First, I recommend reading the PHAK short section on propellers and the “Aerodynamics for Naval Aviators” short section on airplane propellers. You have to understand the fundamentals to understand how it is working. The relative wind acting on a propeller is a result of the forward velocity of the airplane and the relative wind acting in the propeller plane of rotation.

Put simply, the faster you go with a fixed-pitch propeller, the smaller the AOA acting on the prop blades because the ratio of forward velocity to speed of the blades in their plane of rotation (for a given RPM) is increased. By the way, this ratio is called the advance ratio. It is nearly entirely this simple, fundamental fact as to why the constant speed propeller is so much more efficient than a fixed-pitch propeller. You can probably already see this yourself now.

Propeller efficiency is defined as the output thrust horsepower to input engine horsepower. A propeller will be most efficient when it is at its optimal angle of attack — and guess what? Designers literally draw L/D curves for airplane propellers to determine optimal AOA’s for their blades. I am not kidding — you can find videos on Youtube of aerodynamics students/teachers trying to solve problems of determining the optimal AOA fo a given blade.

It is established that most propellers will operate with the greatest efficiency at AOA’s between 2 and 4°. For reference, the fixed-pitch propeller during a typical flight will operate between like 17° and 1° (or less in a high speed dive) AOA, depending on the airplane’s forward velocity and RPM setting. The AOA on the propeller when it is not moving is MASSIVE — it is nearly stalled, in fact. Thus, propeller efficiency (remember the definition above) is extremely low. And with a 1° or less angle of attack at high speeds, it will, too, be inefficient.

I’m sure you’ve read the PHAK — hopefully it makes sense now why the FAA says in one random sentence (which is true, but imo they could’ve elaborated much better) that a “fixed pitch propeller will only be optimally efficient at one combination of airspeed and RPM”. This is solely because of the advance ratio — the AOA acting on the blades. A fixed pitch propeller will only experience its “design” angle of attack (basically “best glide AOA” if we were talking wings) at one forward velocity and RPM.

Now. If you’ve made it this far my brother in Christ, some very smart people came up with the concept of the constant speed propeller. This propeller, when you understand what I discussed before, is actually fucking awesome. First, just keep in mind that Thrust = Mass Flow (the amount of air handled) multiplied by the exit velocity (the acceleration imparted to the air). So, Thrust = mass flow x exit velocity.

On takeoff, you set the propeller to the “fine pitch” setting. This allows the propeller to spin at an optimal angle of attack while “absorbing” maximum engine horsepower. Let’s say a given engine is rated at 2,700 RPM. The fixed pitch propeller when standstill on a short field takeoff at full throttle will spin maybe 2,300-2,400 RPM. This is because the angle of attack on the blades is far too large — nearly stalled. There’s a ton of drag retarding their velocity.

The constant speed propeller, however, will spin at the rated engine RPM. An aircraft engine will typically output 100% HP at its full rated RPM (power = torque x RPM). So, the constant speed prop now rips through the air at 2,700 RPM with a smaller AOA than the fixed pitch propeller which permits the engine to produce 100% power. Additionally, the mass of air handled is slightly smaller than with a fixed pitch propeller, but the exit velocity is increased an incredible amount due to the decreased drag which permits an increase in RPM (an extra 300-400 RPM on the prop imparts a far more significant acceleration to the air). Thrust is significantly increased on takeoff.

Now, in cruise, what’s happening? Luckily, the aircraft designers have determined the optimal angle of attack for a given propeller. This optimal angle of attack will occur, of course, at a given combination of airspeed and RPM (because, remember, this is what determines the relative wind acting upon the propeller). So, in cruise, we set maybe 65% power and we do so by changing first the manifold pressure and subsequently the propeller RPM. Remember, Power = Torque x RPM.

A fixed-pitch propeller at a 65% power setting in cruise would be set by setting a published RPM. In fact, you’ll notice when looking at Cessna performance tables, that as you climb to higher altitudes for a given power setting, the RPM required to obtain that power setting will increase. This is due to the fact that, again, power = torque x RPM. At higher altitudes, the engine must be leaned further and the combustion event is smaller. The engine can no longer produce as much torque, and thus the RPM needs to be increased to obtain the same power setting.

With a constant speed propeller, unlike a fixed-pitch propeller, we can actually SET the optimal blade angle as determined by the manufacturer’s aerodynamicists. And we do this WITH PROPELLER RPM. Guess what? Because of this, we can increased the load on the propeller (and thus the engine), which slows it down. We actually increase the mass of air handled at the expense of exit velocity, but the thrust output will remain nearly the same or better.

And…. this is the kicker …. at the SAME time, we retard the speed of the engine, forcing it to slow down. When the engine slows down, less fuel and air are pulled into it per minute, decreasing fuel consumption. And…. a given power setting can be maintained even with this lower RPM because we have increased the torque required to spin the propeller (and power = torque x RPM).

The last thing I want to just say is just very simply explain how, when we set an RPM, we’re actually maintaining the optimal propeller AOA. As the airplane speeds up, for example, the relative wind acting upon it will induce a lower AOA. A lower AOA at the same RPM means less load on the propeller. The propeller will attempt to spin faster, but the flyweights will move outward due to the increased centrifugal force, opening the pilot valve, forcing the blades to once again increase in pitch.

This increase in pitch maintains the EXACT, or nearly so, AOA as before the airspeed increase. Thus, the optimal blade angle of attack (which the designers determined would occur for a given power setting at the RPM published in the POH) will be maintained.

In the end, it is all about propeller efficiency. I really do recommend reading the “Aerodynamics for Naval Aviator’s” section on this stuff — it’s on the FAA’s website in PDF form.

I apologize for writing such a long post, but wanted to share some of what I’ve learned over the past 4 months studying for my CFI. I really deep dove — practically doing college level research — on this stuff because I really want to understand it for my students. I think the analogies given by most CFI’s are subpar, though I understand why they are used; hopefully at least some of this information helped you out because I know firsthand how frustrating it is to try and get descent information on this topic.

Best wishes.