HELICOPTER TRIM BY PERIODIC SHOOTING WITH NEWTON-RAPHSON ITERATION

The problem of finding a rotor trim solution involves both a search for the correct control settings that will give a desired flight condition as well as the calculation of the periodic solution to the nonlinear rotor equations, given those controls. In the present study, a method is developed whereby the correct controls and periodic solution (i.e., the correct blade initial conditions to yield periodicity) are found simultaneously. The use of initial conditions as unknown variables to obtain periodicity is not new and has been called "periodic shooting". The simultaneous solution of the controls and initial conditions, however, is an innovation developed here. Analysis shows that the new method is computationally superior to other methods in many practical applications. Numerical implementation on nonlinear flap-lag equations verifies the usefulness of the method even under extreme conditions such as instability, resonance, and high advance ratio. A detailed study of the convergence shows that the method may diverge for certain combinations of initial guesses, but that the divergence can be circumvented by simple procedures.