How to Calculate Speed and Propeller Efficiency

These formulas are simply presented for your amusement.  You do not need to know this math or ever work these problems unless you are a speed freak or just like playing with numbers.

Also see

• Model Aircraft Propellers

Calculating Theoretical Speed

Theoretical speed means that the propeller is 100% efficient and that there is no loss due to aerodynamic drag, etc.  A perfect airplane flying in a perfect world.  That's not going to happen here on earth, but this still gives you a starting point.

For this example we'll use an engine turning a 7" pitch propeller at 15,000 RPM.

Convert Revolutions Per Minute (RPM) to Revolutions Per Hour (RPH):

RPM x 60 = RPH

15,000 x 60 = 900,000 RPH

Find Inches Per Hour assuming 100% efficiency:

RPH x Propeller Pitch = Inches per Hour

900,000 x 7 = 6300000 inches per hour

Convert to Miles Per Hour (12" x 5280' = inches in a mile):

6300000 ÷  (12 x 5280) = 99.4 MPH

The bottom line (assuming 100% propeller efficiency and zero airframe drag):

Speed = ( RPM x Pitch ) ÷ 1056

In reality the average sport model with this combination might do 75-80 MPH on a good day.

Calculating Propeller Efficiency

Going a little farther, we can actually set up a speed trial to determine how fast an aircraft is going and then determine propeller efficiency using those numbers (time over distance).

So let's say you time your aircraft on a 100 yard (300 feet) course (upwind and downwind to make it even).  The average time is 2.7 seconds.

Convert the distance covered to miles by dividing distance covered in feet by number of feet in a mile.  There are 5,280 feet in a mile.

300 ÷ 5280 = .0568 miles

Convert elapsed time to hours by dividing time in seconds by seconds in an hour.  There are 3600 seconds in an hour.

2.7 ÷ 3600 = .00075 hours

Find Miles Per Hour:

.0568 ÷ .00075 = 75.7 mph

If our timer was accurate and the distance is accurate then that speed will be accurate.  An easier way is to use a radar gun, but then you don't get to do all this fun math.

Going back to the previous example, let's determine the overall loss of efficiency and then, for convenience, blame it all on the propeller.

Divide actual speed by the theoretical speed using a 100% efficient propeller and an aircraft having zero drag:

75.7 ÷ 99.4 = 76.16% efficiency

Unless we have an onboard tachometer, we do not really know what the RPM of the engine is.  Also, the lack of efficiency could very easily be attributed to the airframe design - not necessarily the fault of the propeller.  Still, it is something to play around with if you are so inclined.

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Copyright © 2003 Paul K. Johnson