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

Abstract

SECTION (B). GEOMETRIC ASPECTS OF TRIMMED FLIGHT The Relation Between the Various Planes of Reference The preceding analytical investigation of the trimmed conditions has been based upon the use of the particular set of axes advocated in Part I. There we took as the dominant axis the axis of the rotor shaft, and regarded as the dominant plane, plane RS, the plane perpendicular to the rotor shaft. We recall that the choice of this plane as a plane of reference was dictated by the importance attached at the outset to the study of the dynamics of the blade motion. We also pointed out that, from the mechani‐cal point of view, plane SP, the plane of the swash‐plate for in the absence of a swash‐plate, the equivalent ‘plane of no‐feathering’), could alterna‐tively be regarded as the dominant reference plane. But now we sec that if we concentrate on the aerodynamic aspect, the prevalence of the ex‐pressions (?i—?0+?0?1) and (?1—?) ascribe prime importance to the axis of the flapping cone. Now just as in the case of the rotor shaft, we chose to specify its direction by a plane perpendicular to it, so here we shall specify the axis of the flapping cone by any plane perpendicular to it. One such plane is the tip‐path plane: another is the plane through the rotor hub parallel to the tip‐path plane. We shall refer to cither plane as the plane TP, and so long as we are only concerned with directions, no ambiguity will be caused. We now have three planes competing for attention, planes RS, SP and TP, and it is our object to link these planes together and see what roles they play in the description of the motion of the helicopter as a whole, having special regard in all this to the particular position of the helicopter's C.G. It may be added that the relationship between these planes is a prominent feature of certain papers [Refs. (2), (10)], and the phrase ‘the equivalence of flapping and feathering’ is there used to describe the resultant findings. It will be shown that there are two different interpretations of this phrase, and that in one sense, what is implied is no more than the equivalence of alternative geometric descriptions of one and the same motion of a helicopter rotor. On the other hand, the phrase may be taken to mean that a rotor having no flapping hinge at all [such as the one analysed by Squire in Ref. (3)] performs effectively in the same way as one free to flap. Indeed, the results of Ref. (3) are frequently used as the basis of many trim and stability calculations of helicopters with freely flapping rotors, despite the lack of a flapping hinge in the calculations of Ref. (3). We shall see that, in general, this procedure is questionable.

Citation

Price, H.L. (1963), "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", Aircraft Engineering and Aerospace Technology, Vol. 35 No. 12, pp. 354-357. https://doi.org/10.1108/eb033809