# Propeller modelling

I need a (very) approximate model of a propeller on an aircraft.

My principal question is this: what would the relationship be between:

• Propeller rate of rotation
• Aircraft speed
• Force generated by propeller

As an aside, what would the relationship be between the above and:

• Energy required to drive propeller?
• Rotational force between the propeller and aircraft body

Any insight would be very helpful, including stating that I haven't given enough information!

Thanks

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Why don't you fix the propeller's efficiency (at say 75%) and then use the formula here as your model? This contains everything you mentioned. –  Glen The Udderboat Feb 10 '13 at 18:45
Thanks - however it still leaves the question of how the thrust force changes with respect to the aircraft's velocity –  Jodes Feb 10 '13 at 20:06
Doesn't it say that, keeping the other stuff constant, thrust times velocity remains constant? For example: if velocity doubles, then thrust halves. –  Glen The Udderboat Feb 10 '13 at 20:17

You have enough information. A propeller is just a complicated sort of wing.

Assume the aircraft is moving forward at an airspeed of, say, 150 km/hr.

Assume the propeller is turning at an angular rate of, say, 40 revolutions per second (hz).

From that, if you look at the propeller surface at a particular radius from the center, such as 1 meter, you can determine the angle of the helical path followed by that part of the propeller through the air, and the speed it is travelling through the air.

Then assume it has a particular angle of attack, like 10 degrees or 0.18 radian, and has a particular "width", which is the chord length of its airfoil. From that, you can figure out how much "lift" and "drag" it is generating, and what the direction of those forces are relative to the aircraft centerline.

Now if you just do that for a range of different radii on the propeller (i.e. perform an integration), you can figure out how much thrust the propeller generates and how much power it needs. Don't forget, that is per propeller blade. Typical propellers have 2 or 3 blades, but can have as many as 6.

This is still just a rough calculation because it depends on things like the shape of the tip of the propeller, just as the shape of an aircraft's wingtips make a difference in how much drag is produced.

Note that if the thrust is greater than the drag on the aircraft, the aircraft will be climbing. If less, it will be descending.

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