Rotor performance and optimum power from finite-state inflow with realistic constraints

Finite-state induced-inflow theory is used to develop an analytical formulation for general performance of the lifting rotor in forward flight with arbitrary loading. The theory incorporates conventional blade-element theory for blade lift and provides the integrated loads and the induced power of the rotor in terms of an arbitrary number of rotor controls such as conventional collective and cyclic pitch as well as higher harmonic radial and azimuthal pitch. The theory provides the basis for a classical quadratic optimization with realistic constraints that is applied to determine minimum induced power for a variety of available control combinations, rotor trim constraints, and operating conditions. The numerical results are presented for an actuator disk with an infinite number of blades, although the formulation is not limited to that case. The findings show significantly increased induced power relative to ideal Glauert power at moderate and high advance ratios that also depends on the rotor moment trim constraints. Higher harmonic and radial blade twist significantly reduce the non-ideal induced power increment. It appears that increasing the available controls enables the optimum solution to redistribute the rotor loading to minimize the induced power. New insights are given for some of the factors that prevent present rotors from achieving Glauert ideal efficiency. Limited comparisons with previous research corroborate the earlier results and demonstrate the versatility of the present formulation.