Analytic solution of in-plane vortex–rotor interactions with arbitrary orientation and its impact on rotor trim

The general aerodynamic problem of arbitrarily oriented in-plane vortex-rotor interaction was investigated in the past only by numerical simulation. Just one special case of in-plane vortex-rotor interaction with the vortex axis in flight direction was recently solved analytically. In this article, the analytical solution for arbitrary in-plane vortex orientation and position relative to the rotor is given for the first time. The solution of the integrals involved as derived here encompasses and simplifies the previous derivation of the special case significantly. Results provide the vortex impact on rotor trim (thrust, aerodynamic rolling and pitching moments about the hub) and the rotor controls required to mitigate these disturbances. For the special case with the vortex axis in flight direction, the results are identical to the former solution and results for the other in-plane vortex orientations and positions agree with the numerical results obtained so far.