Aircraft Power Performance Curves
By Mike Andresen
In last month's article, "Cruise Speeds," we learned how optimal cruise speeds can be derived from an airplane's power and thrust performance curves. We also learned that cruise speeds could be optimized depending on the objective of the flight mission. In this article, I would like to discuss how to determine the performance curves for your airplane and what you can learn from it.
The power required for level flight performance curve is easily determined through flight testing. The data you need to collect is the engine power required for particular airspeeds from stall to cruise. Engine power is determined by manifold pressure and revolutions per minute (rpm) on a variable pitch propeller equipped engine, and by rpm alone on a fixed pitched propeller equipped engine. The conversion from manifold pressure and rpm to power is available in either your pilot operating manual or in the engine manual. If your airplane is fixed pitch equipped you can just record rpm versus airspeed and not worry about the conversion if you like.
The flight test itself is flown at constant altitude, varying the airspeed in 5 kt increments. I like to start at cruise speed and work my way down to stall. You will also need an estimate of the weight of the airplane during the test if you want to convert your power curves to thrust curves. If you want to precisely convert the engine parameters to power, you will also need to record your pressure altitude and outside air temperature.
This flight test should be performed at least four times and for each flap setting. The power versus airspeed is then averaged from all flights and plotted in a spreadsheet graph. You would like to think that your plot will look like the curve in a textbook but it will not. It takes precision flying, averaging over multiple flights, and graphical curve fitting to get a smooth looking graph like the one shown below from my RV-10 flight testing.
The lower end of the power curve is dominated by induced drag and the upper part of the curve is dominated by parasitic drag. As a force, induced drag is proportional to one over airspeed squared, and parasitic drag is proportional to airspeed squared. Total drag is equal to k1/V2 + k2 V2, where v is true airspeed and k1 and k2 are constants chosen to curve fit data to theoretical curves.
The first difference you will notice between the curves below and those in a textbook are that the real life curves don't span over all airspeeds. The lower limit of each curve is limited by the stall speed of the aircraft which is decreased with flap deployment. The upper end of each curve is limited by the maximum flap deployment speeds which also vary with flap settings. The VFE for each flap setting is not normally published for general aviation training aircraft but is for higher performance aircraft.
In previous month's articles we derived optimum climb and cruise speeds from the performance curves. We can now see that each of the V speeds are decreased as flap deflection is increased.
As flaps are deployed, more power is required to maintain level flight. Small initial flap deflections cause noticeable changes in lift without large changes in drag and hence only require small power increases. Larger flap deflections cause considerable changes in drag and require larger power increases. In any case, flap deployment requires more power and hence degrades climb performance (rate) which is a function of excess power.
- First 50% of flap deflection causes >50% total change in lift
- Last 50% of flap deflection causes >50% total change in drag