Rotor Dynamics ROTORCRAFT 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 ultimate object of the present work is the investigation of the dynamic stability of a helicopter. Fundamentally this is the problem of the small oscillations of a body about a steady state of motion when subjected to a field of force comprising aerodynamic and gravitational forces. It may be remarked in passing that there is really no such thing as a steady motion of a helicopter. The rotor forces are continually varying during the course of a revolution, and the notion of a steady motion has to be interpreted as ‘steady on the average’. With this proviso the problem is intrinsically the same as that of the stability of a fixed wing machine, and the problem reduces to finding the variation of the rotor forces when subjected to small disturbances and feeding this information back into the equations of disturbed motion of the helicopter as a whole. Naturally a proper estimation of the forces in the disturbed state depends on a faithful description of the initial steady state, and for this reason the previous account of the steady motion is included. In particular, the increments in the rotor forces due to a disturbance will be functions not only of U, V, W but also of ?0, ?1, ?2 and ?0, ?1, ?2. The flapping angles themselves, however, will vary during the disturbance, and much of the work will be concerned with calculating the effect of this variation on the rotor forces as a whole. In general ? and ? will be fairly small; but, whereas in stability theory the products of small velocity increments are ignored, products here of ? and ? will warrant a great deal of attention. The retaining of second order terms throughout would be a formidable task, but as mentioned earlier, it is possible to enunciate a general principle enabling only the more important products to be selected.