Optimum Loading and Induced Swirl Effects in Hover

Optimum hover performance is the quintessential goal of rotor design. Yet, it is not entirely clear what the optimum loading for a hovering helicopter rotor should be. The Betz solution based on vortex theory is considered the optimum for a propeller, whereas helicopter textbooks often show uniform loading as the optimum based on momentum theory. The difference may in part be due to the presence of an axial climb velocity in the case of a propeller. However, another difference between the two is that unlike the vortex theory, the simple momentum theory ignores the induced swirl. The present work extends typical blade element momentum theory to include the induced swirl. Prescribed circulation distributions for an actuator disk are then examined to better understand the optimum loading condition in hover. When the induced inflow and the induced swirl are solved simultaneously, uniform loading (circulation) does appear to be the optimum, giving a slightly lower induced power than the Betz loading. The blade element momentum theory, with coupled induced inflow and swirl, is augmented with a profile drag model to calculate complete rotor performance, and is applied to several rotor configurations with good success