Barnes, J., "Math Modeling of Propeller Geometry and Aerodynamics," SAE Technical Paper 1999-01-1581, 1999, doi:10.4271/1999-01-1581.
A new implementation of the vortex step method for predicting subsonic propeller blade aerodynamic loading is described. The analysis, taking advantage of the classical work by Rankine, Betz, and Glauert, also accounts for the effects of an axisymmetric nacelle in both the vector boundary condition and Glauert velocity diagram. Wake-induced velocities are examined, including effects of wake extent and “observer” position. A certain “equivalence” is demonstrated for the classical results of Betz, Glauert, Goldstein and Theodorsen for the optimum-wake-induced velocities. The effects of wake continuity and rollup are studied, relative to a simple helical wake. Thrust loading calculations are compared to NACA wake-pressure-derived test data. Rationale and methods for geometry “math modeling” are shown and illustrated. Finally, geometric and aerodynamic models are integrated for the preliminary design of a new propeller. “The propeller vortex sheet is fundamental to the understanding and calculation of the aerodynamic force distribution along the propeller blades.” -- A.B. Bauer (25)