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Aircraft Performance

"Cubic inches make the world go around".
That had been my credo until gasoline prices made me take a more serious look at the performance and efficiency of my Mustang II.

How well does your airplane perform on the power it has and uses?

To find out exactly where your airplane performs best you need to go through a relatively simple set of flight tests. Required is the weight of your airplane, a stop watch and some graph paper. A bit of simple number crunching on a calculator and you'll have some intimate knowledge of the performance characteristics of your airplane.

The first exercise is to measure carefully the rate of sink at various airspeeds. On my airplane I tried this at every 10 mph from 70 to 130 mph. The resulting curve looked like this:

Sink rate curve

Next, calculate the Lift Drag ratio (L/D) at the various speeds. Divide the airspeed by the vertical speed and, presto, you obtain the L/D at that speed. To make this work you need to convert both speeds to the same units, however. So, let's convert vertical speed from ft/ min to MPH. That is an unusual unit for speed to use for vertical speed because our VSIs are not calibrated in MPH but in ft/min. But then airspeed in ft/sec is not the usual calibration either. Aviation is such a fun activity we mix Metric Units with English units, and then hash all those around, just to protect the mystery of flight. Anyway, you need to convert by multiplying the vertical speed in ft/min by 0.01136 that gives you vertical speed in MPH. Don't worry about this, it is all in the interest of science and saving dollars in fuel. For example, let's say that your sink rate is 750 ft/min at 85 mph. To work out the L/D, you do the following: Multiply 750 ft/min x .01136. That is 8.52 MPH . Now divide the airspeed of 85 MPH by 8.52 MPH. You get an L/D of 10. In other words, at 85 mph airspeed your airplane has an L/D of about 10. So, if you are on a 1 mile final you should be about 550' up, no wind. If you do these calculations at the various speeds, you end up with a curve which will look something like this:

Lift - drag cureve

The curve shows that the airplane is most efficient at 85 mph. All other speeds will burn more fuel to obtain a given airspeed.

Now the interesting stuff starts. Let's say you were interested in the Horsepower required to fly at various speeds. Because you now know how much power the airplane consumes while gliding, you know the power required to fly it level at that speed- they are equal. The formula used for finding the numbers to plot on the graph below are obtained by using the formula:

HP = (Sink rate (mph) x Wt) / 377

If the airplane during your tests weighed 1000 lb, and using the L/D of 10 you calculated before at 85 mph, you would calculate the horsepower required at that speed to be 31 HP. Crunching the numbers at other airspeeds, using the changing L/D values, yields a graph resembling this:

Hp vs airspeed curve 1

This graph shows the typical "back side of the power curve" below 85 mph and it indicates that at full power you will never get beyond 130 mph, unless you trade altitude for speed.

If on the same graph above you could also plot the power available from your propeller-engine combination, you could establish the speed at which you would have maximum rate of climb. Those numbers are, however, not easy to come by. Typically, it might look something like this:

Hp vs airspeed curve 2

Where the difference in vertical distance between the upper curve and the lower curve is greatest is where the biggest reserve of horsepower occurs presumably the highest rate of climb. The graph above shows that to be around 90 mph. At 130 mph there is no reserve of power because it is all used to overcome the drag maximum level flight speed.

Because the airplane's efficiency varies with speed, the maximum efficiency (highest L/D) occurs at only one speed, you could calculate the range at various speeds, no wind. To do this you will need the fuel consumption figures from the engine manufacturer. They usually provide good data in their Operator's Manual for your engine. Plotting that fuel burn data at various power settings against the horsepower required at various speeds from the previous graph allows you to derive a curve which resembles the following:

Airspeed vs range curve

Flying too slow or too fast costs you range. It is important to note that the specific speeds you obtain for any of this data discussed here is changed by altitude and weight variations. Done properly, you would have various lines on each graph for differing altitudes and weights. For range, of course, you need to take wind into account.

For those of you who want to be precise at the outset when gathering your data for the initial graph - the sink speeds - you need to calculate what the zero thrust RPM for your propeller is at various speeds. In other words, say you have a 60 (5ft) pitch prop, at 85 mph that prop should turn at 1495 RPM to produce neither thrust or drag. At idle power it will likely show fewer than 1495 RPM at 85 mph, which means the air rushing past the prop is helping to turn it. That means drag not attributable to the airframe but specifically to the windmilling prop. So you want to add enough power during your glide tests to keep the RPM at 1495. (Of course you had your RPM indicator calibrated at the last Annual as per CARs 625 Appendix C). You'll need to calculate what the zero-thrust RPM is at various airspeeds and create a chart to use during tests, if you wish to do this really accurately. The end result will be a very good picture of how clean aerodynamically your airplane is. It would be real interesting to compare your numbers with those of a friend using a similar airplane. I also wonder what impact piloting skills have on these numbers.

Have fun

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Frank Hofmann, AME
Retired Prof. Of Aircraft Maintenance
EAA Technical Counsellor
Copyright © 2003