Note about Self-Induced Velocity Generated by a Lifting-Line Wing or Rotor Blade

摘要

This report presents an elementary analysis of the induced velocity created by a field of vortices that reside in the wake of a rotor blade. Progress achieved by other researchers in the last 70 years is briefly reviewed. The present work is presented in four stages of complexity that carry a lifting-line representation of a fixed wing into a single-blade rotor. The analysis leads to the conclusion that the lifting rotor's spiraling vortex wake structure has very high induced power when compared to the ideal wing. For an advanced ratio of one-half, induced power is on the order of 10 times that of the wing when the comparison is made at wingspan equal to rotor diameter and wing and rotor having equal lift.