THE DA VINCI AERIAL SCREW: A CHARACTERIZATION OF THE AERODYNAMICS, PERFORMANCE, AND ACOUSTICS

Abstract

Aerial screw rotors are high-solidity rotors which rely on a shape-conforming helical vortexat the blade tip– the “da Vinci vortex”– as the primary thrust generation mechanism, analogous to vortex lift on delta wings. The geometry of an aerial screw is defined by key parameters such as the pitch rate (ζ), taper rate (η), number of blades (Nb), and the maximum radius (Rmax). Aerial screws generate higher thrust compared to conventional rotors at similar rotation speeds, with the cost of increased power requirements. This work employs a one-at-a-time approach to understand the effect of varying these design parameters on the aerodynamics, performance, and acoustics of aerial screws using high-fidelity computational fluid dynamics (CFD). The flight states investigated include hover, axial climb, and off-axis climb, primarily for aerial screws with a one-foot radius. The maximum radius is found to positively contribute to the hover efficiency with diminishing returns at larger sizes, attributed to viscous effects becoming less significant at higher Reynolds numbers. An increasing number of blades significantly decreases the figure of merit due to interactional aerodynamics weakening the da Vinci vortex. An optimal linear pitch rate of ζ = 1.2 is found in hover, balancing vortex strength against the torque-wise orientation of the blade’s surface normal vectors. This optimal pitch rate shifts upward with increasing climb speed, reaching ζ = 1.8 at a climb inflow of λc = 0.08, as higher pitch rates better sustain the effective angle of attack against the increasing inflow. In off-axis climb, higher pitch rates produce significantly larger oscillatory side forces and pitching and rolling moments, presenting a key design tradeoff. The taper rate is found to be less influential than the pitch rate in axial and off-axis climb states, where its effect on efficiency becomes nearly negligible. Bilinear variations of pitch and taper rates are explored in hover to further improve aerial screw performance beyond what linear distributions allow. A bilinear pitch distribution transitioning from ζ1 = 1.0 in the first half of the screw to ζ2 = 1.4 in the second half yields a modest improvement over the best linear pitch design. A bilinear taper distribution with an aggressive initial taper of η1 = 0.8 transitioning to an untapered second half achieves a 5% improvement over the best linearly tapered design, by strongly feeding the da Vinci vortex in the first half while maximizing lifting area in the second. Combining the best bilinear pitch and bilinear taper profiles yields a figure of merit of 0.64 in hover — a 13.7% improvement over the best linearly varying design. While this aerial screw outperforms all other screw configurations studied, conventional rotors still achieve higher figures of merit in hover, ranging from 0.73 to 0.77. Phase shifting in azimuthal loads was discovered between linear and bilinear varying designs due to the differencing in local surface inclinations and blade loadings. This finding suggests a potential optimal one-bladed aerial screw which is capable of canceling side forcing, rolling and pitching moments in hover. An aeroacoustic analysis reveals that despite producing higher thickness noise levels than conventional rotors due to their distributed geometry, aerial screws exhibit significantly more favorable perceived noise characteristics. Their low 1/rev blade passage frequencies result in tonal noise components that are heavily attenuated by A-weighting, and their continuous, distributed wake interactions produce a far less impulsive broadband noise signature compared to conventional rotors. The best performing aerial screw achieves total perceived noise levels comparable to a 4-bladed conventional rotor, with a distinctive directivity pattern that is quiet both in-plane and on-axis. These findings suggest a compelling acoustic advantage for aerial screw designs in noise-sensitive practical applications