Approximate effect of blade number on the induced power of lifting rotors at varying wake skew angles

Induced power computations are much easier to perform in the case of an infinite number of blades than they are for a finite number of blades. This is because low-order actuator-disk concepts can be employed for rotors in which the induced flow is assumed to proceed from an infinite number of blades, whereas either high-order actuator disks or vortex-lattice methods are required for rotors with induced flow emanating from a finite number of blades. Therefore, it would be helpful to have approximate correction factors that could be applied to infinite-blade results to capture the effect of blade number on induced power. (Prandtl's famous tip-loss function for rotors is an example of such a correction.) We use results from Prandtl and Goldstein, our own finite-state inflow results, and other induced-power computations in the literature to create such a correction function, useful at all wake skew angles from hover to edgewise flow. Applications to induced power computed by a finite-state method are also given.