After women is over we now go for a cruise experiment it has been the physics behind
so that we understand what you are doing and what you are looking for.
. And you know we want to estimate the drag
polar CD knot +kcL2 essentially we are just image CD knot +kcL2 and as long as for the
low speed we are playing this parabolic equation is valid form is valid we will put the CD
knot +kcL2 as a drag polar of the air plane, that is the purpose for the screws experiment.
And why this is important you can understand that depending upon the value of CD knot K
the drag experienced by the airplane at a given altitude and given speed will vary.
You always want t CD knot to be as slow as possible k should we ask you as possible for
a given here right. You also know that, this CD knot is because of pair is called Paris
Hydra because of shape and the speed etc. However this is primarily, this is the induced
drag which is because of lift, and there is a lift linking vertices which causes Windows
track if you lifting to strike. So this is primarily because of shape and this is family
because of the lift. Now we want to estimate the CD knot and you want to design an experiment
which is known as in our terminology cruise experiment.
. Let us develop the physics behind it, you
know during cruise thrust=drag so what I can write trust= half Rho v2 is CD knot +kcL2,
no problem set forward. Now what is CL you know lift=weight, so I can write half Rho
v2 SCL=W this implies CL= 2w/ rho v2 s. At least what I am cruising lift=weight, So this
equation I have written this will tell me how much CL are flying at a given altitude
at a given speed for a given weight of the airplane at cruise that is important right.
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
2 is whole square, Ok.CL 2 for CL I put this expression, now I expand trust from the engine
is equal to half Rho v2 is CD knot + half Rho v2 is into k into 4w2 / Rho2 V to the
power 4S2. .
Right, now do some simplification, if I do some simplification, and find that let me
write this thrust= half Rho v 2s CD knot plus so this four and two becomes two, row is row1
V squared + V squared X1 so this will be 2 k w2 / 2 k w2 / rho sv2 .Right we see this
what is this T is the thrust available from the engine that it was equal to drag experienced
by the airplane that cruise trust is equal to drag experienced by the range. Now what
I do I multiply both sides by V what I have half Rho V3 s into CD knot+2 k w 2 /by Rho
s v 2 into V. What had but this gives me T into V is equal
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
thrust available from the engine T into V at during cruise means power available, right
and this equal to half Rho v q s CD knot+ 2 k w2 /Rho s v.
. So let me write this here, so I write p available
is equal to half Rho v q s CD knot+ 2 KW 2/ Rho S V , just to make with familiar notation
for power available I use a word letter BHP brake horsepower allow me to write BHP for
power available to give it a understanding that it is coming from the brake horsepower
from the engine .So this will be equal to half Rho V3 s CD knot + 2 k w 2 /Rho s v.
Now what I do I multiply left-hand side and right hand side by V again so I get half Rho
v half Rho s CD knot V4 + 2 k w2 /Rho s. .
Watch out for this expression, what is BHP the information comes from the engine how
we get V where from I get the V that is a question comes from your airspeed indicator
right, okay and you know that in the Air speed indicator you get equivalent airspeed and
what was equivalent air speed you know that it is that speed or we write ½ RhoSLV2E=
½ RhoairV2T . How do you define equivalent air speed the
suppose an airplane is flying at 10 kilometer with some speed V it is experiencing some
dynamic pressure which is equal to half Rho altitude into V true there but if I want to
fly the same airplane at a seal standard sea-level condition duplicating the same dynamic pressure
it was experiencing a 10-kilometer then that speed was with the equivalent air speeders.
. I am equating the actual dynamic pressure
have seen by the airplane equal to the dynamic pressure at sea level condition standard sea
level conditions and what is the speed equal speed that is that v e are equal in speed,
but we will be working with V true so I know that V true equal to Rho C level standard
by low altitude under root into VE. My Airspeed indicator gives me air speed indicator in
airplane gives me the equivalent, but I need to use the true here so I will be using this
relationship to get what is the true speed for that low altitude.
As I told you once you have outside air temperature which you are recording then using P equal
to Rho RT and standard atmosphere you will be able to find out the Rho as P / RT and
pressure comes from the altimeter reading because altimeters are calibrated based on
the static pressure atmospheric standard atmosphere right. So no problem BHP comes from the engine
and I told you the beginning most of such engines which we have propeller-driven IC
backup engine these parameters that will be useful forgetting what is the actual power
delivered by the engine under that condition using the engine chart or a correlation.
. We need to or just measure RPM manifold pressure
and outside air temperature while doing the cruise experiments for rpm less rpm indicator
or the manifold pressure the manifold pressure indicator for outside air temperature this
outside air temperature indicator in cockpit. So you will get all those information right,
so no issues on the BHP and no issue on of the V Rho also you are smart so most of the
thing w you know how to take the weight now I have to use this relationship to get the
value of CD knot and k so how do I plan my experiment to use this relationship to get
the value of CD knot and k let us focus on that.
This is the cruise experiment, so we start from that we have come to this point and started
cruising, so this is record as you start cruising I take down what is the altitude note down
the altitude from the altimeter reading and also seeing the outside air temperature indicator
I note down the outside air temperatures reading. Now what happens you have to cruise the pilot
will do, he will cruise at a speed V1 and you have to note down RPM and manifold pressure,
so once this cruise over aspire to say I will go for another cruise at a different speed
so again you have to note down RPM and manifold pressure again V3 like this five or six points
pilot will give you. .
So what are you going to do with this again comeback here I need to know BHP or the power
available from the engine I need only information RPM manifold pressure and outside air temperature
and there are engine correlation supplied by the manufacturer I can use that and find
out how much power the universe delivering the horsepower black horse power available.
We know from airspeed indicator but you also know that is equivalent air speed so we are
converting into the true airspeed okay. Now if I know these measurements what I will
do that is more important watch if you see that equation if I plot V4 and BHP into V
what sort of relationship it will have BHP into V I call it y. V 4 I call it X ,so half
Rho s CD knot into x+ this I call C. .
So this is typically y equal to MX plus C, so if I plot BHP into V and V to the power
4 then I am expected to get straight line is this part clear, okay. So what we will
do I pick up v1 I will take RPM and manifold pressure and I will compute BHP using outside
air temperature also. .
So this is available this is available this is available to see available so for a particular
v I find how much is this BHP into V that is important one point will come here and
one will come here and we will come here something like this happen and then you have you know
it will be best wicked by straight line because that is what the physics tells you it will
be best fitted by straight line. So do the best fit straight line and this
intercept whatever you get that will reflect the A and the slope whatever you get to measurement
let us say this B then I know A is equal to whatever I get from the graph is equal to
2 K W2/ Rho S and B equal to the slope which is equal to half Rho s CD knot correct please
understand the A and B we are getting from the plot right after plotting the experimental
results there. .
Once I know this my aim was to find k so k will be A Rho s / 2 w2 and CD knot will be
equal to 2B/Rho s ,as simple as that. So get the value of K you get the value of CD knot
so now you postulate the drag polar of this experiment is or the airplane is CD knot+
k CL2 where you have estimated CD knot and k by going through this experimental procedure
clear. .
So this is what is the first cruise experiment and also understand, once I know the CD knot+
k CL2 that is once I know what is the drag polar of the airplane through this experiment
I can easily calculate power required at different speed and that is given as half Rho v2 s half
Rho V3 s into CD knot + k CL2 and CL equal to 2 w/ rho v 2 s so what you can do offline
you can easily plot power required versus velocity or speed please understand.
Now the CD knot value and k value you have already estimated from that experiment so
you know this CD knot and k for different different altitudes where ever you want a
different speed you can plot for required versus V and you will see it will follow this
sort of a trend which you have studied in your classroom right.
. And then if you want to find out if small
available was this let us say of a engine if this is power available then you can find
out what is the speed at which rate of climb will be maximum, I repeat again a CD knot
and K you have estimated from flight test now you are finding power required and the
plotting the power required here, now for different engine setting you want to check
how much rate of climb it can have so I can easily use this plot to find our rate of climb
and how to do that what is the physics behind this.
. Let me discuss so that you are comfortable,
I am sure you have done all these things and this things will be on your fingertips. Remember
this diagram this is the air plane, this is the trust this is the weight the lift and
drag so we wrote for a steady climb that is climbing at the constant speed, I write the
equation like this along the V direction. This is V direction T-D-W sine gamma equal
to M DV/ DT for gamma you know the flight path angle but for a steady climb this gentleman
will become 0 ,so I write this equal to zero, so what you get T- D is equal to W sine gamma
or T into V minus D into V by W is equal to v sine gamma.
. These are all stuff I am sharing with you
multiply by v and then divided by w what is the sine gamma if you recall if the gentleman
is going with v here V sine gamma is the vertical component so this is typically is the rate
of climb okay ,right. So now I can write the rate of climb is equal to TV minus DV by w
so now here you see TV minus DV, DV minus DV is what its power available minus power
required so from this graph you could see this is all available power required so at
different speed this excess power which is difference between power available and power
requirement is going on changing in fact it goes on increasing comes to maximum then again
goes on decreasing right. So with this graph you should be able to see
what is that speed like the v-star activation to the excess power is maximum so that time
you should give this v-star should crush on to rate of climb maximum and that will take
you this part are clear. .
This is the excess power and you can see this excess power is gradually increasing then
again decreasing so there is a point v star where this excess power is the maximum as
his excess power related to rate of climb for this v-star respond to a rate of ground
maximum for that attitude okay these are understanding. So you do it offline now we experiment which
I call climb experiment will essentially see how to get this v-star through experiment.
Again once cruise is over, we say now going for the climb experiment as a ritual note
down the altitude note down the outside air temperature, now this is a V unless the pilot
says I am climbing so note down the is H1 note down what is h2 once he says that my
climb is over. .
So I said V1 is climbing ,this is h1 this is h2 where he says I stop climbing and now
you note down what is the time taken to go from H1 to H2 .Does he stop off nor does people
use the mobile so you could see that rate of climb approximately will be equal to delta
h by delta T if you see my earlier notes this is approximate values it is not very accurate
because the altimeter is calibrated instead most fears so because refer back to my notes
there is a correction of ratio of densities to be applied but mostly we had conduct experiment
within thousand feet so that difference is not much but fundamentally should know I refer
back to my performance lecture. .
On this similarly pilot again will carry out another climb at different climb defendant
speed so have delta H by delta T different values of delta H by delta T for corresponding
to different speeds once you have that, once you have that life is simple what you will
do we will just cross the plot rate of climb which you have obtained three experiment to
this column. .
And we plot this plot will come like this and join them and this is the point if you
see where rate of climb is maximum cycle exist are and to that experiment whatever v star
you get and through this theory whatever you get this v-star are and that v- star should
be closed. Then yes whatever physics we have got that is getting validated. So this is
one of the experimenter are called to climb experiment you can conduct these experiments
at different altitudes and then find out service selling okay but we do not do it here but
you should know this you can do extend this experiment to get service selling etc. right.
I hope I have made it clear what we will be doing after this how to take away that the
physical demonstration where students from MIT Chennai will be conducted be participating
in web and experiment similarly will be doing some cruise experiment some videos will show
you how to take the readings and how to do the calculation this is I told lose 10 hours
module just to warming you up how to conduct experiments. And once you are happy will try
to see that as you present return to invite to all of you here and do the experiment yourself
thank you very much.