This is a function of the advance ratio, i.e. the pitch.

Take a propeller that is 10 ft in diameter with a tip advance angle of say 5 degree. One full rotation of the propeller would thus see that blade going around 31.4 feet (pi times the diameter), and at 5 degree, this would make the tip advance 2.74 feet (I am rounding up my numbers; the actual equation would be SIN(5) * pi * diameter). We can assimilate this advance rate to a screw advancing in solid material (note that the advanced angle is not necessarily the same as the plade angle itself, as there are camber and angle of attack issues, but for this simple analysis, this is good enough)

Now, let's take a point 2.5 feet from the hub, i.e, in the middle of a blade. This point will go 15.7 feet around during a full rotation, and if its advance rate was also 5 degree, would want to move forward only 1.37 feet, i.e. it would work *against* the tip, dragging it down. Since we want the whole propeller to move at the same rate (evidently) for reason of internal stress and efficiency, we have to solve for the advance angle at that point by using the same advance rate per rotation as for the tip, i.e. 2.74 feet.

In this instance, we have to solve for the equation

SIN (angle) * pi * diameter-of-a-point = 2.74

In the case of a point 2.5 feet from the hub, this is

SIN(angle) = 2.74/(pi*5)

and "angle" has to be 10.04 degree.

Repeat this for all the points on the propeller, noticing that the angle has to be 90 degree exactly at the center by the way, and you just defined the required propeller twist.

About 20 years ago, I was involved in wind tunnel testing, and some of the technicians building the aircraft model decided to make a small rubber band powered aircraft in their off hours. The first prop they made (very smooth, those guys were real craftsmen) had the advance angle at zero at the hub and maximum at the tip; and when they showed it to me, I pointed out that the prop would be fingthing against itself. So they made another one, with the angles correct, and they reported the wind through the small prop was so much higher with the second model than the first. At the end of the wind tunnel test weeks, they tested their airplane, and it went magnificiently. With their first prop, I doubt it would even have picked up speed.

Source(s):
Aerospace engineer

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