Minimum Loss Load, Twist, and Chord Distributions for Coaxial Helicopters in Hover

This paper presents an approach for determining the optimal (minimum power) geometry of a hovering coaxial rotor using blade element momentum theory, including swirl. The analysis accounts for the presence of a finite number of blades using the Prandtl tip loss factor, the effect of profile drag using experimentally or computationally determined drag polars, and the mutual interference between the two rotors using an empirically determined influence coefficient method. Numerical results show that including the induced swirl in the model decreases the optimal figure of merit and that swirl has a larger impact at higher disk loadings. At the disk loadings typically found on helicopters, the effect of swirl is relatively small, particularly compared to mutual rotor interference or tip losses. Additionally, accounting for swirl affects the optimal rotor design near the blade root, at locations that would often be part of the root cutout of a realistic rotor.