Expert: Paul Soderman - 7/30/2009

Question
Hello,
is there any simple formula that can be used for the preliminary estimation of the propeller dimension?

I read one that states:

diam =(4*shaft_power/(pi* number_of_blades * blade_load))^0.5

but I don't know what Blade_load actually is and which is a typical value for this parameter.

Thank you very much,
Fede

Answer
Fede
The optimum propeller is one that converts engine horsepower to thrust horsepower with the greatest efficiency.  The equation you cite attempts to relate power to propeller load and area, which doesn't help much.  There is no typical blade load as that depends on the aircraft thrust required. To choose a propeller size, a designer would do a system analysis based on the aircraft mission and aerodynamic requirements.  For example, is the airplane designed primarily for high speed at altitude (fighter) or is takeoff and climb performance more important (cargo plane).  What thrust is required and what horsepower is available. Suppose you have chosen a desired aircraft speed and altitude and computed the rotational speed and power available.  You can then calculate the speed-power coefficient of the propeller.

Cs = (rho V^5/P n^2)^1/5,  where rho = air density, V = flight speed, P = propeller power, n = rotational speed (radians per second)

which can also be written in terms of engine shaft horsepower and rpm.

Using propeller design charts based on propeller tests, one can choose the optimum propeller and blade number.  Of course, other constraints come into play such as ground clearance, tip Mach number, fixed or variable pitch, and so on.  In many cases, the engine and propeller are designed together.  I suggest reading Elements of Propeller and Helicopter Aerodynamics by Daniel Dommasch (chapter 3).
Paul