Analytical Investigation of the Aerodynamic Stability of Helical Vortices Shed from a Hovering Rotor
ROCHESTER UNIV NY
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A small-perturbation stability analysis of a doubly infinite array of interdigitated, right circular helical vortices has been formulated. This array corresponds to the vortices trailed from the tips of the blades of a helicopter rotor or propeller in static thrust or axial flight condition and at great distance from the plane of rotation of the blades. The analysis makes use of the Biot-Savart law of induction and the Vorticity Transport Theorem. The singularities in the Biot-Savart integration for self-induction have been eliminated by substituting approximate functions. Near-singular behavior in other integrals has been minimized by adding and subtracting functions with similar near-singular behavior and which have exact, closed-form integrals.