Rotor Dynamics and Helicopter Stability: Development of a Unified Mathematical Theory of the Steady and Disturbed Motion of a Helicopter with Particular Emphasis on the Dynamical Aspects of the Problem

The need for analysing the trim conditions of a helicopter having a non‐flapping (purely feathering) rotor arose out of the discussion in Part III of the ‘equivalence of flapping and feathering’. The analysis will, however, serve a far more useful purpose, for not only shall we go considerably beyond Squire's two‐dimensional approximate analysis of Ref, (3) by producing an exact three‐dimensional solution of the problem, but we shall also use it in such a way as to enable us to assess the accuracy of our trim solution of the helicopter having a flapping‐cum‐feathering rotor. The word ‘exact’ is here used in the sense of the dynamics of the problem only, and we adopt the same simplifications regarding the aero‐dynamic forces as have been discussed at length in Part II in the section dealing with the incidence and force on a blade element. In particular, we shall assume a constant downwash distribution w, over the rotor disk, ignore the effects of tip losses and blade bending, and also disregard any aerodynamic influences associated with blade stalling, rapid incidence changes and wake effects. Apart from these assumptions there will be no approximations whatsoever, and as these aerodynamic assumptions are common also to our analysis of the feathering‐cum‐flapping rotor, we shall be in position to compare the results of this exact analysis with the results for the feathering‐cum‐flapping rotor.