Piston engines generate power by applying torque to rotate the crankshaft. The crankshaft cannot be mechanically coupled directly to push against the air to drive the airplane forward. That function is performed by the propeller, which takes the power developed by the engine and converts it to thrust.
Proper matching of the propeller to the engine, and the flight condition at which the airplane will operate are essential to getting good performance from the airplane.
As the propeller rotates, it accelerates air aft that in turn generates a reaction force forward on the propeller blades. This reaction force is the thrust that drives the airplane through the air.
The thrust horsepower is the thrust generated by the propeller multiplied by the airspeed (in appropriate units). If the propeller were perfect and had an efficiency of 100%, thrust horsepower delivered by the prop would be equal to the shaft horsepower delivered to the prop by the engine. In the real world, even an ideal propeller of finite diameter cannot achieve an efficiency of 100%, so the thrust horsepower out is always a bit less than the shaft horsepower in. By proper design and selection of the propeller, we can minimize this difference, and maximize performance.
The thrust horsepower delivered by the propeller to the airframe to drive the airplane forward is a function of two things: the shaft horsepower from the engine that is driving the propeller, and the efficiency of the propeller itself. Both of these vary with airspeed and propeller rpm.
As the propeller rotates, the pitch set into the blades gives them an angle of attack relative to the incoming air. This angle of attack causes the blades to develop the aerodynamic lift that generates thrust. The torque of the engine drives the propeller and overcomes the drag of the blades.
For a propeller at a given rpm, the angle of attack of the blades changes with airspeed. As the airspeed increases, the oncoming airflow approaches the propeller disc from the front, which is the “upper” or suction surface of the airfoil of the propeller blades. This reduces the angle of attack of the blades.
The reduction in angle of attack of the blades has two effects: it reduces the lift of the blades (and hence their thrust), and it reduces their drag. Accordingly, as airspeed increases, the power required to turn the propeller at the specified rpm goes down. If the airspeed gets high enough, the angle of attack of the blades becomes negative, and the airstream starts to drive the propeller like a windmill.
Figure 1 shows the power required to turn an example propeller at constant rpm. The example propeller was designed to absorb (be driven by) 75 horsepower at 2600 rpm at an airspeed of 100 knots. At 80 knots airspeed, this same propeller needs 98 horsepower to maintain 2600 rpm. At 120 knots, the prop only needs 39 horsepower to maintain 2600 rpm.
This behavior has several important implications. The amount of power required to drive the propeller at a given rpm is also the horsepower the propeller will apply to the air to make thrust at that rpm and airspeed. A propeller flying faster than its design point can’t absorb the full design power without turning faster than the design rpm.
The second effect is that the engine may not be able to drive the propeller at the rated rpm at airspeeds below the design point. If this is the case, then the propeller will govern the engine to a lower rpm and lower horsepower.
To see how this works, refer to Figure 2, which shows the power absorbed by our example prop as a function of rpm at several airspeeds. The figure also shows the power the engine driving the prop can deliver at full throttle as a function of rpm. If we look at each constant-airspeed propeller power curve in turn, we will find an rpm where the power absorbed by the propeller matches the full-throttle power the engine can deliver. This is the rpm the prop will spin at that airspeed. That equilibrium rpm, in turn, determines how much power the full-throttle engine is developing while turning that propeller at that airspeed.
If we follow the 100-knot airspeed curve, it intersects the engine curve at 75 horsepower and 2600 rpm, which is the design point for this propeller. At 80 knots, the propeller governs the engine down to 2380 rpm, at which it produces 67 horsepower. Reducing the airspeed further, to 60 knots, loads up the prop blades even more, and the prop holds the engine down to 2230 rpm and 64 horsepower.
At 120 knots the picture changes. The propeller cannot absorb the power the engine can produce at full throttle, even if we allow the rpm to increase to 2700. Assuming the airplane gets to that speed, the pilot will have to retard the throttle to avoid overspeeding the engine, so that the power delivered to the propeller will drop to 50 horsepower if the limit is 2700 rpm.
What we see here is the essential compromise inherent in choosing a fixed-pitch propeller. We want the prop to efficiently absorb the cruise power of the engine at our desired cruise airspeed and altitude, but we also need it to be able to deliver enough thrust for takeoff and climb. A cruise-optimized propeller is likely to govern the engine too much at low speed, particularly if the airplane is clean, and relatively fast. The more airspeed difference there is between cruise and climb, the farther the prop will be from its cruise operating condition in climb. This is why we tend to use propellers that are a compromise. They have a bit less pitch than would be optimal for cruise in order to improve takeoff and climb.
The variation of thrust horsepower with airspeed is also affected by the efficiency of the propeller. The propeller efficiency is the ratio between the thrust horsepower generated by the prop and the shaft horsepower required to turn the prop.
Figure 3 shows the efficiency of our example propeller as a function of airspeed and rpm. The important thing to notice here is that the propeller efficiency drops significantly when the propeller is operating far away from its 2600-rpm, 100-knot design point.
Plots like Figure 3 are a bit difficult to use, so propeller designers have evolved a way of combining all of the curves at varying airspeeds and prop speeds into a single curve. We do this by defining a quantity called the “advance ratio” of the propeller. The advance ratio (signified in equations by “J”) is the airspeed in feet per second divided by the diameter of the propeller in feet and the rotational speed of the prop in revolutions per second.
Figure 4 shows the efficiency of our example propeller as a function of advance ratio. Notice that the efficiency of the propeller drops steadily as the advance ratio (and hence the airspeed) drops below the design point. This reduction in efficiency further reduces the thrust horsepower the propeller can produce at airspeeds below the design point. Not only is the shaft horsepower reduced, as we saw earlier, but the propeller is less efficient at converting that lower horsepower to thrust.
Figure 4 also shows why we don’t want to move the design point to too low an airspeed while trying to improve climb. Notice that above a certain advance ratio, the propeller efficiency falls very rapidly. We must ensure that our airplane isn’t trying to cruise here.
Available Thrust Horsepower
In total, the thrust horsepower available from the engine/propeller combination at any given airspeed is the product of the power absorbed by the propeller from the full-throttle engine and the efficiency of the propeller at that flight condition.
The thrust horsepower available from our example engine/prop combination is shown in Figure 5. The maximum thrust horsepower available occurs at the propeller design point for a well-matched engine and prop. At lower airspeed, thrust horsepower is diminished by the combination of the propeller governing the engine to a lower shaft horsepower and reduced propeller efficiency. At higher airspeed, the need to reduce throttle to avoid overspeeding the engine and lower propeller efficiency also reduce the thrust horsepower available.
Matching a fixed-pitch propeller to an airplane is inherently a compromise driven by the relative importance of takeoff roll, climb performance, and cruise performance. If the airplane has sufficient power and is operated off of relatively long runways, we can use a higher-pitched propeller biased towards cruise. Takeoff roll will be higher and rate of climb lower than it would be if the prop had less pitch, but the airplane will fly faster in cruise.
If the airplane has relatively low power-per-unit weight, or if short takeoff and initial climb are most important, then the preferred prop will have a lower pitch that allows the pilot to use more of the engine’s power to accelerate and climb. The price for this will be a lower top speed.
A major advantage of a fixed-pitch prop is that it is lighter, simpler and cheaper than one with variable pitch. For many light aircraft, the compromise in performance is small enough that the lower cost and greater simplicity outweigh the performance hit.
As the airplane gets faster and the speed difference between climb and cruise gets bigger, it gets harder to find a single propeller pitch which produces acceptable climb without seriously limiting cruise speed. At some point this compromise becomes too large, and we must look to variable-pitch and constant-speed propellers to provide good performance over the entire airspeed envelope.
Barnaby Wainfan is a principal aerodynamics engineer for Northrop Grumman’s Advanced Design organization. A private pilot with single engine and glider ratings, Barnaby has been involved in the design of unconventional airplanes including canards, joined wings, flying wings and some too strange to fall into any known category.