THE GENERALIZED ACTUATOR DISK

Abstract
Based upon the classical vortex system representation the induced velocities of a finite-bladed propeller with arbitrary circulation distribution are derived and Fourier analyzed. The zeroth harmonic, or steady component, of the induced velocities is considered in detail and formulas involving only an integration over the blade radius are found. Sample calculations of both the axial and radial velocity components for an arbitrary representative circulation distribution closely approximating the Goldstein optimum are presented. For the special case of a uniformly loaded propeller, expressions for the induced velocity components are given in simple closed form and velocity profiles are compared with the representative results.

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