mike andresenAircraft 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. 

performancecurves1

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.

In General:

  • First 50% of flap deflection causes >50% total change in lift
  • Last 50% of flap deflection causes >50% total change in drag 

performancecurves2

Now that you have reached your cruise altitude, you can switch off the fasten seatbelt sign and take a moment to relax. If you are in a technologically advanced airplane, or carrying a tablet, you are probably looking at multi-colored LCDs throwing all sorts of information at you. My Electronic Flight Information System has readouts of fuel flow, range, miles-per-gallon and indicated/true/ground speeds. Is there a way to minimize fuel flow, maximize MPG, and maximize airspeed all at once? Probably not, but we will explore the factors effecting each and some other performance metrics that we may not normally think about.

 

Maximum Time Aloft

The airplane's time aloft or endurance is its fuel on board (gal) divided by fuel flow (gph). To maximize time aloft, one must maximize fuel capacity and minimize fuel flow. Fuel flow is minimized by using the least amount of power to sustain flight. This is the bottom of the power required for level flight curve. On an endurance flight, as fuel is consumed and the airplane weight decreases the minimum power required will decrease and the throttle can be reduced. To fly for maximum endurance, you will be flying really slow, at or near your Vx speed, so this is rarely done in general aviation. An example of when this would be useful is on an observation mission where the airplane needs to remain on station for the longest possible time.

 

Best Miles per Gallon, Best Range Speed

This probably gets your attention because now we are talking about saving money. The best miles per gallon will result in the maximum range of the airplane. Another way to express it is that this cruise speed will use the least amount of fuel for a given trip distance. The fuel used on a trip depends on fuel flow and the time it takes to make the trip. So now we need to minimize fuel flow (keep power low) but make the trip fast enough to use as little fuel as possible (keep power high!). The middle ground is found at the bottom of the L/D curve of the airplane and is close to, if not the same as, the Vy speed. In the interest of saving fuel, we get to fly a little faster but still at a relatively slow airspeed.

 

Best Speed per Gallon

Optimum cruise speed was derived by B.H. Carson of the U.S. Naval Academy in 1980. For those of you that can remember back that far, this was after the oil embargo. Suddenly the country was focused on the fuel efficiency of cars and airplanes. Carson addressed the question of using miles-per-gallon as the optimizing metric for airplanes. He noted that for airplanes the speed for optimum fuel efficiency was quite slow and utilized only a small percentage of the airplane's available horse power. Instead he derived a new metric, the optimum cruise speed which maximizes the speed of the airplane relative to fuel flow. It is the best speed per gallon-per-hour ratio that can be achieved. The optimum cruise speed that he derived is 1.32 times the best miles-per gallon speed. It is a bit more practical than flying at best range speed.

 

Here are the V speeds discussed in this article derived from the performance charts I measured during the flight test period of my RV-10. The blue line is the thrust required for level flight and is read from the axis on the left in pounds. The red line is the power required for level flight and is read from the vertical axis on the right in horsepower. The maximum endurance speed is a very slow 70 KIAS and only requires 57 horsepower from the 260 horsepower engine. The maximum range speed is 90 KIAS and requires about 100 horsepower. The optimum cruise speed is 120 KIAS, still somewhat slow, but better, and requires around 120 horse power - still only 46% power.

 

Next month we will discuss how to determine these performance curves for an airplane through flight testing.

 

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