Optimum Rotor Performance in Axial Flow by Finite-State Methods

Recent studies have pointed out that conventional lifting rotors in forward flight have efficiencies far lower than the optimum efficiencies predicted by theory. Finite-state inflow models have been suggested as a theoretical basis whereby to study the reasons for this efficiency deficit. In this paper, a finite-state inflow model is utilized to formulate the optimum circulation and inflow distribution for rotors in axial flow. The results show that a formal optimization with finite-state models can be done in closed form and that such an optimization recovers the classical uniform-flow condition (for an actuator disk with an infinite number of blades), the Prandtl solution (for an actuator disk with a finite number of blades), the Betz distribution (for a lifting rotor with an infinite number of blades) and the Goldstein solution (for a lifting rotor with a finite number of blades). Thus, it should be possible to use finite-state models to investigate optimum rotor performance in forward flight.