After a brief discussion of alternative ways in which the drag of an aircraft wing can be derived theoretically, attention is focused on a technique whereby the separate ‘far-field’ components of drag — viscous, trailing-vortex (induced) and wave — are calculated separately. In particular, a new approximate method is described for estimating the wave drag. Based on an exact two-dimensional analysis involving the flow conditions just upstream of the shock wave, a simple formula is derived which, to first order, involves only a knowledge of the Mach number distribution on the surface of the aerofoil ahead of the shock and of the surface geometry at its foot. The accuracy of this formula is assessed for aerofoils by comparison with more exact theoretical results and with experiment. A ‘strip theory’ extension to swept wings is proposed and illustrated by applying it to a particular transport-type wing body combination. Using experimental pressure measurements as input, all three components of drag are estimated theoretically, and by adding their sum to separate balance measurements of the body drag comparisons between ‘theory’ and experiment for the overall drag can be made. These show a satisfactory standard of accuracy, the error varying between —5% and — 1% of the total drag over a wide range of Mach number and lift coefficient.

An exact integral formulation of the two-dimensional full potential equation is presented. The well developed standard surface panel method based on the linear Prandtl-Glauert equation is extended by means of sources in the field surrounding the configuration, allowing the calculation of transonic flows.

A major attraction of the Field Panel Method is that solutions can be obtained using standard surface panelling together with a field grid which has no special form. The surface panels are used to satisfy the boundary conditions so that the field grid does not have to be surface-fitted which is a requirement for existing field methods. Further, the grid need only be in a region close to the configuration where nonlinear compressibility effects are non-negligible and need not extend to the far field as generally required. Grid generation is therefore trivial allowing solutions for arbitrary configurations. Convergence, especially for flows with shock waves, is enhanced by use of a modified Approximate Factorisation scheme. Results for single aerofoils are compared with Garabedian-Korn solutions and show good agreement; and to demonstrate the ease of grid generation, results for multicomponent aerofoils are also presented. Finally, an outline is given of how the method can be extended to threedimensions.

The work was carried out in conjunction with the Department of Applied Mathematics, University of Leeds together with Procurement Executive, Ministry of Defence.

The lateral dynamic stability and control of a large receiver aircraft was considered during air-to-air refuelling. A simple aerodynamic model was developed in order to determine the aerodynamic forces and moments acting on the receiver aircraft due to the tanker aircraft's vortex field. These forces and moments were then expressed in derivative form and included in the linearised equations of motion. Solution of these equations revealed a divergent oscillation, characteristic of air-to-air refuelling and consisting mainly of bank and sideways displacements. An approximation to this mode, which highlights two important aerodynamic derivatives was made. The values of these derivatives depend mainly on the vertical separation between the tanker and receiver aircraft and the ratio of the tanker-to-receiver aircraft wing spans. In flight, it appears that the pilot controls the divergent mode by frequent alternate movements of the ailerons.