# Modelling helicopter flight dynamics: stability under constraint and response analysis

Everybody’s simulation model is guilty until proved innocent. (Thomas H. Lawrence at the 50th Annual Forum of the AHS, Washington, 1994)

5.1 Introduction and Scope

Continuing the theme of ‘working with models’, this chapter deals with two related topics – stability under constraint and response. The response to controls and atmos­pheric disturbances is the third in the trilogy of helicopter flight mechanics topics; where Chapter 4 focused on trim and natural stability, response analysis is given prime attention in Section 5.3. Understandably, a helicopter’s response characteristics can dominate a pilot’s impression of flying qualities in applied flying tasks or mission task elements. A pilot may, for example, be able to compensate for reduced stability provided the response to controls is immediate and sufficiently large. He may also be quite oblivious to the ‘trim-ability’ of the aircraft when active on the controls. What he will be concerned with is the helicopter’s ability to be flown smoothly, and with agility if required, from place to place, and also the associated flying workload to compensate for cross-couplings, atmospheric disturbances and poor stability. Quantifying the qual­ity of these response characteristics has been the subject of an extensive international research programme, initiated in the early 1980s. Chapter 6 deals with these in detail, but in the present chapter we shall examine the principal aerodynamic and dynamic effects, mostly unique to the helicopter, which lead to the various response characteristics. Response by its very nature is a nonlinear problem, but insight can be gained from investigating small amplitude response through the linearized equations of perturbed motion. This is particularly true for situations where the pilot, human or automatic, is attempting to constrain the motion – to apply strong control – to achieve a task. We discuss this class of problems in Section 5.2, with an emphasis on the kind of changes in the pilot/vehicle stability that can come about, therefore maintaining some continuity with the material in Chapter 4. Section 5.3 follows with an examination of the characteristics of the helicopter’s response to clinical control inputs, and the chapter is concluded with a brief discussion on helicopter response to atmospheric disturbances.

Most of the theory in both Chapters 4 and 5 is concerned with six degree of freedom (DoF) motion, from which considerable insight into helicopter flight dynamics can be gained. However, when the domain of interest on the frequency/amplitude plane includes ‘higher order’ DoFs associated with the rotors, engines, transmission and flight control system, the theory can become severely limited, and recourse to more

complexity is essential. Selected topics that require this greater complexity will be featured in this chapter.