Time domain unsteady incompressible cascade airfoil theory for helicopter rotors in hover

A detailed derivation of a finite-time arbitrary-motion incompressible casade theory is presented for both Laplace and frequency domains. Such theories are useful for both aeroelastic stability and response calculations. The generalized cascade lift deficiency function C" is shown to be consistent with the generalized Theodorsen's lift deficiency function when the wake spacing approaches infinity or when the reduced frequency tends to infinity; it also yields a correct value for the zero reduced frequency limit. Efficient numerical procedures are presented for the evaluation of the cascade lift deficiency function. Numerical examples comparing the cascade lift deficiency function with Loewy's rotary-wing lift deficiency function in frequency domain are presented. Fade approximants of the cascade lift deficiency function are constructed using a Bode plot approach that allows for complex poles. A general purpose optimization program is used to determine the coefficients of the approximant.