# Demo a Course Session

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## Demo Video Transcripts

Duration:"00:47:15.1170000"

00:00:30.930 --
OK guys, this is lecture
8C441.

00:00:36.670 --
I think we started problem two
last time, right?

00:00:41.780 --
And I'm not. I remember is that
we already almost done with

00:00:47.420 --
that. But let's just finalize it
again. This is problem tool in

00:00:53.060 --
hand out #2.

00:00:56.140 --
So this is the problem here.

00:00:59.010 --
I think we got. We calculated
the if we go to the most.

00:01:05.460 --
We calculated the location
of the neutral axis and

00:01:10.041 --
that was 6.78.

00:01:13.120 --
Inches and then we calculated
the tracking moment of inertia

00:01:18.570 --
or the correct moment of inertia
which is 4067.

00:01:24.740 --
And then we just applied the.

00:01:28.670 --
Basic basic equation
from the mechanics of

00:01:32.709 --
materials which has.

00:01:35.960 --
This form here F sub C = M
* X divided by the correct

00:01:42.904 --
moment of inertia and we
calculated the stresses here to

00:01:47.864 --
be about 1400 peace sign.

00:01:51.440 --
Right?

00:01:53.290 --
So the last thing that we need
to do is to calculate the

00:01:56.709 --
stress in the steel and the
stresses in the steel as well

00:01:59.865 --
or the stress of the steel F
South. This is the steel

00:02:03.021 --
stress.

00:02:06.600 --
We can still use the same
formula from the mechanics of

00:02:10.835 --
materials, but what we have to
do is we have to multiply that

00:02:15.840 --
by the model ratio and so that
should be N times the moment

00:02:20.845 --
times the distance from the
neutral axis to the centroid of

00:02:25.080 --
the steel which is.

00:02:27.430 --
Do you minus X? That should
be divided by the correct

00:02:30.862 --
moment of inertia.

00:02:33.160 --
Just to make it clear here guys.

00:02:36.820 --
We do have.

00:02:38.840 --
The assumption that at this
stage of loading.

00:02:44.390 --
The stress distribution, if you
check the handout.

00:02:48.710 --
That's the cross section
of the beam.

00:02:51.790 --
And we had, I think the width of
the beam is 12 inches.

00:02:56.030 --
And the total depth
here is 20, right?

00:03:00.290 --
So this is that's the dimension
and the first step. The first

00:03:04.250 --
step that we did last time is to
locate the neutral axis to the

00:03:08.870 --
neutral axis somewhere here like

00:03:10.520 --
that. And the distance or the
location of the neutral axis

00:03:14.940 --
which is X is measured from the
compression side, assuming that

00:03:18.625 --
the main steel is down here,

00:03:20.635 --
similar to. The figures shown
on the handout right so

00:03:27.556 --
this distance here. That's the
6.78 inches, right?

00:03:34.350 --
And based on the bending theory.

00:03:37.090 --
We assume that the stress
distribution at this stage is

00:03:42.360 --
linear like that.

00:03:51.190 --
So the dashed line below the
neutral axis means that

00:03:55.490 --
concrete. These dash line
here means that concrete is

00:03:59.360 --
ignored, so there is no
stresses in the concrete.

00:04:05.540 --
So that's here no.

00:04:08.130 --
I will just. Say no concrete
stresses, and this is the

00:04:12.816 --
stress in the concrete on the
compression side which is F

00:04:17.293 --
sub C and we calculated the FC
here from again the mechanics

00:04:22.177 --
of materials equation is 1400
PS I so this is 14 one 400 PS

00:04:27.875 --
I so the maximum the maximum
compressive stress is located

00:04:31.945 --
on the top surface of the
section, right?

00:04:36.690 --
And then the stresses or the
stresses is usually decreases

00:04:41.460 --
when we. Approach the neutral
axis till we have a zero stress

00:04:46.890 --
zero strain at this point.

00:04:49.550 --
And then stresses will be.

00:04:52.620 --
Converted from compression to
tension, so anything below the

00:04:56.607 --
neutral axis is under tension
and the maximum steel stress

00:05:01.037 --
which is F Subs. Here will be
the modular ratio, and that's

00:05:06.353 --
given as nine times the moment
which is already given as well.

00:05:14.770 --
Now at 70, so that's 70. Kept
foot again. We are working in

00:05:20.698 --
pounds and inches, so that
should be multiplied by 1000.

00:05:26.590 --
Times 12 to have it an pound

00:05:29.740 --
inch. And that should be
multiplied by the distance from

00:05:34.275 --
the neutral axis to the centroid
of the steel, which is this

00:05:38.775 --
distance. So the distance from
here to here. This is guys the

00:05:43.275 --
distance D -- X.

00:05:46.490 --
So the depth of the beam that's.

00:05:49.770 --
Given in the figure, which is 17
inches minus X, which is 6.78

00:05:56.803 --
inches and that should be
divided by the correct moment of

00:06:02.754 --
inertia, which is 4067.

00:06:06.690 --
So if we calculate that in peace
I so the steel stress here would

00:06:12.486 --
be about 19,000 peace sign.

00:06:24.240 --
Yes, So what is the again D is
the depth the depth is measured

00:06:30.988 --
from the compression side.

00:06:33.530 --
To the centroid of the
steel here.

00:06:37.550 --
So this distance here, that's D.

00:06:42.510 --
And the total height of the
section H. That's 20, but the

00:06:46.974 --
depth is 17.

00:06:50.280 --
This makes sense, so now this
is the stresses or the stress

00:06:53.712 --
distribution based on that
stage or based on that

00:06:56.286 --
applied moment. Now let me
ask you a question here.

00:07:00.180 --
What will happen if we increase
at the moment the value of the

00:07:03.911 --
moment given is about 70 Kip

00:07:05.633 --
foot. Right?

00:07:08.880 --
So if we increase this M this.

00:07:12.390 --
Moment here what would happen
to FC&F Steel will go up right

00:07:17.298 --
anwer this moment usually
increases when we increase the

00:07:20.979 --
load applied to the beam. That
makes sense. So when we

00:07:25.478 --
increase the load moments will
be increased. Stresses in

00:07:29.159 --
concrete and stress in the
steel will be increased.

00:07:34.520 --
Til the whole failure of the
beam, right. And then we so

00:07:40.427 --
based on that we will go over
the ultimate strength limit

00:07:44.794 --
state. But before going to the
ultimate strength we just solve

00:07:49.161 --
another problem here guys. And
the same handout before we move

00:07:53.528 --
on to another problem you have.
Do you have any questions here?

00:08:00.690 --
Yes and represent.

00:08:03.060 --
M and this is the modular
issue. Again, this model ratio

00:08:08.100 --
and. This represents the elastic
modulus of the steel divided by

00:08:13.560 --
the elastic modulus of concrete
and why you are doing that, or

00:08:18.780 --
why you are using NB cause this
kind of analysis in concrete

00:08:24.000 --
sections based on something
called the transformed area

00:08:27.480 --
method. So we convert or we

00:08:30.090 --
transfer everything. Into an
equivalent concrete make sense.

00:08:34.450 --
Instead of dealing with concrete
and steel, we.

00:08:39.320 --
We say that no, we will transfer
everything, convert everything

00:08:42.820 --
to an equivalent concrete
section. That's the reason that

00:08:45.970 --
if you check the.

00:08:48.850 --
If you check the hand out the
figure that is drawn on page

00:08:54.804 --
tool, I have something like
this you have.

00:09:01.840 --
Did you see the guys?

00:09:04.360 --
So this is the concrete.

00:09:07.120 --
On the compression side, and
we mentioned that the concrete

00:09:10.600 --
and attention is ignored, so
we converted all the steel on

00:09:14.428 --
the tension side to an
equivalent concrete section.

00:09:20.100 --
And you see that on the finger.
So this is the.

00:09:24.450 --
End times area steam.

00:09:29.220 --
So that's the distance X.
Again, this distance here is

00:09:32.840 --
the D -- X which is from the
neutral axis. This line here

00:09:37.546 --
represents the neutral axis
to the centroid of this team.

00:09:43.060 --
So let's go to problem. Problem
Three is a straight forward. We

00:09:47.908 --
can go over that quickly. So
again in problem 3.

00:09:53.020 --
We need to determine the
allowable bending moment

00:09:55.356 --
that may be applied to the
beam of example tool. So

00:09:58.568 --
we use these numbers here.

00:10:02.840 --
If the allowable stresses is
1350PSI for concrete in

00:10:07.367 --
compression and 20,000 piece I.

00:10:11.660 --
For that, enforcing steel in
tension so it's the same thing,

00:10:16.302 --
just problem Series A
straightforward business that.

00:10:19.256 --
Let's assume guys that I that we
have some limiting values for

00:10:24.320 --
stresses. We call it the

00:10:26.430 --
allowable stresses. So what is
the maximum? Let's say that the

00:10:30.845 --
maximum allowable stresses for
concrete in compression is.

00:10:34.110 --
1350 PS I and the maximum
allowable stresses for the

00:10:40.090 --
steel intention is about
20,000 pieces.

00:10:46.790 --
So can we use these two numbers
to find the?

00:10:52.610 --
Global moment.

00:10:56.190 --
So the allowable moment means
that the maximum moment that

00:11:00.330 --
should be applied to that beam
without exceeding this allowable

00:11:04.470 --
stresses. Right,
which is the same.

00:11:11.050 --
Same equations now if we.

00:11:16.150 --
And also, given that OK, so
the moment equation, same

00:11:19.920 --
thing it's.

00:11:21.970 --
FC. Times I sub CR which
is the correct moment of

00:11:27.980 --
inertia divided by Y. So
this is the just rearranging

00:11:32.270 --
the equation from the
previous problem. Same

00:11:35.273 --
equation. So we do have FC.
This is the allowable

00:11:39.563 --
compressive stresses which
is 1350 that's given.

00:11:44.410 --
Times the correct moment of
inertia, which already

00:11:48.234 --
calculated in problem 2 and that
was 46, four 067.

00:11:53.880 --
And that should be divided by
the value of Y.

00:11:57.840 --
Which is.

00:12:00.000 --
Distance from neutral. The
distance from the neutral axis

00:12:04.680 --
to the compression side, which
is 6.6 point in 76.7.

00:12:11.340 --
So that will bring us up tool.

00:12:17.920 --
A big number.

00:12:20.180 --
Which which is if you
divide the whole thing.

00:12:24.995 --
Let's divide the whole
thing guys by 1000 * 12

00:12:30.345 --
again to convert it to
Capen foot. I think that

00:12:35.695 --
will be 67.5 foot.

00:12:45.270 --
So.

00:12:48.010 --
To make sense so that this
is the moment this is the

00:12:51.694 --
global moment based on.

00:12:54.400 --
The allowable compressive
stresses in the concrete.

00:12:58.400 --
Now we can repeat the same
equation from problem tool

00:13:02.525 --
here for the steel. So the
moment equation based on the

00:13:06.650 --
steel stress that will be what
will be again F sub S.

00:13:11.750 --
Times the correct moment of

00:13:13.790 --
inertia. Divided by the modular
ratio times D -- X.

00:13:20.580 --
Again, this is the same
equation that we just used in

00:13:24.749 --
problem 2, but just
rearranging the equation so

00:13:27.781 --
the steel stress that's
given.

00:13:30.870 --
As 20,000, which is the level
steel stress 20,000 piece I.

00:13:36.970 --
Times the correct moment of
inertia, which is a constant

00:13:43.470 --
number 4067 inch 4.

00:13:48.550 --
Divided by the moderation
which is 9.

00:13:53.880 --
Times D -- X, which is the depth
of the beam 17.

00:13:58.980 --
Minus 6.78.

00:14:03.360 --
Anne. Again, if you divide the
whole thing by 1000.

00:14:10.600 --
By 12 that will give us a

00:14:14.597 --
hard 73. .7 keep foot.

00:14:20.830 --
So we do have two moments now to
a level moments. One is

00:14:24.613 --
calculated based on the.

00:14:26.460 --
Compressive stresses in the
concrete and the 2nd is

00:14:30.240 --
calculated based on the tensile
stress in the steel right.

00:14:35.910 --
So this is the number 67 point.

00:14:39.740 --
Five and the second moment is
73.7 and I think the allowable

00:14:44.432 --
one will be which one?

00:14:47.910 --
Smaller, right? So
that world controls.

00:14:53.760 --
Windows so that will control
67.5. That will be the

00:14:59.490 --
moment controls the.

00:15:04.980 --
Beam.

00:15:07.130 --
Makes sense, yes.

00:15:10.340 --
So the first moment equation you
said why yes, but you just use

00:15:14.786 --
the X value from the past. That
is basically the same thing. Yes

00:15:19.232 --
Simpson something so that the
genetic equation in mechanics of

00:15:22.652 --
materials says M y /, y, right
or myo over I. Sorry so M Y / I

00:15:28.466 --
so this Y the definition of this
wine. Concrete is the distance

00:15:32.570 --
from the neutral axis to the
compression side which is X OK.

00:15:38.620 --
OK questions.

00:15:44.590 --
So let's go to problem 4 then.

00:15:47.790 --
Which is.

00:15:52.550 --
That is a bit interesting
here to have it.

00:15:58.150 --
So for problem 4.

00:16:01.030 --
We have just a weird section.

00:16:07.480 --
So we have a market section
guys like this.

00:16:23.860 --
So.

00:16:25.970 --
And we do have steel bars
down here, so that's the

00:16:29.523 --
tension side.

00:16:32.580 --
Um?

00:16:35.820 --
The total width here is 18.

00:16:39.800 --
That's.

00:16:44.580 --
So.

00:16:46.920 --
6 inches each and the height of
this notch here is.

00:16:52.580 --
About 6 inches.

00:16:55.260 --
Um?

00:16:57.340 --
So the model ratio is given the
value of N is 8.

00:17:02.440 --
And the moment the applied
moment to that beam is about

00:17:06.477 --
110 kept foot.

00:17:10.830 --
So we need to find the game. The
bending stresses in the.

00:17:16.730 --
Concrete and steel.

00:17:19.490 --
So the challenge here
will be locating the

00:17:23.418 --
neutral axis, right?

00:17:26.780 --
How?

00:17:31.150 --
How, how, how, how we find the
neutral axis location here?

00:17:37.970 --
And the moment of inertia for
each square and then translating

00:17:41.919 --
it to no first week before,
before, before we find the

00:17:45.868 --
moment of inertia, we have to
find the neutral axis location.

00:17:49.817 --
We cannot find the moment of
inertia without knowing the

00:17:53.407 --
location of the neutral axis. So
we need to locate Mr. NA.

00:18:00.680 --
And to do that?

00:18:03.320 --
We have

00:18:07.520 --
two options or two scenarios
options, scenarios, right?

00:18:10.832 --
Because we don't know if the
neutral axis will be located

00:18:15.386 --
over here within the notch,
right or outside here.

00:18:21.960 --
Makes sense, so we have two
scenarios. Either the neutral

00:18:24.900 --
axis located. Over the neutral
axis will be less than the six

00:18:29.590 --
inches. The height of this
launch, or it will be greater

00:18:33.242 --
than the six inches, so that.

00:18:36.410 --
The easiest way to do that is
just assume one scenario and

00:18:39.578 --
see. If the scenario is achieved
so you are correct. If not, we

00:18:44.534 --
have to go to the other one. So
in other words, what we can do,

00:18:49.664 --
let's assume that the neutral
axis is located outside the

00:18:53.084 --
match like that. So in this case
this distance here that's our X,

00:18:57.530 --
which is, I think, drawn in the
figure. But just in case. So

00:19:01.976 --
this is the X value. Now to find
the neutral Axis location X.

00:19:07.460 --
We have to take the first moment
of area about that line to be 0.

00:19:13.550 --
So what about this? Can we
guys? You know guys that

00:19:19.182 --
this area here?

00:19:22.500 --
Has nothing right? This is void.

00:19:26.090 --
So the first moment of
area what we can do is

00:19:29.335 --
we can assume the whole.

00:19:32.010 --
The first moment of area of the
whole compression block here,

00:19:36.564 --
OK, which will be what will be B
again. B is the width here.

00:19:44.580 --
Times X. Times X /
2.

00:19:54.150 --
So B * X This is the area
of the concrete rectangle.

00:20:00.280 --
Above the neutral axis.

00:20:02.470 --
Times X / 2 because we're taking
the moment of that area about

00:20:07.514 --
the neutral axis.

00:20:09.300 --
Two more easily calculate the
area, multiply the area where

00:20:12.650 --
distance and the distance is X /
2 because we measure distances

00:20:16.670 --
from. Centroid the centroid
of that shape, which is so

00:20:21.936 --
the centroid of everything
here guys.

00:20:27.010 --
These block here are these box
here the centroid is at the

00:20:30.214 --
middle which is X at distance X

00:20:32.083 --
/ 2 right? Makes sense.

00:20:35.160 --
So this is the X / 2.

00:20:39.510 --
Minus now we need to subtract

00:20:42.258 --
the. The void.

00:20:47.650 --
OK, which will be what?

00:20:50.910 --
6 * X -- 6 So that any of
that voyante is.

00:20:56.950 --
6 by 666 by 6 right,
because this is 6

00:21:00.710 --
inches, this is 6
inches, but that should

00:21:03.718 --
be 6 * 6 times.

00:21:07.520 --
The distance from the centroid
of that void.

00:21:12.040 --
Which is here. To the neutral
axis so that distances.

00:21:19.080 --
X -- 3.

00:21:22.130 --
Three yes X -- 3 because this is

00:21:24.562 --
6 right guys? So make sense.
So this distance here I will

00:21:29.512 --
just draw an error here. So
that's X -- 3.

00:21:34.580 --
So that should be multiplied by
X -- 3.

00:21:40.660 --
And then.

00:21:43.440 --
Another negative sign.

00:21:47.210 --
Will take the first moment of
area of the steel.

00:21:51.720 --
About the neutral axis.

00:21:55.370 --
So the first moment of area of

00:21:56.980 --
this deal will be. The area of
the steel. Sorry N times the

00:22:01.523 --
area of the steel because we
need to transform this steel to

00:22:05.087 --
an equivalent concrete. So
multiply that by N so that's

00:22:08.836 --
N times a sub S which is
area of the steel.

00:22:14.170 --
Times the distance from the
centroid of the steel bars.

00:22:18.850 --
To the neutral axis, which
is this distance.

00:22:23.750 --
This is D -- X.

00:22:27.130 --
So that's times D -- X that
should be 0, so makes sense.

00:22:33.640 --
So if we do that, just let's
plug numbers here, the width B

00:22:40.062 --
is 18 * X.

00:22:42.680 --
Times X / 2 -- 36
* X -- 3.

00:22:51.550 --
Minus N, which is given as eight
times the area of the steel. And

00:22:57.192 --
if you look at the figure, the
area of the steel is given as 4

00:23:03.237 --
#10 four bars number 10 which is
5.06 square inches times D -- X

00:23:08.879 --
D is the depth.

00:23:11.500 --
What is the depth guys? Can
you see that in front of

00:23:14.224 --
you 23 -- X?

00:23:16.440 --
Yeah, so the depth is.

00:23:19.130 --
23 inches, can you see that?

00:23:22.130 --
Minus X = 0.

00:23:25.080 --
So have a nice equation
here and you know that

00:23:27.910 --
you're expert in math.

00:23:30.590 --
It was your magic Calculator to
find what is X.

00:23:36.740 --
So X here will be.

00:23:39.940 --
9.32 inches, which is a
good sign.

00:23:46.370 --
Why it's a good sign?

00:23:50.060 --
It's outside, avoid yes, because
we assumed at the beginning that

00:23:54.383 --
the neutral X is larger than the
six inches depth is away from

00:23:59.492 --
the void. Based on that

00:24:02.435 --
assumption. The exact solution
is 9.32, which is verifying what

00:24:07.570 --
we're what we have assumed to.

00:24:10.770 --
Our scenario is good
makes sense.

00:24:14.280 --
So from here guys, once we have
the neutral axis questions about

00:24:17.892 --
this, yeah, probably know if our
assumption is bad. If it's

00:24:21.203 --
negative or if it's just smaller
now this more if it's 4 inches.

00:24:25.116 --
So in this case that means that
we have to go back and repeat

00:24:29.330 --
everything. That's a good
question. Makes sense guys so

00:24:32.039 --
again. This is now
this is good, right?

00:24:38.020 --
Now if it's bad.

00:24:44.890 --
Which is again or correct.

00:24:48.270 --
FX for some reason 3 inches, so
that's bad. So what should we

00:24:54.549 --
do? We have to neglect all of
that and start over from

00:25:00.345 --
scratch, assuming that the
neutral axis whoops.

00:25:05.910 --
The neutral axis is somewhere

00:25:07.775 --
here. And then you have
to repeat the process to

00:25:10.727 --
find what is the exact X.

00:25:19.470 --
Are you following them here?

00:25:22.340 --
OK.

00:25:25.560 --
OK, so we have X which is good
9.32 Now the second stage step

00:25:30.908 --
is to find.

00:25:33.670 --
The moment of inertia. What is
the correct moment of inertia

00:25:37.784 --
and at 12?

00:25:39.660 --
Have some.

00:25:42.230 --
Computational effort
here to find it, but in

00:25:46.182 --
order to small guys so.

00:25:49.850 --
Step #2

00:25:53.020 --
why find the?

00:25:56.910 --
Cracked moment of inertia. So
the correct moment of inertia

00:25:59.780 --
Now will be a challenge. How
can we find it?

00:26:12.620 --
Let me draw this again here.

00:26:16.930 --
So.

00:26:19.940 --
This is the neutral axis, right?

00:26:25.510 --
So we need to find the moment of

00:26:27.134 --
inertia of two things. For the
concrete and the compression

00:26:30.492 --
side and for the steel and
attention side. So for the

00:26:33.979 --
concrete and the compression
side we have a very weird shape

00:26:37.466 --
because we do have a void here.
So we have many different ways

00:26:41.587 --
to do it OK.

00:26:43.870 --
We know that this
distance now is X.

00:26:47.270 --
Which is 9.32 inches.

00:26:50.720 --
We know that the width here of.

00:26:54.420 --
Of this

00:26:56.250 --
port, 6 inches. Same thing here.

00:27:01.140 --
6 inches So what we can do is
we can divide that weird shape

00:27:06.954 --
into subdivisions or some small
shapes to find the moment of

00:27:10.716 --
inertia of each.

00:27:13.220 --
OK, So what we can do guys?

00:27:17.140 --
Let's do this so that's the
fairest shape here.

00:27:21.820 --
Or the 1st part. This
is the second part.

00:27:26.080 --
And that's the third part.
So this is part one. This

00:27:30.821 --
is Part 2 and.

00:27:33.960 --
This is Part 3.

00:27:36.650 --
So whenever you have a very
weird shape like that, the

00:27:40.236 --
easiest way is to divide it into
small rectangles, because we

00:27:43.822 --
know the moment of an edge of

00:27:46.104 --
each rectangle is. BH
cubed over.

00:27:51.040 --
No. Yes, I know, but this is
about the centroid, but is for

00:27:56.600 --
our case is BH cubed over 3.

00:28:00.830 --
Do you understand why correct?

00:28:03.350 --
No.

00:28:05.830 --
Yes no.

00:28:08.040 --
Why it's over 3? Again, we
mentioned that last time.

00:28:12.780 --
Side note.

00:28:15.830 --
So the BH cubed over 12. This is
the moment of inertia when the

00:28:22.130 --
neutral axis is passing through
the centroid of the area.

00:28:27.470 --
So these BHQ over 12 is the
moment of inertia about this

00:28:32.282 --
line, which is passing through

00:28:34.287 --
the centroid. But if we.

00:28:39.560 --
If we do have the same
rectangle, if we need to find a

00:28:42.810 --
moment of inertia of a

00:28:44.060 --
rectangular section. About a
line passing through its lower

00:28:48.327 --
edge like this.

00:28:51.120 --
Note the centroid, so that
will be BH cubed over three.

00:28:55.652 --
This makes sense.

00:29:01.350 --
Wake up.

00:29:04.610 --
So here we have.

00:29:07.220 --
Oh well, here we have.

00:29:10.630 --
What is the first moment of
inertia? What is the moment of

00:29:14.122 --
inertia of the first part then?

00:29:18.210 --
Six times so B is 6 inches,
right? So six times.

00:29:24.100 --
The height which is 9.32
cubed over.

00:29:31.620 --
3.

00:29:34.200 --
Over 3 * 2.

00:29:36.700 --
Because area one or part one is
similar to Part 2 makes sense.

00:29:43.440 --
OK. Plus the moment of
inertia of the small part,

00:29:48.837 --
which is part number three,
we know that this width is.

00:29:56.280 --
That's six inches, and we know
the height as well this.

00:30:00.250 --
Height is what is 9.32 -- 6,

00:30:03.659 --
right? So that will be 3.3 two?
Yeah that will be 3.

00:30:11.390 --
That would be 3.32 inches.

00:30:15.160 --
So from here, the moment of
inertia of this small part here

00:30:20.632 --
will be the width, which is 6
times the height which is 3.32

00:30:26.560 --
^3 / 3 as well.

00:30:29.990 --
This makes sense. Again, this
tool because we have two

00:30:33.500 --
similar parts which is part
one and Part 2, and this term

00:30:37.712 --
is for part number 3.

00:30:40.990 --
Plus the moment of inertia of
their enforcing steel, which is.

00:30:47.790 --
Lying here in the lower side.

00:30:52.750 --
And that should be an N, which
is the molar ratio that's eight

00:30:58.379 --
times the steel area which is.

00:31:02.460 --
Five point 5.06.

00:31:05.880 --
So this is the in value. This is
the area of the steel times the

00:31:11.520 --
distance from the centroid of

00:31:13.400 --
the steel. Through the neutral
axis, which is.

00:31:19.470 --
9.3 Two yes D -- X
which is 23 -- 9.32.

00:31:28.660 --
So this is 23
-- 9.32 ^2.

00:31:35.970 --
Squared

00:31:38.390 --
OK. Because you know the problem
with this concrete calculations.

00:31:43.139 --
If you forget the square here,
everything down here will be

00:31:47.330 --
missed. Will be missed, right

00:31:50.074 --
so? Please be focused with her
with us. If so, this is the

00:31:55.874 --
moment of inertia that we should
have and that will be about

00:32:00.578 --
10,887 inch 4.

00:32:03.940 --
So at this stage, once you have

00:32:07.580 --
them. Moment of inertia. And
once you have the location of

00:32:12.720 --
the neutral axis, we can easily
move on to find the stresses at

00:32:17.530 --
any. Location across the section
that we have so.

00:32:26.020 --
To find the stresses again will
recall the mechanics of

00:32:30.190 --
materials equation F sub C will
be the moment.

00:32:35.310 --
Times our why?

00:32:37.790 --
Which is equivalent to X to M *
X divided by the correct moment

00:32:42.816 --
of inertia. This is the equation
to find the concrete stress, and

00:32:47.124 --
we do have the moment because

00:32:49.278 --
that's given. 110

00:32:54.900 --
kept foot, so this 110 should be
multiplied by again 1000 * 12.

00:33:03.140 --
Times the distance X which is
the neutral axis, which is 9.32.

00:33:10.700 --
Divided by the correct moment of
inertia, which we just

00:33:15.030 --
calculated the 10,800.

00:33:18.530 --
87 that will give us
like 1130 P sign.

00:33:26.550 --
So about 11130, pyside, that's
the stress in the concrete. And

00:33:31.676 --
for the steel.

00:33:34.280 --
It's the equation. It's N times

00:33:37.730 --
the moment. Times the distance D

00:33:41.562 --
-- X. Divided by the correct
moment of inertia.

00:33:47.550 --
So again, repeating that N is 8.

00:33:52.250 --
The moment is 110.

00:33:55.420 --
Times 12,000.

00:34:00.780 --
Times D -- X, which is
23 -- 9.32.

00:34:07.500 --
That's divided by 10,887. So
if you simplify that, I

00:34:14.680 --
think we'll have about 13,000.

00:34:20.180 --
269 PS I.

00:34:25.080 --
So these are the stresses
in the concrete.

00:34:29.940 --
And in the steel
at the extreme.

00:34:36.360 --
Favor so.

00:34:42.990 --
This makes sense here guys.

00:34:54.060 --
So going back to
this figure here.

00:35:02.750 --
Are you done this part?

00:35:07.540 --
So stressing concrete is about

00:35:09.730 --
11:30. Steel is 13,000.

00:35:13.790 --
So if I ask you to draw the
stress distribution here, so

00:35:17.834 --
that should be the stress
distribution. Again similar to

00:35:20.867 --
what we did last time. We do
have a triangle like this.

00:35:26.800 --
And the maximum stress in the
concrete is in the top surface

00:35:31.120 --
on the compression side, which
is 1130 P sign.

00:35:36.220 --
And concrete on the tension site

00:35:38.836 --
is ignored. And the maximum
stress on the steel level, which

00:35:44.291 --
is down here.

00:35:47.160 --
That is 1113 thousand
269 peace sign.

00:35:57.310 --
So that's the stress
distribution still.

00:36:01.540 --
Perfect linear noise.

00:36:07.200 --
We'd like just to look at this
figure and just have some

00:36:12.084 --
conclusions here so.

00:36:15.990 --
From C 357 guys, you remember
that you know the target

00:36:20.731 --
compressive strength for normal
concrete at 28 days was what?

00:36:25.860 --
Roughly.

00:36:29.650 --
4000 something like that, right?
This for normal concrete that we

00:36:33.610 --
use for bridge decks like 4000.
PS. I so.

00:36:37.970 --
F prime C
at 28 days.

00:36:43.890 --
This should be the target. This
is a very well known number

00:36:48.596 --
in the in the outside the field.
The 4000 piece sign.

00:36:53.790 --
Let's assume that this concrete
that has been used in this

00:36:58.135 --
section has a compressive
strength at 28 days equals 4000,

00:37:02.085 --
right? Now when the moment
applied when the moment.

00:37:10.620 --
When the moment
of 110 kept foot.

00:37:17.570 --
Is applied to that section. How
much concrete stress we got.

00:37:22.890 --
1130 So FC we got

00:37:26.430 --
11. 30 or 1100 thirties
makes sense.

00:37:32.440 --
So this is the
maximum compressive

00:37:34.804 --
stresses on the
concrete when the

00:37:37.168 --
moment was 110.

00:37:39.990 --
The question now is.

00:37:42.790 --
What is the relationship between
the 100 so that 1130 piece I

00:37:47.086 --
compared with the 4000 peace

00:37:48.876 --
sign? Is it like less
than half equals half

00:37:52.564 --
of their value or what?

00:37:56.960 --
It's 11:30 is less than half
of the 4000 is right, so

00:38:04.832 --
when groups when not if when?

00:38:10.580 --
When F sub C, which
is the 11:30 equals

00:38:16.691 --
oh sorry less than
.5 F prime C. The

00:38:22.802 --
target at 20 days.

00:38:26.690 --
OK.

00:38:29.770 --
Stress is for the stress
distribution.

00:38:38.130 --
As assumed to be linear.

00:38:45.390 --
So as long as.

00:38:47.360 --
The compressive stress is
less than 50% of the 28

00:38:53.230 --
days compressive strength.

00:38:57.230 --
The stress distribution
is assumed to be linear

00:39:00.110 --
over the cross section.

00:39:02.930 --
If this number, which is F sub

00:39:05.380 --
C. Exceeds
50%

00:39:11.490 --
of the 4000.

00:39:13.770 --
The stress distribution will be

00:39:16.635 --
nonlinear. Because after that
number after that, sorry after

00:39:20.806 --
that threshold value which is

00:39:22.616 --
the 50%. Concrete the concrete
section will be having major

00:39:27.764 --
cracks and this major cracks
will produce non linearity in

00:39:32.194 --
the concrete behavior.

00:39:34.660 --
And in that stage.

00:39:38.350 --
The actual stress distribution
will be not linear. It will be a

00:39:43.438 --
nonlinear system distribution,
which will be. Other would be

00:39:47.254 --
our topic here so.

00:39:49.690 --
If we go back to the screen.

00:39:52.310 --
So which? Is
showing like this?

00:40:00.050 --
So. So once.

00:40:02.740 --
FC exceeds point 5F.

00:40:06.710 --
Prime, see.

00:40:09.810 --
We now entering the ultimate
flexural strength stage of

00:40:14.697 --
the concrete section and in
that stage.

00:40:19.620 --
And that's the image we do
have the stress distribution

00:40:22.910 --
groups. Can you see that the
stress distribution now became

00:40:26.200 --
nonlinear? So this is just a
3D thing. Just to make sure to

00:40:30.477 --
visualize to make sure that
you understand this. That's

00:40:33.438 --
the width of the section.
That's the height this is the

00:40:37.057 --
C value or the.

00:40:39.930 --
The location of the neutral
axis. So in the uncorrect

00:40:43.380 --
stage we named the location
of the Neutral X as an X.

00:40:47.520 --
Once we jump into the
ultimate stage now we will

00:40:50.970 --
call it C and the strip the
stress distribution now is a

00:40:55.110 --
parabolic or has a public
shape which is not linear,

00:40:58.560 --
and in this case.

00:41:01.640 --
The analysis will be a little
bit different, but again.

00:41:06.570 --
As you know, the ACI dimeric and
concrete Institute committee

00:41:11.540 --
knows that civil engineers are

00:41:14.025 --
lazy, so. And you know, we know
that we are.

00:41:19.790 --
Very strong math, right? So they
switch it or we made the life

00:41:25.406 --
more easier for us.

00:41:27.700 --
So as long as the stresses or
the stress distribution is

00:41:32.034 --
nonlinear and has a public ****
like that we have, we can assume

00:41:37.156 --
it to be or to have an
equivalent stress equivalent

00:41:41.096 --
rectangular stress block similar
to the one that is shown here.

00:41:45.430 --
So in other words, once this is
the actual stress distribution

00:41:49.764 --
for get it, which is a public
complicated shape for get it,

00:41:54.492 --
and then we will assume that the

00:41:57.250 --
section. OPS the section. We
will have a rectangular

00:42:01.474 --
equivalent stress block like

00:42:03.326 --
that. So go back going back to
it again. Sorry this is the

00:42:08.326 --
cross section. I think you
know you're familiar with it.

00:42:11.606 --
Now this is the strain
distribution. Hope So what you

00:42:14.886 --
can conclude here that.

00:42:17.370 --
Regardless of the loading stage.

00:42:20.580 --
The strain distribution is
assumed linear.

00:42:24.850 --
On correct, correct fully
cracked ultimate stage. The

00:42:27.650 --
strain distribution is linear,
but for the stress the situation

00:42:31.150 --
is different. So for the stress
distribution as you can see this

00:42:35.350 --
is the parabolic shape and we do
have the compression force on

00:42:39.550 --
the compression side. This is
the tension force and retention

00:42:43.050 --
side that is complicated for us.
So we will replace these public

00:42:47.250 --
with an equivalent stress block.
2 main important things that you

00:42:51.100 --
must understand when we talk
about Ultimate stage ultimate

00:42:54.250 --
strength. That means that the
concrete, which is the maximum

00:42:59.592 --
maximum stresses and concrete
will start to fail. So the ACI.

00:43:05.410 --
Put a threshold of the ultimate
failure strain, so once you hear

00:43:13.258 --
that the concrete strain reaches

00:43:16.528 --
0.003. That means concrete died.

00:43:22.050 --
Recent.

00:43:24.330 --
When the steel reaches the steel
strain reaches the yield strain.

00:43:30.800 --
That means that steel is filled.

00:43:34.920 --
So in conclusion, here concrete
fails at a strain equals 0.003.

00:43:41.910 --
Steel fields at a strain equal
to the yield strain.

00:43:48.210 --
So these two failure failure
thresholds or values are.

00:43:54.260 --
Or done or made for the
design purpose, so makes sense.

00:44:01.960 --
When we talk about design.

00:44:04.030 --
You have to memorize these two
numbers. However in the lab.

00:44:09.580 --
You should remember that beam.

00:44:11.910 --
That I showed you guys in the
lab when we start pushing the

00:44:16.694 --
beam to the limit, the concrete
strain will exceed .00 three and

00:44:21.110 --
the steel strain will exceed the
yield strength at the final

00:44:25.158 --
filter stage. But we cannot do
that in design and design. We

00:44:29.574 --
have to be very conservative
right? To make sure that the

00:44:33.622 --
beam or the element the concrete
element will not reach the

00:44:37.670 --
ultimate stage, because if it if
that element reaches that, so.

00:44:41.920 --
Everything will fail
immediately, right guys? So we

00:44:44.920 --
have to have a very safety
factor here, and that's based on

00:44:49.420 --
the values that the ACI
specified. So this is the actual

00:44:53.545 --
stress distribution. This is the
equivalent stress block. We

00:44:57.472 --
assume that the actual neutral
axis has a.

00:45:01.410 --
Annotation of C. Here. Once we
transfer that to the

00:45:05.160 --
equivalence, replug the neutral
X is location will be.

00:45:09.560 --
Or will equal to a?

00:45:13.970 --
OK, so this a this is the
neutral axis location the new

00:45:18.770 --
one. What is the relationship

00:45:20.770 --
between A&C? A equals another
factor called beta 1 * C.

00:45:27.630 --
So be ready that because it will
be exposed to about 1000 factors

00:45:32.531 --
from then on. So beta one.
That's the factor that we

00:45:37.055 --
must consider this beta one
depends on the compressive

00:45:40.448 --
strength of concrete. Is normal
concrete high strength, ultra

00:45:43.841 --
high performance? All a that's
will be shown here. So based on

00:45:48.365 --
the concrete compressive
strength, you can determine what

00:45:51.381 --
is the value of beta one going
back to hear the maximum

00:45:55.905 --
concrete stress that is limited

00:45:57.790 --
for design. Is 0.85 times.

00:46:01.490 --
The FC prime don't left .8 Zero
Point 8 five times.

00:46:07.570 --
Is it if Ramsey lifsey prime?

00:46:11.950 --
FC Prime FC prime.

00:46:15.640 --
Fusion FC Prime so .5 so the FC
prime that you got from the

00:46:20.960 --
machine in the lab which is 4000
PS I we will multiply that by

00:46:26.280 --
.85 to have the maximum
compressive stress limit for

00:46:29.700 --
design. Makes sense.

00:46:33.480 --
Break so.

00:46:35.750 --
So it's you guys on Friday. I
haven't hand out here. Please

00:46:40.178 --
take a copy that will use it
next week and maybe Friday and

00:46:44.975 --
it's already posted too similar.

00:46:48.500 --
Thank you.

Duration:"00:47:49.8050000"

00:00:24.990 --
Hi welcome everybody to our 27th
class. I guess I'm not even sure

00:00:28.916 --
if we're In Sync on the web.

00:00:33.100 --
So.

00:00:34.900 --
We second here less than we
just about finished up the

00:00:41.467 --
wireless network section, except
we didn't quite.

00:00:46.770 --
We didn't. We kind of hated for
the last couple of slides and I

00:00:50.998 --
would like to just catch up
there where we left off last

00:00:54.622 --
time hoops with the last slide.
So in our in our hierarchy here.

00:00:59.970 --
Well.

00:01:02.180 --
Here.

00:01:03.740 --
So where we're sitting there at
802 eleven, which was a MIMO

00:01:09.656 --
MIMO scenario and.

00:01:12.140 --
In if you have now this, this
capability can use different

00:01:17.520 --
type of strategies. You might
use actually know aggregation

00:01:21.102 --
and remember aggregation means
putting together or we can have

00:01:25.082 --
where we basically put a bunch
of frames and we put a common

00:01:30.256 --
header in there.

00:01:32.030 --
And when you do that and it's
called a MSUD. So it's basically

00:01:37.802 --
an aggregation where you put in
these packets here, right

00:01:42.686 --
next to each other with one Mac
header. So the advantage of such

00:01:48.458 --
a thing here is of course that.

00:01:53.560 --
You have less overhead, so the
frame overhead compared to its

00:01:57.201 --
alternative, which would be like
where you send it with their own

00:02:01.173 --
Mac overhead so we can look at
this here and you will see that

00:02:05.807 --
the contribution of overhead of
course here is much higher due

00:02:09.448 --
to that, but everything has a
pro Ana con, so everything has

00:02:13.420 --
an advantage and a disadvantage
from a overhead POV. This is

00:02:17.061 --
actually much better because you
have only one header and then

00:02:20.702 --
this case works. Then we have

00:02:22.688 --
four protocol units. Data units,
on the other hand, if we do have

00:02:28.270 --
a corruption, then we have an
issue because that would mean

00:02:32.318 --
that every Mindy header actually
has the ECS the see the error

00:02:36.734 --
correction code over the entire
the CRC, and to say it has the

00:02:41.518 --
CRC over the entire. In this
case 4 frame of four subframe

00:02:45.934 --
frame. Meaning if one goes bad
it has to reset the whole thing.

00:02:51.450 --
And so that is not the case down
here, where now, however, you

00:02:55.688 --
have to carry the burden of.

00:02:58.890 --
Of the different units with
their own headers, so that's

00:03:03.290 --
essentially what we have, and
then you can have, like

00:03:07.690 --
aggregation of multiple scenario
would have like. In this case

00:03:12.090 --
two of those packed together
with one physical header. So

00:03:16.490 --
these are the different options
that we have on the plate. So

00:03:21.770 --
now this was for 802 eleven
North, but it also transfers

00:03:26.610 --
into a 211.

00:03:29.020 --
At 802 eleven AC and in AC we
looked at it. I mean, we had

00:03:35.065 --
several advantages in AC. First
of all, we had a much bigger

00:03:39.901 --
bandwidth. We had 160 megahertz
versus the small.

00:03:44.150 --
40 megahertz that error to
leaven in had we have more. My

00:03:49.514 --
more capability up to 8
doesn't have to be, but up to

00:03:54.878 --
8 different antennas, and we
had a modulation that went

00:03:59.348 --
from 64 quam for the North to
256 quam for the AC. So All in

00:04:06.053 --
all, that is where the big
improvements occur.

00:04:13.990 --
So the advantage is now that if
you have such a scenario, we can

00:04:19.380 --
have actually group, so we can
have different constituents or

00:04:23.230 --
multiple users there. I can have
a multi user MIMO where I'm

00:04:27.850 --
talking to you with one antenna.
I'm talking to you with another

00:04:32.470 --
antenna and that is a very
different scenario in a straight

00:04:36.705 --
out scenario where we have one
antenna. Because I can first

00:04:40.940 --
talk to you and then I can talk

00:04:44.020 --
to you. But here I can actually
split up the streams in

00:04:48.770 --
multiplayer games that are based
now on antennas and that becomes

00:04:52.818 --
a variable. Very powerful means.
So I might have. Now I'm sending

00:04:57.234 --
something to you and I will use
my antennas to have different

00:05:01.650 --
data stream two antennas
directed to one link to more

00:05:05.330 --
antennas, one each going to
another device. So that is the

00:05:09.378 --
kind of advantage that you would
have from, let's say, a router

00:05:13.794 --
point of view.

00:05:15.190 --
The router that is capable of AC
can make these decisions, so if

00:05:20.572 --
you have like 4 different or
eight different people in a

00:05:25.126 --
place, you can have 8 ongoing
communications, otherwise they

00:05:28.852 --
would not be on this at the same
time. So that's a huge advantage

00:05:34.648 --
of this multi user MIMO
capability of AC.

00:05:40.310 --
So if everybody I know if
everybody gets it here, but

00:05:44.281 --
essentially now if I'm
sending it on the downlink. I

00:05:47.891 --
mean I'm sending it towards
you here, I could use now

00:05:51.862 --
different antenna and do it
all at the same time. So that

00:05:56.194 --
is quite some difference in
mentality. There the other

00:05:59.443 --
tool of an NI don't think can
do that. I'm not 100% sure

00:06:04.136 --
but I don't think with the
four in Tennessee.

00:06:10.050 --
So the only disadvantage than
this you have to send them as

00:06:13.878 --
individual frames. He cannot
aggregated. You cannot aggregate

00:06:16.430 --
him in the fashion that we had
here, so this won't work.

00:06:20.850 --
Which is the low overhead, so
we have to go with this right

00:06:23.606 --
here with the higher overhead.

00:06:26.510 --
No, but that's essentially it.
So NAD now, remember AD. The

00:06:30.437 --
biggest thing we should remember
if anything at all like we were

00:06:34.721 --
in a complete different League
here we're switching now from

00:06:38.291 --
the five Giga Hertz to the 60
Giga Hertz Band and that gives

00:06:42.932 --
you a huge advantage of.

00:06:46.070 --
Of bandwidth. The one thing is
you will have very little

00:06:51.031 --
contention there at the moment
and this is in devices will

00:06:55.200 --
trickle in that take over there.
So that's one advantage. There

00:06:59.369 --
is little contention, whereas
the 2.4 giga Hertz range is very

00:07:03.538 --
occupied. Everybody runs on 2.4
less people but more and more

00:07:07.707 --
run on five, and I don't have a
single device that can run on

00:07:13.013 --
60. At this point I think so
that, but that's where things

00:07:17.561 --
are moving so.

00:07:19.160 --
Not everything is always great,

00:07:21.900 --
why? I mean, what are the
disadvantages well?

00:07:26.820 --
You go to higher goal with your
frequencies. The more lost you

00:07:32.436 --
have to endure, so that is one
thing. So higher losses there

00:07:38.052 --
and multipath is also an issue.
Multipath losses are a big

00:07:43.200 --
issue. Remember multipath is
when a signal bounces off

00:07:47.412 --
somewhere. And obviously I get
now are reflection. I get the

00:07:52.560 --
original one. I get the

00:07:54.900 --
reflection but. The reflection
can interfere with my primary or

00:08:00.606 --
original signal. And that can
cause big problems. So it's not

00:08:05.486 --
just that I get an echo, but the
echo messes up my original 1 as

00:08:10.346 --
well. So that is a typical
example of multi loss problems

00:08:13.910 --
here. The next thing that is a
little bit of a pain is you go

00:08:18.770 --
that high with the frequencies
and that will not be able to go

00:08:22.982 --
through objects anymore. So that
is a big problem. For example of

00:08:26.870 --
fear and building. Or if you
want to go through buildings.

00:08:32.840 --
We just ran some examples.

00:08:38.880 --
Just as a little
side note here, we ran just week

00:08:45.930 --
ago, so we're an example where.

00:08:49.670 --
We're having a huge building

00:08:51.235 --
here. So this is a big building
and we're trying out some

00:08:55.543 --
collision. Avoidance
scenarios were.

00:09:00.100 --
In 811 Piso, there's another 802
eleven standard. This one

00:09:03.780 --
happens to be also in the five
Giga Hertz range, but it's only

00:09:08.564 --
for vehicles, and we were trying
to test the impact of.

00:09:13.390 --
These applications where this
vehicle comes and if this one

00:09:17.100 --
doesn't stop, there should be a
alert that tells her if you mean

00:09:21.923 --
watch out, you're on collision
course with some other vehicle,

00:09:25.633 --
so that was the thing and we're
testing. For example, in this

00:09:30.085 --
case, how much buildings would
affect such measurements? And we

00:09:33.795 --
were in the five Giga Hertz
Band, 5 GHz band and this year

00:09:38.618 --
is roughly what did we have? The
150 hundred 50 meter or

00:09:43.070 --
something like that? If I got
the exact dimensions?

00:09:46.810 --
And it turned out that in the
five Giga Hertz Band we had

00:09:50.177 --
fairly good communication, even
though there's no line of sight.

00:09:52.767 --
You don't need that made with
cell phones. You don't need line

00:09:55.875 --
of sight to the tower. I mean,
we're in the building here. It

00:09:59.242 --
works just fine. I'm.

00:10:01.960 --
But if you were and we could run
this very nicely. So we're

00:10:06.068 --
driving, measuring, logging,
everything an yeah work just

00:10:08.596 --
fine. Incidentally, as we're
doing it, one of people that

00:10:11.756 --
there was a car ahead of us and
that car introduced exactly what

00:10:15.864 --
we're testing for, 'cause that
car just about there was a girl

00:10:19.656 --
there on her phone, but she was
paying attention. Run the stop

00:10:23.448 --
sign right in front of me. So
unfortunately it didn't have a

00:10:27.240 --
webcam that would have been
funnier than heck to show at a

00:10:31.032 --
conference. So like you were
testing for this application,

00:10:33.876 --
and guess what happened?

00:10:35.200 --
The exact case that
we tried to test for.

00:10:38.520 --
But if you were to experience,
expect that experience.

00:10:41.445 --
Experiment now in the 60 Giga
Hertz range the reliability

00:10:44.695 --
would definitely much different,
'cause the communications would

00:10:47.295 --
have been much more Hanford by
the building here, which happens

00:10:50.870 --
to be in our case the Wallace
complex. We use that as an

00:10:55.095 --
example. If we had been NYC with
there being cooler 'cause we had

00:10:59.320 --
bigger buildings. But in Moscow
we don't have big buildings.

00:11:04.780 --
So that can be a problem here.
So these millimeter wavelengths

00:11:09.367 --
and remember higher frequency.
The shorter the wavelength.

00:11:13.420 --
They have issues they don't like
to go through objects anymore

00:11:17.061 --
and that becomes a real problem
because that now has more of a

00:11:21.364 --
flavor of line of sight. That's
the big problem that we run

00:11:25.336 --
into. So not everything is
always perfect and this is

00:11:29.773 --
definitely one of them, where
it's a compromise space.

00:11:35.160 --
So the biggest ones here turn
out to be well here we have a

00:11:40.788 --
MIMO antenna conversion here.
We have single one, but we

00:11:44.808 --
have a huge number of channels
due to a big bandwidth at the

00:11:50.034 --
60 giga Hertz Band.

00:11:52.900 --
Then they show you in the
book a nice example here of

00:11:57.256 --
justice, different physical
layers for us, I mean, for

00:12:00.523 --
the most users, the only
thing that matters is the

00:12:04.153 --
bitrate. Here they care about
how fast is it? So we see

00:12:08.509 --
here basically what the
speeds are for.

00:12:12.890 --
480 two 1180 depending on what
the physical layer is, and so we

00:12:17.895 --
can just see what happens here.
The modulation. Incidentally,

00:12:21.360 --
now you probably see what all is
involved. We haven't really

00:12:25.595 --
talked about some of the
flavors. You know, Ï€ / 2

00:12:29.830 --
lalalala so, but you probably
get the feeling of what that

00:12:34.065 --
might be. Phase shift keying
involved. There's a shift there.

00:12:37.915 --
When we looked at phase shift
keying of 0 and 180, we.

00:12:42.970 --
Looked at when you do it
differently, let's say like 90,

00:12:46.391 --
then 270 and so on. So it should
give you an idea what's

00:12:50.434 --
happening here, so hopefully
when you look at it gives an

00:12:53.855 --
idea you might have to kind of
go back and say that guys not

00:12:58.209 --
forgotten what was the
difference between this and

00:13:00.697 --
that. No.

00:13:03.660 --
So this obviously is a frequency
division multiplexing and 16

00:13:07.610 --
qualm just means we have these
different levels there to

00:13:11.560 --
differentiate with. That's the
big one here, so anyway.

00:13:15.680 --
Just kind of cool to see
the differences here.

00:13:22.680 --
So that's on the AD.

00:13:26.310 --
So then what we kind of just
hand waved was the excess an

00:13:31.159 --
privacy information and
anybody that had configured

00:13:33.770 --
wireless router would kind of
have an idea what's involved

00:13:37.500 --
there. The first thing is to
establish station. So if you

00:13:41.603 --
want to hook up to station you
need to have access to it. So

00:13:46.825 --
if you're up to VandalWeb
gold for the first time, well

00:13:51.301 --
it asks you for information
and then it comes in there.

00:13:57.050 --
Once you're on there, well, then
you expect and it turns out to

00:14:01.821 --
be the case here too that there
will be some encryption in place

00:14:06.592 --
and that is now something that's
not the access itself, but that

00:14:10.996 --
deals with the privacy and so.

00:14:14.330 --
The different type of author
mean authorizations

00:14:17.473 --
authentication schemes that are
offered, and the main thing for

00:14:21.963 --
us is just to see what we have
and the typical ones are the

00:14:28.249 --
authentication itself. Do it to
password. You can normally pick

00:14:32.739 --
the parameters for that.

00:14:35.140 --
You can use further.

00:14:38.450 --
Authorization by implementing
things like lists of specific

00:14:41.066 --
devices that you allow and which
ones you do not allow. That is

00:14:45.317 --
much more useful in an office
environment, not at University

00:14:48.587 --
environment, 'cause that would
be a maintenance nightmare or

00:14:51.530 --
maintaining a list where every
day somebody comes and says like

00:14:55.127 --
I got rid of this machine. Now I
have another machine and can you

00:14:59.705 --
lock the new Mac address? That
would be really not a practical

00:15:03.629 --
thing, but in certain
environments I would strongly

00:15:06.245 --
suggest doing exactly that,

00:15:07.553 --
meaning only. Those that have a
particular MAC address can

00:15:11.436 --
actually join such a device, and
the others don't. So just

00:15:15.528 --
because somebody would give you
a password then to have access

00:15:19.620 --
to the note would not get you on
there because you also would

00:15:24.456 --
have to be in the Mac list birth
specifically. I mean there by

00:15:29.292 --
specifically allowing you to do
that, it can become a bummer for

00:15:33.756 --
consumers if they have a guest
network, because once

00:15:37.104 --
established, that's a list.

00:15:38.950 --
The guest network typically also
likes to access such a list, and

00:15:42.514 --
that means now you have many
kind of just give somebody the

00:15:46.078 --
password. So like hey, the
guests are Hello World and then

00:15:49.345 --
it will tell you, well you know
but I don't know you mattress. I

00:15:53.503 --
can't let you in here.

00:15:55.850 --
It's not like I'm VandalWeb
guest. If you have your goal,

00:16:00.158 --
vandals password there when you
can go on and there's no more

00:16:04.466 --
questions asked other than that,
and that makes a lot of sense

00:16:08.774 --
from a privacy point of view. Of
course we want to have

00:16:13.082 --
encryption involved, because
otherwise if you sit there and

00:16:16.313 --
you run an unencrypted
connection, all you need is a

00:16:19.903 --
packet sniffer and you can get
the information. So we've tried

00:16:23.852 --
that before when we used to have
a class here.

00:16:27.910 --
That already class called 421,
which was the data

00:16:30.826 --
communications lab. So it was a
one hour lap. We ran with the

00:16:35.038 --
Klausner. I got rid of it
because it turned out to be too

00:16:39.250 --
much work for one credit hour
class for me and the

00:16:42.814 --
infrastructure also was a little
bit difficult. But let's take a

00:16:46.378 --
look at this here. So we had.
Let's say we have a device here.

00:16:53.420 --
And we have now information
that goes. He ran. It could

00:16:58.458 --
be, it could be.

00:17:01.680 --
On wireless this could be
wireless. Here it could be

00:17:05.370 --
wired, you know it could be
wired here, so we might have

00:17:09.798 --
wired notes here. Or maybe I
have a router here like an 802

00:17:14.595 --
eleven type thing. So Whoops
802 eleven X or some whatever

00:17:18.654 --
you might have here. So now
you're sitting there.

00:17:23.550 --
On a smart phone or
what have you here?

00:17:28.670 --
So if you were to establish,
let's say we pick the no.

00:17:34.800 --
Your other device on
your laptop and your

00:17:37.848 --
establish a telnet
connection. Telnet is

00:17:40.134 --
not, is not.

00:17:44.040 --
Tell that it's not encrypted.

00:17:46.970 --
And you do this in your
favorite coffee shop that uses

00:17:50.567 --
no encryption or at the
airport or in a hotel where

00:17:54.164 --
you just go on and there's no
encryption, and you know when

00:17:58.088 --
that is because there's no
encryption key there, you just

00:18:01.358 --
see the little symbols here
for wireless, but you don't

00:18:04.628 --
see anything next to it, so
you know this is an open

00:18:08.552 --
wireless an. Typically it
tells you it's a non secure

00:18:11.822 --
line, so if you sit there and
you run a packet sniffer.

00:18:20.910 --
And you can download those free
from the Internet and it may be

00:18:24.784 --
there everywhere we use them
always. When we run experiments.

00:18:28.660 --
You can just never packet an.
You can get everything out, so

00:18:32.476 --
we used to do that in the
networking lab, which we did

00:18:36.292 --
not. On Wi-Fi wireless, but we
did it here on such a

00:18:40.108 --
scenario, and so I asked them
to students. So like OK, you

00:18:43.924 --
type in your password you
establish from here as a

00:18:47.104 --
server. So this is server and
this is a client, so I'm

00:18:50.920 --
trying to establish telnet
from here to there.

00:18:54.930 --
So now you start sitting there
is typing telnet and then you

00:18:58.470 --
type your password and you would
think like OK so I should get

00:19:02.305 --
now. The password in the packet.
Well that happens to not be the

00:19:06.140 --
case because we are so slow in
typing that it will already send

00:19:09.975 --
that packet with like 1
character at a time just because

00:19:13.220 --
we are so slow compared to the

00:19:15.285 --
data rate. So what you would
have to do now on a sniffer.

00:19:20.060 --
You would, whether it's wireless
or where it makes the

00:19:22.990 --
difference. Here you would
target a machine. I target this

00:19:25.920 --
particular phony and I said I
want to have only the packets

00:19:29.436 --
that are related to this phone
that I'm trying to bring in, and

00:19:33.245 --
then I look at those packets a
string him up here.

00:19:37.440 --
And then between those packets I
will find the telnet. I mean

00:19:41.280 --
maybe T in here and El in here
and letter at a time and then

00:19:46.080 --
we'll get the password. I will

00:19:48.000 --
get the password. And it will
however only show up if I

00:19:52.353 --
capture all of the packets from
this unit. Here, it's not as one

00:19:56.084 --
might think, like here is the
packet that has the password.

00:19:59.241 --
No, it's just. Too slow, we're
just too slow typing by the time

00:20:03.410 --
we're finally done, each packet
gets sent out by itself.

00:20:08.000 --
And so, in an unencrypted
environment is a real

00:20:12.360 --
problem. If however, you were
sitting in this coffee shop and

00:20:17.156 --
now you use SSH instead of
telnet, then actually this will

00:20:21.952 --
not be a problem because now
your traffic itself with SSH is

00:20:27.184 --
encrypted and you can run a
packet sniffer and all you get

00:20:32.416 --
is rip gibberish.

00:20:34.290 --
You cannot really use that, so
that is the good part. The bad

00:20:38.684 --
part is that often when it
comes, for example to web

00:20:42.402 --
context content. We don't really
know is this not encrypted or

00:20:47.098 --
not. It's not always obvious
whether it is encrypted or not,

00:20:51.300 --
like you're sitting in an
Internet cafe at the McDonald's

00:20:55.120 --
in Paris or who knows were and
you're trying to access your

00:20:59.704 --
account. Is this safe or not?

00:21:03.110 --
You know, and then the
question really depends on the

00:21:06.320 --
application support for
encryption, yes or no. If you

00:21:09.209 --
do have it, yes, if you don't
have it, no. But how do you

00:21:13.703 --
know? And sometimes it's worth
sniffing your own connections

00:21:16.592 --
to see how exposed you are.

00:21:19.680 --
I've done that not too
long ago with the Mail

00:21:23.320 --
client on a machine where
we tried it out and sure

00:21:27.324 --
enough, despite me
thinking we had everything

00:21:29.872 --
set up right.

00:21:32.120 --
We did not have it right and
there was a setting wrong. I

00:21:35.526 --
thought it was unencrypted,
turned out not to be encrypted

00:21:38.146 --
so we could see the password

00:21:39.718 --
flying by. And I thought, like,
woah, woah. Woah. How

00:21:44.310 --
would I have known that an so if
you exercise this somewhere

00:21:48.210 --
where they have a sniffer
running like at the airport, how

00:21:51.785 --
do I know not there's nobody
there that actually just sits

00:21:55.360 --
there praying on just careless
or ignorant users that don't

00:21:58.610 --
really understand it and run it.
So that is a problem. So the

00:22:02.835 --
original able to 11 came with
web that turned out to not be

00:22:07.060 --
that great of a thing. An
incidentally if you own an old

00:22:10.960 --
machine like an old cell phone

00:22:12.910 --
and I. Old iPad or what might be
what you might have. It might

00:22:18.382 --
just basically allow you only to
use these old, not so secure.

00:22:23.840 --
Encryption methods and it might
not let you in. For example, if

00:22:26.984 --
I use web here at the
University, this I know can't do

00:22:30.128 --
that. So if I don't have the

00:22:34.034 --
WPA. Encryption I cannot get on
at all, so they were not allowed

00:22:39.380 --
that. So one has to be aware of
that. Different levels of

00:22:43.340 --
encryption. That's essentially
all I wanted to discuss here. I

00:22:46.640 --
hope you have a feeling for
things that didn't make us any

00:22:50.600 --
experts on wireless, but I
hope you get to feeling for it.

00:22:55.530 --
There are other wireless
definitions there.

00:23:00.570 --
Like I said, we work with 802
Eleven P at the moment, which is

00:23:05.694 --
something like 802, eleven, or
811 a, but it operates for it's

00:23:10.086 --
designed for vehicle and
networks and some of the

00:23:13.380 --
parameters are a little bit
different. Some of the

00:23:16.674 --
parameters like the it's the
back of the medium access

00:23:20.334 --
parameters are different, so
their minor changes, but enough

00:23:23.628 --
to make a difference there.

00:23:28.230 --
Any questions to any
of the wireless stuff?

00:23:38.140 --
Alright.

00:23:40.390 --
When with it.

00:23:43.120 --
We're ready to go for the next
one here, which turns out to be.

00:23:47.770 --
The Internet protocol, so
we're going very. We're

00:23:51.250 --
almost there. I'm almost
at the upper level now.

00:23:56.610 --
We have one more level to go
through, and that's done the

00:24:01.338 --
transport transport layer, but
here we're looking at the

00:24:04.884 --
Internet protocol. IP would be
the Classic One that we have,

00:24:09.218 --
but Internet Protocol it doesn't
have to be IP, we're just

00:24:13.552 --
talking about in general.

00:24:16.930 --
So before we go here, let's just
look at a couple of notations

00:24:21.550 --
or not connotations like couple
of terminologies that they use

00:24:24.850 --
here. I mean one over the
communication network. While we

00:24:28.150 --
know what that is, a bunch of
notes there, I mean for so to

00:24:32.770 --
provide data transfer among
devices attached to the network.

00:24:35.740 --
Of course we have a network of
notes. That's all we have. So

00:24:40.030 --
the network communication
network that facilitates that

00:24:42.340 --
might be in the ether. Might it
be using wire? What have you?

00:24:47.240 --
Then Internet here. That is
a collection of.

00:24:52.680 --
In the networks interconnected
with bridges and routers and

00:24:56.496 --
this and that. So it's a big
mess. A big spaghetti of.

00:25:02.250 --
Smaller, bigger spaghetti of
devices, links, etc networks.

00:25:10.660 --
And then we have intranet and
this is actually when we scale

00:25:15.472 --
it down. Intranet Internet is
bigger in between, intranet is

00:25:19.482 --
inside, so here it's like an
Internet used by single

00:25:23.492 --
organization. So we're basically
running this thing on our own

00:25:27.502 --
and typically it's like for
World Wide Web so.

00:25:32.690 --
So it's like in self, perhaps
even self contained Internet, so

00:25:37.794 --
it's like a part of it. A
smaller contained portion of the

00:25:43.362 --
Internet, Internet. The big
thing, intranet small single

00:25:47.074 --
organization. Child childish
subset. That's what this would

00:25:51.919 --
be. Then we have separate

00:25:54.454 --
subnetworks. If you have a big
network, sometimes she only

00:25:58.671 --
interested in a small portion of
that and we would treat it as a

00:26:03.557 --
subnetwork. It means, like some
constituent network of an

00:26:06.698 --
Internet, meaning a smaller
segment in our organization.

00:26:09.490 --
Here for example, we have
different subnetworks. CS has a

00:26:12.980 --
couple of so then if you're on
these networks more than you're

00:26:17.168 --
in this CSS network.

00:26:19.170 --
And we see later on how one
would treat the addressing of

00:26:23.646 --
the network itself, including
the subnetworks. There's more

00:26:26.630 --
effect. You probably all have
seen in your configurations that

00:26:30.360 --
sometimes you see there is a
subnet mask and the subnet mask

00:26:34.836 --
typically is a mechanism to say,
like all the bits that are one

00:26:39.685 --
later on, get XI mean ended with
the real address to identify.

00:26:44.161 --
That's the network address and
all the ones that have zero.

00:26:48.264 --
That turns out to be.

00:26:50.320 --
The host address, so we see that

00:26:52.917 --
later on. So then we have our
end systems like my laptop, my

00:26:58.284 --
tablet, here that would be an
end system at the moment. So

00:27:02.412 --
that is just something to be
attached and we have

00:27:05.852 --
intermediate systems that would
be some kind of a switch or

00:27:09.636 --
something that can hook up.

00:27:12.170 --
Two or more networks, and so
device used to connect two

00:27:16.350 --
networks and permit
communication between these

00:27:18.630 --
things and we might have them as
bridges or routers where the

00:27:23.190 --
bridge is considered to be a
lower level. It doesn't

00:27:26.990 --
translate, it doesn't do much
thinking, it just forwards.

00:27:30.410 --
That's all they do and then the
router is considered like a

00:27:34.970 --
bridge on steroids. I mean it
would be a router that actually

00:27:39.530 --
looks at things can do certain

00:27:41.810 --
manipulation. Both of them will
send traffic through in One

00:27:46.040 --
Direction if needed or not.

00:27:48.590 --
But this one here operates
at Layer 3, where this one

00:27:52.231 --
operates at layer 2.

00:27:54.600 --
So layer two is a lower layer in
the OS I hierarchy. Remember we

00:27:58.604 --
start out with the physical
layer and work our way up.

00:28:02.490 --
So this is at a lower layer. The
higher the layer, the more

00:28:06.767 --
knowledge you can apply, for
example error checking

00:28:09.399 --
fragmentation, D. Later on we
see that when taking something

00:28:12.689 --
apart of putting it back
together all of that.

00:28:17.110 --
Should not be confused with.

00:28:20.310 --
Terms like I have a layer 2
switch or have a layer 3 switch

00:28:24.398 --
etc. That means simply.

00:28:26.320 --
From a device point of view, how
far do you use hardware control?

00:28:31.820 --
And I can run a Linux box and
we've done that as a router.

00:28:36.370 --
Press your Linux box as a

00:28:38.122 --
router. But I can also get a
layer 3 switch that has this

00:28:43.466 --
hardware encoded and it will be
so much faster than my Linux box

00:28:48.185 --
running as a router.

00:28:51.340 --
So the question is almost how
much how much visibility you

00:28:54.442 --
have in terms of the smarts and
how much of that is implemented

00:28:58.108 --
in hardware that determines the
quality of the speed or the.

00:29:01.970 --
Typically the price tag
also of these devices.

00:29:07.240 --
Alright, so these are the
standard terms that the book

00:29:10.450 --
uses. And we would have no
applications sitting like this,

00:29:15.599 --
so here would be the classic
connection between two hosts A&B

00:29:20.670 --
and they have some applications
that now interface with ports.

00:29:26.220 --
Like if it's a project would be
port 80 if it was a Mail program

00:29:30.480 --
as a port 25.

00:29:32.260 --
So whatever port you might have,
so these applications now want

00:29:35.934 --
to connect to some application
on the other side. That's

00:29:39.274 --
typically what we have.

00:29:41.900 --
Sending something and let's say
I do an FTP which is on port 20

00:29:46.226 --
and 21 if I recall right? So we
would basically establish a

00:29:49.934 --
connection from one year to the
other one. This is the server

00:29:53.642 --
and this is now a client, so I
would say like I want to

00:29:57.968 --
download this file and

00:29:59.204 --
essentially these two.
Logically, connect and request,

00:30:02.158 --
like I say one download so they
would say OK here it comes. This

00:30:08.276 --
is simplified language here.

00:30:10.640 --
So. The application still
themselves would now have these

00:30:15.252 --
access points which are ports,
and then they would form a TCP

00:30:19.680 --
packet. Whether TCP packet. Now
what could be UDP packet as

00:30:23.739 --
well. The main thing is that
transfer transport layer

00:30:27.060 --
protocol we will put that and
box it into the IP packet and

00:30:31.857 --
that's where our attention is
right now. The IEP IP packet is

00:30:36.285 --
the one that has the IP address
of the destination and we have

00:30:41.082 --
to find our way from here to
that other host.

00:30:44.970 --
And we don't even know what's
all in between in this

00:30:48.215 --
particular toy example here,
there are two networks in

00:30:50.870 --
between, so we come from the
host that lives in this

00:30:54.115 --
network. We go through router
that will realize based on the

00:30:57.360 --
adressing, that I use in the
information up here.

00:31:01.450 --
It will. It will figure out that
it has to forward it to that

00:31:07.050 --
site here switching over.

00:31:09.400 --
The IP packet of course will be
then brought down to the lower

00:31:13.248 --
link control to the Mac layer
and then it will back. Here it

00:31:17.096 --
will look at it, receive it,
bring it up, and will look

00:31:20.648 --
inside to peak. Where is it
going to? So it has to look

00:31:24.496 --
into the header of the IP
packet to make that decision.

00:31:29.140 --
So this is a router that has to
know the IP address. Otherwise

00:31:33.066 --
we can do it and then there has
to be a routing table here so

00:31:37.596 --
that it will find out OK. This
particular traffic. Now I'm

00:31:40.918 --
sending out on that physical
port here Becausw the

00:31:43.636 --
destination is attached to this
port and there might be more

00:31:46.958 --
networks in between. This would

00:31:48.976 --
be a very simple. Where
we have one, we have

00:31:53.814 --
a two hop scenario here.

00:31:57.230 --
Two edges in the graph.

00:32:00.950 --
So these are logical
connections and these are

00:32:04.830 --
physical connections here and
again from here to here we

00:32:09.680 --
have logical connections, so
that's how that would work.

00:32:14.045 --
So the first question is,
should IP be connection

00:32:18.410 --
oriented or connectionless?

00:32:21.050 --
And here's an example WHI
perhaps we don't want to have

00:32:26.528 --
connection oriented traffic,
because if we have now.

00:32:31.300 --
The application going from
one machine 8 to be which is

00:32:35.040 --
far away. For example, an
award to use connection

00:32:38.100 --
oriented and would first
have to basically request a

00:32:41.160 --
connection, then the other
side. Like Yup, I can. I can

00:32:44.900 --
do that, so there would be
an accept. Now would

00:32:48.300 --
transfer my file.

00:32:51.160 --
You know one of the time here
and then you have multiple

00:32:55.624 --
exchanges with acknowledgements
and then I would terminate this

00:32:58.972 --
and finish this up and that
would basically use up quite a

00:33:03.808 --
bit of time. Time goes in this
direction and oops, the root

00:33:08.272 --
problem is here in the
establishment of the connection,

00:33:11.620 --
the acceptance, determination
etc in the middle. Here we don't

00:33:15.340 --
have a problem.

00:33:17.900 --
But this of course
is now connection a.

00:33:22.650 --
An established connection, so we
don't want to deal with the

00:33:26.632 --
overhead. Another part is the
whole idea of the Internet in

00:33:30.614 --
its own right. Originally this
came of course from a defense

00:33:34.596 --
point of view. DARPA, DARPA was
the one that actually started

00:33:38.578 --
this whole thing. I mean, that
was under defense thinking, and

00:33:42.560 --
it came in a time where people
were afraid of the Cold War and

00:33:47.628 --
they would say like we don't
want to have a network that

00:33:51.972 --
looks like this here.

00:33:55.490 --
Let's say I have here. Here is
Seattle and here in New York.

00:34:03.010 --
If I had such a network here.

00:34:05.860 --
According to a military thinker,
they would say, well, all you

00:34:09.941 --
need to do is bomb one of these
links here and that's the that's

00:34:15.135 --
the end of the communication
between those two. So the idea

00:34:19.216 --
was let's establish a network
that is interconnected and

00:34:22.555 --
really has bunch of links there.
We don't even know what all is

00:34:27.378 --
available here. So we have a lot
of these things. Now it becomes

00:34:32.201 --
much more difficult to corrupt
such a network by physically.

00:34:36.090 --
Damage in the system so you can
drop a couple of bomb Siri can

00:34:40.024 --
blow this thing up. You can blow
that edge up and you have a

00:34:43.958 --
fairly high resilience there.

00:34:45.720 --
It's not necessarily optimized.

00:34:48.680 --
To be cake connected.

00:34:51.540 --
Remember K connected means
there are at least K disjoint

00:34:54.760 --
paths between any two. We
don't have to have that, but

00:34:58.302 --
from an attacker POV, if I saw
something, I would say like

00:35:02.166 --
what are the two weakest
connected ones, the minimum?

00:35:06.250 --
Cut set.

00:35:08.580 --
Where the weights are equal, for
example, and that would be my

00:35:12.144 --
most efficient attack point.

00:35:15.120 --
Find the one in this
particular case here, while if

00:35:18.450 --
we're interested from here to
here, where do I attack? Well,

00:35:22.113 --
it would be. Basically I take
this no doubt in that no

00:35:26.109 --
doubt, and things are done.

00:35:32.680 --
Well, this is silly exactly
because it's so, so we only are

00:35:36.880 --
two connected here. I can send
it like this or can send it out

00:35:41.780 --
like this. These are vertex.
These are vertex disjoint paths.

00:35:46.110 --
One here.

00:35:49.330 --
And one goes here.

00:35:53.030 --
So these are vertex disjoint

00:35:55.420 --
paths. Edge disjoint would be
different, but edge disjoint is

00:35:59.829 --
a difficult thing to me. Can
knockout an edge alright? Like a

00:36:03.921 --
backhoe is typically the cost
for that. You have construction

00:36:07.331 --
project and somebody ***** into
data cable. That's what would

00:36:10.741 --
happen here. But if a router
goes out, all the links attached

00:36:14.833 --
to the router route. So this is
this is a weaker thing. So at

00:36:19.607 --
the time the thinking was like
let's come up with a highly

00:36:23.699 --
dynamic quickly changing very
easily kind of figure big.

00:36:27.210 --
Mash big mash or should you
smash 'cause that's normally

00:36:31.160 --
considered like a certain
structure, but something

00:36:33.925 --
that's difficult to knockout?
That was the overall

00:36:37.085 --
motivation, and that would
mean such idea here may not be

00:36:41.430 --
it. It might be much better to
set it up in a way that these

00:36:47.355 --
things right themselves.

00:36:49.590 --
Then we have flexibility, send
it there and see how you make it

00:36:53.646 --
to the other side, regardless of

00:36:55.518 --
something failing perhaps. And
that was it. So initially

00:37:00.451 --
developed by DARPA, the D for
defense, of course.

00:37:05.320 --
So it was a defense project and
the Internet protocol IP is

00:37:11.776 --
basically the outcome of this
whole mess, so.

00:37:18.840 --
So now if and that uses
connectionless.

00:37:22.910 --
Connection this communication.
What does it mean? What we set

00:37:25.980 --
something out there packet and
say go and make it to your

00:37:29.971 --
destination off you go.

00:37:32.110 --
So there are huge advantages to

00:37:34.174 --
that. For example.

00:37:38.050 --
Flexible something changes.
This router goes out. This

00:37:40.810 --
router goes out due to
maintenance or what? Who knows

00:37:44.260 --
what? Maybe they have a
thunderstorm. They lost power.

00:37:48.550 --
So we can write differently.

00:37:52.210 --
Robust. Against. All
sorts of things.

00:37:58.950 --
Typically I mean flexibility
would be also like there's a

00:38:02.260 --
quicker link. There's a found
link that is much less

00:38:05.570 --
utilized so I can go there
rather than where there's a

00:38:09.211 --
lot of contention.

00:38:11.700 --
Robust means new links fail. The
systems fail, we can do it and.

00:38:19.780 --
The other thing is, there's no
overhead. There's no other.

00:38:23.590 --
There's no handshaking going on,
their data crams IP is a

00:38:27.781 --
datagram thing. The datagram is
the postcard. You drop it off

00:38:31.972 --
and you think it makes it there,
but there's no guarantee

00:38:36.163 --
datagrams have no guarantee.
It's the postcard of data

00:38:39.592 --
communication. You send it there
and off it goes. We know also

00:38:44.164 --
that we have TCP and UDP.

00:38:48.560 --
And those are TCP is actually
reliable and UDP is also

00:38:52.784 --
datagram. So we would have now
day to cram in a datagram the IP

00:38:58.160 --
packet. The datagram in
the datacom? Then you

00:39:01.019 --
send it off to China.

00:39:03.260 --
The reason we have of course
TNTS UDP to have a port number

00:39:08.187 --
because our IP packet has no
clue what application this is.

00:39:12.356 --
It doesn't know this is for.

00:39:15.570 --
The browser this is FTP. This is
this or that you know. So the

00:39:19.000 --
port number has to be part of
it, and that's at the higher

00:39:22.185 --
level. We stick that into the IP
packet, but the upper layer

00:39:26.666 --
would have to deal, for example
with reliability issues and the

00:39:30.252 --
only one we have there is TCP.

00:39:33.170 --
You DPS no reliability. It's
also a data crime.

00:39:37.250 --
So that is the. This is
advantage. It's not reliable.

00:39:41.848 --
There's no guaranteed delivery.
There's no guaranteed order of

00:39:45.610 --
delivery, meaning I sent three
things out. The last one might

00:39:50.208 --
arrive 1st, and so that becomes
securing problem for the two

00:39:54.806 --
sides. If I send something from
here to there, they can go do.

00:40:00.320 --
Different route so I don't know
what they take. There's no

00:40:03.598 --
guarantee an I might be waiting
here for awhile till that second

00:40:07.174 --
packet arrives because it's
worse. The second packet,

00:40:09.558 --
whereas the second packet and it
might not make it.

00:40:14.010 --
In which case then later on the
layer above would have to say

00:40:18.014 --
like what the heck is going on?
Where is my packet? So that

00:40:22.018 --
would be now where reliability
would be based on TCP and TCP is

00:40:26.022 --
a protocol that actually does do
reliability. There is a

00:40:29.102 --
handshake and if I send
something in order to hear from

00:40:32.490 --
you, I assume you didn't get it
and I would send it again.

00:40:37.840 --
Whether you never got it or
whether your acknowledge was

00:40:40.420 --
lost, for me, there's no
difference in that. All I can

00:40:43.258 --
say is I didn't hear back from

00:40:45.064 --
you. So that's the unreliable

00:40:47.912 --
part here. So now this would be
the typical example of a

00:40:53.250 --
configuration and the packets
that are being used here. For

00:40:57.010 --
example here I have some station
that looks up to a router, then

00:41:01.898 --
it goes through some frame relay
wide area network to another

00:41:06.034 --
router to another station, and
in this case here.

00:41:11.260 --
We want to have a TCP package.
Let's say we do an FTP transfer.

00:41:16.730 --
That would use TCP, whereas if
you were to use, let's say,

00:41:20.738 --
WhatsApp or something like that
audio video that is most likely

00:41:24.412 --
UDP, because So what a frame
missed. No big deal. But if a

00:41:28.754 --
bit flips in a file executor
that we transfer, that would be

00:41:32.762 --
a disaster. So from here it
wants to talk to this site here

00:41:37.104 --
and it does so by now. Sending
an IP packet to the lower link

00:41:41.780 --
control, which then brings it to
the Mac layer, which using the

00:41:45.788 --
physical layer brings it out to
the neighboring device which is.

00:41:49.590 --
In this case, this particular
router in here you would go up

00:41:53.682 --
to ask the question, well,
what's the IP address and I have

00:41:57.774 --
to unpack all the way to here.
Remember the structure is.

00:42:02.180 --
The TCP packet.

00:42:05.410 --
Here with its header.

00:42:07.890 --
Get stuffed into, let's
say the IP packet.

00:42:13.230 --
So now this is a header. This is
now going in here.

00:42:17.970 --
Run and they should try the
other direction here, so this

00:42:21.908 --
is now exactly this thing here
and then. This one here gets

00:42:26.204 --
down until we're at the Mac
layer. So until I'm down here

00:42:30.500 --
at the Mac layer.

00:42:33.620 --
Where is Santas across on the
other side. In the router I have

00:42:37.494 --
to 1st get this the lower link
control data units routes. So

00:42:41.070 --
this is my link control. Then I
open up in a find the IP to get

00:42:45.838 --
the IP address here. So this is
where. Whoops, I'm certainly in

00:42:49.414 --
the header here, so this is I'm
interested in the address.

00:42:55.450 --
So we need to know the
address where this is going,

00:42:58.981 --
the destination address and
that would now be.

00:43:02.750 --
Then we would consult or their
router would consult its routing

00:43:05.588 --
table to decide where does it go
out and it would say OK out of

00:43:09.458 --
this link here. This might be
rather than as many ports 32

00:43:12.554 --
ports or what have you, I don't

00:43:14.360 --
know. Then it would go to the
next router. On this end here.

00:43:20.820 --
Same thing again. They would
have to unpack it all the way to

00:43:24.395 --
here to find out what's the
address and it would forward it

00:43:27.695 --
here. That's why if you think of
the devices themselves, if you

00:43:30.995 --
do that a lot.

00:43:32.790 --
Like a gateway does or high in
high throughput router, you

00:43:36.541 --
better get something that does
most of the work in hardware

00:43:40.292 --
rather than software. If you
configure your Linux system like

00:43:43.702 --
your laptop running Linux as a
router for this you will not get

00:43:48.135 --
any glory for being a high speed

00:43:50.522 --
network. 'cause that would all
be under software control. You

00:43:54.132 --
need hardware controller so the
higher level you can buy, the

00:43:57.190 --
faster it would work. So there
would be essentially happening

00:43:59.970 --
over and over and over until
this system. Here a would talk

00:44:03.306 --
to the one in China which would
be. So we're constantly go up to

00:44:07.198 --
the next one. Look at the table,
go up next one, look at the

00:44:11.090 --
table. What we want to have of
course, and then it will go to

00:44:14.982 --
some links that will either use
satellite to go over the

00:44:18.040 --
continent or it will go through
a cable in the ocean. There will

00:44:21.654 --
be a long link somewhere.

00:44:23.810 --
And the cable will be just about
like 1 cable in reality. Of

00:44:27.892 --
course that cable segments that
have to be powered because

00:44:31.032 --
there's no fiber optics that can
send something over that length

00:44:34.486 --
without nothing coming out. So
every so often you have to have

00:44:38.254 --
a repeat are station and you
have companies that have big

00:44:41.708 --
boats that are traded at Mastec
that would go and maintain those

00:44:45.476 --
huge cables and there would be
there will be a link somewhere

00:44:49.244 --
where that cable will be part of
the Lingard will be 1 edge in

00:44:53.640 --
that link. It will be a fast
edge, so from a router POV

00:44:57.805 --
that will be attached to
very fast device.

00:45:03.010 --
So connectionless is what we
have here and connectionless has

00:45:09.100 --
this. Great thing flexibel

00:45:12.426 --
robust. And it does not do
any additional overhead,

00:45:17.116 --
nor handshaking involves,
so very little overhead.

00:45:21.620 --
So now the big problems when it
comes to Internetworking would

00:45:25.228 --
be like how do I route the

00:45:27.524 --
packets? And how do I find my
way through from here to China?

00:45:32.466 --
Great RFC? Or is it 1088? I
think it's the one that gives

00:45:36.730 --
the tutorial on how this works.

00:45:39.960 --
Take a look at that one. That's
the only one that I know that's

00:45:43.124 --
not a sleeping pill. That's
actually kind of fun to read.

00:45:45.610 --
All the other RFC's are like
Reading man pages for

00:45:47.870 --
entertainment. Then you have to
have a mental problem to do

00:45:52.100 --
that, but not really, but
you know what I mean. They're

00:45:56.096 --
not very entertaining and RFC's
are not entertaining. I think

00:45:59.426 --
it's a 1088 that one actually
because it's a tutorial of how

00:46:03.422 --
it would find its way. The first
issue that we run into is like

00:46:08.084 --
the lifetime of a datagram. How
long should it be defined and

00:46:12.080 --
the problem will be that there
is a potential for example to

00:46:16.076 --
get a datagram into a loop

00:46:18.074 --
situation for example. It could,
it might loop around in such a

00:46:22.095 --
loop, here where. We send it
from here to there that goes

00:46:26.641 --
from here to there goes back
here and then pretty soon we're

00:46:30.229 --
back here and we're whipping
around the loop and there has to

00:46:33.817 --
be a way to kill it off so there
will be a lifetime defined.

00:46:38.760 --
And if you exceed your lifetime,
the router that sees a packet

00:46:42.636 --
with that light would simply
just ignore it, destroy the

00:46:45.866 --
package. Therefore, I mean so
you don't have it then.

00:46:49.650 --
Fragmentation reassembly because
a lot of times we sent something

00:46:52.890 --
and we might not be able to keep
the length of the packet we

00:46:57.426 --
might have to actually chop up
the packet. It depends on what

00:47:01.314 --
we have in terms of the
neighborhood network, what

00:47:04.230 --
technology we have, what
capabilities etc. And so we

00:47:07.146 --
might have to shrink it down,
cut it in half. For example we

00:47:11.358 --
call that fragmentation and at
one point you have to reassemble

00:47:14.922 --
that as well and their issues
that need to we need to look at

00:47:19.458 --
there. And would be error
control and flow control,

00:47:22.202 --
and that's where we start
next time. Have a nice day

00:47:24.996 --
and I see you on Wednesday.

Duration:"01:16:32.4080000"

00:00:21.550 --
OK, a couple things as we get
started. The first one is we

00:00:26.828 --
have the last lab assignment.

00:00:31.670 --
And so this one is going to be a
bus differential protection lab

00:00:35.349 --
and so the on campus students is
pretty much going to be a

00:00:39.028 --
similar setup to what you did
before. You just need to read

00:00:42.424 --
through this and then work with
the TA. As far as if you're

00:00:46.103 --
going to, I think you all of you
have groups that you've been

00:00:49.782 --
doing the labs with the TA. If
you want to stick with those

00:00:53.461 --
groups in those times. If you
wanted to negotiate a different

00:00:56.574 --
time, then you just need to
communicate with him about that.

00:01:02.040 --
Until you have a system and
you're going to look at fault

00:01:05.628 --
at a couple of different
places, this is actually

00:01:08.319 --
should be a little bit shorter
than the last, quite a bit

00:01:11.907 --
shorter than the last lab.

00:01:14.920 --
And so you're really just
going to look at several

00:01:17.710 --
different cases.

00:01:19.710 --
Look at the behavior with this.

00:01:22.940 --
The Engineering Outreach Lab is
going to be similar.

00:01:26.730 --
So this is just the description
of the entering outreach lab.

00:01:31.580 --
And so it's a little bit more
complicated system, but it's

00:01:34.616 --
still the same basic idea.

00:01:36.980 --
And also you have some
information about the CT

00:01:40.410 --
ratio that's was used for this.

00:01:44.480 --
And then this is using that.

00:01:47.590 --
Relay model that the
differential relay model we

00:01:50.462 --
talked about. So again this
is a low impedance restrained

00:01:54.052 --
differential element, so it's
not. It's not a high

00:01:57.283 --
impedance differential
element.

00:02:01.530 --
If anyone has fair time and
wants to create their own

00:02:05.369 --
creative all the create this,
it wouldn't be that hard to

00:02:09.208 --
create a lab for the restraint
for the high impedance

00:02:12.698 --
differential elements. We just
haven't had a chance to put

00:02:16.188 --
together the simulation files.

00:02:18.800 --
So anyway, it's the same idea
you read in the data files.

00:02:24.470 --
Very similar to the handout that
we talked about with the lecture

00:02:28.310 --
last week. All of this stuff
we're reading the comtrade file,

00:02:31.830 --
and so where this really starts
to differ a little bit is

00:02:35.670 --
towards the end of it. Once
we've got the phasers, so we've

00:02:39.510 --
got the things where we're
looking at the voltages in the

00:02:43.030 --
currents, and then we have the
operating restraint current, and

00:02:46.230 --
so one thing that's different
from the hand out before is now

00:02:50.070 --
the. In this case, there's no.

00:02:53.660 --
Nothing where you put in a
multiplier to imitate

00:02:56.297 --
saturation. The simulation data
that you're using for this now

00:02:59.227 --
actually has saturation in it.

00:03:01.850 --
And the case is that you'll be
doing for the on campus

00:03:05.450 --
students in the lab. You're
actually going to be doing

00:03:08.450 --
these with an RTS simulation
instead of using the model

00:03:11.450 --
power system, and so that the
RTS will have setae. Models

00:03:14.750 --
that include saturation, but
you're still going to be

00:03:17.450 --
setting the actual physical
relay.

00:03:21.310 --
And then one of the things that
this is going to show is the

00:03:25.664 --
basically the how they operate.
Quantity changes. So basically

00:03:28.463 --
as it reads through samples,
this thing is moving and then it

00:03:32.195 --
works its way up and then it has
some final value it goes to and

00:03:36.860 --
so you can as you look at these
different cases once you enter

00:03:40.903 --
the slope setting you can
actually look at a little bit

00:03:44.324 --
how the how the value evolves
and when you look at the case

00:03:48.367 --
with the saturation you can
actually see how it.

00:03:51.300 --
Now the saturation changes
what it's what the relay

00:03:54.171 --
element is seeing too, and so
this was a case for an

00:03:57.999 --
internal fault, so it grows
quickly.

00:04:02.860 --
So any questions about that?

00:04:09.170 --
Hey are there any questions
from the last lecture?

00:04:12.680 --
Yeah, so in the last lecture
when you talk about the high

00:04:16.832 --
impedance plus differential
protection, you mentioned that

00:04:19.254 --
for an external fault. Once one
of the see T starts to saturate

00:04:23.752 --
it will dive deeper into
saturation, right? So my

00:04:26.866 --
question is how will that?

00:04:29.160 --
To how will that city begin to
saturate? Like because?

00:04:33.660 --
The currents are all balanced,
right? I mean based on the

00:04:37.972 --
culture of slow, so part of
it's too far into this into the

00:04:43.460 --
hand out so.

00:04:47.760 --
That's the internal fault. So
for the external fault part of

00:04:51.148 --
it's going to be the case that.

00:04:54.690 --
We've got this one. This is 1
heck external fault, right? So

00:04:58.338 --
this is seeing the current from
all of the other feeders or

00:05:01.986 --
other lines going through it,
and so depending on what the

00:05:05.330 --
burden is for this one.

00:05:07.800 --
Oh that 'cause there's
going to be?

00:05:12.460 --
The relay and the and some of
the winding resistance is going

00:05:16.084 --
to be dominant. Burden that
affect saturation in this one in

00:05:19.406 --
a lot of ways.

00:05:21.210 --
So if this one, if there's a
fault with a lot of DC offset,

00:05:25.088 --
especially then this one is
going to start to saturate.

00:05:27.858 --
'cause this is seeing the most
current. I thought there is only

00:05:31.182 --
one button then that's the one
at the end. Well, remember that

00:05:34.506 --
the burden and we look at ACT
when we look at burden.

00:05:40.260 --
Mr Lead wire.

00:05:48.530 --
So the first thing we're going
to have is the CT winding

00:05:51.338 --
resistance. And it's so. So
in this case the Siti

00:05:54.649 --
winding resistance is going
to be the most significant

00:05:57.088 --
one, because once we get to
the terminals of the see T.

00:06:07.470 --
We're basically connecting each
of the CTS.

00:06:12.750 --
In parallel on the secondary
side, right and then once

00:06:16.320 --
they once we have this
parallel combination, then

00:06:19.176 --
that's going. Then we have
the rest of the lead wire.

00:06:25.200 --
And we have the relay out here.

00:06:30.540 --
But there's the secondary
current on the secondary

00:06:33.404 --
winding, and the CT is still
going to see.

00:06:37.340 --
All that current, right?
The current when they sum

00:06:40.328 --
to 0 between.

00:06:44.320 --
We put in a third
CT just to kind of.

00:06:49.030 --
Illustrate this a little
bit more.

00:06:58.680 --
When I talk about connecting
them together right, this is

00:07:01.940 --
where they sum to 0, right?
So if it's if it's an

00:07:05.852 --
external fault.

00:07:12.350 --
So let's say that this is
the one with.

00:07:18.870 --
The external fault, right? So
that's going to have.

00:07:23.100 --
Let's say we have current going
this way and this one. Each of

00:07:26.948 --
these are going to have their
share feeding it right, so this

00:07:30.500 --
one is going to be the sum of
this plus this and so at this

00:07:34.940 --
point here. They're going to sum

00:07:37.224 --
to 0. But this one, each one of
these is going to have its own

00:07:42.072 --
fault current share the
fault current, it's it's

00:07:44.628 --
carrying. It's going to go

00:07:46.048 --
through this resistance. And
so basically what's going to

00:07:49.888 --
drive that start driving in
this one in the saturation is

00:07:53.936 --
going to be a combination of
the voltage drop across this

00:07:57.984 --
plus the ACE asymmetric
current due to the DC offset.

00:08:03.130 --
Remember that as we talked
about with on the BH

00:08:07.030 --
characteristic, the DC offset
is shifting you in One

00:08:10.540 --
Direction and the BH
characteristic.

00:08:17.450 --
And so when we look at this.

00:08:21.080 --
So under normal conditions.

00:08:23.650 --
It's going to be doing
something like this, right? And

00:08:26.760 --
if we have a fault with no set
without significant saturation?

00:08:31.480 --
It's going to be doing some like
this, and so if we have well

00:08:36.324 --
size CTS we may only see
behavior that looks like this.

00:08:40.730 --
But for a bus situation,
sometimes it's hard to get

00:08:44.380 --
around that, but if we add.

00:08:47.510 --
The.

00:08:52.590 --
The DC offset.

00:08:54.830 --
I did not draw that very well,
sorry. So we may start out with

00:09:00.248 --
something like this. Then the

00:09:02.183 --
next cycle. It's going to be
working like this and it's going

00:09:06.480 --
to be following that DC offset,
so it's going to push it into

00:09:10.302 --
saturation. Discuss. The flux
loops are being pushed this way

00:09:13.242 --
by the DC offset.

00:09:15.870 --
And in some cases with a
combination of the of a large

00:09:20.286 --
current and going through
this resistance in a DC

00:09:23.598 --
offset, this one may start to
go into saturation an.

00:09:29.390 --
Lessina cycle.

00:09:31.800 --
Possibly quite a bit less
in the cycle.

00:09:35.790 --
And so that's why that's why
even though you on the surface,

00:09:39.606 --
you would say that there
shouldn't be much voltage across

00:09:42.786 --
this, because these current sum
to zero and the voltage drop

00:09:46.284 --
across this should normally be
negligible. But what's going to

00:09:49.464 --
happen is that the combination
of that fault current going

00:09:52.644 --
through this winding resistance
and the DC offset starts this

00:09:55.824 --
one into saturation. And then
that mismatch current through.

00:10:00.130 --
That saturation goes through
this, and because of that

00:10:03.577 --
compensating resistor that's
going to drive this voltage up.

00:10:08.730 --
But because this is the one
that's already starting to

00:10:12.290 --
saturate and has a lower
impedance than it's, it's

00:10:15.494 --
going to tend to make this
voltage collapse and keep

00:10:19.054 --
these from rising.

00:10:28.560 --
Like I said, it's not. That's a
very good question. 'cause it's

00:10:32.280 --
there's a lot of things that are
not intuitively obvious when we

00:10:36.000 --
look at the high impedance bus

00:10:37.860 --
differential. Because we're
basically using something that's

00:10:42.662 --
inherently nonlinear to work.

00:10:57.580 --
Any other questions for my son?

00:11:06.790 --
OK, so then we're going to start
on. Next, we're going to start

00:11:11.223 --
talking bout transformer
protection and I talked to I did

00:11:14.633 --
a very quick introduction to
some of the some of the issues

00:11:18.725 --
and the difference.

00:11:20.960 --
Things were gonna talk about.

00:11:21.870 --
We're going to talk about.
Fall protection of the

00:11:25.190 --
transformer itself for faults
inside the transformer.

00:11:29.680 --
And then we're also going
to look at protecting the

00:11:32.850 --
transformer, firm
external conditions, and

00:11:34.435 --
this can include faults
external to the

00:11:36.654 --
transformer. Boy, the
transformer is carrying

00:11:38.556 --
the fault currents that
goes that go to it.

00:11:47.680 --
And then there are Transformers
introduce a number of unique

00:11:51.640 --
challenges that we'll talk about
as we go through this.

00:11:56.550 --
So in some ways it will start
out looking at a concept similar

00:12:01.308 --
to what we looked at with the
bus protection. So we're going

00:12:05.700 --
to a lot of the internal fault
protection for Transformers.

00:12:09.360 --
Starts with the idea of
restrained low impedance

00:12:12.288 --
differential element, so it's
kind of build time. We start. I

00:12:16.314 --
started with the bus protection.

00:12:29.630 --
And so one of the things that
the bear in mind as we talk

00:12:35.748 --
about transformer protection is
when we talk about bus

00:12:39.681 --
protection. Fast protection has
a bus fault or misoperation

00:12:43.614 --
where a bus gets tripped when it
shouldn't can have very severe

00:12:48.858 --
operational. Consequences for
our power system. So bus faults

00:12:52.556 --
are actually fairly rare.

00:12:54.760 --
Fat faults that cause were and
the bigger concern is as

00:12:59.028 --
generally going to be external
faults that caused the bus

00:13:02.908 --
protection to miss operate.

00:13:06.160 --
And so that's why the restrained
differential element, the high

00:13:09.640 --
impedance differential element,
have so there so much efforts

00:13:12.772 --
gone into developing and
optimizing those at the relay

00:13:15.904 --
vendors is because they are very
high consequences operationally

00:13:19.036 --
to the system in the short term.

00:13:24.130 --
Transformer failures, on
the other hand.

00:13:44.050 --
Can have longer time
consequences.

00:13:54.730 --
And that's because there are
longer replacement times.

00:13:59.700 --
And in most cases, if an
internal fault happens in a

00:14:04.560 --
transformer.

00:14:06.370 --
There is a good chance that it's
going to evolve to the point

00:14:10.348 --
where it's not something that's
very simply repaired. In some

00:14:13.408 --
cases there are still a number
of cases where they're caught

00:14:16.774 --
fast enough, or it could be
repaired simply, but if it gets

00:14:20.446 --
to severe faults and you'll have
a fire in the transformer, then

00:14:24.118 --
it can be very severe.

00:14:27.950 --
And so there are a number of
things. The number of strategies

00:14:32.750 --
that try to minimize the impact
of transformer faults.

00:14:49.760 --
So one of the big ones is
finding ways to reduce the

00:14:53.252 --
likelihood of them happening.

00:15:05.320 --
And so part of what a lot of
this comes down to is.

00:15:10.900 --
Track external events.

00:15:31.620 --
And it's really the life of
the installation. That's a

00:15:34.010 --
big issue.

00:15:35.620 --
So one of the things that I
mentioned is that we have two

00:15:39.741 --
directions. We're gonna go to,
and they actually are related to

00:15:43.228 --
each other. So one of the big
things that is a has a

00:15:47.349 --
consequense for Transformers is.

00:16:06.620 --
Meeting of the installation
will have a big impact on

00:16:09.700 --
how the life or how long
that installation is going

00:16:12.780 --
to be good.

00:16:23.030 --
Transient overvoltages is
another another issue.

00:16:44.770 --
So what are some of the
things that are going to

00:16:47.168 --
cause a transformer? Cause
heating in a transformer?

00:16:51.350 --
So let's think about a
transformer for a second

00:16:53.690 --
we have.

00:16:56.970 --
So I'm just going to draw a
single phase core.

00:17:01.570 --
So as we've talked about where
we have a single phase core

00:17:05.410 --
and have the low voltage
winding on the inside, an will

00:17:08.930 --
have a higher voltage winding
wrapped around the outside of

00:17:12.130 --
it, right? And then we'll take
those out to the bushings.

00:17:16.690 --
And as I mentioned earlier, we
don't. You don't see a

00:17:20.397 --
transformer core just sitting
out open in the air, right?

00:17:24.360 --
And so usually this is
going to be.

00:17:32.140 --
In a tank.

00:17:37.710 --
Anna's tank is going to be.

00:17:45.730 --
Filled with oil, right? So
usually it's going to be some

00:17:48.271 --
sort of a dielectric oil.

00:18:02.600 --
Is also used as a coolant.

00:18:08.650 --
And so you may look at a name
plate for a transformer, an it

00:18:13.914 --
may say that you have a
transformer that's rated at 15

00:18:18.050 --
MVA, 20 MVA.

00:18:20.300 --
25 NBA

00:18:23.920 --
so why would why would there
be 3 MVA ratings for the

00:18:27.712 --
same transformer?

00:18:34.120 --
Different cooling stages. It's
different cooling stages, so

00:18:37.424 --
this is going to be.

00:18:40.720 --
Basically, entirely
passive cooling.

00:18:45.100 --
So there is going to be there
will be radiator fins or on the

00:18:49.510 --
side of this case on the side of

00:18:52.030 --
that tank. This is going to be.

00:19:03.070 --
Going to be pumps used to
circulate oil to cool the

00:19:06.029 --
transformer or cool the oil so
it's going to circulate because

00:19:08.988 --
there are going to be.

00:19:11.010 --
Different spots in the winding
that are hot spots said certain

00:19:14.156 --
certain points are going to be

00:19:15.872 --
hotter than others. And so if
you don't circulate the coolant,

00:19:19.424 --
there will be a little bit of
natural convection, but you're

00:19:22.262 --
going to. Those hot spots are
not going to be cooled as well.

00:19:26.580 --
And then this is
going to be pumps.

00:19:31.090 --
Plus

00:19:32.920 --
running cooling fans that are
blowing error basically across

00:19:36.997 --
the radiator so that the
radiator works more efficiently.

00:19:45.810 --
So depending in some cases
people will just run these

00:19:49.220 --
all the time. In some cases
they'll based on the load

00:19:52.971 --
conditions, they'll start
and stop this equipment.

00:19:56.890 --
And if you have a transformer
that's always lightly loaded,

00:19:59.290 --
they may not. Run it as. Run to
run them very much at all.

00:20:15.100 --
So other things that could
cause heating.

00:20:23.270 --
So I want to be carrying
harmonic currents.

00:20:38.460 --
Do you know external loads?

00:20:48.380 --
So for example, if we have
a transformer that one of

00:20:52.153 --
the loads.

00:20:54.110 --
Is.

00:20:59.190 --
A dialed dialed rectifier.

00:21:04.740 --
And then we have a voltage
source converter.

00:21:09.580 --
Anyway, have an induction motor.

00:21:17.060 --
If.

00:21:19.260 --
This doesn't have any
compensation.

00:21:28.570 --
The current strong by this
drive are going to look

00:21:30.800 --
something like this.

00:21:34.920 --
And so this is going to
have 5, seven, 1113 and

00:21:39.463 --
basically multiples of
6 plus or minus one.

00:21:47.670 --
Is there going to have other
loads here? But this

00:21:50.100 --
transformer is going to be
carrying this current plus

00:21:52.287 --
whatever loads are here.

00:21:57.000 --
And carrying those harmonic
currents increases Eddy current

00:22:00.808 --
losses in the transformer core.

00:22:04.480 --
And so that the transformer is
going to run hotter.

00:22:23.280 --
And so they actually
you can actually get.

00:22:27.470 --
K factor rated.

00:22:35.920 --
So basically these K factors are
more of a derating factor.

00:22:41.170 --
And so if you have, if you know
you're going to be supplying

00:22:45.642 --
harmonic loads, you can buy a
transformer that has basically

00:22:49.082 --
an extra factor in its MVA
rating to be able to deal with

00:22:53.554 --
harmonics. If you're not, if
you don't have a transformer

00:22:58.028 --
that has any K rating an you
start supplying harmonics,

00:23:01.848 --
then usually you can. There's
there are formulas from the

00:23:05.668 --
IEEE standards that talked
about how you derate the

00:23:09.106 --
transformer, so instead of
being a 15 MVA transformer, it

00:23:12.926 --
may actually be a 12 MVA
transformer due to the extra

00:23:17.128 --
heating from the harmonics.

00:23:19.820 --
And so when someone buys a
transformer, usually you're.

00:23:24.470 --
Part of the data for when
you sign the contract with the

00:23:28.019 --
supplier and stuff like that is
saying well, this is. This has a

00:23:31.568 --
30 year design life for this as
a 25 year design life.

00:23:35.850 --
If you routinely overheat the
transformer, you may take years

00:23:39.750 --
off of that life.

00:23:41.870 --
So we had an outreach student
awhile back that worked at an

00:23:46.334 --
industrial facility that was
basically with zinc smelter.

00:23:50.010 --
And so they had a lot of very
large rectifier loads and so

00:23:54.924 --
they had Trent. They bought
Transformers that had.

00:23:59.340 --
30 year old designlife

00:24:01.880 --
Then they push them kind of
right. It may be a slightly

00:24:07.520 --
beyond their NBA ratings.

00:24:10.240 --
And then they gave this heavy
harmonic loading. So they

00:24:13.060 --
lasted about 10 years.

00:24:18.790 --
An that fit and when I say
lasted about 10 years, they had

00:24:24.237 --
a fault, and so if I did so by
heating the insulation, you end

00:24:30.103 --
up causing the you decrease the
lifespan of the installation and

00:24:34.712 --
your moral an it's more likely
to fail by having our fault. And

00:24:40.159 --
so that's why this external
event, external condition stuff

00:24:44.349 --
matters from the from the
transformer Protection POV.

00:24:52.670 --
So transformer protection will
usually track the loading on a

00:24:56.900 --
transformer an if the
transformer is overloaded, and

00:25:00.284 --
then there are formulas you can
use to figure out how much

00:25:05.360 --
that's affected the life.

00:25:10.980 --
And so some other things that
will go into this are going

00:25:13.776 --
to be over excitation.

00:25:23.720 --
So on a transformer over
excitation basically means

00:25:26.400 --
a steady state.

00:25:34.200 --
However, voltage that means
you're partially saturating.

00:25:57.850 --
Angene why the transformer is
going to produce more

00:26:01.478 --
harmonics because of this?
Because this is a steady state

00:26:05.438 --
sinusoidal condition, these
will be only odd harmonics.

00:26:11.110 --
And often the 5th harmonic is
usually going to be the one

00:26:14.674 --
that's used as sort of the main
detection detector for that.

00:26:21.140 --
But again, because you're
saturating the core.

00:26:26.070 --
What does that? What does
it mean when you saturate

00:26:28.960 --
the core more deeply?

00:26:35.050 --
More excited, you have more
expectations, well over

00:26:37.938 --
expectations. We have more
expectation right? But what

00:26:40.826 --
losses go up?

00:26:44.480 --
The winding losses go up, or
so we're going to increase

00:26:50.200 --
hysteresis losses.

00:26:54.180 --
Remember, hysteresis losses
are basically proportional to

00:26:56.672 --
the area of the hysteresis
loop it follows, so if you're

00:27:00.588 --
over exciting the transformer,
your loop has a bigger bigger

00:27:04.148 --
area, so the losses are going
to be higher.

00:27:24.780 --
Another one that's a big factor
are through faults, which means

00:27:29.345 --
that the transformer.

00:27:52.160 --
So basically, one of the things
that also gets tracked is how

00:27:56.120 --
many, how many faults is this
transformer supplied? What is

00:27:59.420 --
the magnitude of the fault

00:28:01.070 --
current bin? Because. Oh through
fault can cause very substantial

00:28:05.092 --
heating. It may not. It's not
going to last very long, but

00:28:08.764 --
it's going to take a long time.
It's going to take awhile quite

00:28:12.742 --
awhile for the transformer to
cool down from that.

00:28:37.870 --
So even frequent large motor
starting or if the transformer

00:28:42.020 --
is supplying current to
energize other Transformers.

00:28:48.500 --
So for example when.

00:28:53.020 --
I think their procedures have
changed a little bit, but at

00:28:56.771 --
Grand Coulee there's a pumped
hydro storage facility that

00:28:59.840 --
has very large synchronous
Motors. They generally only

00:29:02.568 --
start those Motors once a day
because the thermal shock on

00:29:06.319 --
the Motors every time they
start them is so much that

00:29:10.070 --
they can't start them more
often.

00:29:14.040 --
They redid that facility.

00:29:17.610 --
And within the last.

00:29:20.130 --
Eight years, so I think
they've redone it, so

00:29:23.019 --
it's not quite as harsh.

00:29:26.260 --
But so basically all of
these things get tracked.

00:29:45.910 --
They predict lifespan loss and
we're going to. We're going to

00:29:48.814 --
come back and talk about the
over some of these issues and

00:29:51.982 --
how and how this factors into
the transformer protection later

00:29:54.622 --
in the course. I want to talk
about internal faults. First,

00:29:57.526 --
we're going to come back to

00:29:59.110 --
this. That a good resource for
this. Our textbook does a pretty

00:30:03.945 --
good job with this, but also the
IEEE 30 C 3791.

00:30:08.770 --
Also another good one for
this and or there's some

00:30:11.730 --
other references. We'll talk
about a little bit later.

00:30:21.310 --
And So what I want to start
talking about is now protection.

00:30:27.370 --
For internal faults.

00:30:33.170 --
And will be going through
this over the next couple

00:30:35.320 --
of lectures.

00:30:45.020 --
And so I guess that's one
other sort of structural

00:30:47.990 --
thing. When we look at.

00:30:51.370 --
Large Transformers again.

00:31:13.460 --
I felt it evolved to
the point where there's

00:31:15.485 --
a fire can cause long.

00:31:19.490 --
As I said, long repair times.

00:31:23.550 --
And so some of the things that
you'll see in a substation, for

00:31:29.205 --
example for large transfer
transmission substations

00:31:31.815 --
especially often you'll see
single phase Transformers used,

00:31:35.295 --
and so you'll see.

00:31:40.310 --
Three single phase units, and
actually they are often going

00:31:43.810 --
to be 3 winding Transformers
as we talked about earlier in

00:31:47.660 --
the semester.

00:31:49.800 --
And so they're going to have
their own individual tanks.

00:32:00.700 --
And when you look at the
substation.

00:32:04.490 --
You'll see a wall
that's been placed.

00:32:09.980 --
Between the Transformers.

00:32:13.120 --
So what's the purpose of
that wall?

00:32:16.130 --
Prevent fire from
cleaning, so these are.

00:32:20.530 --
Firewalls raise more of the
archaic usage of the term

00:32:24.070 --
instead of the one that's now
everyone uses when they talk

00:32:27.964 --
about software.

00:32:29.990 --
And so this is basically if
this one has a fault, and as

00:32:34.072 --
a fire, the idea is that
this is that this is going

00:32:37.840 --
to basically make it less
likely for any for the heat

00:32:41.294 --
in the flames to get to this
transformer, so it fails to.

00:32:49.730 --
And a lot of utilities will

00:32:52.352 --
have. A limited number of
spare Transformers that they

00:32:56.392 --
can put in to replace a
failed transformer.

00:33:00.350 --
So.

00:33:03.620 --
This was probably almost 15
years ago. Now there was a

00:33:08.328 --
transformer fault at a 500 kva.
Think it's a 500KV substation in

00:33:13.464 --
the Southwest. An
they did not have.

00:33:18.530 --
Firewalls between the single
phase transformer, so they lost

00:33:22.364 --
all three phases. They had their
spares close enough that it

00:33:27.050 --
actually scorched the paint off
of the tanks, but they actually

00:33:31.736 --
didn't lose the spares.

00:33:36.820 --
But because they lost all three
and they only had three spares,

00:33:41.392 --
then they had to scramble to try
to get spares from other people.

00:33:46.345 --
And I know that one of the
utilities in the northwest

00:33:50.536 --
sentence pairs and they had all
sorts of issues because these

00:33:54.727 --
were 500 kva Transformers, Oran,
high MVA ratings. Just

00:33:58.156 --
transporting them was difficult.

00:34:04.410 --
And I think even
transporting the spares

00:34:06.867 --
took like several months.

00:34:17.190 --
So then actually one of the
things that the.

00:34:21.070 --
US Department of Energy in
the Department of Homeland

00:34:24.814 --
Security been working on in
the last several years, is

00:34:28.974 --
basically trying to form a
kind of a national database

00:34:33.134 --
of transformer spares and
also trying to increase the

00:34:36.878 --
inventory of spares so that
if there is something like.

00:34:42.950 --
High energy electromagnetic
pulse from a nuclear weapon or a

00:34:47.550 --
major Geo Geo magnetic.

00:34:50.070 --
A disturbance for the gym
geomagnetically induced currents

00:34:53.454 --
caused transformer failures that
they've got something that they

00:34:57.261 --
can go to restore power in some

00:35:00.222 --
areas quickly.
Relatively quickly.

00:35:05.270 --
OK, so let's now start talking
a little bit more about the

00:35:08.798 --
Internal fault protection.

00:35:16.340 --
Really, the first line for
this is going to be

00:35:19.390 --
differential protection.

00:35:27.600 --
So as I said, much like
what we were just talking

00:35:31.285 --
about with the.

00:35:33.640 --
Boss protection for the
restrained low impedance

00:35:38.078 --
differential protection.

00:35:42.100 --
So let's start out looking
at a transformer that.

00:35:47.170 --
We have a YY connection.

00:35:51.350 --
And so, let's say it's.

00:35:55.330 --
3:45 KV. 2.

00:36:00.110 --
138 KV.

00:36:07.700 --
And so for the moment,
let's just say it's a.

00:36:11.870 --
2 winding Transformers.
So we're going to have

00:36:14.102 --
three leads coming out.

00:36:34.210 --
Now I have see T is on each
phase and will just look at one

00:36:38.110 --
phase for the moment.

00:36:47.100 --
And so we start out saying,
OK, well, this looks a lot

00:36:50.436 --
like what we talked about
when we anytime we talked

00:36:53.216 --
about differential
protection. So we're going to

00:36:55.162 --
have current if we have
current going this way.

00:37:02.630 --
Then we're going to have.

00:37:06.340 --
Secondary current. That's going
to circulate like this, and.

00:37:12.870 --
I op should be about 0,
right? That would be. That's

00:37:17.666 --
what we would expect.

00:37:23.200 --
Now, unlike the virus
protection, we've got a number

00:37:27.574 --
of factors that complicate this.

00:37:44.360 --
So what do you think? Some
of the complicating factors

00:37:46.660 --
might be?

00:37:49.540 --
Configuration. Well, let's
say they will stick with the

00:37:53.020 --
YY for the moment.

00:37:56.010 --
If it's why Delta that, that
will add, that will be the next

00:37:59.195 --
challenge, will talk about
after we finish this one.

00:38:03.450 --
CD accuracy. Find CD accuracy.

00:38:07.640 --
So ciety accuracy, but
there's actually something

00:38:09.831 --
before that. One is going to
be the CT ratios.

00:38:37.200 --
So we may not get apart. We
may not get a perfect

00:38:40.284 --
cancellation of.

00:38:42.410 --
So let's say that just for
making this easier, let's say

00:38:46.172 --
that this was a 2 to one ratio.

00:38:54.770 --
So let's say that this was
500KV and this was 250KV just

00:38:58.598 --
for nice numbers. Even though
the 2:50 is not something

00:39:01.788 --
you'd run across much.

00:39:04.660 --
Then we would say OK. Well
then this. Let's say that

00:39:07.608 --
this is 1000 to one CT and
this is going to be what?

00:39:15.290 --
Or 1000 to 5C T, and
that's what would this

00:39:17.760 --
would need to be then.

00:39:24.010 --
Remember, this is.

00:39:26.200 --
Two to one is the effective
voltage transformation

00:39:28.680 --
ratio, so the current goes
the opposite, right?

00:39:32.170 --
So so this one would need to
have 500 to 5 setes.

00:39:37.110 --
So that would be one that
would be an example of a

00:39:39.894 --
good cancellation. So
let's say that this was.

00:39:44.450 --
500KV to
250KV.

00:39:50.810 --
And the cities were.

00:39:53.330 --
1000 to 5

00:39:56.690 --
in. 500 to 5 so that's something
that you could pretty easily.

00:40:00.320 --
Fine cities.

00:40:03.260 --
To cancel that right?

00:40:06.340 --
If we look at 3:45 to 138.

00:40:13.080 --
That's not going to be so
easy to find CTS that give

00:40:16.572 --
you a good cancellation on
that. So even if this was

00:40:19.773 --
even if these were still.

00:40:22.920 --
Thousands of five.

00:40:27.930 --
This would need to be
basically 1000 times.

00:40:33.640 --
38 / 345.

00:40:37.240 --
To five.

00:40:43.830 --
And chances are that's not
going to be a nice stock

00:40:47.108 --
number that you're going to
be able to buy in. SNS ET.

00:40:56.510 --
And so it's one that we're we'll
talk about a solution for that,

00:41:01.424 --
but this is basically going to

00:41:03.692 --
be. Having

00:41:06.760 --
taps on the relay.

00:41:10.600 --
So watch mechanical relays. What
they had was they had multiple

00:41:13.625 --
tap points where you could

00:41:15.000 --
connect. The inputs from the
transformer for the differential

00:41:19.010 --
and you could partly correct for
that mismatch to a degree you

00:41:23.690 --
couldn't. You could not connect
4 correct for it perfectly, but

00:41:27.980 --
you could. You could go a long
ways towards correcting it.

00:41:33.160 --
What we'll see in probably not
today. We may. I don't know if

00:41:37.697 --
we get to the example today,
what you'll see in

00:41:41.187 --
microprocessor relays now that's
just a number, so it's just a

00:41:45.026 --
scaling factor, so you can. So
basically you as you enter the

00:41:49.214 --
stuff into the relay for setting
it, you're entering the

00:41:52.704 --
information so the relay
calculates that tap and you

00:41:55.845 --
don't even have to answer.
Calculate it yourself so you say

00:41:59.684 --
OK, here is the MVA rating.
Here's the voltage rating.

00:42:03.680 --
And then at the relay says
OK and this is the rated

00:42:06.980 --
current and just basically
calculates it for you.

00:42:11.830 --
And then you also put the seat.
The actual CT ratios 'cause it

00:42:15.444 --
puts that in as a correction to.

00:42:27.670 --
Another thing you'll see in a
lot of large power Transformers

00:42:31.080 --
is they have taps, right?

00:42:34.410 --
So we may see.

00:42:37.830 --
500KV to 250KV.

00:42:42.510 --
Anne, this could be we could

00:42:46.392 --
have. Plus 2
1/2% + 5%

00:42:53.060 --

5%.

00:42:58.620 --
And these could also have
some different apps. So if

00:43:01.930 --
you start putting.

00:43:04.060 --
If you and so in some
cases, these maybe.

00:43:08.340 --
For lower power ones,
these may be on load. Tap

00:43:11.695 --
changing Transformers where they
can be changed. In other cases

00:43:14.745 --
the transformer has to be D
energized for crew to come in

00:43:18.405 --
and change that tag.

00:43:22.870 --
What what is that tap change
due to the differential current?

00:43:32.540 --
You just change the ratio of the
transformer, right? So you've

00:43:36.984 --
gone to the effort of correcting
for compensating for this, this

00:43:41.428 --
ratio and the CT ratios. Now you
just threw that off because you

00:43:46.680 --
changed the transfer. The power
transformation ratio by 2 1/2%.

00:43:59.070 --
Then another one would be.

00:44:25.660 --
The transformer is always going
to draw some magnetizing current

00:44:28.480 --
if it's energized right.

00:44:32.250 --
And this is something that's.

00:44:34.160 --
Going into the transformer
and not coming out.

00:44:44.190 --
And as we talked about last
time, this might be 2 to 4%,

00:44:48.948 --
maybe 5% of the rated current.

00:45:07.230 --
It will be higher if the
transformer is over excited.

00:45:13.210 --
So there's really two things
that you need to look at with

00:45:16.414 --
over. Excitation is going to be.

00:45:18.830 --
If the over excitation is severe
enough and last long enough you

00:45:23.114 --
want to trip the transformer.

00:45:25.910 --
But you don't want to trip it
because you think it's an

00:45:29.414 --
internal fault, so you don't
want to trip at the instant it

00:45:32.918 --
happens. So there's some
tradeoffs on that, and the

00:45:36.460 --
harmonic content of that's
going to be a factor in how

00:45:39.595 --
the relay responds to it.

00:45:44.120 --
Now there's another issue
that you have to worry about

00:45:46.480 --
with magnetizing current.

00:45:51.280 --
What would that be?

00:45:58.370 --
So we have magnetizing
inrush current.

00:46:09.250 --
So if you energize a
transformer.

00:46:23.570 --
You're going to see a
current that's going to

00:46:25.568 --
start out looking like this.

00:46:28.260 --
And it may take a second or two

00:46:31.508 --
to. One at one to two seconds
to get down to the normal

00:46:36.314 --
magnetizing current.

00:46:40.990 --
So are people familiar?
Why Transformers exhibit

00:46:43.867 --
this behavior?

00:46:52.120 --
So it goes down, it goes back to
our hysteresis characteristic.

00:46:57.400 --
So the transformer is going
to when it's operating is

00:47:00.650 --
going to be.

00:47:03.580 --
Following something that looks
like this, right? So if this is

00:47:07.507 --
B versus H.

00:47:10.670 --
This is proportional to voltage.
This is proportional to current.

00:47:15.790 --
So every time you go through a
sinusoidal cycle, it's going to

00:47:18.982 --
trace this curve, right?

00:47:22.010 --
And so when you deenergize the
transformer, you deenergize

00:47:26.042 --
nearer at a current 0, right?

00:47:29.630 --
And so when the current goes to
zero, you're going to be

00:47:32.654 --
somewhere up here. And so
there's going to be some trapped

00:47:36.706 --
flux on the core.

00:47:38.830 --
When it's deenergized and
depending on where you were in

00:47:42.030 --
that hysteresis cycle, when the
breaker contact cleared or what

00:47:45.230 --
the power factor of the current

00:47:47.150 --
was. Usually the final invoice
and normal routine operation

00:47:51.948 --
when I want to Transformers.

00:47:54.940 --
D energize you open one side,
then you open the other ones

00:47:59.476 --
you're interrupting, basically
just magnetizing current with

00:48:02.122 --
the final. The energizing of
the transformer.

00:48:06.540 --
When you re energize it.

00:48:09.140 --
How is voltage related to
flux in a transformer?

00:48:13.830 --
So V is equal to NDF DT, right?
So the flux in the voltage or 90

00:48:19.014 --
degrees out of phase with each
other. But you can so that the

00:48:23.226 --
voltage here at some point in a
sinusoidal voltage waveform you

00:48:26.790 --
can map that the flux when you
energize it. So when you're when

00:48:31.002 --
you close a circuit breaker,
there's going to be some

00:48:34.242 --
basically effective flux that
you're you're trying to impose

00:48:37.158 --
on that core. So if you're lucky
and you and you pose a circuit

00:48:41.694 --
breaker in the effective flux
for the point on waiver, you're

00:48:45.258 --
closing. It's about what you
trapped on the core.

00:48:48.680 --
Then there's not really
going to draw any current.

00:48:53.430 --
If you're unlucky and you had
trap works up here and you're

00:48:56.562 --
closed when you're somewhere
down like this, now the

00:48:58.911 --
transformer is going to draw a
lot of current to try to

00:49:02.043 --
equalize that flux. And after
magnetizing inrush current.

00:49:06.320 --
And it's very nonlinear current.

00:49:09.000 --
And so this has a lot of
harmonic content. The

00:49:12.210 --
generally it's going to be
dominated by second and

00:49:15.099 --
then 5th and so on. But
it's going to have more

00:49:18.630 --
even harmonics where the
over excitation is only

00:49:21.198 --
going to be odd.

00:49:25.610 --
How's the modern steels that
they're using in newer

00:49:29.615 --
Transformers? Do not have a
sharper second harmonic

00:49:32.839 --
characteristic. They still draw
big magnetizing currents, but

00:49:35.135 --
now there's not as clear a
second harmonic, and we'll talk

00:49:38.292 --
about some of the issues with
that later in the.

00:49:42.650 --
Not this, not later
today, but next week or

00:49:45.570 --
the week after next.

00:49:49.040 --
So you've got these very large
currents again, they're just

00:49:51.940 --
going into the transformer.

00:49:57.860 --
And so you know, if you're doing

00:49:59.764 --
a normal. Registration of the
transformer. Not something

00:50:02.364 --
following like Re closing in a
fault. You might have this side

00:50:06.312 --
open and you energize this side
and so now you're seeing current

00:50:10.260 --
San people have measured
currents as high as 15 per unit.

00:50:16.260 --
If there are a lot of lights,
limits that is partly whether

00:50:19.596 --
the surrounding power system
can supply that much current.

00:50:22.098 --
If there's too much impedance
in the power system that won't

00:50:25.156 --
supply it.

00:50:28.120 --
And so you're doing. You have a
differential element. You're

00:50:31.140 --
going to see. Let's say it's
something more normal, like 5 to

00:50:34.764 --
7 per unit for a second.

00:50:37.980 --
So in electromechanical relays.

00:50:41.570 --
One of the things that they did
initially was basically turn off

00:50:46.274 --
the differential element until
the inrush current period was

00:50:49.802 --
over. They still had issues
where if you had two

00:50:53.199 --
Transformers that were close
together and you energized one

00:50:55.638 --
when the other one was on,
sometimes you had a sympathetic

00:50:58.619 --
trip of the different of the
differential element for the one

00:51:01.600 --
that was already energized.

00:51:07.180 --
Professor, I have a
question on this one, so

00:51:09.952 --
there is no saturation
really, it's just the.

00:51:13.740 --
The core trying to reach that

00:51:15.876 --
flux level. But there's no
saturation, so as.

00:51:21.150 --
It face it, it started has sort
of a saturation effect because

00:51:24.966 --
of where it pushes the flux, but
there really isn't any true

00:51:28.782 --
saturation of the core in this.

00:51:31.560 --
So why isn't it sinusoidal?

00:51:35.990 --
So when you think about the
iron in the core right, you

00:51:40.423 --
basically have a bunch of
magnetic domains that want to be

00:51:44.174 --
in random directions, right? So
let's say that because of the

00:51:47.925 --
trap flux, they're all pointing

00:51:49.630 --
this direction. And for the
inrush you're trying to flip

00:51:53.712 --
them all to go back. Basically
you want the flux to go this

00:51:58.249 --
way, so you need to flip all

00:52:00.692 --
these domains. And.

00:52:03.920 --
They don't, simply.

00:52:06.420 --
Follow a nice thing in
sinusoidal behavior as they flip

00:52:09.250 --
on this. So there's some
resistance. I'm really

00:52:12.652 --
oversimplifying this, but
basically it's it's a

00:52:15.186 --
magnetic. The nonlinear
magnetic behavior of the core

00:52:18.082 --
that keeps it from looking
sinusoidal.

00:52:25.980 --
And this harmonic, and So what
we're going to see in a little

00:52:30.426 --
bit, is that to try to minimize

00:52:32.820 --
this effect. The second
harmonic is often used as a

00:52:37.252 --
as a signature, so if the
second harmonics above a

00:52:40.942 --
certain threshold.

00:52:43.030 --
Then it's got the relay will
block the differential

00:52:46.189 --
element, so you can either do
harmonic blocking or harmonic

00:52:49.699 --
restraint, which is basically
making the slope steeper.

00:52:53.590 --
Now, this raises an interesting
thing. From a relay point of

00:52:57.572 --
view. We talked about digital
filters, right? So here we

00:53:01.192 --
talked about second harmonic. I
talked about fifth Harmonic when

00:53:04.812 --
I talked about over excitation
detecting over excitation.

00:53:09.520 --
So remember what we talked
about with digital filters? If

00:53:12.270 --
we're using cosine filters.

00:53:14.730 --
Well, the is the what is a
cosine filter due to harmonics.

00:53:19.866 --
What's the gain about cosine
filter 0, right? So the relay

00:53:24.574 --
needs a separate.

00:53:26.820 --
Cosign filter that if you want
to measure second harmonic or

00:53:30.582 --
you want to measure 5th harmonic
or any of the others, you need

00:53:35.028 --
to have some separate
filter elements that are going

00:53:38.448 --
to calculate those.

00:53:40.160 --
Because the normal cosine filter
using for your protection

00:53:43.400 --
calculations is going to have a
gain of zero and block those.

00:53:49.450 --
And when you start getting up
to 5th or 7th, now you're

00:53:52.450 --
starting to get up to the range
where the low pass filters,

00:53:55.450 --
anti aliasing filters also
going to have an effect on

00:53:57.950 --
them.

00:54:03.460 --
So when you talk about residual
magnetism, why doesn't it die

00:54:07.387 --
out? So if I'm.

00:54:09.370 --
I'm switching off or closing
opening the breaker in front of

00:54:13.286 --
the transformer at equals to
zero. Eventually the residual

00:54:16.490 --
magnetism should die out, right?
If I'm not energizing it back in

00:54:20.762 --
let's say days or weeks. So does
it die out and not? It does

00:54:25.746 --
decay OK, so basically it's a
it's a thermal process. So

00:54:29.662 --
basically these are going to try
to randomize if the car is warm

00:54:34.290 --
when you demagnetize it, then
they tend to randomize faster

00:54:37.850 --
than if the core is cool as the
core as a transformer cools that

00:54:42.834 --
slows down the rate.

00:54:44.460 --
That randomization OK, but even
if it's gone to zero an you

00:54:48.900 --
closing your somewhere up
here still we're going to have

00:54:52.970 --
some issues on that.

00:54:57.930 --
Awhile back, well actually one
of the Masters students here who

00:55:01.989 --
works at Sweitzer. Now guy named
Doug Taylor looked at using a DC

00:55:06.786 --
source to preflex the
transformer so you could put

00:55:10.476 --
the trap flux at a known at a
known point and then if you have

00:55:16.011 --
Breakers with individual phase
control then you can control

00:55:19.332 --
when you close them.

00:55:22.220 --
They also are using variations
of that an like.

00:55:28.760 --
There's been a lot of stuff
looking at that in Europe, for

00:55:32.324 --
example, in some of the offshore
wind farms where they basically

00:55:35.591 --
are in a system that can't
supply that magnetizing current

00:55:38.561 --
to magnetize the core, because
there isn't a source strong

00:55:41.531 --
enough to provide it out there.

00:55:44.090 --
And so they want to be able to
close the Transformers with no

00:55:48.276 --
inrush. And so rather than pre
flexing the cores, they're

00:55:52.692 --
looking at trying trying to
dissipate the flux in the

00:55:56.960 --
core so that they can bring it
to zero, and then they do

00:56:02.004 --
individual phase control on the
Breakers to minimize the inrush.

00:56:07.670 --
Also the whole pre fluxing
minimize trying to get the

00:56:10.730 --
known side of inrush makes a
big difference. If you have a

00:56:14.402 --
five legged core versus the
three legged core.

00:56:18.190 --
So when you see the anticipated,
basically they figure out at

00:56:21.644 --
what time or what voltage at
what point in the voltage the

00:56:25.412 --
breaker was opened, and then
based on that they calculate the

00:56:28.866 --
residual magnetism and the
decay, and then they open

00:56:31.692 --
individual phases at different
times. Or they close them, they

00:56:34.832 --
close them at specific times.
OK, so the Breakers are always

00:56:38.286 --
going to try to open it. A
natural current 0. Sure, an

00:56:42.054 --
there are actually some big
problems if you don't open it in

00:56:45.822 --
natural current 0, because then
you can get very big.

00:56:49.350 --
Transient response if you do
a current shopping.

00:56:53.590 --
So the parasitic capacitance
of the winding will interact

00:56:56.560 --
with the magnetizing branch,
and you can see like 2 / 2

00:57:00.520 --
per unit voltage.

00:57:03.600 --
Even if you're chopped
like half an amp.

00:57:11.700 --
That's a topic more for
you. See 524 though.

00:57:20.290 --
OK, so any other questions
related to the magnetizing.

00:57:24.950 --
Current behavior.

00:57:27.630 --
So these are all things that
need to be accounted for in

00:57:31.758 --
creating the differential
element an in setting like

00:57:34.510 --
the slope and the minimum
operate current.

00:57:39.090 --
The other one to look at is
going to be the transformer

00:57:42.342 --
phase shift.

00:57:49.760 --
So I started out drawing a
YY transformer.

00:58:00.000 --
So the other thing we have to
look at is Delta Y.

00:58:04.150 --
Or why Delta Transformers?

00:58:22.310 --
And so in North America there's
an ANSI IEEE standard so that

00:58:27.926 --
the phase shift is generally
very predictable, right?

00:58:33.330 --
And what's the standard?

00:58:37.720 --
Sorry. The high side
is leading by $30.

00:58:59.020 --
So V line the neutral in
the high voltage side leads

00:59:01.902 --
vilanda neutral in the low
voltage side by 30 degrees.

00:59:06.370 --
The Power systems textbook I
used when I was an undergrad

00:59:10.055 --
gave the impression that
whenever you had a Y Delta

00:59:13.405 --
transformer or the Y side always
led the Delta side by 30 degrees

00:59:17.760 --
because the author in.

00:59:20.620 --
All the cases he had run
across the Y side was always

00:59:24.328 --
a high voltage transformer,
'cause he'd always worked in

00:59:27.109 --
transmission and never worked
in distribution.

00:59:38.430 --
And so. So one of the
effects were going to have

00:59:42.274 --
obviously is the 30 degree
phase shift this also.

00:59:58.400 --
The Delta Y connection also

00:59:59.820 --
impacts the. Turns ratios right.
So now you've got this other

01:00:03.574 --
sqrt 3 that gets put in there in
addition to having.

01:00:11.110 --
The voltage
transformation ratio.

01:00:14.910 --
That sqrt 3 shows up in the
current so that reflects

01:00:18.320 --
back to the CTS.

01:00:23.620 --
And let's say that we have a
Delta Y grounded transformer.

01:00:28.640 --
So this side.

01:00:41.830 --
When we're measuring the phase
currents, there's going to be 0

01:00:45.537 --
sequence current on this side,
but there won't be on this side.

01:00:53.200 --
And so even some Even so, one of
the things that you have to be

01:00:57.550 --
careful of his solutions to try
to fix this phase shift.

01:01:01.490 --
And fix this also after account
for this. So I said that they

01:01:05.871 --
are one of the solutions that
people did for less mechanical

01:01:09.578 --
relays. Had to have an extra
step added to it because of

01:01:14.094 --
the zero sequence kind.

01:01:26.250 --
So if we have a transformer.

01:01:47.130 --
So we can look at the CTS.

01:01:51.140 --
So for electromechanical relays.

01:02:00.880 --
The common solution in this for
this was going to.

01:02:06.860 --
To use the CT connections to
help cancel for the cancel this.

01:02:12.520 --
And so.

01:02:16.250 --
So one option.

01:02:31.830 --
Would be to connect the CTS on
the Y grounded side in Delta.

01:02:38.340 --
And the CTS and the
Delta side and Y.

01:02:57.440 --
You need to make sure you
connect the Delta properly to

01:03:01.092 --
cancel the shift. But So what
that means is that the that the.

01:03:07.110 --
Phase currents that the
Delta phase currents.

01:03:12.580 --
Well, include the zero
sequence current that's going

01:03:15.148 --
to circulate in that Delta,
but then the line currents

01:03:18.358 --
coming off the Delta which go
to the differential relay

01:03:21.568 --
will not have.

01:03:23.640 --
That current

01:03:29.600 --
morning your device is running
low on memory.

01:03:37.470 --
So one of my colleagues has a
sledgehammer. He brings the

01:03:40.737 --
class for people whose cell
phones make noise during class.

01:03:47.100 --
The new phone is trying to
shut it down.

01:03:52.290 --
And so this is so, you still
will run across substations that

01:03:57.018 --
have the CTS wired this way from
the electromechanical relays.

01:04:03.920 --
And then a second option.

01:04:16.440 --
Would be the connect.

01:04:18.660 --
This it is an Y and
this it isn't Delta.

01:04:24.240 --
So yes, there's a problem
with this one, right?

01:04:30.810 --
So now the.

01:04:35.270 --
The differential element on
this, the current that goes to

01:04:38.140 --
the differential an element from
this side, it's going to include

01:04:41.297 --
zero sequence current. The one
in this one won't, right.

01:04:45.970 --
So this one is going to need.

01:04:55.020 --
So basically this one needed
an auxiliary set of current

01:04:58.210 --
Transformers that would block
the zero sequence current by

01:05:01.081 --
basically circulating it in
the auxiliary Transformers and

01:05:03.633 --
not have a go to the
differential element.

01:05:26.570 --
So now if you go to a
substation where it's new

01:05:31.553 --
construction and it's
designed not anticipating

01:05:34.271 --
that there's going to be
microprocessor relays

01:05:37.442 --
protecting this.

01:05:47.680 --
Now the seats are going to be
why on both sides and there

01:05:51.632 --
will be a ground reference in
the seat path.

01:06:19.860 --
And it will also the CTA will
basically perform calculations.

01:06:24.340 --
To compensate for the phase
shift an it's going to

01:06:28.920 --
perform another calculation
to remove I 0.

01:06:35.480 --
And these are actually going to
be matrix multiplications.

01:06:48.380 --
So I have a handout that.

01:06:51.350 --
Maybe I will pass it
out today. You need to

01:06:53.950 --
remember to bring it.

01:06:57.250 --
Don't be sorry.

01:07:13.600 --
And so.

01:07:18.360 --
This first calculation is
basically.

01:07:23.660 --
Typical calculation
that you would see.

01:07:27.220 --
Done in the relay.

01:07:29.840 --
For the.

01:07:32.120 --
As an intermediate step
for going to the

01:07:35.264 --
differential element.

01:07:37.540 --
So you're gonna have.

01:07:40.570 --
You're going to have the primary
currents. Then they're going to

01:07:44.112 --
be divided by the current

01:07:45.722 --
transform transformation
ratio. Remember, these are

01:07:48.686 --
why connected.

01:07:54.000 --
And then there's also going to
be this tap calculation, and

01:07:57.744 --
the other hand out goes into
more detail about the how this

01:08:01.488 --
tap is calculated. And then
there's going to be a correction

01:08:06.020 --
matrix, so the correction matrix
the output is going to be the

01:08:09.920 --
secondary current with the phase
and zero sequence correction.

01:08:16.110 --
And so the current from both
windings are going to. So this

01:08:20.190 --
is actually. This would be the
primary side, and then we're

01:08:23.930 --
going to secondary sidewinding.
So this is actually.

01:08:27.470 --
The power transformer primary.

01:08:53.070 --
And then the correction matrix,
or a number of correction matrix

01:08:58.240 --
we can do. And so when I say
matrix zero, that is using the

01:09:04.820 --
IC Clock terminology. So if we
think about o'clock, we're going

01:09:09.990 --
to have 12369, etc and then 12.

01:09:13.890 --
12 is also equal to 0, right?

01:09:19.820 --
And so if we have a Y
connection with, if you say

01:09:24.212 --
that we have basically our
phase, a voltage is going to

01:09:28.238 --
be here at an angle of 90
degrees. That's our zero

01:09:32.264 --
position.

01:09:37.340 --
And so the Matrix Zero is
assuming we have a Y

01:09:40.783 --
connection and we're not
trying to do any reversal of

01:09:43.913 --
the voltages, so this will be
just the identity matrix.

01:09:53.370 --
And then where matrix one is the
one o'clock position and this is

01:09:59.129 --
one that in.

01:10:00.540 --
South America is often
referred to as the DAB and

01:10:03.490 --
this would be a Delta.

01:10:08.250 --
AV connection so that means
that the first winding of the

01:10:11.583 --
Delta is connected from A to
B. The second line will be to

01:10:15.522 --
see the third one will be see
to a. This gives you remember

01:10:19.461 --
North America. You're limited
to either plus 30 degrees or

01:10:22.491 --
minus 30 degrees when you're
going from Y to Delta. So all

01:10:26.127 --
we care about in North
America is going to be the D1

01:10:29.763 --
in the D11 connection.

01:10:33.240 --
And then we have the D11
connection, and so if we

01:10:37.398 --
compare these all it's
doing is exchanging

01:10:40.044 --
which rows are have the.

01:10:43.410 --
Then have the different
column combinations.

01:10:47.840 --
And so, well, we'll talk about
this a little bit more, applying

01:10:52.172 --
it in the other example.

01:10:54.970 --
And then, as I mentioned, we
have that we need that zero

01:10:58.054 --
sequence removal matrix too.

01:11:03.900 --
And so that's what this
one does.

01:11:08.460 --
And so this is
mathematically reproducing

01:11:10.410 --
the effect of the current
circulating in the Delta.

01:11:20.750 --
Anworth this what this is
coming from?

01:11:24.700 --
A very good reference for
summarizing this is.

01:11:31.420 --
A paper that was written by.

01:11:35.230 --
I group from Basler
Electric John Horack.

01:11:37.659 --
Actually, I have a link to
on their class links web

01:11:41.476 --
page. I have a link to
webpage it he's got put

01:11:45.293 --
together an extensive web
page was protective

01:11:47.722 --
relaying. Related links.

01:11:51.260 --
And so I did not. I gave you
copy. It's, uh, some of the

01:11:54.676 --
pages from this paper. I have
links to the whole paper on

01:11:57.604 --
the course web page. That's
the on campus students. There

01:12:00.044 --
were some of the pages that
I'm going to talk to talk

01:12:02.972 --
about today and next time.

01:12:06.810 --
So this is just showing sort
of the connection information

01:12:10.070 --
as a reference for the rest
of this paper.

01:12:16.410 --
So.

01:12:18.450 --
He has uppercase letters to
indicate the primary lowercase

01:12:22.635 --
to do the secondary.

01:12:25.520 --
And then he has the third of the
terminal ends an the.

01:12:31.060 --
So this would be the
polarity end of the wine,

01:12:33.656 --
and this is the nonpolarity
end of the winding.

01:12:40.150 --
And so. This is one of the
things that you go through.

01:12:45.030 --
You're going to find different
people in different places, use

01:12:48.580 --
somewhat different notation so
we see UV WABC.

01:12:52.070 --
And so on.

01:12:59.290 --
And so if we wanted to build a
YY transformer in a typical

01:13:05.166 --
North American connection so
when we see the W1W 2W3, those

01:13:10.138 --
are referring to the winding.

01:13:14.330 --
The windings of the six
windings that produced the

01:13:17.372 --
three phase transformer.

01:13:21.590 --
And then it's not very
obvious, but these are his

01:13:24.910 --
polarity marks for those
windings.

01:13:28.910 --
And so H1X1 this is
high voltage. This is

01:13:31.664 --
low voltage and so on.

01:13:34.330 --
And so mapping these this is how
they would map.

01:13:39.870 --
Tell the two winding sets.

01:13:47.510 --
And so winding one and
winding 4 on the same course.

01:13:50.282 --
So these two are going to be
in phase with each other.

01:13:55.700 --
And so you can use this to
build the diagram for how

01:13:59.168 --
the transformer ones relate
to how the windings relate

01:14:01.769 --
to each other.

01:14:06.900 --
And so then he goes on
to look at.

01:14:15.830 --
So the basically the Y zero
is the one that's most

01:14:19.669 --
common in North America.

01:14:24.100 --
And so we can look at things
that change polarities by so

01:14:27.556 --
the Y four is now we're
shifting things down to the

01:14:30.724 --
4:00 o'clock by putting
winding one connected to Phase

01:14:33.316 --
V.

01:14:35.850 --
White and then we can just
look at all these different

01:14:39.546 --
combinations. WHI Six is just
reversing the polarity so the

01:14:42.906 --
polarity marks reversed
unwinding one.

01:14:47.440 --
And so this is another one
that is more of an industrial

01:14:51.076 --
power systems one, but you'll
sometimes see Transformers

01:14:53.500 --
with wired opposite of the
polarity marks.

01:14:57.580 --
Then he goes through the same
thing with Delta windings.

01:15:02.450 --
So the. And so next time
we'll go back and look at

01:15:06.270 --
this in terms of a Y Delta
transformer. How we do the

01:15:09.054 --
plus 30 if the Y is a high
side, how we do the minus 30?

01:15:12.534 --
If the why is the low side?

01:15:17.010 --
And so this paper goes on to
kind of lead into deriving

01:15:21.402 --
those connection matrices.

01:15:24.560 --
And so we'll finish talking
about this paper next time, and

01:15:28.014 --
then we'll talk about the.

01:15:31.130 --
Example handout so that
we're going to apply these

01:15:34.622 --
connection matrices to
measurements for a fault.

01:15:38.450 --
We can look at an internal
fault or an external fault. We

01:15:42.458 --
can also look at what happens
if somebody accidentally left

01:15:45.798 --
ascete shorted in the
substation and how that plays

01:15:48.804 --
through these connection
matrices.

01:15:51.560 --
So with that, well, any
questions before we stop.

01:15:55.730 --
OK, and just a reminder for
the outreach students.

01:15:58.115 --
There is no class on campus
next week, so there will be

01:16:01.295 --
no new lectures for a week.

01:16:05.650 --
OK, that's all done.

Duration:"00:40:29.6340000"

00:00:29.460 --
Hi, welcome back.

00:00:33.550 --
So we're going to resume chapter
two. We are in the section on

00:00:39.738 --
project management planning
tools and the next thing I

00:00:44.022 --
wanted to talk about was sipoc
diagrams. And really, there's

00:00:48.782 --
this one and one other slide
coming up here, which probably.

00:00:54.840 --
I mean I I would characterize
them as a project management

00:00:59.405 --
planning tool, although they're
really most relevant if you're

00:01:03.140 --
doing process improvement. And
again, many of us as a part of

00:01:08.120 --
our role as a project manager
have some element of process

00:01:12.685 --
improvement that has to be done.
Anna Sipoc diagram might be

00:01:17.250 --
something you would use and this
is basically where OK, let's.

00:01:23.170 --
Um?

00:01:25.970 --
This is where you would
basically identify these

00:01:29.314 --
dimensions of your process. You
want to look at suppliers inputs

00:01:33.912 --
to the process, what the process
itself is, what are the outputs

00:01:38.928 --
and who are the customers. So in
this case this is a process for

00:01:44.780 --
making pizza, so you know it
looks at our suppliers are

00:01:49.378 --
inputs or process our outputs in
our customers. You can read

00:01:53.976 --
those you know and maybe.

00:01:56.160 --
We're doing this because our
we've been getting.

00:02:02.040 --
You know complaints about how
long it takes to make pizzas in

00:02:06.936 --
our particular business, and we
might want to take a look at how

00:02:12.240 --
can we improve that? And you
want to kind of take this broad

00:02:17.544 --
perspective so you're not
necessarily honing in on

00:02:20.808 --
something which maybe isn't
going to solve your problem? It

00:02:24.888 --
may be an issue, but it might
not be related to the particular

00:02:30.192 --
metric you're trying to solve,
so it's a good way.

00:02:34.400 --
To tackle process improvement I
you know I'll be honest in

00:02:40.516 --
research and development. We
didn't really use sipoc

00:02:44.964 --
diagrams, or I hadn't seen
amused. But when I I did a

00:02:51.636 --
about 18 month rotation into our
customer service business and

00:02:57.196 --
they they always had teams who
were doing process improvements.

00:03:04.180 --
Particularly within call
centers, and they use sipoc

00:03:08.180 --
diagrams. You know it was
amazing what they what they

00:03:13.180 --
did with these as a method
to truly understand where

00:03:18.180 --
to focus their efforts.

00:03:22.470 --
Racy, racy diagram. You
kind of look at this and

00:03:25.600 --
say, well, is that really
a project management tool?

00:03:29.530 --
We will hit on this a little
more when we talk about

00:03:35.326 --
communication, which is, I think
in the leading chapter, but a

00:03:40.639 --
raci diagram is a very important
tool to have if you work in any

00:03:47.401 --
kind of environment that has
more than one team in more than

00:03:53.197 --
a handful of people, because it
helps you identify who's

00:03:58.027 --
responsible for particular sets

00:03:59.959 --
of work. Who is accountable?

00:04:03.880 --
And by that I mean who's making
decisions and who has ultimate

00:04:08.740 --
ownership, who's consulted? So
who are stakeholders in the

00:04:12.385 --
process and who might need to be
consulted before you make a

00:04:17.245 --
decision or take some action and
who just needs to be informed

00:04:22.105 --
and? You know an example. If you
work in a team where maybe

00:04:28.100 --
you're part of a matrix
organization and we'll talk

00:04:31.880 --
about that in our next chapter
on organizing. But say you have

00:04:36.920 --
multiple teams that are a part
of a project.

00:04:41.330 --
Um? You want to make sure
you're very clear about who's

00:04:47.120 --
doing what to get pieces of the
project done, in particular for

00:04:52.184 --
a matrix. It's also very
important to understand who's

00:04:55.982 --
making the final decision,
because everyone might think

00:04:59.358 --
they're making the decision
right there. They are managing a

00:05:03.578 --
team. Why aren't they
responsible? Well, in fact, if

00:05:07.376 --
you're part of a matrix
organization, you may have a a

00:05:12.018 --
program manager or.

00:05:13.370 --
A project management
organization who does in fact

00:05:16.770 --
have the final authority on the
work that gets done. People who

00:05:21.870 --
are informed might be the
managers above you. You've taken

00:05:26.120 --
some course of action and it was
clear you had the ability to

00:05:31.645 --
make that decision, but it's
good to let other people know

00:05:36.320 --
who might. Maybe just be
interested or who may need to

00:05:42.153 --
take other action based on
something you do, and so they

00:05:47.070 --
might be in inform you can find.

00:05:51.420 --
Lots of examples on line for how
you might fill that out, but

00:05:56.685 --
it's a good tool to get clarity
and alignment within a project.

00:06:03.340 --
Risk analysis.

00:06:06.440 --
You know, again, we've probably
all done risk analysis at some

00:06:12.347 --
level. I just, you know, pulled
in this example where it's

00:06:18.254 --
basically identified 10 risks
that have been deemed to be

00:06:23.624 --
project risks. It talks about
the worst case scenario, what

00:06:28.994 --
happens in case of that coming
to bear, and then you basically

00:06:35.438 --
do a qualitative and

00:06:37.586 --
quantitative. Assessment and
ultimately come up with the risk

00:06:42.148 --
rating. You can come up with
much simpler ways of looking at.

00:06:48.040 --
You could identify your risk.
Basically make an assessment of

00:06:52.950 --
the likelihood of it happening,
and then maybe you do some

00:06:58.351 --
assessment of what's the impact
and then basically multiply

00:07:02.770 --
those together and that's your
risk assessment. You can make it

00:07:08.171 --
as complicated. Or as simple
as needed. The point here

00:07:12.574 --
though is every project that
you manage. You should at

00:07:16.754 --
least do a very high level
risk analysis, typically as a

00:07:21.352 --
part of a you know if you're
following some kind of a

00:07:26.368 --
structured project management
lifecycle.

00:07:29.290 --
When you're doing your initial
project planning, you would

00:07:33.232 --
likely do a very high level risk
analysis and then have.

00:07:38.860 --
You know, figure out what your
cadence is for going back and

00:07:44.920 --
assessing where things
are. Have new risks, come up,

00:07:49.970 --
etc. The you don't want to
just put a lot of effort into

00:07:55.670 --
doing a risk analysis and then
and then never come back

00:07:59.520 --
around to in fact evaluating
it. They can be very helpful

00:08:03.370 --
in helping you mitigate issues
that may come up.

00:08:08.990 --
A quality management plan is
another example of a project

00:08:13.070 --
management tool you might use.
If you're in the quality area or

00:08:17.966 --
if you have any responsibilities
for quality and you know this is

00:08:22.862 --
something very simple which is
looking at what's the particular

00:08:26.942 --
characteristic you're looking
at. Why is it important? How are

00:08:31.022 --
you going to test for quality?
Who's going to do it, and then

00:08:36.326 --
simply a status?

00:08:39.040 --
My guess is most businesses
probably have a you know more

00:08:43.803 --
specific template you might use
as a part of a quality

00:08:48.566 --
management plan. But again, the
point here is.

00:08:53.060 --
Always be thinking about that.

00:08:56.750 --
Even you know we all have a
need to be delivering the

00:09:02.431 --
highest quality and most value
we can of whatever we do for our

00:09:08.112 --
business. And so you want to be
thinking about how can I, you

00:09:13.793 --
know what's important for me in
my team in order to deliver on

00:09:19.474 --
that high quality. So this is an
example of that. Another quality

00:09:24.718 --
tool is a failure. Modes,

00:09:26.903 --
effects analysis. And this
again, is where you're really

00:09:32.193 --
looking at. Different in this
particular case, we're

00:09:36.585 --
looking at different process
steps and identifying

00:09:40.428 --
potential failure modes.

00:09:43.460 --
What are the effects of those
modes? Assessing severity? How

00:09:47.870 --
frequently is it likely to
occur, etc. And ultimately,

00:09:51.839 --
you're going to come up with an
overall risk priority number,

00:09:56.690 --
and I have seen these use

00:09:59.336 --
pretty. Sensibly in various
research and development type

00:10:03.988 --
teams. And there are good.

00:10:07.450 --
You know fairly simple way to do
a pretty in depth analysis and

00:10:12.845 --
get an understanding of where in
fact you might be want to. You

00:10:18.240 --
might want to be investing
effort in order to prevent some

00:10:22.805 --
issues from happening.

00:10:26.740 --
Dmax

00:10:29.110 --
define measure, analyze,
improve, control is.

00:10:33.660 --
Probably a process improvement
approach. You might be familiar

00:10:37.449 --
with if you've done that as a
part of your role and again.

00:10:44.350 --
You know, when I was working in
R&D we were doing lots of

00:10:50.122 --
process improvement. We probably
weren't as rigorous as we could

00:10:54.562 --
have been at using something
like Demac as a model for doing

00:10:59.890 --
our process improvement, but
it's a good approach to

00:11:03.886 --
methodically walk through a
process improvement approach. It

00:11:07.438 --
can be for a very simple
improvement in each of the steps

00:11:12.766 --
might be quite short.

00:11:15.670 --
But it helps you think.

00:11:19.220 --
I guess more completely about
all the elements of the

00:11:24.240 --
problem in what you're trying
to do to improvement, so

00:11:29.260 --
definitely worth looking into
if you have an element of

00:11:34.280 --
process improvement in your
job and it's something that's

00:11:38.798 --
talked about pretty
extensively in the process

00:11:42.312 --
improvement class.

00:11:47.130 --
So wrapping up the discussion on
action planning, you know just a

00:11:52.470 --
couple of comments that I
thought were worth including.

00:11:56.475 --
You know. Oftentimes when we're
managers, we think it's our job

00:12:01.370 --
to do all the planning and it
is, you know, it is the role of

00:12:08.045 --
the technology and engineering
managers to do the planning. But

00:12:12.495 --
be sure to involve the people
who do the work.

00:12:17.020 --
In the planning where you can
now you don't want to go to

00:12:22.077 --
extremes. I was talking to a
friend of mine who works at a

00:12:27.134 --
very large company who's in the
midst of, I guess a very

00:12:31.802 --
horrendous product release and
everybody is getting really

00:12:34.914 --
nervous that they're going to be
late and so every day.

00:12:40.230 --
The senior vice president calls
every single engineer into a

00:12:45.140 --
meeting at 7:00 AM to walk
through their action planning

00:12:50.050 --
for the day. Now, do you think
that's really productive? The

00:12:55.451 --
answer is no, because a it's
people are, you know, people who

00:13:01.343 --
can are quitting because they're
there. It's ridiculous, you

00:13:05.762 --
know. So that's an example where
there's people at too high of

00:13:11.654 --
levels. Involved in the planning
with the doers. That's not the

00:13:16.110 --
intent here, but the intent is
if I'm a project manager and I'm

00:13:21.193 --
planning the next project, it
would behooves me to have a

00:13:25.494 --
session with the engineers at
some point. Not that you

00:13:29.404 --
necessarily want to ask them to
sit with you for two days to do

00:13:34.878 --
all of your scheduling, but you
probably want to have a.

00:13:40.510 --
You're kind of a validation

00:13:43.590 --
that. That you're on track
because a you want them to buy

00:13:48.525 --
into that plan. If you're
expecting them to deliver it.

00:13:52.990 --
Similarly, if you're doing
strategic planning, if you're

00:13:57.110 --
more senior executive and you're
doing strategic planning, always

00:14:01.745 --
involve your staff in that you
know that's a great opportunity

00:14:07.410 --
for a. Regular, you know, a
quarterly staff offsite to not

00:14:13.952 --
only build and foster teamwork
among the team, but.

00:14:19.410 --
Drive good alignment on that
strategic plan because

00:14:22.530 --
ultimately the people in your
team are the ones who are going

00:14:27.210 --
to have to do the work, so use
those planning.

00:14:32.220 --
Opportunities as a way to
drive alignment.

00:14:36.310 --
Use computer based tools when
you have access to them, and

00:14:41.403 --
again similarly to don't go
crazy involving people. Don't go

00:14:46.033 --
crazy with it mean there's some
really incredible tools out

00:14:50.663 --
there to do scheduling and
things like that, but if you

00:14:55.756 --
have, you know 1000 or 2000
tasks in a schedule is just too

00:15:01.775 --
unwieldy to manage, so use them
when they make sense

00:15:06.405 --
Alternatively. Use simple tools
when they make sense.

00:15:10.980 --
If you're doing software
development, you know everybody

00:15:14.940 --
is familiar with Agile there is.

00:15:19.200 --
Kind of an element of agile for
very simple projects where you

00:15:23.820 --
can basically use a con Bon
bored. So if you're fixing

00:15:28.055 --
defects for example in a
product, it's very easy to use a

00:15:32.675 --
con Bon bored to show how you
know when the defect gets

00:15:37.295 --
accepted into the system, who's
working on it when it's done,

00:15:41.530 --
when it's tested, when it's been
deployed to a customer, for

00:15:45.765 --
example. That's a very visual
way. You don't need a very

00:15:50.000 --
complex. Tool to track that
work, but the visual kambam

00:15:54.290 --
board is a good way to keep
everybody up to date. So figure

00:15:59.269 --
out what you need and don't
don't apply technology where you

00:16:03.482 --
don't need to.

00:16:06.430 --
Make sure you're looking at
risks in doing contingency

00:16:10.084 --
planning where you need to, and
you might have to go back and

00:16:15.362 --
iterate on the planning process.
You may say you do your planning

00:16:20.234 --
as you know your project
manager. You do some planning,

00:16:24.294 --
you have a review, say with your
team and there were some things

00:16:29.572 --
that you missed. Well, you gotta
go back and iterate. It's not

00:16:34.444 --
you don't need to feel like.

00:16:37.040 --
Iteration is a bad thing
because it's an opportunity

00:16:40.532 --
to get things right.

00:16:43.550 --
So I think those are some things

00:16:45.496 --
that. That you can keep in mind.

00:16:49.330 --
Hey, the last couple of topics
are issuing policies and

00:16:53.990 --
basically documenting
procedures, and I think

00:16:56.786 --
typically when we hear oh gosh,
you know I have to do I have

00:17:03.310 --
to generate policies that can
take a very negative connotation

00:17:07.970 --
in really policy czar directives
intended to address repetitive

00:17:12.164 --
questions, issues of general
concern, and really to drive

00:17:16.358 --
equity across your workforce. So
here's some good examples.

00:17:21.090 --
Hiring and firing guidelines.
You want to make sure that

00:17:25.700 --
you've got strong policy's for
expectations around hiring, and

00:17:29.849 --
also around terminating people.
You know, it's your it would be

00:17:34.920 --
a very uncomfortable environment
if there were no guidelines for

00:17:39.530 --
how people were terminated.

00:17:42.120 --
Equal opportunity policies might
be an example. Performance

00:17:47.760 --
appraisals are something that.

00:17:52.420 --
You are necessary in the
workplace and you want to be

00:17:57.073 --
able to do those
consistently. You might be in

00:18:00.880 --
a business where a drug
policy or drug testing is

00:18:05.110 --
mandatory.

00:18:07.090 --
So you know, these are some
examples of things where you're

00:18:11.875 --
really trying to.

00:18:14.680 --
Make sure there's equity and
address repetitive concerns.

00:18:19.008 --
Policies are there to save
management time. No, they're

00:18:23.877 --
not intended to generate lots
more work.

00:18:29.400 --
They are intended to capture it.
You know, the experience and

00:18:35.263 --
past learning of the company and
hopefully facilitate delegation

00:18:40.060 --
if there are clear policies in
place, then for example, if I'm

00:18:46.456 --
a senior level executive and
there are clear policies around

00:18:51.786 --
travel expenses and trip
reports, I could perhaps

00:18:56.050 --
delegate the ability or delegate
the responsibility to my

00:19:00.847 --
administrative assistant. To
look at those and approve them,

00:19:05.030 --
for example. That might be, that
might be something.

00:19:10.350 --
If that's allowed in
your particular

00:19:12.636 --
business, but basically
you're trying to figure

00:19:15.303 --
out a way to be
consistent on things

00:19:18.351 --
that are going to come
up over and over again.

00:19:25.340 --
Policies will apply uniformly to
all employees. They should be

00:19:30.930 --
pretty permanent. You don't want
to be changing policy's real

00:19:36.520 --
frequently, and hopefully they
foster corporate objectives. You

00:19:40.992 --
know you don't want to have
policies that really are in

00:19:47.141 --
conflict with things.

00:19:51.100 --
Things that are valued at the
corporate level, and so I think

00:19:55.780 --
you need to think about when you
need to have policy's.

00:20:00.420 --
You might have policies about
working at home. That's probably

00:20:04.720 --
the one that has come up several
times through the course of my

00:20:10.310 --
career. I can remember when
working at home or remote, you

00:20:15.040 --
know. Being a remote worker
located in a different geography

00:20:20.542 --
just wasn't an accepted Norm,
and I can remember the first

00:20:26.020 --
time we had to address this was
we had a very Senior High

00:20:32.494 --
performing engineer. Needed to
move to Wyoming because of some

00:20:37.780 --
family things with his wife and.

00:20:41.500 --
So we you know the question was
do we let him resign or do we?

00:20:47.480 --
Basically, craft a policy about
a remote worker and so we did

00:20:54.152 --
and it was interesting because
that got tested.

00:21:01.080 --
Over and over again in terms of
people you know other people

00:21:05.064 --
wanting to take advantage of
that, and it was interesting

00:21:08.384 --
because you know what? If you
have somebody who comes in,

00:21:12.036 --
wants to be a remote worker, but
there may be some kind of middle

00:21:16.684 --
of the road performer, well, how
do you know? Then you have to

00:21:21.000 --
start thinking about. Do you
have to create a policy that so

00:21:24.984 --
regimented in terms of if you
come with the request to work at

00:21:29.300 --
home? You need to be?

00:21:31.550 --
In the you know, whatever top
two tiers of performance you

00:21:36.686 --
know etc., etc.

00:21:40.230 --
Think we tried to have a policy
that was more general.

00:21:46.710 --
Probably the biggest challenge
we had was when we started

00:21:50.680 --
working with teams in other
geographies where suddenly you

00:21:54.253 --
know we worked a lot with India
and that was not a commonplace

00:21:59.414 --
thing to have people working at
home and but then they started

00:22:04.178 --
raising that with their
management and it was

00:22:07.354 --
interesting because then when I
had my assignment in Singapore,

00:22:11.324 --
that was probably one of the
first policy things we had to

00:22:16.088 --
come up with was.

00:22:17.800 --
What are we going to do? How are
we going to create a work at

00:22:23.650 --
home policy for an environment
that historically did not permit

00:22:27.550 --
that? So again, you know.

00:22:30.060 --
That's something that came up
many years ago, and it's evolved

00:22:34.614 --
overtime. I think in general,
when I was when I retired from

00:22:39.582 --
HP, we were going back to a
policy of everyone being back on

00:22:44.964 --
site so things can swing
pretty radically and come full

00:22:49.518 --
circle based on the needs of the
business. I think that's the

00:22:54.486 --
main thing you have to keep in
mind is you may create a policy.

00:23:02.020 --
If the business needs change,
you may have to go back and

00:23:06.400 --
revisit that policy and there's
nothing wrong with doing that.

00:23:11.820 --
Procedures, it's kind of the
same, you know, we think about,

00:23:16.275 --
oh, brother, you know I have to
follow a set of procedures to

00:23:21.540 --
doing something, and it's really
you're trying to standardize

00:23:25.185 --
work that benefits from.

00:23:28.560 --
Procedures, because you're doing
it over and over again, you've

00:23:32.670 --
got or you're.

00:23:34.890 --
You have some kind of
certification, perhaps that

00:23:37.810 --
is dependent on having a
procedure to ensure that

00:23:41.095 --
work is done a certain way.
Or maybe you have a say to

00:23:45.840 --
health and safety thing
where certain types of

00:23:48.760 --
manufacturing wastes have to
be disposed in a certain way

00:23:52.410 --
and you need to follow
procedures in order to

00:23:55.695 --
ensure health and safety of.

00:23:59.040 --
The workforce and.

00:24:02.560 --
So again, depending on the type
of work you're doing, the

00:24:07.301 --
procedures you're involved with
are going to be quite different.

00:24:11.611 --
If you're in an R&D team, the
product management lifecycle is

00:24:16.352 --
a procedure that establishes and

00:24:18.507 --
standardizes how. The work is

00:24:21.446 --
going to. Or the steps if
you will. At a high level the

00:24:27.586 --
work is going to follow and what
is going to happen at each of

00:24:32.878 --
those checkpoint or handoff
process is that would be a

00:24:37.036 --
procedure if you're working in.

00:24:40.210 --
You know a part of the business
where you're installing devices

00:24:45.072 --
or you're in your field.
Engineer installing devices at

00:24:49.050 --
customer sites. It's important
you have an installation manual

00:24:53.028 --
so you can follow the
appropriate steps for ensuring

00:24:57.006 --
that things are done
appropriately. So again, it's

00:25:00.542 --
not to create a bunch of
overhead and procedures for

00:25:04.962 --
every single thing you do, but
it is important to.

00:25:10.590 --
Make sure that when you need a
procedure, you get 1 written

00:25:16.026 --
appropriately. Actually this
here we go. You want to.

00:25:20.930 --
Preserve the best way to get
the work done. So how can

00:25:24.182 --
you be efficient?

00:25:26.460 --
It can help you know.
Oftentimes, procedures are one

00:25:29.997 --
of the outcomes of a process
improvement approach. You want

00:25:33.927 --
to ensure that you have
standardized action you want to

00:25:37.857 --
simplify things, and in
particular it's a way to save

00:25:41.787 --
some of your corporate memory.
How do things get done? What's

00:25:46.110 --
the right way to do things?
What's the procedure for testing

00:25:50.433 --
your device now? It doesn't
matter if somebody leaves the

00:25:54.363 --
company, you know how things get

00:25:56.721 --
done. Because you have that
documented in the form of a

00:26:00.770 --
procedure. So again, you don't
want to overdo it, but you want

00:26:05.812 --
to have good procedures when
they make sense.

00:26:10.940 --
When you want to develop a
procedure, again, concentrate

00:26:15.251 --
on the critical work. Look at
the inputs and outputs of

00:26:20.520 --
what's happening. You might
even use a sipoc diagram as

00:26:25.310 --
input to detailing or
developing a new procedure.

00:26:29.142 --
You need to talk about or
think about the

00:26:33.453 --
characteristics.

00:26:35.620 --
Proposed the procedures and then
figure out the regular timeframe

00:26:40.290 --
that you're going to come back
and review. These probably most

00:26:45.427 --
important is making sure that
the people who are involved in

00:26:50.564 --
doing the procedure have an
opportunity to give input before

00:26:55.234 --
you go develop something in
handed off to them and inspect.

00:27:00.371 --
Expect them to do it I ideally
you'd like to have their input.

00:27:06.510 --
In the creation of the
procedure in some way,

00:27:10.164 --
certainly you want to have the
review of people who are going

00:27:15.036 --
to have to execute the
procedure before you turn them

00:27:19.096 --
loose.

00:27:24.630 --
We talked about different types
of planning. We talked, we

00:27:28.350 --
started out with some discussion
on strategic planning.

00:27:32.300 --
How do we figure out what are
the right things to do in our

00:27:36.612 --
business and then? As we
transition into operation

00:27:39.725 --
planning, what are some of the
tools to help us get things done

00:27:43.898 --
the right way? Just some things
to keep in mind.

00:27:50.730 --
Validate your assumptions.
You're going to want to go out

00:27:55.160 --
there, and even if you're
planning a project that's a

00:27:59.590 --
follow on project that you've
done five times, something will

00:28:04.020 --
be different, so be sure to make
sure you're getting appropriate

00:28:08.893 --
information. You're doing some
of that forecasting. You're

00:28:12.437 --
looking at alternatives, but
really validating that the

00:28:15.981 --
assumptions you're making are

00:28:17.753 --
correct. From a people
perspective, involve the

00:28:21.938 --
right people.

00:28:24.250 --
One of the things that.

00:28:27.140 --
You know? Is important is
consider what we used to call it

00:28:32.860 --
the with them. What's in it for
me. For all stakeholders

00:28:37.458 --
involved in your planning so
involved the people are going to

00:28:42.474 --
do the work. If you're making.
If you're planning some things

00:28:47.072 --
that are going to be done
differently, you know, introduce

00:28:51.252 --
those changes in a way that
maybe you can't avoid resistance

00:28:55.850 --
but you manage it and.

00:28:58.530 --
Will in the chapter on
leading will talk a little bit

00:29:03.054 --
about John Carter's eight step
change management approach.

00:29:06.620 --
This is a perfect opportunity
for where if you're doing some

00:29:11.504 --
planning, that's going to

00:29:13.280 --
involve. Someone elses work
being done a different way?

00:29:17.756 --
Don't discard the need to do
some active change management

00:29:21.626 --
and at a minimum this
consideration of what's in it

00:29:25.496 --
for me for all your
stakeholders will help you

00:29:28.979 --
think through that.

00:29:31.250 --
Be sure to understand the
benefit versus the cost. You may

00:29:36.398 --
come up with a great plan to do,
you know, some great product,

00:29:42.482 --
but. Is the benefit there? Is it
going to cost so much that you

00:29:49.085 --
know you're never going to
recoup what you've put into it?

00:29:53.430 --
You really have to think about
benefits versus costs. Make sure

00:29:57.775 --
when you're doing your planning

00:29:59.750 --
have. A series of small steps
along the way. This allows you

00:30:05.036 --
to get some small wins. It also
allows you to make course

00:30:09.788 --
corrections if you do a project
management plan that goes

00:30:13.748 --
basically from investigation to
and say you have one task which

00:30:18.104 --
is develop the product and then
your product is done, your

00:30:22.460 --
opportunity for making midcourse
corrections is not very good in

00:30:26.420 --
that case, so you need to figure
out what's that right level of.

00:30:31.860 --
Um?

00:30:34.160 --
What's the right level you
need to break that work

00:30:37.740 --
down such that you have
the control you need, and

00:30:41.320 --
in particular the ability
to make these corrections.

00:30:46.160 --
You want to be anticipating
changes in future conditions,

00:30:49.742 --
and again, this is where you
may be thinking about

00:30:53.722 --
contingencies, and you may
have to apply a formal change

00:30:57.702 --
management process if needed.
And Lastly, of course, make

00:31:01.284 --
sure you get the commitment of
the resources you need to

00:31:05.662 --
achieve the objectives. It's
great to have a wonderful

00:31:09.244 --
plan, but if you don't have
the ability to deliver on it,

00:31:14.020 --
then that.

00:31:16.040 --
Is very discouraging
for people overtime.

00:31:22.030 --
I think wrapping up, then, you
know, planning. I think it's

00:31:26.848 --
probably fairly obvious to all
of us we plan in every part

00:31:32.542 --
of our lives really, but it is a
very important function in

00:31:37.798 --
engineering management and
technology management and the

00:31:40.864 --
key activities we talked about
were the need to forecast action

00:31:45.682 --
planning. Of course, related to
both strategic planning and

00:31:49.624 --
tactical planning, issuing
policies and establishing

00:31:52.252 --
procedures. You know, oftentimes
we think that forecasting and in

00:31:57.313 --
particular strategic planning,
are only activities by the high

00:32:01.696 --
level executives. In my, you
know, kind of my opinion is

00:32:07.053 --
don't discount those activities
at any management level in the

00:32:11.923 --
organization, because if you're
if you understand what the

00:32:16.306 --
strategic plan is at the top
levels of your business,

00:32:21.176 --
ideally. Eat their cascaded to
each level so each level then

00:32:27.150 --
could take those objectives in
based on the work they are

00:32:32.562 --
responsible for. Create their
key objectives that link to the

00:32:37.482 --
overall objectives above them
and then ultimately if you take

00:32:42.402 --
that to the you know kind of the
final step. Each individual on

00:32:48.798 --
your team hopefully has a set of

00:32:52.242 --
performance objectives.
Ideally they can see within

00:32:55.435 --
their performance
objectives how they fit

00:32:57.889 --
within the context of the
team and how the work they

00:33:02.388 --
are doing is going to
contribute to the success

00:33:06.069 --
of the team's objectives.
The teams objectives.

00:33:10.010 --
Hopefully are linked to the
team or manager above them,

00:33:15.390 --
etc and so it really allows
clear line of sight from every

00:33:21.846 --
single person in your business
or team up to the high levels

00:33:28.302 --
of the organization and.

00:33:32.270 --
My my personal opinion is
that every single manager

00:33:36.437 --
should take the time to do
that at the level that's

00:33:41.530 --
appropriate for where their
team fits in the

00:33:45.234 --
organization.

00:33:46.850 --
And then I think, Lastly
operational planning, you know.

00:33:50.970 --
Really forms the basis for much
of what we do.

00:33:55.400 --
And so you need to figure out
what are the tools that are

00:33:58.871 --
important for you to do.

00:34:01.960 --
Here's just an example of you
know how you might have to think

00:34:06.926 --
a little bit strategically, and
this was question 2.2 at the

00:34:11.128 --
back of the textbook and it

00:34:13.420 --
says. So the company has
always been focused on the

00:34:18.105 --
high quality, high priced
end of the market.

00:34:22.500 --
Now, market intelligence
indicates that some competitors

00:34:26.399 --
are planning to enter the low
price, low quality into the

00:34:32.526 --
market. What would you do?

00:34:38.660 --
It's an interesting question
because from a strategy

00:34:44.460 --
perspective you probably
have focused on.

00:34:50.170 --
Well, you obviously have focused
on the high end element of the

00:34:55.090 --
market. Probably everything in
your company is structured

00:34:58.370 --
around that. You certainly want
to figure out how to protect

00:35:04.074 --
that Mitch if you will, but
likely if you do nothing.

00:35:09.820 --
Your business will
slowly be eroded by.

00:35:15.220 --
People who are anticipating this
kind of low, low price, low

00:35:19.972 --
quality product by the
competition and there's a number

00:35:23.860 --
of options you could explore.

00:35:26.890 --
You could really look at the
option of partnering with

00:35:32.160 --
someone and you know, importing
a low price, low quality

00:35:37.430 --
product, perhaps you.

00:35:40.640 --
Label it as you know you work
with somebody by the technology

00:35:45.416 --
and label it as your own.

00:35:49.650 --
That would certainly be a way to
quickly get a product into the

00:35:55.448 --
market with the least amount of
investment necessary. Of course,

00:35:59.908 --
you know the downside of that is
if it really is low quality and

00:36:06.152 --
your brand has been all about
high quality, what does that do

00:36:11.504 --
to your customer base? They may
not be accepting of that, so you

00:36:17.302 --
have to think through.

00:36:19.810 --
That may be a really good
thing to do, but what are

00:36:23.830 --
the implications? So there
you would probably need to

00:36:26.845 --
do some scenario planning
and think through that you

00:36:29.860 --
could certainly.

00:36:33.610 --
Follow the competition more
closely and perhaps start

00:36:37.418 --
preparing to take your product.
You know, kind of downmarket

00:36:42.178 --
some. That obviously takes a
much bigger investment and takes

00:36:46.938 --
a longer period of time.

00:36:52.620 --
That might be a way to get
started on this notion of having

00:36:58.002 --
a second brand if you will
within your business. So you

00:37:02.556 --
could still maintain that high
price, high quality brand and

00:37:06.696 --
basically Re brand of product
line that's targeted at a lower

00:37:11.250 --
end of the market.

00:37:15.260 --
Yeah, I think the point is
though, you probably can't.

00:37:18.870 --
You know doing nothing is
probably a recipe for

00:37:22.119 --
failure. So in a case like
that, you need to think

00:37:26.090 --
through.

00:37:27.600 --
From a strategic planning
process, what are your options?

00:37:32.082 --
What makes sense and they can

00:37:35.070 --
range from? Investing in new
product development for that low

00:37:39.856 --
end of the product line,
recognizing that takes a long

00:37:43.426 --
time. You can do nothing at the
other end of the spectrum, which

00:37:49.104 --
probably is going to be.

00:37:52.510 --
It's going to impact your
business overtime or you

00:37:55.876 --
come up with something in
the middle. Which is this

00:37:59.616 --
idea of partnering with
somebody. And each of those

00:38:02.982 --
will have pros and cons and
benefits and risks, and that

00:38:07.096 --
would be an assessment you
have to make.

00:38:12.090 --
So I think what you can see and
will see this probably in every

00:38:17.928 --
chapter in the textbook.

00:38:20.730 --
Engineering management or
technology management is usually

00:38:24.335 --
not very black and white.

00:38:28.130 --
There is always this kind of,
typically a Gray, you know a

00:38:33.314 --
Gray area in the middle, and
that's where we want to take

00:38:38.498 --
advantage of all the tools we
have available to us. You want

00:38:43.682 --
to certainly apply critical
thinking as you're looking at

00:38:47.570 --
homework assignments that are
case studies. There's typically

00:38:51.026 --
not going to be necessarily a
right and wrong answer.

00:38:56.730 --
So what's going to be important
is are you able to think through

00:39:02.099 --
and analyze the particular
situation and use the tools at

00:39:06.229 --
hand to come up with some
possible options? So don't get

00:39:10.772 --
hung up on.

00:39:13.250 --
So you know I have to do a case
study and it's going to be. It

00:39:16.770 --
has to be. You know, if I don't
get this right answer, I'm not

00:39:21.339 --
going to get 100%. That's not
really the case. There's going

00:39:24.518 --
to be a lot of flexibility. The
main thing is to think

00:39:27.986 --
critically and apply the tools
that you have at hand.

00:39:32.010 --
So with that next, the
next lecture we will talk

00:39:38.090 --
about Chapter 3, which is
focused on organizing and.

00:39:45.870 --
Will look at a number of
different organization

00:39:48.742 --
structures when you might
use them. Some of the pros

00:39:52.332 --
and cons, and so I think
it will be an interesting

00:39:56.281 --
discussion. So thanks bye.

Duration:"00:52:28.7600000"

00:00:30.200 --
Yes.

00:00:33.030 --
So today we will continue
discussion about the

00:00:35.870 --
modified, all the method and
Runge Kutta methods. So we

00:00:39.420 --
will talk about the formulas
and then accuracy and so on.

00:00:43.325 --
So I give you hand out and
the problem. I'll use it

00:00:47.585 --
today so that we can cover a
little bit faster. And then

00:00:51.845 --
I'll spend time on other
material. OK, so.

00:00:58.460 --
In there you remember in all
this method in order to go from

00:01:03.751 --
point X&YN to point XN plus one
1 + 1, essentially with another

00:01:09.042 --
next index, we only use
information from the previous

00:01:12.705 --
point. So in a modified or leave
use information from 2 points

00:01:17.589 --
and we use oil as step to go to
the point X N + 1 NU N +

00:01:24.915 --
1. This is predicted point.

00:01:27.950 --
And then be available slope at
the predicted point and we use a

00:01:33.059 --
slope at initial, not initial.
But the point that we start

00:01:37.382 --
start from and then we average
these slopes defined slope

00:01:41.312 --
alone, which we find essentially
construct line right tangent

00:01:44.849 --
line and then we find
approximation at the next step.

00:01:48.779 --
So I also wrote this method last

00:01:51.530 --
time. So you can either define
predictor which is the Oilers

00:01:57.000 --
step and then this is slope at.

00:02:01.370 --
.1 right and here we have slope
at .2 and then we average slopes

00:02:07.082 --
and this is how we find the
next. The next point all we can

00:02:12.794 --
write down these slopes
explicitly. So K1 is a slope at

00:02:17.282 --
point. XNYN and then we use it
to March to find point you and

00:02:22.907 --
plus one. Then we find K2 slope
at the second point and then we

00:02:27.793 --
take every to the slopes
defined. And if you don't want

00:02:31.632 --
to use K1K2 and just write this
in terms of an even without you

00:02:36.518 --
N + 1, then you just write
explicitly all the expressions

00:02:40.357 --
for for you and plus one. So
this is a first step. Predictor

00:02:44.894 --
does not change and in the
second step in the character.

00:02:48.970 --
You have your own plus one
equals UN plus H / 2, so you

00:02:53.702 --
take average. This is your slope
at point XYN. This is your point

00:02:58.096 --
and you X N + 1 right here. This
is your predicted point. U N + 1

00:03:03.842 --
essentially just written

00:03:04.856 --
explicitly. OK.

00:03:09.510 --
Modified the oldest method uses
two term approximation from the

00:03:13.990 --
Taylor series right. The
constant term and the linear

00:03:18.022 --
term. The modified Euler method
uses. Also next terms uses

00:03:22.502 --
quadratic term in the Taylor
expansion, so if we go back to

00:03:27.878 --
their tail expansion then
modified Euler will use up to

00:03:32.358 --
age squared term. So this means
that the first time that you

00:03:37.734 --
neglect will be proportional to

00:03:39.974 --
H cube. Right next will be age
to the 4th. Each of the 5th and

00:03:45.450 --
if H is small then this will be
a dominant term. So air local

00:03:50.070 --
error over one step will be
proportional to H cube.

00:03:54.290 --
And then you find cumulative
error after multiple steps right

00:03:58.000 --
after. If you're going from zero
to X final, then the error will

00:04:02.823 --
be proportional to age squared,
so similar usually you lose one

00:04:06.904 --
order when you sum the errors
you find cumulative error. So

00:04:10.985 --
since modified term all this but
it matches the 1st three terms

00:04:15.437 --
in the Taylor series up to and
including termination squared,

00:04:19.147 --
the local area is proportional
to each cube, but the cumulative

00:04:23.228 --
error is proportional to age

00:04:25.083 --
squared. So if air is
proportional to H squared

00:04:28.998 --
and instead of H, you take
H / 2, what would happen

00:04:32.910 --
with the error?

00:04:35.610 --
As will decrease by
approximately 1 force, right? So

00:04:38.265 --
if you see so, this is a way how
you can check that your method

00:04:42.690 --
is quadratic. So so this means
that your method is quadratic,

00:04:45.935 --
so your error is proportional to
each squared. Let's say you

00:04:49.180 --
write a program and how would
you verify that? Yes, the method

00:04:52.720 --
is programmed correctly. So what
you can do you take you take a

00:04:56.555 --
test problem for which you know
exact solution, so you can look

00:05:00.095 --
at the error because error would
be the difference between exact

00:05:03.340 --
solution and numerical solution.
So you go from.

00:05:06.430 --
Initial time to some final time
final point, and you compute

00:05:11.457 --
solution at the final point.

00:05:14.530 --
And you look at the error right?
And then you decrease error by

00:05:18.391 --
half and look how the error will
change. So if error bill

00:05:21.955 --
decreased by by half, this means
that you have a linear method.

00:05:26.250 --
If it decreased by quarter, than
its accuracy is quadratic.

00:05:32.310 --
OK. So this is a way to verify
that your program is is correct,

00:05:37.448 --
and then once you verify your
code then you can change

00:05:41.034 --
equation. You can change
function, then you can more or

00:05:44.294 --
less thing that your program is
reliable, computes correctly, so

00:05:47.554 --
this is what happens with the
error. Is H decreased by half

00:05:51.466 --
then the arrabelle because by by
a factor of four and just for

00:05:55.704 --
comparison. Again for all this
method it's a linear

00:05:58.638 --
convergence. So if you decrease
age by half your error will also

00:06:02.550 --
decrease approximately by half.

00:06:05.710 --
OK.

00:06:11.410 --
And so essentially we know the
methods we just. I can just

00:06:15.442 --
rewrite it may be in the way
that is more convenient for for

00:06:19.810 --
programming. So if we want to
solve initial value problem with

00:06:23.506 --
some initial condition. So what
do we need? We need initial

00:06:27.202 --
condition right? So X not, why
not? We also know we need to

00:06:31.570 --
know the step size and how many
steps we have to perform right

00:06:35.938 --
function F is known. So once you
have equation you can find

00:06:39.970 --
function F so again.

00:06:41.420 --
Then before you need to compute
'cause you have some homework

00:06:46.051 --
that you have to actually
implement by hand or using

00:06:50.261 --
Calculator. So write down the
formulas before you substitute

00:06:54.050 --
values right so?

00:06:56.320 --
You can, we can use either write
this in terms of predictor

00:07:00.256 --
corrector or we can use this
slopes K1K2 to write the method

00:07:04.192 --
so XN plus 1 = X N plus H. So
every time you increment by H

00:07:09.440 --
right and also we can write

00:07:11.408 --
that. H is X final minus X
starting divided by number of

00:07:17.326 --
steps right or number of steps
is X final minus 0 / H right?

00:07:23.150 --
So if if you know number of
steps you know initial point

00:07:28.142 --
terminal point then you can
find step size or vice versa.

00:07:32.718 --
If you know step size you can
find number of steps.

00:07:39.730 --
OK, predict this step is
just the oldest method.

00:07:43.490 --
Right and then corrector? So
predicted allows you to find

00:07:46.940 --
this predictive point you N + 1
and then corrector will find

00:07:51.080 --
slopes at both points and
average them to find exponent.

00:07:55.210 --
OK, and again Alternatively this
is using the K1K2 and but

00:07:59.687 --
essentially the same.

00:08:01.550 --
OK, so whatever way you
prefer, you can use.

00:08:08.170 --
OK, any questions here.

00:08:14.070 --
So let's look at the example.

00:08:16.890 --
So in this example you have to
implement modified order in.

00:08:23.520 --
And solve the problem in 2

00:08:24.972 --
steps. So equation is Y prime
equals X + y -- 1 squared.

00:08:30.250 --
Initial condition by 0 = 2. So
find Y at. So you start from X

00:08:35.575 --
equals. O you go to X =
0.2 in two steps means that step

00:08:42.728 --
step sizes. 0.1 right again,
it's a 0.2, so H is 0.2

00:08:49.380 --
-- 0 / / 2 zero point
1 which is written here.

00:08:56.710 --
Initial condition X00Y0 stole
from here number of steps two

00:09:02.050 --
and then H you find.

00:09:06.260 --
Their function function F
function F is the right inside

00:09:09.760 --
of your equation.

00:09:12.550 --
OK, and I know it's tempting to
write down right away their

00:09:17.230 --
solutions, but take some time.
Just write down the formulas in

00:09:21.520 --
terms of X&YN, it's easier than
to substitute. I mean, if you

00:09:26.200 --
program something then you just
program with indices and then it

00:09:30.490 --
computable repeat, write your
computations. But when you do by

00:09:34.390 --
hand then you have to keep track
of X0X1Y0Y1 and then here you

00:09:39.460 --
have you also UN to worry about.

00:09:43.700 --
So you write down the formula.
So this is your next.

00:09:46.850 --
Approximation of X. This is
your predicted value just

00:09:50.540 --
using the Euler's method,
because this is your function

00:09:54.230 --
F at X&YN and then.

00:09:57.420 --
This is your next approximation.

00:10:00.110 --
By using the previous and
the average of slopes.

00:10:04.030 --
OK.

00:10:06.520 --
So for all this method to go
from one point to another, you

00:10:11.109 --
do one is 1 stage method because
you only use one point for the

00:10:16.051 --
modified order, it is 2 stage
because you have predictor an

00:10:19.934 --
you have character. So each step
has two parts.

00:10:24.160 --
OK.

00:10:26.920 --
So if we take so here, we
have N equals.

00:10:33.010 --
Zero, so when N = 0, I have X
1 = X O plus H. We find 0.1,

00:10:40.462 --
which is what supposed to be
predicted point Yuan Yuan plus

00:10:45.016 --
one. Will you one and then it's
Y0 plus HX0Y0 and you substitute

00:10:50.398 --
values you get 2.1. So this is
your predicted value and then

00:10:55.366 --
you can use it in the next stage

00:10:58.678 --
defined. Correction, OK, so this
is your essentially. This is the

00:11:02.650 --
same as what you have here.

00:11:05.450 --
So it might be more beneficial
to use key one key two if you

00:11:10.014 --
want to reduce time on writing
because you have to rewrite

00:11:13.600 --
this. And this is your slope at
the predicted point. Again, just

00:11:17.512 --
write down X0Y0X1U one before
you substitute values, because I

00:11:20.772 --
mean you see that becomes messy.

00:11:29.940 --
OK, so then we substitute values
and we obtain approximation. So

00:11:33.845 --
so we did two stages, but this
is the first step.

00:11:38.670 --
OK, it's not 2 steps first step.
So now we use N = 1 and

00:11:45.525 --
this allows us to find X2U2 and
Y2. So X2 is exam plus H, so

00:11:52.380 --
we have you too is a prediction
using the Oilers step from Point

00:11:58.321 --
X one U-1 and then you do is
correction with average of

00:12:03.805 --
slopes. Again as you see, right
down X one U1X1X2U2 and so on.

00:12:09.880 --
And then approximate and
then substitute values.

00:12:16.130 --
So finally so this is our
approximation of a solution at

00:12:19.639 --
0.2, and again this is not exact
value, right? It's only

00:12:23.148 --
approximation because we use out
of infinitely many terms in the

00:12:26.657 --
Taylor series, we only use 3.

00:12:29.290 --
So H is finite, right? So
definitely we have an error. OK,

00:12:33.442 --
so schematically what is going
on here? You start. Your initial

00:12:37.248 --
condition was at 02 right? This
is your point.

00:12:42.180 --
Predictor brings you
to point X one U-1.

00:12:47.560 --
You find slope at this point at
X1. You want you find slope at

00:12:54.224 --
X0Y0. You average corrector
gives you point X1Y1.

00:12:59.420 --
This is your first step, but

00:13:01.412 --
still stages. Then again from
point X1 U one you find

00:13:06.648 --
predictor X2U2 right YouTube
means has index as Y two. So

00:13:11.510 --
please different letter. But
it is the same index and then

00:13:16.372 --
you've added slopes at X
11X2U2 average them and this

00:13:20.792 --
gives you correct correction
point X2Y two again two stage

00:13:25.212 --
but it's one step.

00:13:31.180 --
OK.

00:13:33.760 --
Any questions here?

00:13:36.930 --
So example have either Euler or
modified Euler method to

00:13:40.870 --
implement by hand, which means
the step size will be generously

00:13:45.204 --
large, maybe like one or
something that doesn't require

00:13:48.750 --
because you cannot use
calculators for the test there

00:13:52.296 --
'cause I don't know which device
you bring mini. Something

00:13:56.236 --
computer that has access online
and so on. So the algebra will

00:14:00.964 --
be simple enough that you can do

00:14:03.722 --
by hand. But for me, even if you
have to perform 2 steps.

00:14:08.650 --
I need to see that yes, you
know what is initial

00:14:11.411 --
condition. What is the next
point and so on. So it will

00:14:14.423 --
not be a lot of steps, but at
most Euler or modified Euler.

00:14:18.810 --
OK, your homework has more steps
to perform, so you're welcome to

00:14:23.358 --
use whatever calculators
computers to get the values, but

00:14:26.769 --
you have to write down. Then you
can probably minimize number of

00:14:31.317 --
things that you write.

00:14:33.600 --
OK, your project Modeler
project is based on

00:14:36.888 --
implementing these methods
actually not implementing.

00:14:39.354 --
Using them to solve
problems because the

00:14:42.231 --
programs functions are
available on the course

00:14:45.108 --
websites. You just have to.

00:14:49.070 --
Maybe on Monday I'll bring the
laptop so I'll show you where

00:14:52.646 --
files are and how to use them.

00:14:57.500 --
OK so next method.

00:15:00.250 --
To consider is so called 1st
order on the quota method.

00:15:06.320 --
And the idea here is the
falling. So we saw from their

00:15:10.880 --
modified all the method that if
we use information from two

00:15:15.060 --
points then we get more accurate

00:15:17.340 --
approximation. Right, so can we
use more points to get the even

00:15:22.577 --
more accuracy and the question
the answer is yes. So in this

00:15:27.101 --
case we use four points.

00:15:29.560 --
So we go from .1.

00:15:32.980 --
2.2 Essentially this is your
order step. We get point .2.

00:15:38.645 --
Then we use this slope K2 to
go to .3.

00:15:44.670 --
We use the .3 slope. Do you go
to .4 and then we take weighted

00:15:50.790 --
average of the slopes at this

00:15:53.238 --
point? OK, so OK.

00:15:57.250 --
Um?

00:16:00.400 --
So which points we use? We use

00:16:03.529 --
point X. We use point in the
middle of this interval at X N +

00:16:08.925 --
H / 2 and here we have two
points to use and we also use

00:16:13.050 --
point at X = N + 1.

00:16:16.350 --
So do we? Do we give the same
weight essentially the sum of

00:16:21.316 --
slopes over 4? No, we give
twice more weight at points

00:16:25.518 --
in the middle.

00:16:36.200 --
And this is last page that you
have an I I did not print. I

00:16:42.095 --
have a few more pages, but.

00:16:45.910 --
I'll explain what we have here.
So if you have.

00:16:51.170 --
Probably let let me use, maybe
maybe maybe this so you don't

00:16:55.094 --
have this page, but this is a
recap of the last page, so you

00:16:59.672 --
have to want to solve the 1st
order equation with some given

00:17:03.596 --
initial. So I'll bring a copy of

00:17:05.885 --
this next time. So what you do
you find the slope at .1. This

00:17:11.178 --
is where you start.

00:17:13.540 --
Then you match half step to .2
using this slope.

00:17:19.110 --
So you have you have X N + H
over to you. This is your X

00:17:25.462 --
displacement an in. Why you do
Oilless step with step size H of

00:17:30.623 --
it but slow K1.

00:17:33.320 --
So once you have this
point, you use this point

00:17:37.380 --
to evaluate slope.

00:17:39.970 --
So I compute slope K2 and I find

00:17:43.858 --
.3. By marching again from KXAN
half step and using alone Def

00:17:50.700 --
line with slope Cato.

00:17:53.650 --
OK, this gives me point X 3.3,
so from .3 then we match full

00:18:00.090 --
step to find point for using
Slope case 3.

00:18:05.020 --
Once you have all these four
slopes, you have weighted

00:18:08.630 --
average so you have you give
weight 1 to the first point and

00:18:13.323 --
to the last point, but two
weights to the .3 and two and

00:18:18.016 --
three. So overall you have for
slopes six slopes. So you divide

00:18:22.348 --
age by 6.

00:18:24.130 --
So this is your average
weighted slope.

00:18:28.090 --
OK, and then you can write this
slope like even if you don't

00:18:32.640 --
know this. So you use
information from four points. OK

00:18:36.140 --
to find, so this is a full stage

00:18:38.940 --
method. Anne.

00:18:43.250 --
In order to go from X&YN 2 X N +
1 one plus one, it is still

00:18:49.098 --
using only one previous point,
right essentially, but it does

00:18:52.538 --
it in four in four stages.

00:18:55.260 --
OK.

00:19:01.760 --
OK, So what I can say
here is there wrong accoutre

00:19:08.756 --
force order matches there?

00:19:14.230 --
The local error in their own
decoder 1st order method is of

00:19:18.406 --
order H as a power 5.

00:19:21.980 --
OK, but when you find cumulative
error then you lose one order

00:19:27.476 --
and then overall the error is.

00:19:31.300 --
Proportional to H is about four
and you can. You can appreciate

00:19:35.116 --
it if H is let's say 0.01 to 10
to the point is the power of

00:19:40.204 --
negative one right? All this
method will have error also of

00:19:43.702 --
the order of 10 to the minus

00:19:45.928 --
one. Right modified order will
have error to the order 10 to

00:19:50.999 --
the minus. Two but longer code
will have error of the order 10

00:19:56.205 --
to the minus four right? So you
see that it's occasionally.

00:20:00.180 --
Logic difference in the in the
accuracy. So all this method in

00:20:03.744 --
order to get the same accuracy.

00:20:06.480 --
You need to use smaller H. Ruby
code allows you to use larger

00:20:11.992 --
step size. Because the the error
is small and So what you save,

00:20:17.542 --
you save the number of steps.
But again, remember that one

00:20:21.634 --
step of the longer quota has

00:20:23.866 --
four stages. So at each stage
you have to evaluate function

00:20:28.565 --
and function evaluation may be
consuming, so that's so. That's

00:20:32.015 --
why it's not very cheap method
because at every step you have

00:20:36.155 --
four function evaluations.

00:20:39.020 --
OK.

00:20:40.850 --
How do we check that method is
first order accurate? If we

00:20:45.686 --
decrease H by half, their level
decreased by a factor of.

00:20:55.410 --
If H is replaced with H / 2,
so the arrabelle decreased

00:20:59.622 --
by a factor of.

00:21:03.430 --
22 to the power. 416 right so
this is, you see, is a

00:21:08.929 --
significant difference between
this method and that method OK?

00:21:14.650 --
Which method you would
like to use if you have

00:21:17.570 --
to solve your problem?

00:21:22.740 --
So you have a choice. You have
three methods and you have to

00:21:27.095 --
implement MCF thread programs,
foiler for modified or Lefranc

00:21:30.110 --
equal to which method you
would start with.

00:21:33.900 --
If you want to solve the
problem that you don't know

00:21:36.595 --
solution about anything about.

00:21:39.660 --
Probably oil it while it's easy
to implement, its lately least

00:21:43.037 --
accurate, but it's easy to
implement, and for example, if

00:21:46.107 --
you programmed at an, you see
that it doesn't work. Maybe

00:21:49.484 --
there is no point of investing
time, right? But if you know

00:21:53.168 --
that yes solution exists, an
that gives you what you need,

00:21:56.545 --
you can start with all the
method just to get a feeling of

00:22:00.536 --
what solution is going to do.
But then if you need to have

00:22:04.527 --
more accuracy, or let's say if
you have to compute for long

00:22:08.211 --
time and maybe. Many points
then you probably would use on

00:22:12.492 --
GeForce order method. Matlab
in fact has so called variable

00:22:15.782 --
Force 5th order method ricotta
which allows us to change the

00:22:19.401 --
step size depending on the
estimate of the error. So they

00:22:23.020 --
have some estimate of the
error in air is small. Then

00:22:26.639 --
you can use largest largest
step. If estimate becomes

00:22:29.600 --
large then you decrease the
time step so it's not

00:22:32.890 --
constant, is not the same
method that would be

00:22:35.851 --
considered here.

00:22:37.550 --
OK, I mean whatever Matlab
built-in function solver.

00:22:42.500 --
OK, so an example and I'll have
this available on the course

00:22:47.564 --
website and then I'll give you a
hand out next time just to show

00:22:53.472 --
you what what is going on in
this ricotta method. So if we

00:22:58.958 --
want to solve this initial value
problem starting from .12 and

00:23:03.600 --
finding oh at 1.4 in two steps
using force ordering decoder

00:23:08.242 --
method, so two steps means that.

00:23:11.460 --
What is H we go from 1 to 1.4.

00:23:15.900 --
Each is.

00:23:19.750 --
So age is 1.4 -- 1 / /
2, so this will give us.

00:23:27.190 --
Zero Point 4 / 2 will be 0.2,
right? So this is your step size

00:23:32.515 --
capital N number of steps is 2
inside of each step. How many

00:23:37.130 --
stages do you have?

00:23:39.330 --
Four stages right? So 4th
function evaluations. So for

00:23:42.480 --
each stage you have to write
K1K2K3K four and then the

00:23:46.330 --
weighted average to find next

00:23:48.080 --
approximation. So K1K2K64
will be different for

00:23:51.738 --
inside of each step.

00:23:55.390 --
OK, so H with no envy, no
initial condition. X Zero is

00:23:59.626 --
one, XY0 is 2 OK, what is a
function function is X + sqrt y.

00:24:04.921 --
This is your function F so F of
XNYN is X N + sqrt y N.

00:24:12.780 --
OK, and then you carefully
substitute these values, right?

00:24:16.263 --
I mean it's OK for demonstration
purposes, so you probably want

00:24:20.520 --
to have this done by computer
right? Unless function is simple

00:24:24.777 --
that you can, you can do it. OK,
so gave one is a slope at first

00:24:30.969 --
point. In this case at X0Y0,
right? You find Cato is you

00:24:35.613 --
March, you replace X with 0 + H
to point in between and Y zero.

00:24:41.418 --
You follow The Cave one slope.

00:24:45.130 --
Right, so this is your X value.
This is your why value once you

00:24:48.882 --
have them, you substitute them
in the function, so you replace

00:24:51.830 --
X with this. Why is that?

00:24:54.140 --
Annual value it so this gives
you slope K2 then use K2 here to

00:24:59.768 --
find .3 again. X is just half
step away while zero plus K 2 *

00:25:05.798 --
H / 2 This is your ex. This is
your Y value you put in the

00:25:12.230 --
function you evaluate. Finally K
4 you much full step.

00:25:16.890 --
Use slope case 3. This is
your X value. This is your.

00:25:20.694 --
Why will you find slope K 4?
You take weighted average.

00:25:24.181 --
You get next approximation.

00:25:31.380 --
OK, so now what you found
you found.

00:25:37.130 --
X1 is 1.2 and
Y one is 2.5201.

00:25:45.570 --
So now you use this.

00:25:47.540 --
To do another step so we have
two steps here to do.

00:25:51.350 --
Right, so we have this and then
again K1K2K3K four. But now

00:25:56.990 --
instead of X0Y0 you have X1Y1.

00:26:00.690 --
Just indexes shifted and so on,
so I'll have this online and

00:26:05.034 --
I'll bring this on Monday.

00:26:09.020 --
OK, any are there
any questions yes.

00:26:14.720 --
This is based on.

00:26:17.670 --
Next one you just. Right, you
found this one from the previous

00:26:22.220 --
right step and then you just
keep it the same, but you keep

00:26:26.640 --
adding. So what I do OK, I have
formulas dependent on X&YN

00:26:30.720 --
right? So here I had to use.

00:26:34.040 --
My end was zero.

00:26:37.050 --
So I replace end with zero
everywhere before I try to

00:26:41.285 --
compute anything. So in the next
stage I have to use N equals.

00:26:46.910 --
1.

00:26:48.560 --
OK so I replace.

00:26:51.160 --
SNV X1 Y end with Y1 and
similarly everything else but

00:26:56.011 --
K1K2K3 will be different now
from the previous case from the

00:27:00.862 --
previous step. So I have F of
X1Y1 compared to.

00:27:06.930 --
F of X0Y0 I have for K2 I have F
of X1 plus HY one plus K 1 * H

00:27:14.250 --
/ 2 I have here with HO, but
this key one and escape one of

00:27:19.740 --
the same. OK, so at every
state at every step you

00:27:24.894 --
K1K2K3K four will be
different, so he probably

00:27:28.142 --
technically we have to write
down another index an, but

00:27:32.202 --
it just will increase. It
will be very cumbersome. So

00:27:36.262 --
so all slopes are different.
So for each step you

00:27:40.322 --
recompute your slopes.

00:27:44.870 --
OK, that's why.

00:27:47.280 --
Write this before you implement
your substitute values.

00:27:52.260 --
OK, right X 0X1YY1Y2 and
so on.

00:28:00.600 --
This will not be on the test.

00:28:04.540 --
OK, but it is in the homework so
so you have to do it.

00:28:10.850 --
OK, any other questions?

00:28:16.150 --
So more about numerical
methods. So we teach a

00:28:20.236 --
course which is now taught
between three department's

00:28:23.868 --
mathematics, physics, and
engineering is typically

00:28:26.592 --
chemical genius teaching and
then so this method are

00:28:30.678 --
studied in more details, but
not only this, but also

00:28:35.218 --
root, finding methods, argon
values, eigenvectors,

00:28:37.942 --
solving linear systems. So
maybe I should write so.

00:28:47.210 --
More about.

00:28:58.720 --
Anne.

00:29:01.050 --
428 and there's also so this
physics for 28 and engineering.

00:29:07.850 --
So it is the same course. I
mean, of course the also

00:29:12.602 --
graduate version.

00:29:15.760 --
529 I think and physics.

00:29:20.070 --
528 So it's slightly dependants
who is teaching, but we cover

00:29:24.437 --
the same material, so professors
from different departments POV

00:29:28.010 --
alternate, but we have the same
syllabus to follow.

00:29:36.920 --
No, normally you choose
whatever flavor you want on

00:29:40.664 --
your transcript, but that's
the only difference.

00:29:46.810 --
OK questions.

00:29:51.800 --
So.

00:29:53.810 --
I'll start Chapter 3, which
is linear equations of

00:29:57.689 --
higher order.

00:30:16.410 --
So far we've dealt only with
first order linear equations,

00:30:20.940 --
but we will look at their
methods that will allow us to

00:30:26.376 --
solve equations of high order
and linear equations do not

00:30:30.906 --
require. Coefficients to be
constantly constant, but we will

00:30:35.444 --
for simplicity we will start
with questions of miss

00:30:39.656 --
constantly efficients. OK, so
let's just recall the definition

00:30:43.868 --
of the linear equation of ends
order so linear.

00:30:51.720 --
And order.

00:30:54.120 --
Differential equation. Has
function derivative, second

00:30:58.768 --
derivative, and so on up the
derivative order NPL linearly in

00:31:04.675 --
the equation so?

00:31:07.440 --
Hey Ann.

00:31:13.720 --
Plus a N -- 1.

00:31:21.670 --
Loss etc plus a 2X.

00:31:25.550 --
D2Y T X ^2.

00:31:29.040 --
Plus a one of X.

00:31:34.190 --
Plus a 0 times function Y

00:31:37.382 --
equals. Some function that does
not depend on why.

00:31:44.150 --
So remember.

00:31:46.460 --
How, how, how we define linear
function we defined in a

00:31:50.673 --
function is a X + B right? So
your independent variable AP is

00:31:55.652 --
linearly means raised to the
power one. So now in the linear

00:32:00.248 --
differential equation you have
the same but for the function

00:32:04.078 --
derivative, second derivative
and up to the ends of the

00:32:07.908 --
derivative. These are the
functions of X only.

00:32:11.540 --
Right then they don't
involve why dependence are

00:32:14.716 --
of X is right inside.

00:32:18.020 --
Can be 00 but linearity means
that you don't have y ^2.

00:32:22.604 --
Don't have y * Y prime and so
on so so they appear linearly

00:32:27.952 --
same way as X appears in the
linear function.

00:32:32.770 --
In this case, we multiply by
constant in the equation. In

00:32:36.268 --
the case of, the equation,
coefficients can be functions

00:32:39.130 --
of X at most.

00:32:41.960 --
OK. So if.

00:32:46.070 --
Oldest coefficients.

00:32:51.390 --
Constants.

00:32:57.190 --
Then we have equations with
constant coefficients.

00:33:00.960 --
Then differential equation is.

00:33:05.460 --
A linear.

00:33:08.260 --
Differential equation with.

00:33:13.190 --
Constant.

00:33:18.560 --
Coefficients. And these are,
these equations are

00:33:23.016 --
typically easier to solve.
Otherwise equation has

00:33:26.103 --
variable coefficients.

00:33:36.630 --
This differential equation is.

00:33:41.680 --
Linear, viz.

00:33:48.200 --
Variable coefficients.

00:33:53.330 --
OK.

00:33:55.070 --
If you have a linear
equation an if right hand

00:33:59.190 --
side is identically zero,
then we have linear

00:34:02.486 --
homogeneous equation and in
fact homogeneous equation

00:34:05.370 --
only can be introduced for
linear equations. I mean

00:34:09.078 --
sometimes can be introduced
for nonlinear, but typical

00:34:12.374 --
is for linear equations.

00:34:15.830 --
Then

00:34:19.440 --
linear differential equation.

00:34:22.060 --
Is homogeneous.

00:34:29.190 --
Otherwise.

00:34:35.270 --
Linear differential equation is.

00:34:42.490 --
Nonhomogeneous

00:34:47.710 --
let's look at some examples that
we've just trying to classify

00:34:51.593 --
and then to analyze the order if
it is linear. If it is

00:34:56.182 --
homogeneous or non homogeneous.

00:35:01.010 --
So Y double prime plus X
y = 0. So what is the

00:35:05.716 --
order of this equation?

00:35:09.740 --
2nd order.

00:35:12.000 --
Is it linear or nonlinear?

00:35:16.800 --
Linear right? Because XY is
multiplied by a function of

00:35:21.040 --
XY, double prime is multiplied
by one. So linear is a

00:35:25.704 --
sensitive linear. Is it
homogeneous or non

00:35:28.672 --
homogeneous?

00:35:32.050 --
Homogeneous because there is no
function that only depends on X

00:35:36.428 --
rated 0 so homogeneous.

00:35:42.100 --
Coefficients are constant
or variable.

00:35:46.930 --
Variable because we have X
right? So this.

00:35:55.180 --
Variable coefficients. OK.

00:35:59.730 --
What about this equation?

00:36:03.530 --
X ^2 y double prime minus two XY
prime plus Y to the XY equals

00:36:10.640 --
two X -- 1.

00:36:13.550 --
Order

00:36:15.760 --
2nd. Is it linear or nonlinear?

00:36:25.740 --
OK, so we have Y times each of
the XY prime times minus two XY

00:36:30.630 --
double prime times X squared. We
have termed it depend on on why

00:36:34.868 --
is it in this form?

00:36:38.870 --
That you have derivatives
multiplied by at most

00:36:41.350 --
functions of X.

00:36:43.760 --
Yes, so it is linear, right?

00:36:46.730 --
Is it homogeneous since it is
linear or not homogeneous?

00:36:51.860 --
None, because we have
to explain this one.

00:36:56.590 --
So, nonhomogeneous? And
coefficients are variable

00:37:00.892 --
variable right? Because we have
functions so this.

00:37:07.660 --
Variable coefficients.

00:37:12.280 --
OK, next example.

00:37:15.440 --
Is 2 Y triple prime minus three
Y prime plus seven Y equals

00:37:22.499 --
luxury four X ^2 -- 1?

00:37:26.490 --
OK, the order of the equation is
3 third order.

00:37:35.940 --
Is it linear or nonlinear?

00:37:42.440 --
Huh?

00:37:43.970 --
Linear or nonlinear?

00:37:47.530 --
Why is it nonlinear?

00:37:52.610 --
We have function multiplied by 7
derivative multiplied by

00:37:57.002 --
negative three, so the order to
multiply by two.

00:38:03.220 --
Linear.

00:38:07.420 --
What is in here an is 3.

00:38:10.950 --
Look for linear equation. You
have function multiplied by at

00:38:14.430 --
most, so this this may be

00:38:16.518 --
constant. Or maybe some function
of X. This functional effects

00:38:20.159 --
may be nonlinear, but we look at
the look at the YY prime Y

00:38:24.373 --
double prime up to the highest
order derivative, not in terms

00:38:27.684 --
of X in terms of Y.

00:38:30.880 --
OK. So equation is.

00:38:34.260 --
Linear.

00:38:36.670 --
Since it is linear, is it
homogeneous or homogeneous?

00:38:41.910 --
Non, because of the logarithm
of X ^2. So nonhomogeneous

00:38:46.250 --
and coefficients are.

00:38:48.580 --
Constant rate with
constant coefficients.

00:38:54.990 --
OK and last example.

00:38:59.640 --
White triple prime my
plus 2Y double prime

00:39:04.216 --
minus y * Y prime +7.

00:39:08.920 --
The order is.

00:39:11.750 --
So the order. 3rd order.

00:39:16.710 --
Linnaean olenia.

00:39:21.560 --
Nonlinear because we have y * y
prime right nonlinear.

00:39:28.920 --
We cannot say if it is ominous
nonhomogeneous becausw we don't

00:39:33.980 --
have linearity to say this.

00:39:38.200 --
OK.

00:39:40.660 --
So big chunk of this course will
be devoted on the 2nd order well

00:39:45.924 --
probably not sister going to
order, so essentially it's

00:39:49.308 --
easier probably to solve 2nd
order equations, especially when

00:39:52.692 --
you consider with variable
coefficients. But the method

00:39:55.700 --
that we will develop for
equations with constant

00:39:58.708 --
coefficients can be easy.

00:40:00.470 --
Applied to the 2nd order first
Order 5th order intense order I

00:40:06.086 --
will have 19th order example to
consider. So yes.

00:40:15.070 --
It is defined only for linear
for linear equations, so.

00:40:21.530 --
I've seen some definitions that
say if identical is zero

00:40:24.950 --
solution satisfies equation,
then you can think of this as

00:40:28.370 --
homogeneous. In this case it
won't be because if you have

00:40:32.132 --
zero then this is 0. This is non
0 but typically homogeneous is

00:40:36.578 --
only for linear equations
because you have some relation

00:40:39.656 --
to linear algebra. So linear
systems, linear equations so

00:40:42.734 --
that that's the reason. So once
you may have a question on the

00:40:47.180 --
test to classify equation
equations and then so similar

00:40:50.258 --
like like we we've done here.

00:40:52.400 --
You look at the order if it
is linear then you can think

00:40:56.716 --
it's homogeneous,
nonhomogeneous, but if it's

00:40:58.708 --
not linear then you just
stop.

00:41:01.720 --
OK.

00:41:06.820 --
OK, so let's start with
second order linear

00:41:10.396 --
homogeneous equations so.

00:41:15.190 --
So we consider 2nd.

00:41:19.420 --
Modern.

00:41:24.600 --
Linear homogeneous
differential equations.

00:41:30.280 --
We will first address the
problem when we have none of

00:41:34.031 --
them, we have homogeneous
equation. Once we know how

00:41:37.100 --
to solve homogeneous then we
will study how to solve

00:41:40.510 --
nonhomogeneous equations
because there are different

00:41:42.556 --
methods how to address this
problem. OK, so in general,

00:41:45.966 --
if you have second order
linear equation then you can

00:41:49.376 --
write it in just using some
coefficients which are

00:41:52.445 --
functions of X.

00:41:55.200 --
A1 of X.

00:41:57.440 --
Divide the X + A zero
XY homogeneous. This means very

00:42:03.776 --
inside is 0.

00:42:15.190 --
And so let's look at example and
then we will try to establish

00:42:20.546 --
some properties of solutions to
the homogeneous equations.

00:42:25.750 --
So example is.

00:42:38.500 --
Let's let's let's do 2 examples,
so example a.

00:42:43.530 --
X ^2 D two YG X
^2 -- 2 X divided X.

00:42:51.680 --
Plus plus two y = 0.

00:42:54.760 --
So you can see it is
second order, right?

00:42:58.620 --
It is linear 'cause you have y *
2 divided you exams minus 2X and

00:43:03.480 --
this is also linear term and it
is not just homogeneous because

00:43:07.368 --
there is no function that only
depends on X and not multiplied

00:43:11.256 --
by wire derivative and.

00:43:13.310 --
My first statement
is that the X ^2.

00:43:17.680 --
Is a solution of this equation.

00:43:21.770 --
How do we? How do we verify that
this function is a solution?

00:43:27.300 --
We have the substitute and check
if you get identity right. OK,

00:43:30.840 --
So what do we have? If X squared
is a solution, what is the

00:43:34.970 --
derivative of this solution?

00:43:37.500 --
2X and 2nd derivative will be 2,
so we have X ^2 * 2 -- 2

00:43:44.572 --
X times. Two X + 2 times
function. So do we have 0?

00:43:51.430 --
We have two X ^2 -- 4 X
squared plus two X squared

00:43:55.863 --
right, so cancels so 0 = 0.
So this means that X squared

00:44:00.296 --
is a solution of the
equation. What happens if we?

00:44:05.020 --
Multiply this function by
by constant.

00:44:09.370 --
By some arbitrary constant.

00:44:13.130 --
The claim is that this is
also a solution.

00:44:18.740 --
So C One is an arbitrary
constant.

00:44:25.870 --
Indeed.

00:44:27.990 --
1st Order derivative will be 2 C
1X and 2nd order derivative will

00:44:32.839 --
be 2C1, right?

00:44:35.290 --
So we have X ^2 * 2 C
1 -- 2 X times 2C. One X

00:44:43.162 --
+ 2 * y C One X ^2.

00:44:48.260 --
C1 is present in all the
terms, right and otherwise

00:44:51.760 --
you have two X ^2 -- 4 X
squared X squared, so so this

00:44:56.660 --
is also zero. So again, if
you take a solution of a

00:45:00.860 --
linear homogeneous equation
multiplied by arbitrary

00:45:02.960 --
constant, you still get the
solution, so this will be

00:45:06.460 --
still a solution.

00:45:08.850 --
So similarly.

00:45:11.370 --
And you can verify that X
is a solution.

00:45:18.240 --
The first derivative is.

00:45:20.930 --
One second derivative is 0,
right? So we have X ^2 * 0

00:45:26.819 --
plus. I'm sorry minus.

00:45:32.040 --
Minus two X * 1 + 2 times
function you can see that

00:45:37.318 --
this is 0.

00:45:40.060 --
And if I multiply this solution
by an arbitrary constant, I also

00:45:44.452 --
get a solution.

00:45:49.450 --
Let's say C 2 * X is a solution.

00:45:55.110 --
And we can verify this by
substitute and so again, second

00:45:58.883 --
derivative will be 0, so we have
X, y ^2 * 0 -- 2 X times C 2

00:46:05.057 --
+ 2 * C Two X.

00:46:07.860 --
Zero and finally, if you
consider linear combination of

00:46:12.225 --
these two functions.

00:46:14.860 --
In linear combination is you
multiply function by constant by

00:46:19.410 --
different constant and you add

00:46:21.685 --
so C1. X ^2 + C
two X is.

00:46:27.720 --
Also a solution.

00:46:33.150 --
OK, let's let's verify, because
probably those cases are easy to

00:46:36.560 --
see. This one is a little bit
tricky. OK, so we have X squared

00:46:40.900 --
times second derivative. What is
the 2nd derivative here?

00:46:45.460 --
To see one right plus zero.

00:46:48.830 --
Minus two X times first order

00:46:51.908 --
derivative 2C1X. Plus C2.

00:46:56.020 --
And plus two times functions, so
C One X ^2.

00:46:59.830 --
Plus it 2X.

00:47:02.870 --
Do we have here?

00:47:06.240 --
So if I look at terms with C1.

00:47:10.270 --
I have two X ^2 -- 4 X squared,
two X squared, they cancel.

00:47:18.040 --
In terms with C2.

00:47:21.470 --
Minus two XY2 plus to exit to

00:47:24.837 --
also cancel. Right,
and this is here.

00:47:29.070 --
So 0 = 0.

00:47:36.510 --
So what we showed here is that
if you have linear homogeneous

00:47:41.178 --
equation an if you have
solutions, you form linear

00:47:44.679 --
combination. So you multiply by
constants and you add and you

00:47:48.958 --
have you keep them arbitrary.
Then result is also a solution

00:47:53.237 --
to this equation.

00:48:01.930 --
So maybe just another
example be.

00:48:05.740 --
G2Y G X ^2 +

00:48:09.486 --
3. Divide X + 2 *
y = 0 again. This is second

00:48:17.322 --
order equation. Linear
homogeneous coefficients are.

00:48:22.880 --
Constant variable so 2nd order.

00:48:29.390 --
Linear homogeneous.

00:48:34.050 --
With constant coefficients.

00:48:39.860 --
And the claims here are that E
to the minus X is a solution. So

00:48:44.615 --
at this point I'm not saying how
we find them, we will. We will

00:48:49.053 --
know this soon, but let's just
just check. So if you have it to

00:48:53.491 --
the minus X derivative will be
minus E to the minus X second

00:48:57.612 --
derivative will be with the plus
sign, right? So you have either

00:49:01.416 --
the minus X + 3 * E to the minus
X minus sign plus two times

00:49:06.488 --
function E to the minus X.

00:49:10.010 --
You get 0 right, and similarly
if you multiply by constant.

00:49:16.900 --
Is a solution.

00:49:20.190 --
That I will not verify, but
you can see that this is also

00:49:23.284 --
straightforward to do.

00:49:27.080 --
And then another solution here
available is E to the minus, 2X

00:49:32.864 --
is a solution.

00:49:38.360 --
And if we multiply by constant,
it is a -- 2. X is a solution.

00:49:45.230 --
And finally, linear
combination is.

00:49:50.340 --
Also a solution.

00:49:53.260 --
OK.

00:49:56.540 --
So so the result is how much
time do I have left?

00:50:05.830 --
One minute. OK, so I'll
I'll write the just result

00:50:09.690 --
so theorem.

00:50:12.320 --
So principle.

00:50:15.760 --
Of linear superposition?

00:50:22.460 --
It only works for linear
homogeneous equations, so given.

00:50:28.790 --
2nd order equation.

00:50:39.160 --
2nd order.

00:50:42.280 --
Linear.

00:50:44.550 --
Homogeneous equation.

00:50:51.200 --
If. Why one
of XY2 of X?

00:50:56.650 --
Our solutions.

00:51:01.250 --
Of this differential equation.

00:51:05.810 --
Then

00:51:08.050 --
their linear combination.

00:51:15.580 --
C1Y one of X + y two
Y2FX is also solution

00:51:21.212 --
of the same equation.

00:51:37.400 --
See once you're here.

00:51:41.630 --
C1C2 are arbitrary constants.

00:51:50.360 --
And similar result holds 4th
order equations, right? So this

00:51:54.430 --
doesn't change. OK, so I guess
I'm out of time, any questions?

00:52:01.690 --
OK, thank you and drive safely.

Duration:"01:13:24.6740000"

00:00:28.270 --
Alright, welcome class. Today
I'll we've got. It's one of my

00:00:33.242 --
favorite lectures is today, so
I'm happy to share that joy with

00:00:38.666 --
all of you for class today.
Alright, before we get going you

00:00:44.090 --
got your homeworks back just so
that you know there are some

00:00:49.514 --
issues. A number of issues arose
in this homework assignment, so

00:00:53.720 --
in problem 5 two finding the
velocity downstream of the shock

00:00:57.724 --
appeared to be a problem. I
think we talked a little bit

00:01:02.092 --
about that last time problem 5
seven finding the velocity

00:01:05.732 --
downstream of the shock appeared
to be a problem as well, and

00:01:10.100 --
then finding the change in
pressure in problem 20 was a

00:01:14.104 --
problem. Please the solutions
are all on baby learn. Go look

00:01:18.108 --
at that and make sure that you
can get those assignments done.

00:01:22.630 --
OK, I think for probably 5 two
that a lot of you solve that as

00:01:26.590 --
a moving shock problem, and
that's going to screw you up

00:01:29.494 --
from the get go. So it's just a
stationary shock, that is, that

00:01:32.926 --
is a bread and butter. Normal

00:01:34.510 --
shock problem. OK, so make
sure that again, compare

00:01:38.642 --
your solutions your homework
with with the solutions that

00:01:42.476 --
are available online and
make sure that you can solve

00:01:46.736 --
the problems correctly. OK,
alright anybody go to the go

00:01:50.996 --
to career fair yesterday.

00:01:54.000 --
OK, engineers were in huge
demand. I walked through, talk

00:01:58.920 --
to some of the employers navair.
We have sent a number of

00:02:04.824 --
students to navair. They're
looking for 250 engineers.

00:02:10.730 --
So if you're looking for
work, it's a great place to

00:02:14.173 --
go, and you can apply gas
dynamics to it. OK, you get

00:02:17.929 --
to work at airplanes to work
on jets. I mean, how cool is

00:02:21.998 --
that? OK, so I've got just a
little bit of information

00:02:25.441 --
here. If you are interested,
come on by after class, OK?

00:02:31.020 --
Let's get on. Let's get on here.
Alright we are going to be

00:02:35.622 --
reviewing oblique shockwaves,
and then we're going to see some

00:02:39.162 --
applications of those
shockwaves. We're going to see

00:02:41.994 --
why, why airplanes are designed
the way they are now that we

00:02:46.242 --
know about oblique shockwaves
here. OK, we're going to learn

00:02:49.782 --
about supersonic diffusers, and
that's just a fancy name for an

00:02:53.676 --
inlet to a jet aircraft. That's
all it is. OK, so we're going to

00:02:58.632 --
learn about jet inlets today.

00:03:00.550 --
We learn about reflected
shockwaves and you have a

00:03:04.087 --
homework problem on reflected
shock waves and then we'll talk

00:03:08.017 --
a little bit about the
differences between subsonic and

00:03:11.554 --
supersonic aerodynamics. OK, so
before we get going a couple of

00:03:15.877 --
principles I want you to keep in
your noggins. What we talk about

00:03:20.986 --
some of our material today. OK,

00:03:23.344 --
First off. The change of entry
is equal to that of the negative

00:03:29.051 --
natural log of the stagnation
pressure ratio. OK, so if you

00:03:33.022 --
want to minimize the losses, if
you want S 2 -- S one to be

00:03:38.437 --
close to 0 or as small as
possible, you want this ratio

00:03:42.769 --
here on the right hand side to
be as close to one as possible.

00:03:47.823 --
Can peanut to ever be greater
than peanut one.

00:03:55.460 --
Because then what would
happen to S 2 -- S one? What

00:03:58.820 --
happens and what that would
violate what law?

00:04:02.550 --
Second law of Thermo dynamics.

00:04:05.170 --
If Pete shot 2 or greater than
peanut one, that would be. That

00:04:10.084 --
would be negative.

00:04:12.000 --
Change there due decreasing the
entropy. OK, not going to

00:04:15.740 --
happen. Alright, second thing
to keep in mind we haven't. We

00:04:20.390 --
haven't developed this
relationship, but we will

00:04:22.826 --
later on a semester. But I
want you to keep this in mind

00:04:27.350 --
now and that is that the
thrust generated an engine is

00:04:31.178 --
related to the stagnation
pressure.

00:04:34.310 --
OK, the higher the stagnation
pressure, the greater the thrust

00:04:38.460 --
that you can develop.

00:04:41.550 --
OK so again keep that in mind.

00:04:45.250 --
Stagnation, that the decrease in
stagnation pressure is related

00:04:48.382 --
to the losses in the flow.

00:04:51.090 --
The thrust is related to the
stagnation pressure. OK here we

00:04:55.248 --
go. Oblique shockwaves. This is
just a review from what we did

00:04:59.784 --
last time, so.

00:05:01.790 --
We talked about. In fact, this
is a hint for the first problem

00:05:05.755 --
we've talked about mock waves.
That was the 2nd second lecture

00:05:09.110 --
I think second or third lecture
in class and a mock wave occurs

00:05:13.075 --
when there is just a very small
disturbance. We could measure

00:05:16.430 --
the angle and once we measure
the angle we could calculate

00:05:19.785 --
with the model number was OK.
That's a hint for one of your

00:05:23.750 --
homework problems. OK, now
instead of just having a small

00:05:28.140 --
disturbance, just like a little
Nick in the wall, now there's

00:05:32.375 --
going to be a large wedge or
large angle right here. OK, when

00:05:37.380 --
that occurs, we have an oblique
shockwave that forms, so flow

00:05:41.615 --
comes down. This way it has to
be supersonic. Makes this turn

00:05:46.235 --
through this turning angle
Delta. It creates a shock,

00:05:49.700 --
creates an oblique shock that
has an angle of beta associated

00:05:53.935 --
with it right there.

00:05:56.110 --
OK, so again the turning angle
Delta, the shock angle, beta,

00:06:01.962 --
animac angle, mu.

00:06:04.730 --
Make sure we've got those down
there. OK, very good. An oblique

00:06:08.714 --
shock forms when a flow turns
into itself, so you have a flow

00:06:13.030 --
that's coming down this way, and
it's kind of like blocking it

00:06:17.014 --
off. OK, so flow comes in gets
directed up into itself. An

00:06:20.998 --
oblique shockwave forms were
going to talk next week about

00:06:24.318 --
what happens when you have a
supersonic flow and the flow

00:06:27.970 --
turns away from itself.

00:06:30.170 --
OK, for now the flow is
turning into itself. An

00:06:34.110 --
oblique shockwave forms, so
here's something that's very

00:06:37.262 --
important to know. After
that oblique shockwave, then

00:06:40.414 --
the flow follows the wall,
so we have here flow that's

00:06:44.748 --
coming out in this duct.
Supersonic flow makes it

00:06:48.294 --
turn Delta right here,
creates an oblique shockwave

00:06:51.446 --
that has an angle beta here
and the direction of the

00:06:55.780 --
flow is with the wall.

00:06:58.900 --
OK, yes.

00:07:05.750 --
The Mach angle is going to be
somewhere likely in between

00:07:09.281 --
those right there. OK, so
usually in oblique shock,

00:07:13.356 --
oblique shock problems, we don't
use the mock angle very much.

00:07:19.170 --
OK so I just included it in this
just so that you saw in fact,

00:07:23.325 --
the reason it's the dotted line
is it's an imaginary angle. In

00:07:26.649 --
this problem, just so that you
could distinguish the two other

00:07:29.696 --
angles from that. That's the
only reason why it's there, so

00:07:32.743 --
we're primarily going to be
concerned with the turning angle

00:07:35.513 --
and the shock angle.

00:07:37.330 --
OK, alright so here's a duct
again. The flow follows the wall

00:07:41.398 --
in that direction. Here we have
flow in. This wedge comes down

00:07:45.466 --
this way. Supersonic flow gets
turned up at this angle Delta.

00:07:49.195 --
The flow follows the wall so we
get the direction of the flow

00:07:53.602 --
there. This total angle right
here is called the included

00:07:56.992 --
angle of the wedge.

00:07:59.190 --
Gate we're going to talk later
on today about what happens when

00:08:03.186 --
you have a wedge like that at an
angle of attack and see some of

00:08:08.181 --
the differences there. That's
coming later on today. This just

00:08:11.511 --
review from last time. OK, we
talked last time and showed how

00:08:15.507 --
the turning angle Delta, the
shock angle, beta, and the

00:08:18.837 --
upstream Mach number M someone
are related to each other

00:08:22.167 --
through this oblique shock
equation. OK, so in any kind of

00:08:25.830 --
problem you're going to get two
of those three values.

00:08:29.230 --
You'll get Delta. You'll get
beta or M's of 1. Any two of

00:08:33.624 --
those, and if you know two,
you can use the relation to

00:08:37.680 --
get three there OK. Appendix
three. We talked about the

00:08:41.060 --
oblique shock chart. That's
this right here. Here we have

00:08:44.440 --
the shock angle. Here is the
turning angle right here, and

00:08:48.158 --
each one of those lines
corresponds to a Mach number.

00:08:52.600 --
OK, so three variables here.
That's all related through this

00:08:57.210 --
relationship again man use com
problem. OK, it's going to make

00:09:02.281 --
your life much easier. Solvable
shot problems. OK, alright or

00:09:06.891 --
your app? OK, good.

00:09:11.900 --
Right also recall that for every
for every Mach number and

00:09:16.828 --
turning angle combination, so
you have an upstream Mach number

00:09:21.308 --
Anna turning angle combination.
There is a maximum turning angle

00:09:25.788 --
associated with that that
maximum turning angle

00:09:28.924 --
corresponds to whether or not
you have an attached oblique

00:09:33.404 --
shockwave right across here, or
a detached shockwave. OK, if the

00:09:38.332 --
turning angle is greater than
the maximum turning angle.

00:09:42.430 --
For that Mach number, then you
have a detached shockwave. OK,

00:09:46.071 --
it's going to behave like a
normal shock right up there if

00:09:50.043 --
the turning angles less than the
maximum turning angle you have

00:09:53.684 --
an attached shockwave. How do
you know what that maximum

00:09:56.994 --
turning angle is? Well, if you

00:09:58.980 --
go up here. Each one of these
lines corresponds to a Mach

00:10:03.215 --
number. This let's if we look at
2.2 right here. Here's the line

00:10:07.700 --
from lot number of 2.2. This
maximum point right there? The

00:10:11.495 --
tip of that little thumb that
comes out there. If you go down.

00:10:16.950 --
You can read off what the
maximum turning angle is going

00:10:21.064 --
to be. The turning angle is
greater than that. Then what

00:10:25.178 --
is 2? That's about 25 or so
degrees right there. The

00:10:29.292 --
turning angle is greater than
25 degrees from lot #22 you

00:10:33.406 --
have a detached shockwave.

00:10:36.350 --
OK.

00:10:39.160 --
That's a review from last
time. Any questions?

00:10:43.410 --
Any questions at all? Yes.

00:10:48.860 --
Could you speak a little
louder so I can hear very

00:10:50.598 --
well?

00:10:54.770 --
OK, so the very first slide
right there. OK, the thrust is

00:11:00.158 --
proportional to the stagnation

00:11:01.954 --
pressure. So the higher the
stagnation pressure, the higher

00:11:05.830 --
the thrust, the lower the
stagnation pressure, the lower

00:11:08.665 --
the thrust. OK.

00:11:12.750 --
Good, any other questions?

00:11:16.350 --
OK, not not everything. Fly
straight and level.

00:11:21.600 --
OK, so you could have say a
wedge like we have here, so the

00:11:26.822 --
wedge is going to have some
included angle right here, but

00:11:30.925 --
now this wedge, the wedge itself
is bent down a little bit.

00:11:36.800 --
OK, so that means, so that means
we're going to have different

00:11:41.528 --
conditions on the top and on the
bottom of our wedge, right here.

00:11:47.250 --
OK, remember the flow follows
the wall, so we have a flow

00:11:51.582 --
direction here and a flow
direction here. Let's just let's

00:11:55.192 --
just draw this out here so we
can see get an idea for what's

00:12:00.246 --
going on. OK, so let's say that
we have a wedge here.

00:12:06.910 --
OK it has.

00:12:09.370 --
This angle Delta, so a total
included angle of 2D right

00:12:14.122 --
across there we have flow that
comes down this way some

00:12:18.874 --
supersonic flow. And the
shockwave forms here. Anna

00:12:23.336 --
Shockwave forms here.

00:12:25.360 --
OK.

00:12:27.030 --
Nothing big there. Could you
solve that problem if you knew

00:12:29.197 --
what the Mach number in the

00:12:30.379 --
turning angle was? Yeah, OK,
look at com property. You get

00:12:33.832 --
the shock angle you could figure
out what the pressure in each

00:12:36.880 --
one of those regions are.

00:12:39.610 --
And the directions of the flow.
You could figure out what the

00:12:43.162 --
temperature is. All sorts of
stuff. So now let's take this

00:12:46.418 --
wedge here and. Turn it up a
little bit this way.

00:12:52.620 --
OK, so now we're going to have
an angle of attack on this

00:12:57.924 --
wedge here. So now all
exaggerate my turning angle.

00:13:01.596 --
So let's say that looks like
this and like this, and the

00:13:06.492 --
flow comes this way. So the
wedge still has a total

00:13:10.980 --
included angle of 2D. But now
here is the centerline of the

00:13:15.876 --
wedge.

00:13:17.620 --
It makes an angle of attack.

00:13:20.610 --
Alpha

00:13:24.430 --
everybody see that.

00:13:27.700 --
OK, immediately, what could you
see? What's going to be

00:13:30.570 --
different on the top part of the
wedge compared to the bottom

00:13:34.014 --
part? What's different
geometrically?

00:13:38.940 --
I heard somebody say someone.

00:13:44.040 --
Less flow.

00:13:46.830 --
OK, that might be the case.
There's only going to be

00:13:50.680 --
differences. What's the turning
angle for the flow on the top

00:13:54.530 --
compared to the floor on the

00:13:56.630 --
bottom? What's the
turning angle?

00:14:00.610 --
So this half angle here is is

00:14:03.795 --
Delta. Right that half angle
there is Delta, so knowing

00:14:07.531 --
that the half angles Delta and
you have an angle of attack

00:14:10.879 --
Alpha, what's the turning
angle there at the top?

00:14:16.590 --
It should be smaller.

00:14:18.900 --
Delta. Minus
Alpha.

00:14:24.390 --
Right?

00:14:26.250 --
What's the turning angle going
to be on the bottom?

00:14:31.610 --
Little bit here. How do we do
it this way? So here is that

00:14:35.796 --
wedge it's coming in this way.
So now the turning angle top

00:14:39.384 --
and bottom is Delta OK if it's
just going in horizontally

00:14:42.673 --
here I take that angle down,
has an angle of attack Alpha.

00:14:46.261 --
So what's the turning angle
here at the bottom?

00:14:52.800 --
Here we go here. The turning

00:14:55.416 --
angles Delta. By now add.

00:14:59.570 --
An angle attack Alpha,
what's the? What's the

00:15:01.770 --
turning angle on the bottom?

00:15:04.500 --
Delta plus Alpha.

00:15:06.820 --
So now I'm going to have a
shockwave here and a shockwave

00:15:11.692 --
here, but this turning angle
here at the bottom is going to

00:15:16.564 --
be Alpha plus Delta.

00:15:19.630 --
And here on the top, it's
going to be.

00:15:23.780 --
Alpha minus depends on which one
of those two is larger, but you

00:15:27.589 --
see, there's going to be
different between those two

00:15:30.226 --
angles there. OK, so now let's
think about this. You can you

00:15:33.742 --
see clearly, can you see clearly
that there's going to be a

00:15:37.258 --
larger turning angle at the
bottom and at the top you buy

00:15:40.774 --
that? I mean, if I kept this
angle of attack this way,

00:15:45.395 --
eventually that's going to have
no shockwave on top.

00:15:48.910 --
When Alpha is equal to Delta,
when that turning angle is the

00:15:52.006 --
same as the wedge angle, there's
no. There's no big shock that

00:15:55.102 --
forms, it's just a straight

00:15:56.392 --
line. OK, so now keep
that in mind. So which

00:16:00.337 --
of those two shockwaves
is going to be stronger?

00:16:08.500 --
Which is going to have the

00:16:10.666 --
highest change. Across there,
what's going what, what? What do

00:16:14.858 --
you see with the flow going on
there? Have a have a higher

00:16:19.421 --
turning there at the bottom.

00:16:22.230 --
Stronger shock. And the bottom
everybody see that? OK, think of

00:16:26.998 --
it this way, you are turning
that air in the higher

00:16:30.650 --
direction, you're deflecting it
more on the bottom then you are

00:16:34.302 --
the top. OK, so there's going to
be a stronger shock.

00:16:39.130 --
On the bottom.

00:16:41.670 --
And this is going to be a weaker
shock here at the top.

00:16:46.670 --
OK, where is going? Where is the
highest pressure going to be?

00:16:54.980 --
Top or on the bottom. The
highest change in pressure on

00:16:58.687 --
the top is if we call this
region one and this region 2 and

00:17:03.405 --
this region 3. Where's the
higher pressure going to be in

00:17:07.112 --
region 2 or region three there?

00:17:09.920 --
Region 2.

00:17:12.000 --
That's why it's a stronger
shock. There's a larger increase

00:17:15.510 --
in the pressure, so here P2.

00:17:18.380 --
Is going to be greater than P1
everybody by that.

00:17:23.310 --
K. Aerodynamicists what's
that going to generate?

00:17:30.450 --
You have a wedge. Here you
have an angle of attack right

00:17:33.906 --
here. The pressure on the
bottom is higher on the is the

00:17:37.362 --
pressure on the bottom is
higher than the pressure on

00:17:40.242 --
the top. What do you get lift?

00:17:43.660 --
That's supersonic aerodynamics,
right there in a nutshell.

00:17:47.680 --
There's no nice curved airfoils.

00:17:51.800 --
OK, with this wedge right here,
just just giving it an angle of

00:17:56.701 --
attack in a supersonic flow,
you're going to generate a

00:18:00.471 --
higher pressure on the bottom
then you will on the top and you

00:18:05.372 --
generate lift. Out of that?

00:18:09.570 --
OK. Next week, we'll talk more
about supersonic airfoils

00:18:13.434 --
because there's one other.
There's one other key ingredient

00:18:16.116 --
that we need to know more about
that, but this is the crux right

00:18:20.288 --
here. OK, just because of that
pressure difference because of

00:18:23.697 --
the way that you have a
stronger shock on the bottom

00:18:26.370 --
then you have on the top,
you're going to get higher

00:18:29.043 --
pressure on the bottom and
lift.

00:18:33.590 --
That's supersonic aerodynamics
right there, OK questions.

00:18:39.810 --
Alright.

00:18:41.650 --
Let's talk about diffusers.
Now diffuser that is just a

00:18:45.160 --
fancy name for a jet inlet
for the intake. That's where

00:18:49.021 --
the air comes into the
airplane. Let's see now what

00:18:52.531 --
we can do in our now. Now
that we know about oblique

00:18:56.743 --
shockwaves and normal shocks,
let's apply those to see if

00:19:00.253 --
we can figure out why
diffusers are designed the

00:19:03.412 --
way they are here. OK, again,
here's the equation that we

00:19:07.273 --
started out class with.

00:19:10.200 --
That to minimize the change in
entropy, we want to keep peanut

00:19:14.988 --
two as high as possible. OK, in
supersonic aerospace design

00:19:18.978 --
that's called pressure recovery.
We want to recover as much

00:19:22.968 --
pressure as possible here. OK,
we want to keep peanut to as

00:19:27.756 --
high as possible here, OK?

00:19:30.640 --
So let's look at a couple of jet
inlet designs and see how the

00:19:35.792 --
stagnation pressure is going to
be here. OK, good, so we're

00:19:39.840 --
going to look at two inlets.

00:19:42.930 --
Air is coming into both of
those inlets out of Mach

00:19:46.131 --
number of 2.5.

00:19:48.080 --
OK, in the first inlet design
all we have is a normal shock.

00:19:54.510 --
OK, what is the stagnation
pressure loss going to be in

00:19:58.019 --
that normal shock? OK.

00:20:00.340 --
Then we're going to have
we're going to have air that

00:20:04.311 --
comes in again. Same lot
number 2.5. Everything is the

00:20:07.921 --
same. It's going to go
through a turn of 18 degrees.

00:20:12.930 --
So it's going to create an
oblique shock. That's going to

00:20:16.263 --
slow it down, and then it goes
through a normal shock.

00:20:20.720 --
OK, now you might ask, why does
it have to be a normal shock at

00:20:25.550 --
the end there? So for jet
turbine airplanes, the air inlet

00:20:29.092 --
always has to be subsonic.

00:20:31.720 --
OK, if you have jet turbines,
OK, compressor blades that are

00:20:35.350 --
spinning that air has to go into
that turban, sub sonically.

00:20:38.980 --
Otherwise you get shock waves
that form along the blade, and

00:20:42.610 --
that's not a very good process.
OK, so the idea in the jet

00:20:46.900 --
aircraft supersonic air comes
in, you slow it down, recover as

00:20:50.530 --
much pressure as possible that
sends it through the jet turbine

00:20:54.160 --
and then it goes out the

00:20:56.140 --
exhaust. OK, that's that's the
process here. Alright, let's

00:21:00.488 --
look at this.

00:21:02.860 --
Get your books out.

00:21:07.380 --
And we have our very first inlet
design right here, and let's see

00:21:13.893 --
what's going on here. OK, we
have an inlet.

00:21:19.020 --
To this aircraft looks like

00:21:20.845 --
this. Looks like this here comes
in at a Mach number of two

00:21:28.330 --
point 5K and as it enters this
inlet here a normal shock.

00:21:35.800 --
Forms right at the inlet.

00:21:38.020 --
OK.

00:21:40.550 --
Good. We have that.

00:21:44.610 --
Will have that P1 is equal to 70
kilopascals and that T one is

00:21:49.902 --
equal to 200 degrees Kelvin.

00:21:52.880 --
OK, we want to know.

00:21:56.420 --
How much stagnation pressure is
lossed in this process? Right

00:22:00.720 --
here? OK, so you can go to your
normal shock tables. So go to

00:22:06.740 --
your normal shock tables and
figure out for this inlet

00:22:11.040 --
design, what peanut too.

00:22:13.470 --
Over P, not one, is equal to.

00:22:21.160 --
What do you get?

00:22:26.200 --
24 nine. 0.499 can we round
that up to .5?

00:22:32.970 --
OK, that says that you have
already lossed half the

00:22:39.180 --
available thrust.

00:22:42.040 --
In this design.

00:22:44.360 --
It's not very good.

00:22:46.970 --
That's terrible. OK, all the
available thrust that you could

00:22:51.050 --
to generate to make your plane
go faster. You've lost half of

00:22:55.250 --
it just because it sends through
a normal shock.

00:22:59.940 --
OK, not good.

00:23:01.900 --
Not good, OK? Let's look at the
second design now, here. So

00:23:06.460 --
let's go to the computer so we
can see that again. So here now

00:23:11.780 --
we have a wedge right here. Flow
comes in supersonically. There

00:23:15.960 --
is an oblique shock that's
formed, and then a normal shock

00:23:20.140 --
that's formed here on the
inside. OK, this normal shock,

00:23:23.940 --
right? There is called the
terminal shock. It's the very

00:23:27.740 --
last shockwave in the system.

00:23:30.830 --
OK, remember as the air crosses
it goes through the inlet an

00:23:34.634 --
approaches the engine. It has to

00:23:36.536 --
be subsonic. OK, so it goes.
It's subsonic across a normal

00:23:41.039 --
shockwave. That's how it finally
is going to slow down here. OK,

00:23:45.371 --
so let's calculate this problem
right here, OK?

00:23:49.250 --
So we have a wedge. Looks like
this and we have the top of

00:23:56.586 --
the inlet right there here.

00:24:00.630 --
OK, the flow comes in at a Mach
number of 2.5 and there is an

00:24:07.605 --
oblique shock. That forms right
across there and then a normal

00:24:13.078 --
shock right down here.

00:24:16.400 --
OK, we were given in this
problem. This has a turning

00:24:21.834 --
angle. Delta is 18 degrees.

00:24:25.040 --
OK, let's we have three
different flow regimes here, so

00:24:29.800 --
let's call this region 1.

00:24:32.980 --
Call this region 2 and
Region 3 right there.

00:24:40.950 --
OK.

00:24:44.430 --
Are we good? Are we good
with the visual here?

00:24:48.220 --
Pretty straightforward problem.
We are now two separate

00:24:51.948 --
shockwaves. OK, so now you want
to get your app out here for M1

00:24:58.472 --
equal to 2.5 and Delta of 18
degrees right there tell me what

00:25:04.530 --
you get. First off for M2 and
then tell me what P not 2 /

00:25:11.520 --
P nought one is.

00:25:17.040 --
See if it comes with my
numbers here.

00:25:20.840 --
Yep, 1.739 is the Mach
number in region 2 peanut

00:25:26.720 --
two over peanut one.

00:25:30.750 --
1.

00:25:32.240 --
8870.88 seventh OK, I got 7 as
well. I thought I heard you say

00:25:38.372 --
6.8877 really that's one part
out of 88,000. I'm not going to

00:25:43.628 --
worry about that too much. OK,
we go there.

00:25:48.520 --
OK, you could go com prop gives
you that you could go to the

00:25:52.300 --
charts and get the same thing.
No big deal. Now what's the next

00:25:55.810 --
step in the problem?

00:25:57.580 --
What do we do?

00:26:00.860 --
It's a normal shock problem.

00:26:03.140 --
OK, so when we get to more
complicated problems, we're

00:26:06.580 --
going to use the same process.
You just go through a serially.

00:26:10.708 --
What's going on here? It's an
oblique shock problem and then a

00:26:14.836 --
normal shock problem, but the
Mach number in region 2 is

00:26:18.620 --
different than the model number
in region 1, so you just have to

00:26:23.092 --
keep that into consideration
there. OK, so for now we know

00:26:26.876 --
what the model number in Region
2 is. So from the normal shot

00:26:31.348 --
tables now. Read off

00:26:34.622 --
M3. And read off now
Peanut three over peanut two.

00:26:40.574 --
What do you get?

00:26:48.350 --
What's M3 go into the normal
shock tables for an M2 that you

00:26:52.198 --
could say that's one point 7
four just to read it off there?

00:26:56.990 --
What do you get?

00:27:01.730 --
0.63 should it be subsonic?

00:27:06.860 --
Better be 'cause it's going
across a normal shockwave right

00:27:09.980 --
there. What is peanut three over
Peanut 2 for that normal shot?

00:27:18.500 --
Say that again.

00:27:20.480 --
.8 Four K
0.84.

00:27:26.690 --
OK, so we're going to look at
some trends here before we

00:27:31.718 --
calculate our final number
'cause we want to know what

00:27:35.908 --
peanut three is compared to
peanut one? That's our. That's

00:27:40.098 --
our stagnation. Pressure loss
from this region to this region

00:27:44.288 --
right here. Look at look at
these two numbers right here for

00:27:49.316 --
model number of 1.739. You lose

00:27:51.830 --
16%. Of your stagnation

00:27:54.416 --
pressure. If you go up from
1.742 amount number 2.5, you

00:28:00.560 --
lose half. Of your
stagnation pressure.

00:28:04.960 --
OK, let's look at those
trends here.

00:28:09.680 --
OK, if you look at the normal
shock tables right here.

00:28:15.730 --
Here is Peanut peanut, two
over peanut one right there

00:28:20.070 --
for this mock number. Notice
that to a mock number, let's

00:28:24.844 --
just say right here at amount
number of 1.58 you lose 10%

00:28:30.052 --
of your stagnation pressure.

00:28:32.900 --
OK, for model number of 1.2 you
only lose 1%.

00:28:39.190 --
Of your stagnation pressure. OK,
if you go to a Mach number

00:28:45.430 --
of two right. Over here you lose

00:28:49.070 --
28%. Of your stagnation

00:28:51.705 --
pressure. Everybody see what
those values are coming from.

00:28:55.460 --
So. You're an aircraft designer.
What should you do?

00:29:02.410 --
What should you do?

00:29:06.830 --
How about if you take this
right here? Shouldn't you slow

00:29:10.350 --
that flow down as much as
possible? It's going to have

00:29:13.870 --
to go through a normal shock.

00:29:17.110 --
But then you want that
normal shock right there to

00:29:19.910 --
be as weak as possible.

00:29:22.460 --
Everybody see that. OK, so let's
calculate now Peanut 20 excuse

00:29:28.168 --
me peanut three over peanut one
that is the stagnation pressure

00:29:33.459 --
loss from this region to this
region right here. OK so.

00:29:40.270 --
Peanut 3 / P nought one is
equal to P not 3 / P

00:29:47.452 --
not two that's this.

00:29:50.370 --
Multiplied by peanut
two over peanut one.

00:29:57.110 --
We know those two values .8.

00:30:00.330 --
877 times
.84.

00:30:07.840 --
I get a value
of 0.745.

00:30:18.740 --
Compare values again. What have
you done to your aircraft?

00:30:25.130 --
You have improved the pressure
recovery by 25 points.

00:30:33.850 --
Instead of losing half of it,
instead of losing half of your

00:30:37.786 --
stagnation pressure, now you
lose just one quarter of it.

00:30:41.890 --
And what have you done?

00:30:44.210 --
All you did was put a little
wedge at the inlet right there.

00:30:51.440 --
OK, This is why I wanted you to
keep in your noggins. Delta S

00:30:56.410 --
changing entropy over R is equal
to minus natural log of the

00:31:00.670 --
stagnation pressure loss.

00:31:02.590 --
Stagnation pressure is directly
related to the thrust, so now

00:31:06.890 --
you have made your aircraft.

00:31:09.930 --
Actually 50% better you've
improved in performance.

00:31:14.170 --
And all you did was put a wedge
here before that terminal shock

00:31:19.110 --
is the only thing you did.

00:31:22.570 --
And you can get more thrust out

00:31:23.592 --
of your play. Is that
cool or what?

00:31:26.920 --
OK, let's see. Here's an F-14 in
low, by the way. Actually,

00:31:31.240 --
before we get to that before we
get to that here.

00:31:36.750 --
Let's go to let's go to the
overhead here. Could you see

00:31:41.526 --
that a natural extension to this
problem might be if now you have

00:31:46.700 --
a wedge and you have a 9 degree

00:31:49.884 --
turn. And then, and another nine
degree turn here and then.

00:31:57.270 --
It goes to the inlet right
here. What have you got?

00:32:02.140 --
M1 is equal to 2.5. You'll
have an oblique shock that

00:32:06.144 --
forms there.

00:32:08.700 --
The flow follows the wall. You
have another oblique shock here.

00:32:15.650 --
Your total turning angle is 18
degrees, just like you did

00:32:19.236 --
before, but now you send it
through two oblique shockwaves,

00:32:22.496 --
not just one. And then you have
your terminal shock right there.

00:32:27.110 --
OK, as it goes into the inlet
right here. So you have

00:32:30.446 --
region 1, Region 2, Region 3,
Region 4. How would you solve

00:32:33.782 --
that problem?

00:32:37.080 --
Same way that we did the first
problem. It's an oblique shock

00:32:40.488 --
across here with the turning
angle of nine degrees and some

00:32:43.612 --
Mach number. Then over here
you have a new model number M2

00:32:47.020 --
Anna Divina, same turning
angle of 90 degrees there and

00:32:49.860 --
then you have a normal shock.

00:32:52.990 --
OK, in this design here Peanut
4 divided by peanut one is

00:33:00.550 --
equal to 0.79.

00:33:03.680 --
So you've improved the
performance from 70 from losing

00:33:08.891 --
25% to losing 21%.

00:33:12.880 --
OK.

00:33:14.970 --
Alright, now we can look at F-14

00:33:18.309 --
Tomcat here. Here
is that inlet OK.

00:33:24.060 --
Uh, let's see what you can see
here. OK, so actually, actually

00:33:27.852 --
here we'll look at it from here
and then we'll see the picture.

00:33:31.960 --
So this is an F-14 Tomcat. We
saw this in class last time

00:33:36.068 --
here. Here are the inlets here.
Actually, if you look in the

00:33:39.860 --
overhead here, there's an inlet
and there's an inlet there.

00:33:43.020 --
Notice it has a sharp leading

00:33:44.916 --
edge. OK, if you look at it on
the side right there.

00:33:50.410 --
OK, there it has a very sharp
leading edge. If you look

00:33:55.078 --
inside right here, zoom in.
I'll just a little bit more.

00:33:59.357 --
You can see there's a hinge
there and a hinge there.

00:34:06.080 --
So what this airplane is
designed to do is that depending

00:34:10.469 --
on the speed, this inlet right
here can change angles.

00:34:16.310 --
OK, and and what is going to be
The upshot of changing the

00:34:20.561 --
angles? What is that? What is
the trying to do?

00:34:25.230 --
Recover the pressure.

00:34:28.310 --
So now let's go look at the
computer. You can get a better

00:34:32.301 --
idea of what it looks like here.
There you can see a hinge Anna

00:34:36.599 --
plate right there. Here you can
see another hinge and another

00:34:40.960 --
plate right there. So in this
aircraft that's going to produce

00:34:44.645 --
three oblique shockwaves at the
inlet, one at the very front. So

00:34:48.665 --
you can't see it. But that's
right that first inlet. This is

00:34:52.685 --
where the second oblique
shockwave forms. Here's where

00:34:55.365 --
the third oblique shockwave
forms. And then inside here is

00:34:58.715 --
where the normal shock form. So
very nice everybody see that we

00:35:02.735 --
can see it both at the inset
right, right there in the upper

00:35:07.090 --
right corner. Thanks in the
control room. That's very good,

00:35:10.878 --
OK? So good again, depending on
the speed of the aircraft and

00:35:16.140 --
its conditions, it automatically
adjusts the angles there.

00:35:20.410 --
To maximize the pressure
recovery and generate the most

00:35:23.209 --
stress in the airplane.

00:35:25.910 --
Is that cool or what? That's
awesome. That is awesome

00:35:29.210 --
engineering design right there.
OK, so here. Here's a little

00:35:32.510 --
schematic of the inlets here.
Here, the first one we see what

00:35:36.470 --
the flow pattern looks like for
subsonic speeds, so obviously

00:35:39.770 --
there's going to be no shock
waves that form there, so the

00:35:43.730 --
plane has to take off and ask to
fly subsonic Lee at some point.

00:35:48.350 --
So it comes through here. It's
got a little. It's got a little

00:35:52.640 --
bleed or there at the top. Air
comes in this way and it goes

00:35:57.260 --
and notice here. It's always a

00:35:59.240 --
subsonic diffuser. Because you
want the air going into the

00:36:02.668 --
engine and the jet turbine
engine here to be subsonic. OK,

00:36:06.364 --
when it gets to transonic
speeds, so that's from a model

00:36:10.060 --
number of .8 to about 1.2 ish in
that range. OK, notice that you

00:36:14.764 --
have a normal shock that forms
right there in the front, or

00:36:18.796 --
you're worried about the losses
across that normal shock.

00:36:22.990 --
Because why Jesus? Why is that?

00:36:29.130 --
The upstream lot number here is
really close to one and so the

00:36:33.745 --
stagnation pressure losses for
Mott numbers close to one are

00:36:37.295 --
don't say negligible, but are
pretty small, so not to worry

00:36:41.200 --
about that, OK?

00:36:43.700 --
In and out at supersonic speeds,
look at this. There is an

00:36:48.068 --
oblique shockwave right there.
There is an oblique shockwave

00:36:51.344 --
right there. There is an oblique
shockwave right there and here

00:36:55.348 --
you can see the actuators. This
is what moves those plates into

00:36:59.716 --
position to get the get the best
pressure recovery and then

00:37:03.720 --
finally at this point is the
terminal or the normal shockwave

00:37:07.724 --
right there behind that shock
the flow subsonic and it goes

00:37:11.728 --
into the diffuser right here.

00:37:16.760 --
So now you could look at a jet
aircraft and say I know why

00:37:19.406 --
it's designed that way.

00:37:21.270 --
To maximize stagnation pressure
to maximize the pressure

00:37:25.382 --
recovery. OK, unfortunately,
this plane does not fly anymore,

00:37:30.008 --
but just to let you know, there
are aircraft companies are

00:37:35.662 --
looking to redesign or to remake
this aircraft. In some sense,

00:37:41.316 --
this is a supersonic transport
designed to fly from either

00:37:46.456 --
France or London, Paris or
London across the Atlantic Ocean

00:37:51.596 --
supersonically. Has a
cruising speed of Mach number

00:37:55.373 --
of two and land in New York
OK. If you are ever in

00:38:01.340 --
Seattle, there's the Museum
of Flight just South of

00:38:05.471 --
Seattle off of off of Hwy 5.
I think there.

00:38:11.840 --
And there's a super Sonic.

00:38:14.670 --
There's there's this airplane
there you can go check out OK,

00:38:19.730 --
look at the intakes here at the

00:38:22.950 --
bottom. OK, notice also even
before we get there, notice the

00:38:28.090 --
Delta wing shape right there,
because when this is flying

00:38:32.130 --
supersonically you want that
conical you want the airplane to

00:38:36.170 --
sit inside that conical
shockwave right there. Then as

00:38:39.806 --
it goes down inside here, notice
the angle of those inlets right

00:38:44.654 --
there. Let's take a look and see
what those inlets look like

00:38:49.502 --
right here. So you can see says
danger. It's got hinges here.

00:38:54.620 --
And here as well.

00:38:57.370 --
So is this plane screws in over
the Atlantic Ocean, creating

00:39:01.165 --
shockwaves? You remember the
shockwave sounded like.

00:39:04.390 --
That's why it doesn't fly over
the continental United States

00:39:07.750 --
flies over the ocean. OK, that
those plates can go up and down

00:39:12.118 --
depending on its speed and the
other conditions of the flight

00:39:15.814 --
there. To maximize the pressure
recovery before it goes into the

00:39:19.510 --
engine there. OK fact, here's a
schematic of that of that.

00:39:23.206 --
What's called the shock train?
OK, so here's the first

00:39:26.566 --
shockwave that's an oblique
shockwave. You know what? You

00:39:29.590 --
know, what oblique shockwaves
are. So you can look at this

00:39:33.286 --
intelligently. Here's the 2nd.

00:39:34.700 --
Oblique shockwave right here.
These are actually compression

00:39:37.756 --
waves and we'll talk about
these next week, right here and

00:39:41.958 --
then another shockwave here. So
1/2 compression, 3 right there

00:39:45.778 --
and then finally the terminal
shock there on the inside.

00:39:49.598 --
That's the normal shock.
Downstream of that it's

00:39:52.654 --
subsonic flow and goes into the
engine.

00:39:57.790 --
OK, and again you can adjust.

00:40:00.320 --
That ramp right there to
maximize the pressure recovery.

00:40:05.120 --
Good, here is a MIG fighter
aircraft, so this is a this is a

00:40:10.776 --
Russian Russian jet. It was used
after World War Two during the

00:40:15.624 --
Korean War. OK, but notice it's
design here. There's a spike

00:40:20.068 --
that sits there right in the
center so the air comes in and

00:40:25.320 --
hits that spike. And what's
going to form when it hits the

00:40:30.168 --
spike? An oblique shockwave.
Actually, in this case of

00:40:33.804 --
conical shock, but.

00:40:35.090 --
Not a normal shot. OK can
you see? Yeah you can see

00:40:39.074 --
on the screen there can you
see this line right there?

00:40:44.140 --
What do you think that is?

00:40:47.670 --
An angle change.

00:40:50.040 --
So it comes in and the initial
change in the flow is half

00:40:54.408 --
whatever that conical angle is
right there. Then it hits this

00:40:58.104 --
an another oblique shockwave
forms follows the wall, and it

00:41:01.464 --
eventually goes into its inlet
right here and down inside

00:41:04.824 --
there's going to be normal
shock.

00:41:08.700 --
OK. Here's another one right
here. This is from a. I think

00:41:14.908 --
this is an F-104 Starfighter, so
again, an older supersonic jet

00:41:19.506 --
fighter here. You can see the
inlet right here, Annacone.

00:41:24.480 --
OK, so the flow goes over this
and forms a conical shockwave.

00:41:28.032 --
Here it's probably a little
hard to see on your on your on

00:41:31.880 --
the TV screens there, but you
see these two little Nicks

00:41:35.136 --
right up there. OK, this cone.
In fact you could see it right

00:41:38.984 --
there from this line that cone
can move in and out.

00:41:45.180 --
So again, depending on the speed
of the aircraft that cone is

00:41:49.476 --
going to go out or kind of go in
to generate whatever sort of

00:41:54.488 --
oblique shockwave you need to
maximize the pressure recovery.

00:41:57.710 --
OK, this is an older fighter
aircraft in the 1960s and so

00:42:02.006 --
that moving the moving inlet
technology isn't quite as mature

00:42:05.586 --
as it was for the SST, and some
of the other aircraft. OK, but

00:42:10.598 --
the same principle holds. It
adjusts this cone, moves in and

00:42:14.536 --
out so that.

00:42:15.760 --
So that the flow field generates
the maximum amount of pressure

00:42:20.380 --
recovery in the airplane, Sir.

00:42:24.030 --
Square.

00:42:28.080 --
It depends. OK, so that's
that's a great question. It

00:42:31.390 --
depends on where you put the
inlets. Usually on the side

00:42:35.031 --
of the aircraft, right? Here,
'cause the flows coming right

00:42:38.341 --
down the this part of the
fuselage. It tends to hug the

00:42:42.313 --
wall a little bit better.
Then you haven't inlet here.

00:42:47.170 --
That that really isn't going to
work for the F-14 Tomcat because

00:42:50.698 --
of the armaments and other stuff
that you had on the side there.

00:42:54.520 --
So depends on the design.
Depends on the design there and

00:42:57.754 --
how you want your fuselages to

00:42:59.518 --
work there. OK, any questions?

00:43:04.170 --
OK, this is a

00:43:08.162 --
subsonic turbofan. Jet inlet.

00:43:13.490 --
Can you tell the difference
between that inlet and the other

00:43:16.548 --
inlets that we saw before?

00:43:18.940 --
OK, are shockwaves
going to form here?

00:43:23.530 --
Negative. OK, So what you see
here are nice curved surface

00:43:27.710 --
is you don't see any sharp
surfaces on a subsonic

00:43:31.510 --
aircraft. OK, nice curved
surface. Is there? These

00:43:34.550 --
compressor blades spin this
way and compress the air as it

00:43:38.730 --
goes inside and comes out the
engine. There's already coming

00:43:42.530 --
in subsonic Lee.

00:43:44.800 --
OK, so that's the difference
between a subsonic inlet and

00:43:50.530 --
a supersonic inlet.

00:43:53.990 --
OK, let's just hypothesize
here. Let's say that we use

00:43:57.790 --
this plane in a fly
supersonically. What's going

00:44:00.830 --
to form on the outside right
there?

00:44:05.640 --
Shock waves normal shocks,
oblique shocks. What do

00:44:07.976 --
you think?

00:44:10.770 --
OK, since that surrounded
surface right there, it's not

00:44:13.443 --
a sharp surface. You're
likely going to get a

00:44:16.116 --
detached bow shock that's
there. And what kind of

00:44:18.789 --
losses are associated with
that?

00:44:21.710 --
Huge.

00:44:23.390 --
OK, we've just shown here that
in oblique shockwave the losses

00:44:26.195 --
are less than for a normal shot.

00:44:28.930 --
OK. Good alright?

00:44:34.390 --
Questions on this?

00:44:37.270 --
We'll talk more. We'll talk more
about it. OK, alright, you're

00:44:41.615 --
going to have a homework problem
or some homework problems

00:44:45.565 --
related to reflected shockwaves.
OK, so let's look at this. Let's

00:44:49.910 --
look at this particular diagram

00:44:51.885 --
right here. So we have
flow that's in a duct.

00:44:56.706 --
Duct is coming down here
has a Mach number of one.

00:45:01.403 --
It's coming down
Supersonically and now

00:45:03.965 --
here we have an angle
change of 12 degrees.

00:45:08.840 --
OK, so what's going to happen?
Well, add this for this Mach

00:45:12.368 --
number and this turning angle of
12 degrees you're going to get a

00:45:16.190 --
shock angle. And
the flow turns Y.

00:45:21.340 --
The flow follows the wall.

00:45:25.050 --
OK, so it's going to come down
this way and it sees this little

00:45:28.858 --
change right there and it
changes direction, so it's going

00:45:31.578 --
down horizontally and then it
turns up 12 degrees.

00:45:35.290 --
OK. Then the flow comes this way
right here, and then it sees

00:45:41.310 --
this wall on the top side right

00:45:43.830 --
there. So now the flow is going
to change directions again.

00:45:50.270 --
So it's coming down.

00:45:52.620 --
It goes up 12 degrees. It's
going to hit the wall on the top

00:45:56.134 --
that's parallel to the bottom
wall on the other side. Here,

00:45:58.895 --
it's going to hit that wall and

00:46:00.652 --
change directions again. So now
this direction of M3 is the same

00:46:05.413 --
as M1. The directions the same.

00:46:08.890 --
How would you solve that
problem?

00:46:15.480 --
Could you solve the problem from
Region 1 to region 2?

00:46:20.110 --
You know in one you know the
turning angle. You could get the

00:46:23.711 --
shock angle and you could get
the Mach number right there.

00:46:27.490 --
In order to see that.

00:46:29.570 --
OK, how would you solve it from
Region 2 to region 3?

00:46:35.010 --
Same thing.

00:46:37.270 --
However, however, are the
turning angles the same?

00:46:43.260 --
Turning angles are the
same, what's different?

00:46:48.640 --
Get shock angles gonna
be different? How does

00:46:51.016 --
M2 compared to M1?

00:46:53.850 --
Smaller.

00:46:56.800 --
OK, so you solve it from
Region 1 to region 2.

00:47:00.672 --
From this Mach number M1
and that turning angle.

00:47:05.060 --
Then you're going to calculate
or determine what your M2 is.

00:47:09.100 --
And then solve this turning
angle problem right here with

00:47:12.900 --
M2, not M1.

00:47:14.930 --
M2 with the turning angle
of 12 degrees and it comes

00:47:18.590 --
out this way right here.

00:47:22.260 --
Everybody see that.

00:47:26.100 --
That's all reflected shock is
all. Reflected shock is, it's

00:47:29.490 --
just, it's just another in a
series of oblique shockwaves as

00:47:33.219 --
it comes down the duck there.

00:47:36.080 --
Nothing more than that. OK, and
all because of the changes here

00:47:40.892 --
in the angles.

00:47:43.790 --
OK.

00:47:45.780 --
I believe that you have a
homework problem, will just

00:47:49.960 --
outline it here. OK, you have
a homework problem.

00:47:55.230 --
Let's see here.

00:47:57.330 --
Have a duct comes down here and

00:48:00.032 --
there's some. Change here Mitch
was at 5 degrees.

00:48:06.100 --
We talked about this in class. I
think this is 5 degree change

00:48:10.247 --
here. OK then you have another

00:48:12.161 --
wall. Here, and this is bent
down at 2 degrees.

00:48:22.770 --
2 degrees right there.

00:48:24.960 --
OK, so you have a flow.

00:48:28.100 --
Coming down this way, M1, what's
going to form first?

00:48:34.060 --
What do you get? 'cause of
this turn right up there?

00:48:39.150 --
An oblique shot.

00:48:41.360 --
So I'm going to be shocked
that comes here.

00:48:44.960 --
OK, and this region 1 this is
Region 2 right here. Given

00:48:49.124 --
that turn and that model
number, can you find the

00:48:52.594 --
pressure and all the good
stuff in region two there?

00:48:58.020 --
It's just an oblique shock
problem. OK, now remember the

00:49:02.180 --
flow follows the wall.

00:49:04.750 --
So now it's coming down
here at 5 degrees.

00:49:08.290 --
OK, coming in this direction.

00:49:10.440 --
However. This turn, this wall at
the bottom is not.

00:49:16.700 --
5 degrees.

00:49:19.680 --
OK.

00:49:22.000 --
Let's do a hypothetical. If this
wall did come down at 5 degrees.

00:49:29.360 --
What would form from region 2 to
this region down here?

00:49:33.910 --
Actually nothing.

00:49:37.550 --
'cause it's going to go down
this duck and turn this way.

00:49:41.650 --
You could have a normal shock
sometime later on there, but you

00:49:44.134 --
all you do is turn in the flow.

00:49:46.860 --
OK, if this were five degrees.
However, now this angle is 2

00:49:52.872 --
degrees from the horizontal.

00:49:55.800 --
So guess what's going to form.

00:49:59.270 --
No big shockwave.

00:50:00.590 --
Right here.

00:50:04.110 --
OK.

00:50:06.530 --
I will leave it up to
your geometrical Wiles

00:50:09.959 --
to figure out what this
turning angle has to be.

00:50:15.750 --
Actually kind of hinted on how
you could solve it. OK, the

00:50:19.698 --
turning angle is what you're
going to figure out. OK, this

00:50:23.317 --
turn here is 2 degrees. What is
the turning angle of that flow?

00:50:30.880 --
Think about it, yes.

00:50:36.130 --
What is the form here? Because
this is where it's being turned.

00:50:43.390 --
OK, so it's coming OK. So the
reason the reason it's attached

00:50:46.762 --
here 'cause the flow comes down
and that's where it turns.

00:50:50.780 --
OK, so in this problem it's just
kind of hypothetical that had

00:50:54.416 --
this turn right. Here we have
all the conditions such that

00:50:57.749 --
this oblique shockwave comes
down right to that point.

00:51:02.210 --
OK, now it's being turned again.

00:51:06.130 --
From here. Again, if this wall
were turned down 5 degrees, it

00:51:10.540 --
would be parallel with the one
at the top. It's only turned

00:51:14.308 --
down 2 degrees.

00:51:16.480 --
So that means there's an
angle change there. An since

00:51:19.360 --
there is an angle change
right there, and oblique

00:51:21.952 --
shockwaves going to form.

00:51:25.180 --
That makes sense. You
still look.

00:51:28.740 --
How about how about since since
we're talking about fine

00:51:33.030 --
degrees, let's blow up the
picture a little bit. OK, let's

00:51:37.749 --
say this makes a turn of of,
let's say, 20 degrees.

00:51:43.660 --
K and this makes a turn of five
degrees. Let's just say so this

00:51:50.310 --
is 20 degrees.

00:51:53.010 --
So we have an oblique
shockwave that's here OK. Can

00:51:55.750 --
you see now? The flow follows
the wall. It's going to come

00:51:59.038 --
down this direction right
here, but what does it see

00:52:01.778 --
when it hits that wall?

00:52:05.170 --
Can you see how it's getting

00:52:06.370 --
bent up a little bit? OK, so
this was 20 degrees. We said

00:52:10.610 --
that this is 5 degrees right
here, so it's running into

00:52:14.185 --
this wall so it has to change
directions.

00:52:18.030 --
That's why I emphasized the flow

00:52:19.572 --
follows the wall. Comes down
here now it's going to get bent.

00:52:24.990 --
Here, if this were 20 degrees

00:52:27.810 --
down here. If this bottom were
bent at 20 degrees in, that flow

00:52:31.563 --
would just follow the wall all

00:52:32.721 --
the way through. But now it's
only turned 5 degrees though,

00:52:36.032 --
so there's an angle change and
you create an oblique

00:52:38.722 --
shockwave and the flow is
going to follow this wall.

00:52:42.520 --
So I've exaggerated the
angles here.

00:52:46.330 --
But it's the same principle
about what's going on in that

00:52:48.574 --
part of the problem.

00:52:50.620 --
Good good.

00:52:53.310 --
Anybody else?

00:52:55.490 --
OK, don't let reflected shocks
get to you. It's nothing but a

00:53:00.074 --
series of single oblique
shockwaves, so if you can

00:53:03.512 --
solve one oblique shockwave,
you just add on whatever the

00:53:07.332 --
turns are and keep going from
there. It's all it is OK.

00:53:11.916 --
Don't let it intimidate you.

00:53:15.230 --
OK, let's see. We got here.
Let's look at now the inlets

00:53:22.334 --
to the SR-71.

00:53:25.560 --
OK, here we go right here and
notice that these inlets are

00:53:32.196 --
spiked. OK, so you see this
spike right here. This is where

00:53:38.151 --
the air enters OK, and guess
what those spikes move in and

00:53:42.963 --
out depending on the speed of

00:53:45.369 --
the aircraft. To recover as much
stagnation pressure as possible.

00:53:51.030 --
OK, let's see what the shock
train looks like for this. In

00:53:55.650 --
fact, we'll do that little inset
trick again in the room. There.

00:54:00.270 --
Let's go to the computer. OK,
and here is what that here's

00:54:04.890 --
what the inlet to the SR-71
looks like. Check this out. Here

00:54:09.510 --
is the first oblique shockwave
that's formed because of the

00:54:13.360 --
nose cone. OK, so it comes down
this way. It follows the wall

00:54:20.088 --
comes in here now this is the
first. This is the cowl lip

00:54:26.172 --
right there, so there's a second
oblique shockwave and then this

00:54:31.320 --
inlet is designed to go through
now a number of reflected

00:54:36.468 --
shocks, 123456 oblique

00:54:37.872 --
shockwaves. Before it reaches
its terminal shock, right

00:54:40.942 --
there and then, the flow
subsonic all the way through

00:54:43.802 --
there. Why is that?

00:54:47.590 --
What's that going really
fast? OK, this this

00:54:52.510 --
particular design? This
aircraft recovers. I think

00:54:56.815 --
it's 97% of the stagnation
pressure.

00:55:03.140 --
It cruises that amount number of

00:55:04.886 --
three. Remember the problem that
we had earlier in class? We had

00:55:09.650 --
a model number 2.5. It just went
through a normal shock. It lost

00:55:14.070 --
half of its stagnation pressure
through this design right here.

00:55:17.470 --
Sending it through all these
small oblique shockwaves. OK,

00:55:20.530 --
this small weak shockwave
oblique shockwave. Then it

00:55:23.250 --
recovers more that pressure, it
just sends it through a bunch of

00:55:27.330 --
'em before it goes through that
final normal shock, which is a

00:55:31.410 --
very weak and or shockwave.

00:55:34.230 --
So this particular inlet design
then slows the fluid down the

00:55:38.927 --
air down very efficiently.

00:55:41.330 --
It loses 3% of the
stagnation pressure.

00:55:45.970 --
That's awesome. That is awesome.
OK, and again as this is taking

00:55:50.960 --
off and landing and cruising up
to speed that cone goes in and

00:55:55.601 --
out there again to maximize the
pressure recovery as it goes

00:55:59.528 --
through those. Parts
right there.

00:56:03.290 --
I love that, OK?

00:56:07.030 --
Will talk about ramjet engines
now before we talk about ramjet

00:56:11.584 --
engines. Let's talk, let's just
talk general engine like

00:56:15.310 --
internal combustion engines
first, so we have some. We have

00:56:19.450 --
some members of the snowmobile
team here is that right? OK,

00:56:24.004 --
what is what is the pressure
ratio in your combustion engine?

00:56:28.558 --
So pressure ratio. So that means
the air goes into the piston

00:56:33.526 --
cylinder head. There piston

00:56:35.182 --
compresses it. So the pressure
gets high. What does that

00:56:38.986 --
increase in pressure? What is it
about? About 10K so air comes in

00:56:43.367 --
an atmospheric pressure. You
compress it to get high pressure

00:56:46.737 --
so you have fuel that's in there
air at high pressure you ignite

00:56:51.118 --
it so you have high temperature,
high pressure air that expands

00:56:54.825 --
the piston goes down right? So
that's that's the compression

00:56:58.195 --
ratio in an aircraft engine will
be there. OK, so now let's think

00:57:02.576 --
about that problem. Let's think
about that problem an for. Right

00:57:06.283 --
now we're going to hypothetical.
Let's pretend no shocks.

00:57:09.410 --
Let's just pretend no shocks.
OK, no shocks here. So I have

00:57:14.138 --
air that's coming this way and
it goes into an engine right

00:57:18.866 --
here. And let's just say.

00:57:22.230 --
Let's just say that I want
to have that same pressure

00:57:26.850 --
recovery here P.

00:57:29.660 --
If I write it down, I kind of
give it away here. I'll just

00:57:34.280 --
call it P2 over P1, no shocks.
Remember the hypothetically no

00:57:37.910 --
shockwave here, so the air comes
in and that pressure goes up by

00:57:42.200 --
10. So we want that increasing
pressure to be 10. OK, let's

00:57:46.160 --
just say that no shocks, so
remember what happens to the

00:57:49.790 --
speed of the flow of the
pressure goes up? What happens

00:57:53.420 --
to the speed the flow goes down?
OK, so let's look at now. This

00:57:58.040 --
air that comes in.

00:57:59.440 --
It has some static atmospheric
pressure. It's going to slow

00:58:02.870 --
down before it gets into the

00:58:04.928 --
compressor blades. Right here.
OK, well actually no no.

00:58:08.617 --
Compressor blades here. It's
just going to come down and it's

00:58:12.148 --
going to slow down and let's
just say that the Mach number is

00:58:16.321 --
about 0. Let's just say so. We
slow it down a bunch there. What

00:58:20.258 --
kind of pressure are we talking
about there for the model number

00:58:22.586 --
0? Stagnation, so look
up in your tables. Look

00:58:27.046 --
up in your tables for P,
not over P equal to 10.

00:58:33.800 --
What do you get?

00:58:37.010 --
Peanut over P is equal to 10, so
you go to the isentropic tables.

00:58:48.610 --
2.16 is perfect.

00:58:52.210 --
So now think about this engine
design. Think about this. So M1

00:58:57.166 --
is 2, what do we say? 2.16 that
we said 2.16. OK so think about

00:59:03.361 --
this. You could have an engine
design where you take high speed

00:59:08.317 --
air that goes into it and all
you have to do is slow it down.

00:59:15.790 --
And what happens to the
pressure?

00:59:18.830 --
Goes up yeah supersonic flow
that enters this and there's

00:59:22.310 --
this right here you don't have
to have any compressor blades.

00:59:26.138 --
You don't have to have a piston
to compress the air. All you're

00:59:30.662 --
doing is slowing the air down.

00:59:34.510 --
By slowing it down.

00:59:36.550 --
From what number of two .16 to
about zero could be a model

00:59:40.190 --
number .1 whatever it's going
to be slightly you get a

00:59:43.270 --
pressure increase of 10.

00:59:45.740 --
OK, that is essentially how
now we can go to our

00:59:51.306 --
computer here. That is how a
ramjet engine works.

00:59:57.240 --
It has no moving parts.

01:00:01.640 --
There are no compressor blades,
there are no Pistons.

01:00:05.250 --
All it does is take air that
comes in right here. Obviously

01:00:11.154 --
high speed air slows it down
that's slowing down. Is the

01:00:16.566 --
compression process.

01:00:19.020 --
You inject fuel into it,
combust it, and comes out

01:00:21.800 --
the nozzle right there.

01:00:25.930 --
That's what are antigens?

01:00:28.290 --
No moving parts. What's the
downside to it?

01:00:32.870 --
How does it have to work?

01:00:35.270 --
You already have to be traveling
at a Mach number of two.

01:00:39.440 --
OK, ramjet engine doesn't work
when you're on the runway an you

01:00:42.980 --
accelerate down and go up.

01:00:45.080 --
That's all subsonic flow. You
have to get that pressure

01:00:49.000 --
increase by the speed of the air
going into that to get it up

01:00:54.488 --
there. OK, ramjet engines
typically function at a Mach

01:00:58.016 --
number of about 3:00, so if
you're looking here in our

01:01:02.328 --
tables here for a model number
of three, look at what that

01:01:07.032 --
pressure increase would be about
36 times. That's assuming no

01:01:10.952 --
shocks, so assuming no shocks
was obviously in this problem,

01:01:14.872 --
they're going to be shocked

01:01:16.832 --
there. OK, so for a ramjet
engine to work, you already

01:01:22.730 --
have to be flying at
supersonic speeds.

01:01:27.800 --
Happens is that they'll have a
little rocket boost, or, uh,

01:01:31.727 --
it's usually a rocket boost.
Or actually, in the case of

01:01:35.654 --
this aircraft that this does
have, this does have ramjet

01:01:39.224 --
engines in it, so there's a
jet turbine engine here, and

01:01:43.151 --
it actually ducks the flow
around that engine and turns

01:01:46.721 --
it into a ramjet engine,
flying fast enough.

01:01:50.900 --
OK, so this is a combination
jet turbine and ramjet engine.

01:01:56.125 --
There OK, obviously we want to
recover as much pressure as

01:02:01.350 --
possible so here.

01:02:04.250 --
Then yeah, right there. OK, so
let's look at here's another

01:02:09.904 --
diagram of it. Here's the cone
here on the inside. Notice that

01:02:16.072 --
you see oblique shockwaves.
There an look at the shock train

01:02:21.726 --
1234556 oblique shockwaves, so
it's slowing it down through a

01:02:26.866 --
series of oblique shockwaves.
Before the terminal shock right

01:02:31.492 --
there. So now it's subsonic

01:02:34.062 --
flow. Then in that subsonic
flow, you inject the fuel. You

01:02:37.730 --
combust it. Here the flame
holders and then it comes out

01:02:40.766 --
the backside right there.

01:02:43.760 --
So it uses the fact that you
transforms high speed flow

01:02:47.511 --
with low pressure, high
speed, low pressure to low

01:02:50.580 --
speed, high pressure flow,
just by slowing it down.

01:02:55.170 --
OK, good, that's how ramjet
engine works. A scramjet engine

01:02:59.110 --
is a supersonic combustion
ramjet engine that's the SC in

01:03:03.050 --
the scramjet, so now it slows it
down, but there is no terminal

01:03:08.172 --
shock. OK, you have supersonic
combustion that occurs in this

01:03:12.112 --
region and goes out the back.

01:03:15.430 --
For scramjet engine, you
typically flying around 7:00 AM

01:03:19.111 --
on #7 or 8.

01:03:23.120 --
OK, we'll talk about that in

01:03:25.346 --
class. Alright.

01:03:29.020 --
Let's let's now talk a little
bit about the difference between

01:03:33.145 --
subsonic and supersonic
aerodynamics. OK, so here is

01:03:36.145 --
this is this is a subsonic
airfoil right here at the top

01:03:40.645 --
and and we have a supersonic
airfoil here on the bottom, can

01:03:45.145 --
you see the difference between
those two? This is kind of fat

01:03:49.645 --
in the front, got a rounded
edge? Kind of hard to see the

01:03:54.520 --
rounded edge, but here's the
supersonic airfoil down there.

01:03:57.895 --
Thin with a sharp leading edge.

01:04:00.830 --
OK, this is at subsonic speeds
here at transonic speeds. Now

01:04:05.274 --
shockwaves begin to form here at
the top because you've got this

01:04:10.122 --
rounded front here and this thin
supersonic airfoil, oblique

01:04:13.758 --
shockwaves start to form OK,
it's in the transonic regime,

01:04:17.798 --
but now look here in the
supersonic regime. Notice that

01:04:21.838 --
there is a bow shock that forms
in front of the airfoil.

01:04:27.260 --
And now for supersonic airflow.
You see these oblique shockwaves

01:04:30.660 --
that form. OK.

01:04:33.930 --
Let's talk about this. So here
we have you have a subsonic.

01:04:42.130 --
Airfoil looks something like
that, and here we have a

01:04:46.630 --
supersonic airfoil thin and
sharp right there. OK, subsonic.

01:04:53.020 --
Super Sonic

01:04:56.470 --
K alright.

01:04:59.660 --
This is this is a great airfoil
in subsonic flow.

01:05:04.690 --
Pilots, what kind of
airfoil is that in subsonic

01:05:07.543 --
flow right there?

01:05:09.800 --
Andrew.

01:05:11.690 --
It's not. It's awful, right?

01:05:15.500 --
OK, so subsonic flow this kind
of what you learned in is what

01:05:19.933 --
you learned in your influence
classes. You know you get a nice

01:05:24.025 --
smooth flow that's over there.
It flows faster on the top then

01:05:28.117 --
on the bottom, so you have a
lower pressure region on the top

01:05:32.550 --
so it generates lift. Here this
airfoil is awful subsonic Lee.

01:05:38.290 --
OK, so now let's go. Let's go.
This is a subsonic airfoil and

01:05:42.788 --
supersonic airfoil, and here
both Mach numbers are less than

01:05:46.248 --
one lot number less than one
right here. And this is just

01:05:50.400 --
kind of flow over this way. Now
let's let's beef up things here.

01:05:56.050 --
Mott numbers greater than
one lot. Numbers greater

01:05:58.810 --
than one. We have a nice,
beautiful rounded airfoil

01:06:01.915 --
right there in a supersonic
flow. What's going to form?

01:06:06.780 --
What's going to form
right up there?

01:06:09.310 --
A detached bow shock or
it's going to be pretty

01:06:13.250 --
much normal shock.

01:06:16.630 --
Right across here and right
across there, what forms and

01:06:21.430 --
supersonic flow in our
supersonic airfoil right here?

01:06:26.780 --
What forms? Oblique shocks

01:06:31.050 --
here. In here.

01:06:34.520 --
OK.

01:06:36.070 --
Can you see the conundrum?

01:06:38.930 --
Between subsonic and supersonic.

01:06:43.060 --
Airfoil or aerodynamic design?
What is good subsonic Lee?

01:06:49.830 --
Is awful supersonically

01:06:53.520 --
OK, this is one reason why
airplanes in the 1940s.

01:06:57.390 --
Propeller driven aircraft
couldn't break the sound

01:07:00.099 --
barrier.

01:07:01.910 --
OK, that they would use subsonic
airfoils. That's what they knew.

01:07:07.150 --
They started getting up into the
transonic regime and all of a

01:07:11.734 --
sudden these bow shocks form the
drag went Sky high. That's what

01:07:16.318 --
that's what the sound barrier is
is extreme increase in the drag

01:07:20.902 --
propeller driven aircraft
couldn't overcome that. So now

01:07:23.958 --
we have a supersonic airfoil
design like we see here, which

01:07:28.160 --
behaves awfully. Terribly in

01:07:31.124 --
subsonic design. Or in subsonic
flows I should say, but

01:07:36.008 --
beautifully in supersonic flows.

01:07:39.650 --
So now. Aircraft designers have
to balance those two out when

01:07:44.556 --
you're making aircraft. If you
fly supersonically if you if you

01:07:48.450 --
fly supersonic fighter jet, do
you ever fly subsonic Lee in it?

01:07:52.698 --
You gotta take off, you have to
land and I presume you want to

01:07:57.654 --
land safely, right?

01:07:59.610 --
Yeah, you know. Depends on the
pilot I guess. OK, so that

01:08:04.206 --
means. So that means the
aircraft designer has to take a

01:08:08.419 --
supersonic airfoil and make it

01:08:10.334 --
function. For the time that that
plane is in flight, subsonic

01:08:14.100 --
Lee. We see that.

01:08:18.050 --
And there are tricks and will
show some tricks that that

01:08:22.340 --
designers use. In fact, one of

01:08:24.680 --
'em is. You can kind of see

01:08:27.635 --
here. That in the root of
this airplane, right here, it

01:08:32.190 --
has a very thick airfoil
right there in there, but

01:08:35.590 --
when it expands out, if you
look at the wings, the wings

01:08:39.670 --
are actually pretty thin.

01:08:42.910 --
OK, so this plane actually uses
a lot of the fuselage and put it

01:08:47.446 --
this way. Uses a lot of this
fuselage. That flat area right

01:08:51.334 --
there to generate lift when it's
taking off and landing. You see

01:08:55.222 --
how that see how that works
there and then. As it goes

01:08:59.110 --
supersonic, it comes back here.
It uses these airfoils that are

01:09:02.674 --
actually pretty thin, not as
soon as other aircraft OK, but

01:09:06.238 --
you see then the conundrum that
designers have to work with when

01:09:10.126 --
they develop airplanes like

01:09:11.422 --
that. Let's look at the
SR-71 and check out this

01:09:15.407 --
wing right here.

01:09:17.720 --
OK, put in the background. Look
at that. That is really thin.

01:09:21.344 --
That's a very sharp edge by the
way. The Museum of Flight has an

01:09:25.572 --
SR-71, so when you're in Seattle
you can look at all these

01:09:29.196 --
airplanes OK, this has very thin
wing. It's kind of hard to

01:09:32.820 --
notice, but do you see that
there's a little kind of a

01:09:36.444 --
divot? A little curve right

01:09:37.954 --
there? You see that.

01:09:41.120 --
Right there.

01:09:43.380 --
And there this is the
aerodynamicists answer to the

01:09:46.719 --
subsonic supersonic flow
conundrum. Here it's got a

01:09:49.687 --
little curve, so it has a little
curvature in that airflow right

01:09:54.139 --
there so that it can take off
and land somewhat safely. You

01:09:58.591 --
get better control on that.

01:10:00.820 --
It's not a straight flat airfoil
as it goes across there.

01:10:04.620 --
OK, same thing on the other side
you can see you can kind of see

01:10:09.375 --
that curve right there.

01:10:12.360 --
OK.

01:10:14.330 --
Good, I just want you to

01:10:16.430 --
appreciate. The difference here
of the designs of what a

01:10:20.262 --
supersonic aircraft does and
what a subsonic aircraft does.

01:10:23.034 --
Let's look at two of 'em here.

01:10:25.890 --
OK, the plane on the left is a
P51 Mustang, a workhorse in

01:10:32.338 --
World War Two great great
airplane fun fact. This went

01:10:37.298 --
from this. Went from initial
design when pencil first went to

01:10:42.754 --
paper to prototype in 90 days.

01:10:48.400 --
Now, remember the United States
was on war footing at the time,

01:10:52.684 --
so it had to get things out
quickly, but this plane was

01:10:56.968 --
designed in that length of time
there. Look at underneath here.

01:11:00.895 --
These are external fuel tanks.

01:11:03.960 --
See that right there? See
one there there in there?

01:11:07.650 --
What's that shape?

01:11:10.050 --
It's like a teardrop design.

01:11:11.980 --
Right? Here is, I think this is
an F15 right here. Same kind of

01:11:17.335 --
design. Look at the inlet right
there. You know now why those

01:11:21.115 --
inlets are designed the way they
are. Look at those external

01:11:24.580 --
tanks. What does that look like?

01:11:28.640 --
Kind of a bull. It's got
a very sharp point there

01:11:31.896 --
and there. Why is that?

01:11:36.080 --
Minimize what? Drag, let's look
at those. So the P51 Mustang has

01:11:42.820 --
a teardrop shape.

01:11:45.740 --
External fuel tanks.

01:11:48.260 --
Which turns out to be wonderful
for subsonic flows.

01:11:52.980 --
OK, this minimizes both the
pressure and the friction drag.

01:11:57.990 --
OK, if I had that fuel tank
flying supersonically, what

01:12:01.190 --
would you see?

01:12:03.850 --
Normal shock bow shock right
there in the front. Great sub.

01:12:09.295 --
Sonically awful supersonically.

01:12:11.550 --
OK, the F15 right there has a
tank that looks like this.

01:12:19.070 --
Right there sharpoint. So now
you get oblique shockwaves that

01:12:24.200 --
form minimizing the drag.

01:12:28.290 --
Appreciate now the difference
between subsonic flows and

01:12:31.818 --
supersonic flows in aircraft
design. Good any questions?

01:12:37.110 --
OK. Dismiss, good luck.

01:12:41.790 --
And let me know if you have
any questions on the

01:12:44.375 --
homeworks at all.

01:12:46.510 --
What a beautiful day for gas
dynamics. I can't believe

01:12:49.330 --
they pay me money to teach
this class.

01:12:53.230 --
I should have to
pay to teach it.

01:12:56.740 --
Have a great day.

Duration:"00:49:15.0530000"

00:00:27.640 --
Alright, for today we're going
to start in Chapter 3. We're

00:00:31.336 --
going to go over. Some were
basically kind of reviewing at

00:00:35.032 --
this point, so a couple of
things to show everybody on the

00:00:39.064 --
website. Is if we go to I have
to move this up here. Sorry I

00:00:45.806 --
forgot I have a preview in a
program one so up here the

00:00:50.928 --
lectures we have. Intro class
review so for this I have been

00:00:55.656 --
an I will continue to do so.
Uploading my intro class of

00:01:00.384 --
lectures. Hopefully most of
these links should work OK good

00:01:04.324 --
and they were working on the
right files. That's even

00:01:08.264 --
important. Super important

00:01:09.446 --
actually. So there's the.

00:01:13.100 --
And.

00:01:14.470 --
Basic Intro class review
lectures. Like I said, I'll

00:01:16.882 --
be putting up a whole bunch
more, especially as we run

00:01:19.830 --
into more stuff that's more
pertinent to the stuff we're

00:01:22.510 --
looking at and or reviewing.

00:01:25.260 --
And on today's we are going to
be in Module 3 which just from

00:01:28.550 --
correspond to chapter three. I'm
not quite sure why use the term

00:01:31.370 --
module, but I did and there it
is, so we're using it.

00:01:35.560 --
So here my links are working.
Yeah, I have a few more links

00:01:39.408 --
for other things to look at, so
my central limit theorem we're

00:01:42.960 --
going to talk about that today
review that I have two

00:01:46.216 --
different lectures for that.
One of 'em actually shows a

00:01:49.176 --
simulation which will be. I
don't know. I always enjoyed

00:01:52.136 --
this simulation. Once I finally
thought so it was kind of nice

00:01:55.688 --
to see. And we're also going to
go through this probability

00:01:58.944 --
distributions handout. I wasn't
actually going to put this up

00:02:01.904 --
and I'm going to do most of it
on the document camera, but.

00:02:07.070 --
I decided to at the last minute
and it literally is a last

00:02:10.567 --
minute hand out, so don't expect
anything gorgeous. No pretty

00:02:13.257 --
colors, sorry, no pretty colors
here. Have a couple of nice

00:02:16.216 --
looking tables or just not
sitting where I want them to,

00:02:19.175 --
but the handout itself will work
just fine, and that's actually

00:02:22.134 --
primarily we're going to go
through today and then we'll see

00:02:25.093 --
if we get a chance to look at at
least one of these central limit

00:02:29.128 --
theorem. Handouts, so today we
are going to look at this, but

00:02:33.546 --
we are going to walk through all
this, so we want to do most of

00:02:37.836 --
this on the document camera, but
I wanted to show something

00:02:40.982 --
first, because, well, this thing
can graph so much nicer than I

00:02:44.414 --
can. So alright first.

00:02:49.140 --
We need to review some
basic terms from

00:02:53.228 --
probability and we want to.

00:02:57.150 --
Zoom in just to hear will come
back to the computer in just a

00:03:02.358 --
bit. So remember, we're going
to be talking about is

00:03:06.078 --
probability distributions.

00:03:10.950 --
We'll start out with this simple
case just to work through. Now

00:03:14.826 --
that we're going to get into a
super highly complex one, but

00:03:18.702 --
will start out with a simple
case. Alright, so we have this

00:03:22.578 --
hypothesize data, and that's
what this worksheet that I made

00:03:25.808 --
is going to basically following
through it. Oh, sorry

00:03:28.715 --
hypothesis. Can you tell that to
normal term? I use hypothesized.

00:03:36.740 --
Population.

00:03:41.420 --
And it's an old example. It's
probably not extremely current

00:03:45.010 --
in terms of its probabilities.
Fitting it is OK. It will still

00:03:49.318 --
work. So here we have the number
of TV sets that are owned.

00:03:55.960 --
Per household.

00:04:01.570 --
Nowadays it might be more
more interesting to look at

00:04:05.960 --
phones or computers, but
everybody's got something

00:04:09.033 --
alright. So in this
population, well, we can

00:04:12.545 --
either have the TV's can take
on values of 0123 or four. Do

00:04:18.252 --
I have for USF 4?

00:04:21.920 --
And then we have some
probabilities associated

00:04:23.845 --
with those.

00:04:26.400 --
P of TV's.

00:04:29.250 --
So the probability of those.

00:04:31.860 --
So I'm just going to write

00:04:33.006 --
another wreath. We can make
a nice pretty table here

00:04:35.404 --
when we're done.

00:04:40.190 --
Alright.

00:04:42.870 --
OK, so this example is at least.

00:04:46.220 --
Now might be over 10 years old,
but it's at least 10 years old.

00:04:50.100 --
So the probability that probably
not quite so accurate anymore,

00:04:53.140 --
but that's OK for what we want
to do here. So this is the

00:04:57.396 --
number of TV sets owned per
household. And if you want to

00:05:01.044 --
think about it this way for
remember what this term is is

00:05:04.692 --
the number of TV's this is going
to be a random variable.

00:05:10.630 --
Which remember is kind of like a
function of valued function.

00:05:15.910 --
So a specific value of our
distribution has a specific

00:05:19.610 --
probability associated with it.

00:05:23.440 --
Alright.

00:05:25.470 --
So actually, let's make a nice
table. I should have done that

00:05:28.350 --
to begin with, but whatever.

00:05:30.770 --
I do things the hard
way sometimes, so TV's

00:05:34.991 --
probability of TV's.

00:05:43.660 --
Your attentive and you
want to redo it, go

00:05:45.928 --
for it, I understand.

00:05:48.120 --
Probably not necessary, as long
as you got all your information,

00:05:51.442 --
but nice little table.

00:05:54.160 --
I could have done it vertically,
whatever it however you want to

00:05:57.280 --
look at it. Either way, this
will get us the basic idea.

00:06:02.790 --
And that's where my graph comes
into play and I totally draw it.

00:06:06.287 --
But really, my my little my
little handout can show so much

00:06:09.515 --
better than I could ever draw
it. So if you want to look at

00:06:13.281 --
that real quick on the computer
that is distribution TV's.

00:06:17.910 --
Thought about playing with
colors, but I just left alone.

00:06:20.390 --
Figured you could get the gist
of it. So we got our 20% here at

00:06:24.110 --
zero and two 40% at one and then
our 10% at three and four.

00:06:28.490 --
Alright. So back to
our examples here.

00:06:35.110 --
So one of the things, well, we
have many things of interest

00:06:38.254 --
that we'd like to look at
about. One of the major things

00:06:41.398 --
we want to look at is to look
at some of our summary

00:06:44.804 --
statistics, and while looking
at this, it would probably be

00:06:47.424 --
nice to know on average, how
many TV's are owned per

00:06:50.306 --
household. So we want to find a
mean.

00:06:53.970 --
And we also call this here
in. With this we call this

00:06:58.134 --
an expected value.

00:07:02.070 --
Expected value alright, so an
expected value is a mean, but

00:07:06.756 --
unlike our continuous
distributions versus discrete

00:07:09.312 --
and this is more of one of those
discrete answers 'cause you

00:07:14.424 --
can't own. 1 1/2 television
sets. You could on average but

00:07:19.110 --
not. Literally.

00:07:22.380 --
You probably don't want broken
ones. I think they think they're

00:07:26.208 --
counting functional TV's not
nonfunctional TV's as well, so

00:07:29.340 --
this would be discreet.

00:07:33.200 --
So basically you want to think
about it that your your variable

00:07:36.344 --
in our book uses why a lot
versus X, but pick a letter. It

00:07:40.012 --
doesn't really matter. I'm going
to use why just because their

00:07:42.894 --
book does, but what was I going
with? This whole number values?

00:07:46.860 --
That's what these
things can take on.

00:07:50.850 --
There's an S there. There we go.

00:07:54.640 --
So this mean here the way we're
going to compute it is because

00:07:59.359 --
it's basically it's a weighted
average, so not every value of

00:08:03.352 --
our random variable TV's.

00:08:05.560 --
Takes on equal probabilities,
they don't have equal

00:08:08.240 --
probabilities, so we have a
weighted average that we're

00:08:11.255 --
going to do.

00:08:13.440 --
And.

00:08:15.690 --
Since we're dealing with the
population, this is what we

00:08:18.900 --
call deductive because we
know exactly what's going to

00:08:21.789 --
be happening in the
population versus a sample,

00:08:24.357 --
and most of our exploration
there is going to be

00:08:27.567 --
inductive, but this ones
deductive, because we can

00:08:30.135 --
actually see what's actually
happening, so we're going to

00:08:33.024 --
call this thing mu the
population mean of the

00:08:35.913 --
distribution, some other
notation E of Y, like

00:08:38.481 --
function notation.

00:08:41.180 --
And to calculate this is the

00:08:44.180 --
sum. So Sigma sum at
each Y times its

00:08:50.164 --
corresponding probability.

00:08:53.320 --
They just calculate about
products and add them all up.

00:08:59.830 --
Alright, so why not? We're here.
We should do this, for example.

00:09:05.870 --
So to calculate our expected
value of Y or mean for this

00:09:11.258 --
we would take zero times its
probability.

00:09:15.950 --
Plus one, so I was trying to
parenthese ahead of time times

00:09:19.922 --
the probability of 1.

00:09:22.890 --
Two times its probability plus
three times .1.

00:09:30.060 --
There's four times by 1.

00:09:33.490 --
There's also and then
we get a lovely 1.5.

00:09:38.590 --
Oops, sorry, papers got broken.

00:09:42.410 --
So on average, we could
expect a household to

00:09:45.830 --
have about 1 1/2 TV's.

00:09:49.290 --
It's like the 1 1/2 kids thing,
though obviously we can't have a

00:09:51.994 --
half a TV or a half a kid, but
it's an average, even if it's

00:09:55.114 --
not a part of the original

00:09:56.362 --
distribution. And that's OK.

00:09:59.780 --
So. This, unfortunately, you're
going to have to torture with my

00:10:03.740 --
drawing anyways. If I drew out
our little distribution.

00:10:09.860 --
So this will be our probability.

00:10:12.750 --
We have wide on the X axis.

00:10:16.310 --
Let's see here.

00:10:18.840 --
So I'm just kind of
guesstimating I'm not an artist

00:10:22.290 --
by any stretch of the
imagination. I can draw a decent

00:10:26.085 --
Bell curve. And occasionally
decent rectangles.

00:10:31.040 --
Pretend those are both .1 and
the other ones are point 2.4,

00:10:35.348 --
point 2.1. .1 there we go.

00:10:40.090 --
So if we imagine where we put
the mean, that would be right

00:10:43.639 --
about here. Well, this is
basically what we would consider

00:10:46.369 --
this center of mass. So if we
actually try to balance this

00:10:49.645 --
thing on, that's exactly the
point where it would balance the

00:10:52.648 --
center of mass right there. And
that's where that mean is.

00:10:59.580 --
I think I just wanted to
touch you with my drawing.

00:11:01.395 --
That's not what I think I
needed to do here.

00:11:04.750 --
Right, and of course we love
measures of location. That's

00:11:08.310 --
what the mean is. But we also
love measures of spread so we

00:11:12.938 --
can see how much variation we
actually have. So this is our

00:11:17.210 --
measure.

00:11:19.070 --
Of spread.

00:11:21.380 --
Variation.

00:11:27.190 --
It's one of 'em, but this
one in particular.

00:11:31.040 --
The variance.

00:11:34.270 --
Is the average.

00:11:40.050 --
Important work here squared.

00:11:43.820 --
Distance.

00:11:46.410 --
Each point is from its mean.

00:11:53.280 --
Remove there.

00:11:59.540 --
So we can see how much variation
we have in our data. Points were

00:12:03.670 --
in relation to the center.

00:12:05.750 --
Of the distribution.

00:12:11.170 --
At see here it's units.

00:12:14.290 --
R-squared units.

00:12:22.720 --
Measurement but yeah.

00:12:25.130 --
But it's not on the same scale
as the mean, so not all the

00:12:29.568 --
time. Is this the one we want to
directly deal with? But we still

00:12:34.006 --
have to calculate it. So to do
that it's it's Greek symbol is a

00:12:38.444 --
Sigma squared. Yeah,
my Sigma is mostly OK.

00:12:42.810 --
And one of my friends used to
draw it and it looked like a

00:12:44.896 --
Theta and I was like Theta

00:12:45.790 --
squared shoes. Now it's a Sigma.
OK, mine supposed to be a Sigma

00:12:50.030 --
at mostly kind of looks like
one. You can also use via Y. Now

00:12:54.930 --
this V here is going to denote
the actual true variance.

00:12:59.660 --
And of course, since we're
dealing with the population,

00:13:01.694 --
that's OK. 'cause that's what
we're going to be looking at.

00:13:04.180 --
But that reason I brought that
up is that will come into play

00:13:07.118 --
here in just a bit, so.

00:13:09.070 --
Keep that in the back of your

00:13:10.183 --
head, all right. So
what we're going to do

00:13:14.456 --
is look at Y minus mu.

00:13:18.550 --
Quantity squared times the
probability of Y, so we'll take

00:13:23.300 --
each squared difference of each
value between it and the mean.

00:13:29.170 --
Look at that squared distance
and multiply it by the

00:13:32.280 --
probability of that data point
and that gives us.

00:13:35.970 --
What we're looking for in terms
of the variation.

00:13:42.290 --
Alright. So of course we're
going to do that.

00:13:48.350 --
And I got a little carried away
on my hand out, which is OK and

00:13:52.910 --
carried away in a good way, sort
of. It might be a little

00:13:56.862 --
redundant for you, but I did
actually expand some of these

00:14:00.206 --
formulas a little bit more, but
I did show the actual work later

00:14:04.158 --
on, so we will actually do this.
So Sigma squared is the variance

00:14:08.110 --
of Y. So we're going to take the
first data point, which is a 0.

00:14:13.780 --
Minus the mean.

00:14:15.750 --
Squared and the probability of
zero was a .2.

00:14:21.720 --
And we get to do this for all

00:14:23.704 --
five values. So next one 1 --
1 1/2 ^2 * .4.

00:14:33.350 --
I have the right table. I'm
just making sure I have the

00:14:35.318 --
right values OK.

00:14:37.450 --
And the next one 2
-- 1 1/2 ^2 * .2.

00:14:43.550 --
I have to move it down page
or move it down the line.

00:14:47.400 --
3 minus the mean squared times
.1 and the last one 4 -- 1 1/2

00:14:53.715 --
squared times point. That's a
two up there. Sorry times .1.

00:15:01.080 --
Well, you know this stuff and
all these lovely little.

00:15:06.550 --
Squared differences in products
all add up to 1.45.

00:15:14.620 --
Ann, if at anytime you're
working through this on your own

00:15:17.887 --
and you get a different number
than I do, don't hesitate to say

00:15:21.748 --
something. It happens,
unfortunately, but it happens

00:15:23.827 --
and I won't be offended.

00:15:27.730 --
I used to wonder why I was like

00:15:29.498 --
why. How is it so easy to make
mistakes? And I think it's

00:15:33.506 --
actually really easy on this end
'cause you get caught up in what

00:15:36.665 --
you're doing. You don't think
about something that you're

00:15:38.852 --
dealing with right this moment
when you're trying to talk about

00:15:41.525 --
something 5 minutes ahead of you
know and think 5 minutes ahead.

00:15:44.441 --
Yeah, it's interesting, alright,
but if I do make a mistake,

00:15:47.114 --
don't hesitate to let me know.

00:15:49.900 --
So. Of course, the variance
leads us to the next one, which

00:15:55.212 --
is the standard deviation anisur
standard measurement of spread.

00:16:02.230 --
And.

00:16:04.320 --
So it's a again a
measure of spread.

00:16:09.480 --
Variation that's an
R in there, sorry.

00:16:12.890 --
It is the average distance.

00:16:17.670 --
Without the squared.

00:16:20.910 --
Each point is from its mean.

00:16:23.690 --
Oh, there's an end in there.

00:16:32.600 --
So.

00:16:36.450 --
It's just the square root of
the variance, and since it's

00:16:39.365 --
really what we end up wanting
to do because its units of

00:16:42.545 --
measurement are the same as the
mean, so they have single non

00:16:45.725 --
squared units of measurement.

00:16:47.830 --
It has seem.

00:16:55.120 --
Units of measurement azzameen

00:17:00.870 --
which is good? Want to keep
things on the same scale?

00:17:06.180 --
And it literally is just the
square root of the variance.

00:17:14.510 --
The positive square root,
of course.

00:17:19.220 --
Remember, standard deviations
invariances cannot be negative.

00:17:21.789 --
They can be 0.

00:17:23.810 --
Which is not very exciting, but
they can't be negative.

00:17:27.280 --
'cause if there is zero, you

00:17:28.678 --
have identical data points.
Which I suppose is not

00:17:31.805 --
necessarily that it's not
super exciting. There could be

00:17:34.550 --
a good case for it, but it
might not be that exciting to

00:17:38.515 --
look at. So Sigma without the
squared is our notation.

00:17:43.890 --
So SD of Y.

00:17:46.650 --
Probably, but as of why, but
that might mean something else

00:17:50.005 --
in a different class, so I use
SD and so we just take the

00:17:54.275 --
square root of our variance.

00:17:56.910 --
Or the square root of Sigma
squared. Either way for us in

00:18:01.962 --
this example, is sqrt 1.45.

00:18:05.720 --
Which is fire Mario 1.2?

00:18:13.770 --
Or something close.

00:18:22.100 --
Alright, this would be great if
we could always get population

00:18:25.070 --
values and we would never have
to worry about doing. You know

00:18:28.310 --
we'd always be able to know
everything about the population.

00:18:32.020 --
Not always the exact case in
life. Unfortunately, there's a

00:18:36.010 --
lot of unknown.

00:18:38.650 --
And it's a two point 1.20 that
some decimals off the end, but I

00:18:42.458 --
just found it to 1 decimal place
as far as your work goes most of

00:18:46.538 --
the time using significant
digits is not a horrible idea,

00:18:49.258 --
but I would say except in a rare
case when we get to the last

00:18:53.338 --
chapters, you probably don't
need to carry it more than two

00:18:56.330 --
to four decimal places are last
chapters or there are some

00:18:59.322 --
concepts where we're going to
have a small value, some sort of

00:19:02.586 --
density value which is very
similar to like a growth or

00:19:05.578 --
decay rate, so you'd probably
more like a decay rate, so you

00:19:08.842 --
probably want to make sure you
might want to carry those out a

00:19:12.378 --
little bit further, but.

00:19:13.640 --
The most part significant digits
or two to four decimal places

00:19:17.457 --
will be more than sufficient for
what you need.

00:19:22.630 --
But unfortunately we don't have.

00:19:26.030 --
Population values all the time.
He did. Life would be simple and

00:19:29.510 --
then we wouldn't probably need a
whole discipline called

00:19:32.120 --
statistics for all this stuff
because we wouldn't know the

00:19:35.020 --
entire population. But since we
don't, we have to use

00:19:37.920 --
statistics. So what we're going
to do is take samples and that's

00:19:41.400 --
really what you're doing. Here
is looking at the samples from

00:19:44.590 --
surveys and what have you and
trying to make estimations. Our

00:19:47.780 --
main estimations are going to be

00:19:49.520 --
a mean. A total which you may or
may not have dealt with in your

00:19:55.123 --
intro class and a proportion.
There are others, of course, but

00:19:58.764 --
those are our main.

00:20:00.180 --
Three statistics of interest
while we're here in this course

00:20:02.840 --
and those would be the main
three statistics of interest in

00:20:05.766 --
surveys as well. So.

00:20:08.360 --
And of course with that we
always want to have a variance,

00:20:12.284 --
so we getting back to
calculating this all right now.

00:20:16.590 --
You've probably seen that
there are different.

00:20:20.540 --
Calculations formulas for
population versus sample values.

00:20:25.880 --
So let's kind of take a peek at

00:20:28.336 --
the differences. Population.

00:20:33.650 --
Versus sample.

00:20:36.980 --
So population value for a mean.

00:20:40.470 --
Is mew. I'm going to write the
word meaning here so we know

00:20:44.698 --
what this is at first case. It's
been a little while since you've

00:20:47.402 --
seen some of these. So if we
knew every single value in the

00:20:51.642 --
population, we would sum all of
those up. So I'm going to use.

00:20:55.516 --
Not that you can tell the
difference, but that's supposed

00:20:58.496 --
to be a capital Y versus a small
way. Usually my capital wise are

00:21:02.668 --
straight just lines and my lower
case. Why is usually kind of got

00:21:06.542 --
a curve to it?

00:21:08.830 --
I'll usually remind you as we
get there, so we take every

00:21:12.514 --
value of the population.

00:21:14.700 --
And we divide it by. Now we have
a new symbol, big End. Big N

00:21:19.875 --
represents population size.

00:21:22.480 --
I'm actually going to write
that on my previous sheet of

00:21:25.351 --
paper that I'm going to bring
down Tuesday here, so an is

00:21:28.483 --
always your sample size.

00:21:32.560 --
And Big N is going to be
your population size.

00:21:37.320 --
Which is actually important.
In this course we need to

00:21:39.380 --
know that for the surveys and
stuff that we were analyzing.

00:21:45.350 --
Alright.

00:21:48.520 --
Before a sample.

00:21:51.400 --
Ala carte, why bar could be X
bar. Yeah, Brooke. Uses why

00:21:54.856 --
we're going to stick with guys.
We would take the sum of all of

00:21:58.888 --
our sample. Observations and
divided by the number of

00:22:03.687 --
observations in our sample.

00:22:06.980 --
Depending on how we draw a
sample, these could be

00:22:10.090 --
identical. But it's not going to
happen terribly often, except in

00:22:14.340 --
my example. Today it was
coincidence. I swear I actually

00:22:17.390 --
do a random sample, and the
thing we're going to look at

00:22:21.050 --
today, and it turned out that
the sample mean is going to end

00:22:25.015 --
up being exactly the population
mean, but that doesn't always

00:22:28.065 --
happen, but it should be most of
the time, pretty close.

00:22:33.250 --
Alright, variance.

00:22:36.060 --
So we call it Sigma squared.

00:22:40.420 --
I'm going to actually give
you two different derivations

00:22:43.183 --
of the same formula.

00:22:46.410 --
There's one you've seen before.

00:22:47.860 --
Maybe sort of. So why that
should be an eye for each

00:22:52.895 --
individual observation minus mu?

00:22:55.150 --
Quantity squared
divided by big N.

00:22:58.680 --
Or in the discrete case, what
you saw earlier?

00:23:04.730 --
That was the sum Y minus mu
quantity squared times the

00:23:09.427 --
probability of Y.

00:23:15.730 --
Alright.

00:23:19.650 --
S squared following the same
sort of formula over here.

00:23:24.040 --
It's going to be.

00:23:27.980 --
The sum why I -- Y bar quantity
squared. We divide that by

00:23:33.661 --
little N -- 1.

00:23:36.370 --
Because it came from a
sample and we're losing

00:23:38.773 --
some information. If you
look there at the formula

00:23:41.176 --
I have. Why bar versus mu,
since we don't know mu, we

00:23:44.380 --
lose. We lose our
information. A degree of

00:23:46.516 --
freedom. So that's why
we're dividing by N -- 1

00:23:49.186 --
little N -- 1.

00:23:51.980 --
But in the population case,
we wouldn't actually lose any

00:23:55.010 --
information because we have
it all. So, and we're using

00:23:58.040 --
the real mean.

00:24:01.050 --
This one here. Technically we
still use via why, but it's more

00:24:05.154 --
ha with a hat on it, so anytime
you see a hat on something

00:24:09.942 --
that's usually called an
estimator and you're actually

00:24:12.678 --
going to see a hat on a V. More
often than not. So this one

00:24:17.808 --
implies that we actually do

00:24:19.518 --
know. All the values and
population. Here we are

00:24:23.030 --
estimating the variance, so it's
the estimated variance of Y.

00:24:27.750 --
And it really isn't going to
look hugely different.

00:24:36.970 --
As well, calculate the expected

00:24:38.450 --
value of Y. Or mew hat.

00:24:42.130 --
Yeah, this book likes to use
hats on things, so if you

00:24:44.962 --
haven't seen that too much
before, we're going to have

00:24:47.322 --
hats. Lots of hats.

00:24:51.340 --
Standard deviation, well,
that's actually.

00:24:57.180 --
Not that exciting or different
than what we were used to. So

00:25:01.212 --
Sigma is the square root of
Sigma squared and over here S is

00:25:05.580 --
sqrt X ^2.

00:25:11.650 --
Alright.

00:25:15.800 --
Trying to keep my pages and
pages in line here so in our

00:25:21.065 --
statistical studies we love to
take samples and we make

00:25:25.115 --
inferences from those samples
about the larger population. So

00:25:28.760 --
we want to make.

00:25:30.980 --
Well, it's an inference is an
educated guess, but we're using

00:25:34.126 --
data and facts to back that up.
So it is an educated guess.

00:25:37.844 --
Guess sounds so. I don't
know Willy nilly versus.

00:25:42.350 --
An educated statement I don't
know, but that's what we're

00:25:45.690 --
going to do. So a lot of times
we want to make inferences about

00:25:50.366 --
unknown population parameters.
So what do we do? We use our

00:25:54.040 --
sample statistics, so we're
going to get back to our TV

00:25:57.714 --
example. 'cause it's completely
exciting an in our TV example.

00:26:04.140 --
TV simple. Let's say I took
a sample an it's not a very

00:26:09.301 --
big sample, it's only a
sample size 4.

00:26:13.970 --
An out of this sample, we knew
that we could have values that

00:26:18.169 --
were 0123 or four, but in this
particular sample my values

00:26:21.722 --
were. Those are my sorry. These
are supposed to be my curly

00:26:25.598 --
braces, but I suck at drawing
them, so that's what it is.

00:26:30.900 --
These were my data points.

00:26:34.650 --
There we go.

00:26:37.580 --
2013

00:26:42.340 --
now just for reference, our
population had a sample or

00:26:44.780 --
had a size 4 as well, but
we're going to take a sample

00:26:47.952 --
of size 4 and it could have
been any values Now notice.

00:26:52.870 --
We actually had five different
values that could happen. We

00:26:55.460 --
only chose for actually so big N
is. I have a big I have a typo

00:26:59.604 --
on my thing. I gotta fix it big
and is actually 5 here, alright?

00:27:04.520 --
So let's estimate mu. So
mu hat. We usually just

00:27:07.920 --
call that Y bar X bar.

00:27:11.360 --
Pick a letter well, minus a few
of 'em till pigsie.

00:27:17.060 --
But here it is. When we
use the sum of our values

00:27:21.296 --
divided by your sample
size. So we can do that.

00:27:27.960 --
Divided by 4, why are we doing
it this way? Well in this case.

00:27:33.280 --
We're kind of assuming that
they didn't have different

00:27:36.286 --
probabilities from our sample
when we actually went to those

00:27:39.626 --
probabilities were different
based on numbers in a

00:27:42.298 --
household, but from our
sample, each of these had an

00:27:45.638 --
equal chance of being chosen.

00:27:48.740 --
So we do this and
like I said before.

00:27:54.130 --
We actually get.

00:27:56.190 --
The same number, or pretty close
to it, 6 force. I don't know.

00:27:59.986 --
Today is one of those days.

00:28:02.510 --
One of my favorite teachers in
the math Department, so some

00:28:05.370 --
days are Calculator days, even
for the most simple things like

00:28:08.230 --
1 1/2. Which I already told you
it was the same, but all of a

00:28:12.991 --
sudden my brain said no, you
must test it again. So even

00:28:16.195 --
though I calculated it 2 hours
ago, evidently I needed to do it

00:28:19.666 --
again. Alright now your sample
mean is not always going to be

00:28:22.870 --
equal to your population mean.
It should be relatively close

00:28:25.540 --
most of the time this just
happened have been one of those

00:28:28.744 --
samples that I happened to draw
and I did actually honestly draw

00:28:31.948 --
it randomly. And it just
happened to be that this sample

00:28:35.507 --
mean was the same as a
population mean, which is OK,

00:28:38.290 --
that's not a bad thing.

00:28:41.470 --
But now we're going to get
into calculating our variance

00:28:46.070 --
and standard deviation.

00:28:49.020 --
So here's our variance. We
can call it Sigma squared

00:28:52.170 --
hat or Sigma hat squared,
probably Sigma hat squared.

00:28:56.380 --
Or you just call ask word
that works too.

00:28:59.750 --
We're going to use the other
formula, the second, well, the

00:29:02.335 --
first one I drew out, but not
the first one we actually used.

00:29:06.540 --
Why I -- Y bar quantity squared
divided by N -- 1?

00:29:12.260 --
That's the one we're
going to use.

00:29:16.480 --
Amazon to all this
lovely fun stuff.

00:29:22.350 --
And we got a zero. Remember
using the values from the sample

00:29:25.878 --
and not the actual population.

00:29:28.710 --
1 -- 1 1/2 squared and
3 -- 1 1/2 ^2.

00:29:38.620 --
Bye bye oh I was gonna say
4 -- 3. Now the answer is

00:29:42.904 --
three 4 -- 1.

00:29:47.900 --
We had five thirds or 1.67.

00:29:53.010 --
Versus what was it before 1.45?

00:29:58.000 --
So a little more variation in

00:29:59.842 --
this. Particular sample,
then there wasn't a

00:30:01.996 --
population, that's OK.

00:30:05.390 --
And then for the standard
deviation.

00:30:08.780 --
Sigma hat or S just take the
square root of your S ^2.

00:30:15.100 --
Anne will get.

00:30:17.490 --
Our standard deviation 1.29.

00:30:22.170 --
As probably.

00:30:28.010 --
Alright.

00:30:30.940 --
Not very exciting, but I thought
we do a nice little nice

00:30:34.816 --
overview. Just remind you so for
random samples from infinite

00:30:38.046 --
populations, which is what we're
kind of doing. The expected

00:30:41.276 --
value of the sample mean.

00:30:43.670 --
Is usually the true meaning that
leads us toward what we're

00:30:47.850 --
looking at next, which is not
just probability distributions,

00:30:51.270 --
but distributions of statistics.

00:31:02.590 --
Sample statistics so
distributions of sample

00:31:05.278 --
statistics, or in other
words, sampling

00:31:07.966 --
distributions. That's
usually the more common

00:31:10.654 --
terminology.

00:31:16.340 --
So just a reminder, what a
sampling distribution is is that

00:31:21.235 --
it looks it's the distribution.

00:31:28.200 --
Of all possible samples, Whoops,
there's 2 S is there?

00:31:37.310 --
Of a sample statistic.

00:31:46.050 --
We like that we have a specific
theorem that we really really

00:31:50.106 --
like. And I need to go find that
real quick here now. We probably

00:31:56.269 --
going to look through one of
these on the computer up here,

00:32:00.985 --
but it didn't want to go

00:32:03.343 --
through. Well, I wanted to show
I didn't want to necessarily go

00:32:06.891 --
through both of 'em 'cause the
other one really just kind of

00:32:09.663 --
summarizes this whole thing
together. So that's something

00:32:11.511 --
you can look at the other link
for. It's called CLT 2.

00:32:15.230 --
But we're going to do is we're
going to look at the sampling

00:32:18.961 --
distribution an. I actually
have a couple of examples to

00:32:21.831 --
show through simulation how
this actually works and why

00:32:24.414 --
we're still able to actually
use a normal model. Most of

00:32:27.571 --
the time for analysis, and
we're going to do a normal

00:32:30.728 --
model in this classroom as
well for this course.

00:32:34.600 --
Not all your surveys are going
to have variables that follow

00:32:38.131 --
normal models. OK, not all of
'em, but provided we look at we

00:32:42.304 --
have large enough samples and
what have you most of the time

00:32:46.156 --
we should be OK, but not every
time. There are exceptions to

00:32:50.008 --
that rule always. So first thing
you should always do graph your

00:32:53.860 --
data if you don't know what your
data looks like visually, then

00:32:57.712 --
you're only getting probably
about 1/3 to half of the

00:33:00.922 --
picture. So alright, so we're
gonna look at the central Limit

00:33:04.453 --
theorem. And for that one, our
sampling distribution of the

00:33:08.129 --
sample mean is approximately
normal with a mean mu and

00:33:11.539 --
standard deviation of the
sampling distribution of the

00:33:14.267 --
sample mean. Is Sigma divided
by square root of N. So since

00:33:18.359 --
we're looking at the
distribution of the sample

00:33:21.087 --
mean, we don't just use our
variance, we take the variance

00:33:24.838 --
divided by N or the standard
deviation divided by the

00:33:28.248 --
square root of N. We call that
Sigma over square root of N.

00:33:32.681 --
We used to call that a
standard error.

00:33:36.760 --
That is provided that N is
sufficiently large. This theorem

00:33:39.570 --
can also apply to other
statistics, which is really,

00:33:42.099 --
really handy because we're going
to be using those other

00:33:44.909 --
statistics as well. The sample
proportion an one of 'em I

00:33:48.000 --
didn't actually have on here.
The sample total which could be

00:33:51.091 --
used in case I don't know if you
guys have ever dealt with the

00:33:55.025 --
total before, but it could be
nice, say for an airline we need

00:33:58.678 --
to know how many passengers are
boarding the plane right? And

00:34:01.769 --
the other thing we do is we
weigh how much your bags weigh.

00:34:05.810 --
We need to know the weight of
your bags, how much junk

00:34:09.002 --
you're taking with you on the
plane, in addition to the

00:34:11.928 --
weight of everything else on
the plane, the humans on the

00:34:14.854 --
plane, everything.

00:34:16.640 --
So it might be nice to know what
the average weight per person

00:34:20.085 --
should be. The maximum average
weight per person, but that's

00:34:22.735 --
not the only thing of interest.
It could actually be of interest

00:34:25.915 --
to look at the entire plane full
of people's total weight. That's

00:34:29.095 --
just one example. It's not the
only one, but it's one of the

00:34:32.540 --
few examples that you could use
a total for, and so that's how

00:34:35.985 --
that's going to play in when we
start getting to that.

00:34:39.770 --
Alright, so for the most part,
the sample size should be

00:34:43.752 --
approximately at least 30.

00:34:46.100 --
If your distribution wasn't
already normal to quote

00:34:48.956 --
unquote, guarantee the
normality I say and kind of

00:34:52.169 --
using that term guarantee a
little. Loosely, there's no

00:34:55.382 --
guarantees, but to get us
the approximate normality,

00:34:58.238 --
we should have a sample size
of at least 30. Now, if your

00:35:02.879 --
original distribution you
already know is inherently

00:35:05.378 --
normal, that sample size
stipulation is not required.

00:35:08.234 --
You could have a sample size
is smallest 2.

00:35:12.850 --
But if you don't know anything
about your original

00:35:15.613 --
distribution, always safer to
take a sample size of at least

00:35:18.990 --
30. That being said, in surveys
we take, sample size is usually

00:35:22.674 --
of probably at least 10 or more
times than that than 30, so.

00:35:27.480 --
And we're going to sample
proportion. We usually want to

00:35:30.000 --
sample size of at least 60. Most
of your information from sample

00:35:33.024 --
surveys, alot of time, not most
or all. But a lot of times are

00:35:36.552 --
going to be percent, so that
would be of interest.

00:35:39.800 --
And again, I said here, if
you're just distribution is

00:35:42.520 --
already inherently normal, your
sample size stipulation can be

00:35:44.968 --
ignored. It's not that you're
ignoring it, but it's not. It's

00:35:47.960 --
not relevant to what you need to
worry about it, alright?

00:35:52.040 --
This one sorry. The book I was
using used pie instead of P for

00:35:56.184 --
the proportion. Now it should be
like most. I'm an intro books,

00:35:59.736 --
they always use P, but as soon
as you hit like our 431 class,

00:36:03.880 --
that book uses pie 'cause
everything else uses a Greek

00:36:06.840 --
letter. Why not? So why not
intro class? Well unfortunately

00:36:09.800 --
will never find that answer out
but we still go back to P in

00:36:13.944 --
this book. This book uses P for
that terminology just to kind of

00:36:17.792 --
let you know. But you can
interchange it with pie. It is

00:36:21.344 --
the same basic thing.

00:36:23.990 --
Alright, so in shorthand
notation. Our sample mean X bar

00:36:28.110 --
or why bar is distributed
normally with a mean mu and the

00:36:33.054 --
Sigma sub X bar is another
notation for that standard

00:36:37.174 --
error. Sigma over square then.

00:36:41.150 --
Same thing for the one for the
proportion and the total would

00:36:44.042 --
work as well. I thought this was
my updated file that showed.

00:36:47.630 --
Totals so all this is nice and
interesting in review. You'd not

00:36:51.950 --
be calculating Z scores in here.

00:36:54.890 --
So if you're hoping to see Z&T
scores in here, I'm actually

00:36:58.454 --
going to see those, but that's
OK, Alright? This is the

00:37:01.721 --
important part, so we actually
see how this distribution works

00:37:04.691 --
and how the central Limit
Theorem helps us to look at

00:37:07.958 --
normality. So we're actually
going to look at a distribution

00:37:10.928 --
that's already normal, so it's
not going to be that exciting

00:37:14.195 --
when we take the look at the
sampling distribution, it's

00:37:17.165 --
still going to be normal. There
are going to be some

00:37:20.432 --
differences, but then we're
going to look at an exponential

00:37:23.402 --
distribution, which is obviously

00:37:24.590 --
not. A normal Bell curve
distribution and a binomial

00:37:27.672 --
distribution, just so you can
see how the central Limit

00:37:31.062 --
theorem works on even the non
normal distributions.

00:37:35.200 --
You don't ever have to reproduce
this unless you want to, and

00:37:38.608 --
which case if you want to borrow
my code, just ask me, But what

00:37:42.584 --
this does is I'm basically going
to take this is in our command,

00:37:46.276 --
so our norm. And you plug in how
many values you want into that.

00:37:50.969 --
That will give you random
numbers generated from a normal

00:37:53.659 --
distribution. If you don't
specify the mean and standard

00:37:56.080 --
deviation, it will assume the
mean is 0 and the standard

00:37:59.039 --
deviation is 1, just like the Z

00:38:00.922 --
distribution. So we needed.

00:38:04.070 --
And in this case I actually gave
it a different mean in a

00:38:08.256 --
different standard deviation
than the Z distribution. So I

00:38:11.154 --
took a sample of 500.

00:38:13.810 --
Out of a normal distribution and
I set the mean at 100 and the

00:38:18.612 --
standard deviation at 10 and I
said, oh, let's look at the mean

00:38:23.071 --
so mean for that particular
sample was 100.25.

00:38:26.970 --
So close.

00:38:29.170 --
And here's our histogram. So the
spread on this one goes from

00:38:33.898 --
about 65 to 135, give or take.

00:38:39.630 --
And another random sample
just to show the mean change

00:38:42.480 --
to her. But we're still right
around that 100 mark.

00:38:46.440 --
And then. For some silly reason,
I decided I need to put a curve

00:38:51.432 --
on it. I hardly ever put curves
on my on my distributions like

00:38:54.890 --
this, but this one was like I'm
going to put that curve on

00:38:58.348 --
there. So there it is. So it is
a normal distribution still

00:39:01.540 --
spread out between 65 and 135
center right about 100.

00:39:05.510 --
Oh, rest of my code fell
off, sorry.

00:39:09.260 --
Alright, so for this simulation
process I'm setting the mean and

00:39:12.714 --
the standard deviation. I'm
going to take samples of size

00:39:16.232 --
5 and I'm going to do that 500
times. We're going to have 500

00:39:20.236 --
samples of size 5, so we can
look at the means of all of

00:39:24.240 --
those, and that's what I'm
calculating here.

00:39:28.350 --
And then we look at histogram
and there is the distribution of

00:39:32.898 --
the sampling distribution of the
sample mean. So the spread

00:39:36.688 --
changes 'cause we're dividing it
by the square root of N. So it's

00:39:41.615 --
now spread from about 85 to
maybe 115 versus 65135.

00:39:46.160 --
So the curve got skinnier and a
little bit taller and that

00:39:50.324 --
happens. But it's still a
normal distribution, but

00:39:53.151 --
this is now the distribution
of X bar versus X.

00:39:56.910 --
And they are just kind of
arbitrary values. I guess I

00:39:59.968 --
just. Grabbed grabbed a mean
in a standard deviation and

00:40:03.884 --
just used it so.

00:40:05.900 --
Normal spread change though.

00:40:08.720 --
That's important to look at.

00:40:10.480 --
Exponential distribution. I
don't know why I really like

00:40:12.919 --
this distribution. If you took
201 or 251 then chances are you

00:40:16.171 --
probably didn't see this. You
may have heard about it, but you

00:40:19.423 --
probably didn't see this. If you
take 301, they may have seen

00:40:22.675 --
this, but don't stress it if you

00:40:24.572 --
haven't seen it. I'm not going
to test you on this formula,

00:40:29.394 --
but this just shows you the
formula I'm using, so it's an

00:40:33.786 --
exponential distribution.
Exponential is really great

00:40:35.982 --
for modeling the waiting time
between events.

00:40:39.620 --
Other processes too, but that's
one of its big big draws.

00:40:43.920 --
Now let's see. Here we are going
to be looking at this with this

00:40:47.784 --
one. We're going to use a
distribution with a rate of 1.

00:40:52.180 --
Alright, so random number
again, a different

00:40:54.595 --
distribution R has told
whole bunch of different

00:40:57.355 --
distributions. You can
randomly generate numbers

00:40:59.425 --
out of which is great.

00:41:03.170 --
We need N.

00:41:05.160 --
Anna rate. So with this one
we're going to sample size 500.

00:41:10.040 --
We will find the mean.

00:41:11.880 --
That's pretty close to 1.

00:41:14.470 --
That sample #1 sample #2.

00:41:18.450 --
Actually knows same sample.
This sample number one.

00:41:21.362 --
Sorry, obviously not a
normal distribution.

00:41:25.370 --
And do it again. This time the
mean was to even just a hair

00:41:28.968 --
lower. But we're still pretty
close to the one mark.

00:41:33.720 --
There we go. Being silly had to
add that curve in again. So

00:41:37.984 --
there's our our curve or
exponential curve and the

00:41:40.936 --
regular distribution of it.

00:41:43.260 --
So now we're going to do the
same thing, except for I'm

00:41:46.776 --
going to be taking samples
of size 30 and I'm going to

00:41:50.292 --
take 500 samples of size 30
to calculate. 500 means joy.

00:41:54.530 --
It's kind of fun to do. Well,
this is the first time so.

00:41:58.840 --
This one, a sample size of 30
almost gives it the normality.

00:42:03.016 --
It's not perfect, but it's.

00:42:05.570 --
Close enough, that's the one
thing that's hard to once you

00:42:08.309 --
get out. Intro class is
looking at some of these

00:42:10.799 --
curves, and some of these they
might not look normal to. You

00:42:13.787 --
might want to go. Some of
these are going to be normal

00:42:16.775 --
enough. This one is actually
good.

00:42:19.450 --
Obviously not exponential
anymore and then binomial. So

00:42:23.266 --
remember binomial distribution
is one of those discrete

00:42:27.082 --
distributions for absence or
presence, so success or failure.

00:42:33.220 --
So this one is again 500
samples with a binomial

00:42:38.020 --
distribution. Its probability
of success was .8 an. We did

00:42:42.820 --
sample sub size 10.

00:42:46.370 --
But this person will probably do
500, though again binomial. You

00:42:49.967 --
can randomly generate, so this
first one is actually 500. Later

00:42:53.564 --
on when we do, the 500 samples
were going to take 500 samples

00:42:57.815 --
of size 30. I think or is it 10,
probably 10? I don't know. I'll

00:43:02.530 --
double check. I looked through
it today and then I forgot.

00:43:06.200 --
So the eight the mean should
be 8, so the mean for a

00:43:11.127 --
binomial is N * P, so 10 times
.8 gives us 8 and this one's

00:43:16.812 --
pretty darn close 7.98.

00:43:20.370 --
Not even a continuous
distribution.

00:43:25.820 --
There we go again, and this one
that means just a hair over

00:43:29.668 --
eight. OK, so that was our
second random sample and there's

00:43:32.924 --
our second. Histogram.

00:43:36.780 --
Same process we're doing
samples of size 10, but

00:43:39.012 --
we're taking 500 of them.

00:43:42.220 --
And look at that all of a
sudden. It's not the prettiest

00:43:46.084 --
thing I've ever seen, seen
prettier distributions, but

00:43:48.660 --
it's still approximately
normal.

00:43:51.700 --
Excuse me, centered right about
8:00, so that's what the central

00:43:54.989 --
limit Theorem does. Remember,
when I took my intro course, I

00:43:58.278 --
was just like it was just kind
of this concept. You had to just

00:44:02.464 --
think about it was like, OK, I'm
sure I'll use it, but actually

00:44:06.351 --
saying it for me it made a huge

00:44:08.743 --
difference this other. Thing
that you get Lord death right?

00:44:12.372 --
I zoomed in, sorry this other
one that you can look at is

00:44:16.090 --
just moves a nice little
handout that my 200 level class

00:44:19.236 --
professor had given to us. So I
asked him if I could steal it.

00:44:23.240 --
Well, I said I asked him if I
could borrow it so I said well

00:44:27.530 --
can I. Can I borrow it and give
it to my class and you said OK,

00:44:32.106 --
that's fine so I stole it.
There it is but I did I did put

00:44:36.396 --
his name down there so.

00:44:39.460 --
Alright. So we're looking at
this thing. We're probably not

00:44:43.222 --
gonna be able to finish this up
today, which is OK. We can

00:44:46.576 --
finish this up later, but we can
kind of set ourselves up for the

00:44:50.188 --
end of this. So what we
want to do?

00:44:54.510 --
Is we have our population
at see here.

00:44:59.810 --
I left my pen open, sorry.

00:45:03.800 --
So this is our original
population values.

00:45:08.530 --
And we're going to.

00:45:11.320 --
I think in this case just
take samples.

00:45:19.530 --
Size 2

00:45:22.310 --
just keep simple.

00:45:25.620 --
Now.

00:45:28.390 --
In this case.

00:45:31.100 --
This is this is our population
and this is the number the

00:45:35.132 --
sample size we're going to do.
We want to actually look at all

00:45:39.500 --
possible samples for this so.

00:45:49.860 --
All possible samples.

00:45:54.600 --
From in this case, what we're
doing is those were the number

00:45:58.344 --
of TV's in the House, but what
we're going to do is we're going

00:46:02.712 --
to be looking at from 4 houses.

00:46:06.240 --
So let's say we have House 1-2,
three and four.

00:46:13.590 --
So this has a population of
four different.

00:46:19.210 --
Possibility so for houses
small town. There we go

00:46:22.666 --
more than Moscow.

00:46:26.250 --
One of the things we got
excited about when I was a kid

00:46:29.396 --
we were driving. I think we
were driving to California and

00:46:32.058 --
we were driving through
southern Idaho really late

00:46:33.994 --
tonight. My dad got all excited
how to wake all of us up. It

00:46:37.382 --
was like 3:00 o'clock in the
morning. 'cause one of the

00:46:40.044 --
towns we came from California
so this was a pretty cool

00:46:42.706 --
concept to us. 'cause it was
cute, neat. One of the towns

00:46:45.610 --
actually like listed on the
animals and I can't remember

00:46:48.030 --
what town it is but listed all
the animals, the cows, the

00:46:50.934 --
humans telling my dad had to
wake us all up. Look, look at

00:46:54.080 --
this look at this.

00:46:57.060 --
Alright, so small town that was
a small town, not as small as

00:47:01.038 --
this little town we're going to
deal with, so we're going to

00:47:04.710 --
sample the houses. And then
we're going to ask them.

00:47:11.280 --
How many?

00:47:13.980 --
TV's do you own?

00:47:20.060 --
All right, we're going to look
at all possible samples.

00:47:25.100 --
So if we just line 'em up.

00:47:29.080 --
One and two can be one of
the samples 'cause we're

00:47:31.621 --
taking samples of size 2.

00:47:34.540 --
Now we're obviously going to
assume something here that's

00:47:37.528 --
going to be kind of important
for us to talk about. Kind of

00:47:41.844 --
important. That's an
understatement.

00:47:44.660 --
Is that we're doing this?

00:47:49.350 --
Without replacement.

00:47:52.210 --
So what I'm doing here is
that when I choose a house,

00:47:56.086 --
it can no longer be chosen
for the observation #2. So

00:47:59.639 --
if it's been chosen for
observation number one, it

00:48:02.546 --
can't be chosen again for
observation #2, so we

00:48:05.453 --
couldn't go to the House
number one twice or House

00:48:08.683 --
number 2 twice, etc.

00:48:12.680 --
Now two and three can be
chosen, and this is all

00:48:15.969 --
possible samples. It's not
what we actually did, but

00:48:18.660 --
we're looking at the
possibilities.

00:48:21.830 --
I don't know. I like Roman
numerals. I always have it

00:48:24.888 --
thing from when I was a kid.
I apologize, but I'm not

00:48:28.224 --
that sorry.

00:48:31.500 --
So these are all possible
samples. We had six of them.

00:48:37.480 --
And that's where we get to pick

00:48:39.545 --
up next time. Figure out what
to do with this thing.

00:48:46.780 --
And that's it, and we will
finish this tomorrow or

00:48:49.910 --
finish this next class.