WEBVTT
Kind: captions
Language: en
00:00:13.870 --> 00:00:20.610
After women is over we now go for a cruise
experiment it has been the physics behind
00:00:20.610 --> 00:00:26.880
so that we understand what you are doing and
what you are looking for.
00:00:26.880 --> 00:00:30.000
.
And you know we want to estimate the drag
00:00:30.000 --> 00:00:38.180
polar CD knot +kcL2 essentially we are just
image CD knot +kcL2 and as long as for the
00:00:38.180 --> 00:00:45.329
low speed we are playing this parabolic equation
is valid form is valid we will put the CD
00:00:45.329 --> 00:00:53.770
knot +kcL2 as a drag polar of the air plane,
that is the purpose for the screws experiment.
00:00:53.770 --> 00:01:00.499
And why this is important you can understand
that depending upon the value of CD knot K
00:01:00.499 --> 00:01:07.170
the drag experienced by the airplane at a
given altitude and given speed will vary.
00:01:07.170 --> 00:01:13.979
You always want t CD knot to be as slow as
possible k should we ask you as possible for
00:01:13.979 --> 00:01:19.980
a given here right. You also know that, this
CD knot is because of pair is called Paris
00:01:19.980 --> 00:01:27.190
Hydra because of shape and the speed etc.
However this is primarily, this is the induced
00:01:27.190 --> 00:01:34.180
drag which is because of lift, and there is
a lift linking vertices which causes Windows
00:01:34.180 --> 00:01:39.670
track if you lifting to strike. So this is
primarily because of shape and this is family
00:01:39.670 --> 00:01:48.080
because of the lift. Now we want to estimate
the CD knot and you want to design an experiment
00:01:48.080 --> 00:01:52.310
which is known as in our terminology cruise
experiment.
00:01:52.310 --> 00:01:55.610
.
Let us develop the physics behind it, you
00:01:55.610 --> 00:02:13.470
know during cruise thrust=drag so what I can
write trust= half Rho v2 is CD knot +kcL2,
00:02:13.470 --> 00:02:23.560
no problem set forward. Now what is CL you
know lift=weight, so I can write half Rho
00:02:23.560 --> 00:02:42.330
v2 SCL=W this implies CL= 2w/ rho v2 s. At
least what I am cruising lift=weight, So this
00:02:42.330 --> 00:02:47.620
equation I have written this will tell me
how much CL are flying at a given altitude
00:02:47.620 --> 00:02:53.200
at a given speed for a given weight of the
airplane at cruise that is important right.
00:02:53.200 --> 00:03:07.640
So now what I do I write this as T=half Rho
v2 s CD knot+ k for CL I put it 2w/ rho v
00:03:07.640 --> 00:03:22.709
2 is whole square, Ok.CL 2 for CL I put this
expression, now I expand trust from the engine
00:03:22.709 --> 00:03:41.459
is equal to half Rho v2 is CD knot + half
Rho v2 is into k into 4w2 / Rho2 V to the
00:03:41.459 --> 00:03:43.129
power 4S2.
.
00:03:43.129 --> 00:03:55.680
Right, now do some simplification, if I do
some simplification, and find that let me
00:03:55.680 --> 00:04:09.670
write this thrust= half Rho v 2s CD knot plus
so this four and two becomes two, row is row1
00:04:09.670 --> 00:04:32.250
V squared + V squared X1 so this will be 2
k w2 / 2 k w2 / rho sv2 .Right we see this
00:04:32.250 --> 00:04:40.470
what is this T is the thrust available from
the engine that it was equal to drag experienced
00:04:40.470 --> 00:04:48.060
by the airplane that cruise trust is equal
to drag experienced by the range. Now what
00:04:48.060 --> 00:05:07.139
I do I multiply both sides by V what I have
half Rho V3 s into CD knot+2 k w 2 /by Rho
00:05:07.139 --> 00:05:17.740
s v 2 into V.
What had but this gives me T into V is equal
00:05:17.740 --> 00:05:37.530
to half Rho v q is CD knot+ 2 k w 2/ Rho s
v, correct. What is T into V, this was t was
00:05:37.530 --> 00:05:45.800
thrust available from the engine T into V
at during cruise means power available, right
00:05:45.800 --> 00:05:58.099
and this equal to half Rho v q s CD knot+
2 k w2 /Rho s v.
00:05:58.099 --> 00:06:06.650
.
So let me write this here, so I write p available
00:06:06.650 --> 00:06:30.800
is equal to half Rho v q s CD knot+ 2 KW 2/
Rho S V , just to make with familiar notation
00:06:30.800 --> 00:06:40.270
for power available I use a word letter BHP
brake horsepower allow me to write BHP for
00:06:40.270 --> 00:06:46.690
power available to give it a understanding
that it is coming from the brake horsepower
00:06:46.690 --> 00:07:00.350
from the engine .So this will be equal to
half Rho V3 s CD knot + 2 k w 2 /Rho s v.
00:07:00.350 --> 00:07:09.729
Now what I do I multiply left-hand side and
right hand side by V again so I get half Rho
00:07:09.729 --> 00:07:25.219
v half Rho s CD knot V4 + 2 k w2 /Rho s.
.
00:07:25.219 --> 00:07:35.571
Watch out for this expression, what is BHP
the information comes from the engine how
00:07:35.571 --> 00:07:45.940
we get V where from I get the V that is a
question comes from your airspeed indicator
00:07:45.940 --> 00:08:05.210
right, okay and you know that in the Air speed
indicator you get equivalent airspeed and
00:08:05.210 --> 00:08:15.380
what was equivalent air speed you know that
it is that speed or we write ½ RhoSLV2E=
00:08:15.380 --> 00:08:20.800
½ RhoairV2T .
How do you define equivalent air speed the
00:08:20.800 --> 00:08:26.039
suppose an airplane is flying at 10 kilometer
with some speed V it is experiencing some
00:08:26.039 --> 00:08:33.349
dynamic pressure which is equal to half Rho
altitude into V true there but if I want to
00:08:33.349 --> 00:08:39.750
fly the same airplane at a seal standard sea-level
condition duplicating the same dynamic pressure
00:08:39.750 --> 00:08:44.660
it was experiencing a 10-kilometer then that
speed was with the equivalent air speeders.
00:08:44.660 --> 00:08:47.620
.
I am equating the actual dynamic pressure
00:08:47.620 --> 00:08:51.720
have seen by the airplane equal to the dynamic
pressure at sea level condition standard sea
00:08:51.720 --> 00:08:58.260
level conditions and what is the speed equal
speed that is that v e are equal in speed,
00:08:58.260 --> 00:09:06.769
but we will be working with V true so I know
that V true equal to Rho C level standard
00:09:06.769 --> 00:09:18.880
by low altitude under root into VE. My Airspeed
indicator gives me air speed indicator in
00:09:18.880 --> 00:09:27.790
airplane gives me the equivalent, but I need
to use the true here so I will be using this
00:09:27.790 --> 00:09:32.540
relationship to get what is the true speed
for that low altitude.
00:09:32.540 --> 00:09:40.870
As I told you once you have outside air temperature
which you are recording then using P equal
00:09:40.870 --> 00:09:51.709
to Rho RT and standard atmosphere you will
be able to find out the Rho as P / RT and
00:09:51.709 --> 00:09:56.680
pressure comes from the altimeter reading
because altimeters are calibrated based on
00:09:56.680 --> 00:10:05.370
the static pressure atmospheric standard atmosphere
right. So no problem BHP comes from the engine
00:10:05.370 --> 00:10:11.209
and I told you the beginning most of such
engines which we have propeller-driven IC
00:10:11.209 --> 00:10:21.210
backup engine these parameters that will be
useful forgetting what is the actual power
00:10:21.210 --> 00:10:27.360
delivered by the engine under that condition
using the engine chart or a correlation.
00:10:27.360 --> 00:10:30.250
.
We need to or just measure RPM manifold pressure
00:10:30.250 --> 00:10:36.230
and outside air temperature while doing the
cruise experiments for rpm less rpm indicator
00:10:36.230 --> 00:10:40.810
or the manifold pressure the manifold pressure
indicator for outside air temperature this
00:10:40.810 --> 00:10:45.050
outside air temperature indicator in cockpit.
So you will get all those information right,
00:10:45.050 --> 00:10:51.290
so no issues on the BHP and no issue on of
the V Rho also you are smart so most of the
00:10:51.290 --> 00:10:56.220
thing w you know how to take the weight now
I have to use this relationship to get the
00:10:56.220 --> 00:11:04.260
value of CD knot and k so how do I plan my
experiment to use this relationship to get
00:11:04.260 --> 00:11:07.590
the value of CD knot and k let us focus on
that.
00:11:07.590 --> 00:11:13.459
This is the cruise experiment, so we start
from that we have come to this point and started
00:11:13.459 --> 00:11:25.510
cruising, so this is record as you start cruising
I take down what is the altitude note down
00:11:25.510 --> 00:11:33.449
the altitude from the altimeter reading and
also seeing the outside air temperature indicator
00:11:33.449 --> 00:11:41.050
I note down the outside air temperatures reading.
Now what happens you have to cruise the pilot
00:11:41.050 --> 00:11:54.370
will do, he will cruise at a speed V1 and
you have to note down RPM and manifold pressure,
00:11:54.370 --> 00:11:59.670
so once this cruise over aspire to say I will
go for another cruise at a different speed
00:11:59.670 --> 00:12:09.620
so again you have to note down RPM and manifold
pressure again V3 like this five or six points
00:12:09.620 --> 00:12:13.029
pilot will give you.
.
00:12:13.029 --> 00:12:20.880
So what are you going to do with this again
comeback here I need to know BHP or the power
00:12:20.880 --> 00:12:28.139
available from the engine I need only information
RPM manifold pressure and outside air temperature
00:12:28.139 --> 00:12:32.620
and there are engine correlation supplied
by the manufacturer I can use that and find
00:12:32.620 --> 00:12:39.450
out how much power the universe delivering
the horsepower black horse power available.
00:12:39.450 --> 00:12:44.010
We know from airspeed indicator but you also
know that is equivalent air speed so we are
00:12:44.010 --> 00:12:50.880
converting into the true airspeed okay.
Now if I know these measurements what I will
00:12:50.880 --> 00:13:03.570
do that is more important watch if you see
that equation if I plot V4 and BHP into V
00:13:03.570 --> 00:13:11.769
what sort of relationship it will have BHP
into V I call it y. V 4 I call it X ,so half
00:13:11.769 --> 00:13:17.570
Rho s CD knot into x+ this I call C.
.
00:13:17.570 --> 00:13:24.720
So this is typically y equal to MX plus C,
so if I plot BHP into V and V to the power
00:13:24.720 --> 00:13:32.542
4 then I am expected to get straight line
is this part clear, okay. So what we will
00:13:32.542 --> 00:13:41.490
do I pick up v1 I will take RPM and manifold
pressure and I will compute BHP using outside
00:13:41.490 --> 00:13:42.490
air temperature also.
.
00:13:42.490 --> 00:13:47.560
So this is available this is available this
is available to see available so for a particular
00:13:47.560 --> 00:13:54.550
v I find how much is this BHP into V that
is important one point will come here and
00:13:54.550 --> 00:13:58.149
one will come here and we will come here something
like this happen and then you have you know
00:13:58.149 --> 00:14:03.759
it will be best wicked by straight line because
that is what the physics tells you it will
00:14:03.759 --> 00:14:09.160
be best fitted by straight line.
So do the best fit straight line and this
00:14:09.160 --> 00:14:17.149
intercept whatever you get that will reflect
the A and the slope whatever you get to measurement
00:14:17.149 --> 00:14:25.010
let us say this B then I know A is equal to
whatever I get from the graph is equal to
00:14:25.010 --> 00:14:39.340
2 K W2/ Rho S and B equal to the slope which
is equal to half Rho s CD knot correct please
00:14:39.340 --> 00:14:45.370
understand the A and B we are getting from
the plot right after plotting the experimental
00:14:45.370 --> 00:14:47.180
results there.
.
00:14:47.180 --> 00:14:57.670
Once I know this my aim was to find k so k
will be A Rho s / 2 w2 and CD knot will be
00:14:57.670 --> 00:15:07.199
equal to 2B/Rho s ,as simple as that. So get
the value of K you get the value of CD knot
00:15:07.199 --> 00:15:14.560
so now you postulate the drag polar of this
experiment is or the airplane is CD knot+
00:15:14.560 --> 00:15:22.569
k CL2 where you have estimated CD knot and
k by going through this experimental procedure
00:15:22.569 --> 00:15:23.569
clear.
.
00:15:23.569 --> 00:15:31.440
So this is what is the first cruise experiment
and also understand, once I know the CD knot+
00:15:31.440 --> 00:15:41.240
k CL2 that is once I know what is the drag
polar of the airplane through this experiment
00:15:41.240 --> 00:15:52.540
I can easily calculate power required at different
speed and that is given as half Rho v2 s half
00:15:52.540 --> 00:16:09.589
Rho V3 s into CD knot + k CL2 and CL equal
to 2 w/ rho v 2 s so what you can do offline
00:16:09.589 --> 00:16:16.029
you can easily plot power required versus
velocity or speed please understand.
00:16:16.029 --> 00:16:21.459
Now the CD knot value and k value you have
already estimated from that experiment so
00:16:21.459 --> 00:16:26.610
you know this CD knot and k for different
different altitudes where ever you want a
00:16:26.610 --> 00:16:32.230
different speed you can plot for required
versus V and you will see it will follow this
00:16:32.230 --> 00:16:36.660
sort of a trend which you have studied in
your classroom right.
00:16:36.660 --> 00:16:41.760
.
And then if you want to find out if small
00:16:41.760 --> 00:16:48.490
available was this let us say of a engine
if this is power available then you can find
00:16:48.490 --> 00:16:58.210
out what is the speed at which rate of climb
will be maximum, I repeat again a CD knot
00:16:58.210 --> 00:17:03.509
and K you have estimated from flight test
now you are finding power required and the
00:17:03.509 --> 00:17:11.940
plotting the power required here, now for
different engine setting you want to check
00:17:11.940 --> 00:17:19.010
how much rate of climb it can have so I can
easily use this plot to find our rate of climb
00:17:19.010 --> 00:17:21.730
and how to do that what is the physics behind
this.
00:17:21.730 --> 00:17:25.949
.
Let me discuss so that you are comfortable,
00:17:25.949 --> 00:17:31.760
I am sure you have done all these things and
this things will be on your fingertips. Remember
00:17:31.760 --> 00:17:50.210
this diagram this is the air plane, this is
the trust this is the weight the lift and
00:17:50.210 --> 00:18:04.070
drag so we wrote for a steady climb that is
climbing at the constant speed, I write the
00:18:04.070 --> 00:18:16.039
equation like this along the V direction.
This is V direction T-D-W sine gamma equal
00:18:16.039 --> 00:18:25.799
to M DV/ DT for gamma you know the flight
path angle but for a steady climb this gentleman
00:18:25.799 --> 00:18:35.549
will become 0 ,so I write this equal to zero,
so what you get T- D is equal to W sine gamma
00:18:35.549 --> 00:18:42.700
or T into V minus D into V by W is equal to
v sine gamma.
00:18:42.700 --> 00:18:46.409
.
These are all stuff I am sharing with you
00:18:46.409 --> 00:18:53.280
multiply by v and then divided by w what is
the sine gamma if you recall if the gentleman
00:18:53.280 --> 00:19:02.140
is going with v here V sine gamma is the vertical
component so this is typically is the rate
00:19:02.140 --> 00:19:13.240
of climb okay ,right. So now I can write the
rate of climb is equal to TV minus DV by w
00:19:13.240 --> 00:19:23.360
so now here you see TV minus DV, DV minus
DV is what its power available minus power
00:19:23.360 --> 00:19:28.460
required so from this graph you could see
this is all available power required so at
00:19:28.460 --> 00:19:35.730
different speed this excess power which is
difference between power available and power
00:19:35.730 --> 00:19:40.860
requirement is going on changing in fact it
goes on increasing comes to maximum then again
00:19:40.860 --> 00:19:45.159
goes on decreasing right.
So with this graph you should be able to see
00:19:45.159 --> 00:19:51.690
what is that speed like the v-star activation
to the excess power is maximum so that time
00:19:51.690 --> 00:19:56.890
you should give this v-star should crush on
to rate of climb maximum and that will take
00:19:56.890 --> 00:20:01.230
you this part are clear.
.
00:20:01.230 --> 00:20:07.140
This is the excess power and you can see this
excess power is gradually increasing then
00:20:07.140 --> 00:20:12.500
again decreasing so there is a point v star
where this excess power is the maximum as
00:20:12.500 --> 00:20:17.950
his excess power related to rate of climb
for this v-star respond to a rate of ground
00:20:17.950 --> 00:20:25.290
maximum for that attitude okay these are understanding.
So you do it offline now we experiment which
00:20:25.290 --> 00:20:34.640
I call climb experiment will essentially see
how to get this v-star through experiment.
00:20:34.640 --> 00:20:42.970
Again once cruise is over, we say now going
for the climb experiment as a ritual note
00:20:42.970 --> 00:20:51.090
down the altitude note down the outside air
temperature, now this is a V unless the pilot
00:20:51.090 --> 00:20:59.200
says I am climbing so note down the is H1
note down what is h2 once he says that my
00:20:59.200 --> 00:21:00.480
climb is over.
.
00:21:00.480 --> 00:21:10.029
So I said V1 is climbing ,this is h1 this
is h2 where he says I stop climbing and now
00:21:10.029 --> 00:21:19.880
you note down what is the time taken to go
from H1 to H2 .Does he stop off nor does people
00:21:19.880 --> 00:21:27.950
use the mobile so you could see that rate
of climb approximately will be equal to delta
00:21:27.950 --> 00:21:34.950
h by delta T if you see my earlier notes this
is approximate values it is not very accurate
00:21:34.950 --> 00:21:41.789
because the altimeter is calibrated instead
most fears so because refer back to my notes
00:21:41.789 --> 00:21:46.880
there is a correction of ratio of densities
to be applied but mostly we had conduct experiment
00:21:46.880 --> 00:21:52.429
within thousand feet so that difference is
not much but fundamentally should know I refer
00:21:52.429 --> 00:21:55.330
back to my performance lecture.
.
00:21:55.330 --> 00:22:04.950
On this similarly pilot again will carry out
another climb at different climb defendant
00:22:04.950 --> 00:22:12.770
speed so have delta H by delta T different
values of delta H by delta T for corresponding
00:22:12.770 --> 00:22:20.039
to different speeds once you have that, once
you have that life is simple what you will
00:22:20.039 --> 00:22:29.320
do we will just cross the plot rate of climb
which you have obtained three experiment to
00:22:29.320 --> 00:22:30.920
this column.
.
00:22:30.920 --> 00:22:43.779
And we plot this plot will come like this
and join them and this is the point if you
00:22:43.779 --> 00:22:52.029
see where rate of climb is maximum cycle exist
are and to that experiment whatever v star
00:22:52.029 --> 00:22:57.250
you get and through this theory whatever you
get this v-star are and that v- star should
00:22:57.250 --> 00:23:05.179
be closed. Then yes whatever physics we have
got that is getting validated. So this is
00:23:05.179 --> 00:23:11.080
one of the experimenter are called to climb
experiment you can conduct these experiments
00:23:11.080 --> 00:23:18.350
at different altitudes and then find out service
selling okay but we do not do it here but
00:23:18.350 --> 00:23:26.730
you should know this you can do extend this
experiment to get service selling etc. right.
00:23:26.730 --> 00:23:33.909
I hope I have made it clear what we will be
doing after this how to take away that the
00:23:33.909 --> 00:23:39.450
physical demonstration where students from
MIT Chennai will be conducted be participating
00:23:39.450 --> 00:23:45.130
in web and experiment similarly will be doing
some cruise experiment some videos will show
00:23:45.130 --> 00:23:51.580
you how to take the readings and how to do
the calculation this is I told lose 10 hours
00:23:51.580 --> 00:23:58.299
module just to warming you up how to conduct
experiments. And once you are happy will try
00:23:58.299 --> 00:24:08.120
to see that as you present return to invite
to all of you here and do the experiment yourself
00:24:08.120 --> 00:24:12.870
thank you very much.