# How can I get the velocity-power curve for a particular aircraft?

The answer for How does wind affect the airspeed that I should fly for maximum range in an airplane? refers to a velocity/power-required curve.

As far as I can tell, this curve can't be deduced from information in the flight manual.

I suppose one could experiment and determine what power setting is required in order to maintain level flight at a bunch of airspeeds (or for a glider, record the sink rate, which is proportional to the negative of the power-required, at a bunch of airspeeds). Would that be accurate enough? Are these curves available from the manufacturer?

• I would expect the curve to be included in the flight manual. Several of them, for different weights, in fact. – Jan Hudec Apr 30 '14 at 17:43
• @JanHudec Are they though? If so, please write that as an answer. None of the aircraft I have flown have included this curve in the flight manual. – user2168 Apr 30 '14 at 17:51
• I don't know. I don't have any actual pilot operating handbook around. – Jan Hudec Apr 30 '14 at 17:58
• @JanHudec Yeah, you would think that. Unfortunately, I haven't seen this chart in an AFM or POH either. – Lnafziger Apr 30 '14 at 18:19
• @Lnafziger: And have you seen newer avionics displaying the relevant $V_x$/$V_y$ as appropriate? The "green dot" speed in Airbus is supposed to be this, so the avionics would have to know the power curve. – Jan Hudec Apr 30 '14 at 19:03

You are right, this curve has to be tested. Of course, during development a lot of simulation and wind tunnel testing is done to get the power required, but it still needs to be confirmed in flight test. The interaction of power plant and airframe can be quite complex, and only testing will ensure that the data is correct.

If it is not part of the manual, the plane's manufacturer will certainly have the power curves. Did you ask them for the data? And I would expect that you will find some data points in any handbook which will allow you to approximate the power curve. Start from the trim condition (basically, thrust equals drag) and calculate the curve with the help of a parabolic polar. Like that:

$$T = c_D\cdot q\cdot S$$

$$P = T\cdot v = (c_{D0} + \frac{c_L^2}{\pi\cdot AR\cdot\epsilon})\cdot v^3\cdot\frac{\rho}{2}\cdot S$$

Of course, now you need to get the zero-lift drag coefficient $c_{D0}$ somehow from one datapoint in the manual. Same goes for values like propeller efficiency or intake losses, because the listed power of the engine will not be what is effectively employed to generate thrust.

Nomenclature:
$T$ thrust
$v$ airspeed
$q$ dynamic pressure
$\rho$ air density
$S$ wing area
$c_L$ lift coefficient
$AR$ aspect ratio of the wing
$\epsilon$ the wing's Oswald factor