The high level of vibration experienced on the helicopter has been an unfortunate feature of the vehicle throughout its existence, and considerable efforts have been expended over many years in attempts to reduce vibration to levels typical of other forms of transport. Much has been achieved, but as the forward speed increases some components of rotor generated vibration increase very rapidly and consequently, at the increased cruise speed of modern helicopters, vibration can still be high. Also, the requirements have become more stringent, due partly to what the passengers or crew are prepared to tolerate, and partly to the complexity of the tasks required of the crews, especially on military machines.

Viscous/inviscid interaction techniques for calculating the flow about multiple-element aerofoils have been under development in the UK for the last decade producing such programs as MAVIS and HILDA. These methods give reasonable predictions of the lift for viscous attached flow, but fail to give an estimate of the maximum lift and the associated flow separations on the aerofoils. The methods also fail to give adequate predictions of the drag for both attached and separated flow. The disappointing performance of the methods in predicting maximum lift stems primarily from the use of direct methods to solve the first order boundary-layer equations, whilst the poor drag predictions arise from inadequate methods for predicting the development of the flow over the flap. The assumption of incompressible flow could also be a contributory factor in both cases. Methods of overcoming the first restriction are described by using a more appropriate coupling between the inviscid and viscous flows which properly assigns the correct role to each partner in the coupling: this approach is illustrated by ‘semi-inverse’ and ‘quasi-simultaneous’ couplings of a finite-element method for the compressible inviscid flow with an integral method for the boundary layers and wakes. Some methods for calculating the compressible flow about multiple-element aerofoils are also reviewed. However these improvements do not give an adequate estimate of the drag so possible improvements to the calculation of the flow over the flap are discussed.

The objective of this paper is to present the principles of a mathematical model of aircraft prescribed motion. Requirements imposed on the aircraft motion are treated as program constraints on the system and both the transient dynamic solution of motion equations and the control ensuring the exact realisation of the prescribed motion are obtained as a result. The approach used is equivalent to the Lagrange multiplier method, generalised for the purpose of this paper. It consists of the solution of the set of differential/algebraic equations of index exceeding three. The presented mathematical model has been applied to the simulation of aircraft prescribed motion in a loop. The flight along an ideal circle and the flight with additionally demanded constant velocity are described. Some results of numerical calculations are demonstrated.