How To Determine The Part-Throttle RPM of a Fixed Pitch Propeller At a Given Horsepower
by
Stan Hall
Technical Advisor, Engineering, EAA Chapter 62

To get the most life from an aircraft engine while at the same time getting acceptable airplane performance the engine manufacturers commonly recommend their engines not be operated continuously over 75% of their full throttle rpm. We have thus come to accept this rpm as a standard "cruising" rpm.

The problem is, how does the pilot of an airplane equipped with a fixed pitch prop know when he is pulling 75% since the only power-related instrument he has is the tachometer and the tach doesn't tell him directly?.

So, the question arises, to throttle back to 75% power should he come back 25% of the distance the cockpit control provides? No, because the only point on the throttle he knows at least roughly what the power is, is full throttle. Or, should he throttle back to 75% rpm as shown by the tach? No again because the relationship between prop rpm and engine rpm is far from linear. It is, in fact, exponential. The power absorbed by a fixed pitch propeller is proportional to the cube of its rpm. Thus, if he reduces the rpm by a quarter he can expect a power reduction of almost a third - and an IAS far less than he had anticipated.

But the tach can indicate the power - you can mark it. A way to determine where to put the tach to yield a 25% power reduction is to refer to the graph shown here. Enter the full throttle (F.T.) level flight prop rpm on the left and draw a horizontal line to the right to intersect with the line labelled 75% F.T. hp then down. Read the part-throttle rpm at the bottom. An example using the Super Cub PA-18-150 is shown. At 2700 full throttle rpm the graph shows the rpm at 75% F.T. power to be 2451 rpm. The Super Cub's owner's handbook shows 2450 rpm.

The graph is based on the use of the so-called "Propeller Load" equation which is.

HP2 = HP1 (RPM2 /RPM1 )3     (eq. 1)
where HP2 = part-throttle hp, HP1 = full throttle hp, RPM2= part-throttle rpm, RPM1 = full throttle rpm

Since we're looking for RPM2 we rewrite the equation to:

RPM2 = (RPM13(HP2/HP1))1/3    (eq. 2)

Something interesting happens here. Note that HP2 / HP1 is a ratio of two horsepowers, not the horsepowers themselves. Since for the 75% power case the ratio is .75 we rewrite the equation again and get:

RPM2 = (RPM13 x .75)1/3     (eq. 3)

This is the equation upon which the graph is derived. What this new equation says is, the only things you need know to determine the Part - throttle rpm are the full throttle rpm and whatever percent of full throttle power you choose. The actual horsepower isn't directly involved except as reflected in the rpm at which it is driving the propeller.

If you don't know how fast your propeller turns at full throttle in flight, find out by hopping into your vehicle for a short, full throttle test on a nice, calm "standard" day, level and at the altitude at which you usually like to fly. You will likely get a more realistic number this way than by reading in the owner's manual whnt the manufacturer claims for his brand new engine - while running in a test cell at close to sea level, with no ram air and no engine installation losses such as you most certainly have in your aircraft.

Back to the graph. If you don't like graphs and/or don't want to go to the trouble of calculating the cruising rpm from the equations 1 show, following is a table which lists a selection of power percentages and multipliers which go with them. Pick out a percentage you like and multiply your full throttle rpm by the multiplier shown. The result will be the corresponding rpm.

Power Percentage Multiplier
75 O.91
70 O.89
65 O.87
60 O.84
55 O.82
50 O.79

Stick a little piece of tape on your tachometer at that rpm, and "cruise" at that power setting. In fact, stick several pieces of tape there, each at one of your chosen power settings. Now you can fly, knowing whenever the tach needle is on one of the marks, what percentage power you're pulling.

If you have the very good fortune to know what your full throttle horsepower is, instead of identifying the tach marks only by power percentage, annotate the actual horsepower too. Since you know the full throttle rpm you can figure the horsepower at any other rpm by using equation l, the propeller load equation. However, if you're not at ease with fractional exponents you may need a calculator that is.

You can have all kinds of fun putting this information to work by, for example, determining fuel consumption versus power, range versus power, etc. Who knows where all this fun can lead?

A final comment about the graph. While the maximum rpm shown on the graph is 4000, engines such as 2-strokers frequently turn at over 6000 rpm. This is too fast for an efficient propeller and so these 2-strokers are often equipped with a propeller speed reduction unit (PSRU). Since the graph deals only with prop rpm and not engine rpm all one has to do in such cases is to divide the full throttle engine rpm by the speed reduction factor to get back on the graph. For example, the graph will work even if your 2 to 1 PSRU is bolted to some wild, screaming fire breather which turns at 8000 rpm. Even so, a prop turning at 4000 rpm is likely to show poor efficiency. Better to use a higher speed reduction factor. But that's a story for another time.