Catto & Prince Props (long)

[elippse]

"As stated previously, 2 blades are more efficient than 3. Less drag=More speed and efficiency."
This is one of those "every knows" things, but they never tell you why. They call up some nebulous thing called "tip loss", but don't or can't explain it. I have in front of me two pictures; one is of the A400M turboprop with eight-blade props, the other is of a fixed-pitch, 18 or 20-blade, fixed-pitch prop, which is the fan on the front of the new Mitsubishi MRJ and Pratt & Whitney's GTF engine! Let's look at this thing from the stand-point of a wing. I have two wings of 100 sf; one is 20' span by 5' chord, the other is 28.3' span by 3.54' chord. Each wing during one second of flight intercepts a volume of air which is a tube of the diameter of the wing span and the length is the forward velocity fps. For a given velocity the longer wing will intercept twice the volume of air as the shorter wing, and so twice the mass. Since lift is a force proportional to m-dot v, where v is the downwash, (F=MA), the longer wing will have half of the downwash of the shorter wing. Any energy put into the air is energy lost, so the shorter wing loses twice the energy to the air in producing lift; its L/D will be half as good as the longer wing. This is known as "induced loss" or "induced drag", the result of producing lift. This is why a high aspect ratio wing has a much better L/D than a lower aspect ratio wing of the same area. So let's apply this same thinking to the number of blades on a prop. Let's take and compare a four-blade prop to a two-blade prop of the same diameter. As in the wing, each blade intercepts a volume and mass of air contained in a tube which has the diameter of the prop and the forward velocity of the plane. Since the four-blade intercepts twice the mass of the two-blade, and thrust is m-dot v, the downwash v from each blade will be only half as much as the two-blade, ergo each blade operates at twice the L/D of the two-blade for the same total amount of thrust, and each blade has only twice the amount of loading, so its area and parasite drag will be half as much. Additionally, its tip vortex will be half as great since that is proportional to loading of the blade. That is why multi-blade props have better static thrust and climb. But, if you make a multi-blade prop with klunky, high-drag blade-root shapes, it will not cruise as fast as the two blade. That's why there were streamlined cuffs put on prop blades of planes such as the P-51, to cut down on the prop drag. If you know of any technical argument that will explain why multi-blade props are not as good as two-blade props, please share it here so that we may all learn!

[smokyray]

Paul,
Obviously, excellent point. Here are several engineering examples I found that cover some of the ground, but not all of it.

Smokey
HR2

Propeller Blade design
A further consideration is the number and the shape of the blades used. Increasing the aspect ratio of the blades reduces drag but the amount of thrust produced depends on blade area, so using high aspect blades can lead to the need for a propeller diameter which is unusable. A further balance is that using a smaller number of blades reduces interference effects between the blades, but to have sufficient blade area to transmit the available power within a set diameter means a compromise is needed. Increasing the number of blades also decreases the amount of work each blade is required to perform, limiting the local Mach number - a significant performance limit on propellers.
A propeller's performance suffers as the blade speed exceeds the speed of sound. As the relative air speed at the blade is rotation speed plus axial speed, a propeller blade tip will reach sonic speed sometime before the rest of the aircraft (with a theoretical blade the maximum aircraft speed is about 845 km/h (Mach 0.7) at sea-level, in reality it is rather lower). When a blade tip becomes supersonic, drag and torque resistance increase suddenly and shock waves form creating a sharp increase in noise. Aircraft with conventional propellers, therefore, do not usually fly faster than Mach 0.6. There are certain propeller-driven aircraft, usually military, which do operate at Mach 0.8 or higher, although there is considerable fall off in efficiency.

There have been efforts to develop propellers for aircraft at high subsonic speeds. The 'fix' is similar to that of transonic wing design. The maximum relative velocity is kept as low as possible by careful control of pitch to allow the blades to have large helix angles; thin blade sections are used and the blades are swept back in a scimitar shape (Scimitar propeller); a large number of blades are used to reduce work per blade and so circulation strength; contra-rotation is used. The propellers designed are more efficient than turbo-fans and their cruising speed (Mach 0.7–0.85) is suitable for airliners, but the noise generated is tremendous (see the Antonov An-70 and Tupolev Tu-95 for examples of such a design).


Propeller Efficiency

In addition to the engine efficiency factors described above the piston and turbo-prop aircraft must also contend with the efficiency of the propeller at converting the power into thrust. The following discussion about propeller efficiency applies equally to piston and turbo-prop aircraft.

Propeller efficiency refers to the percentage of Brake Horsepower (BHP) which gets converted into useful Thrust Horsepower (THP) by the propeller. The propeller is never 100% efficient. Therefore the propeller efficiency is always a number less than one. The definition is:

Neta is propeller efficiency.

In the last chapter we saw that the efficiency of a wing (as measured by the maximum L/D ratio) depends upon the aspect ratio of the wing and the angle of attack at which the wing operates. The efficiency of a propeller depends upon the same things. In other words propellers with high aspect ratios will be more efficient than short stubby propellers. Additionally, each propeller will have an optimum angle of attack. When operated at the optimum angle of attack the propeller will be most efficient.

So, all we have to do is figure out what affects the angle of attack of a propeller.
Propeller Angle of Attack
Some propellers have more than two blades but all the concepts developed here will still apply.

Each blade cross-section is moving along an arc around the crankshaft as well as traveling forward. As a result its motion is a helix.

Before we consider the full helix motion let us look at the simpler case where the engine is running but the aircraft is not moving. (For example the pilot is standing on the brakes while running the engine up, just prior to a short field takeoff.)
Propeller blade angle as the angle between the chord of the propeller airfoil and the arc of rotation (i.e. 90 degrees to the crankshaft.) On a constant speed propeller this angle is variable. On a fixed pitch propeller it is fixed.

The rotational velocity is the speed of rotation, which depends upon the rpm (n) of the engine and the diameter (D) of the propeller blade (the green vector in the diagram.)

In our example there is no forward speed. Therefore, the blade angle and the angle of attack are the same.

Effect of TAS on Propeller Angle of Attack

The important things to note are:

1. Propeller angle of attack Decreases as TAS increases
2. Propeller angle of attack Increases as rotational velocity increases (rpm x Diameter increases)

We therefore know that the thrust produced by the propeller, which is nothing more than lift by another name, will decrease as the TAS increases because the propeller will be operating at a smaller angle of attack. This will reduce the coefficient of lift for the propeller and thrust will drop off. When the pilot increases rpm the angle of attack of the propeller will increase. Thus, thrust will increase and the aircraft will accelerate.
Propeller Efficiency
As we learned before, any given wing will have a certain angle of attack at which it if most efficient. This will be true for the propeller as well. It is after all just a wing flying around in a helix pattern. Since the angle of attack of the propeller depends on both rpm, diameter and TAS, the propeller efficiency will vary according to the ratio of these factors. The ratio Velocity/rpm x diameter is called the Advance Ratio. The most efficient J depends upon the propeller blade angle. Course propellers (large blade angles) will be more efficient at larger advance ratios. Fine pitch propellers will be more efficient at small advance ratios.
When choosing a fixed pitch propeller an aeronautical engineer usually chooses one, which is optimum for cruise. However, s/he might choose one, which is optimum for climb if designing a seaplane, tow plane etc.
With a fixed pitch propeller, getting the ideal advance ratio while also keeping the aircraft's wing at the ideal angle of attack for best range will be almost impossible. That is why constant speed propellers are desirable for cross-country airplanes.

With a constant speed propeller the blade angle will vary from a small angle to a large angle. (The low and high pitch stops.) This allows the propeller to be efficient (i.e. operate at the optimum angle of attack) at a variety of advance ratios.

End

[elippse]

Smokey: If you have seen Jack Norris' new book on prop design, you will see that he says that the elliptical loading I chose in the design of my props is actually superior to the Betz, Goldstein, Theodorsen loading which had previosly been thought the most efficient. He says that now the theoretical efficiency limit is about 95%. From my testing, it appears mine perform at about 90%+ in cruise. Ask Tom Aberle how he likes the four-blade on his biplane racer that got his speed from 220 mph to 252 mph!

[smokyray]

Thanks Paul, look forward to reading up...

Smokey
HR2