Calculation of the pressure distribution over a wing at sonic speeds

Abstract

A method is developed for the calculation of the pressure distribution and the aerodynamic forces and moments acting on a wing at incidence, a wing in (steady) roll and a wing in (steady) pitch. The calculation is based on the assumption of an inviscid potential flow and is restricted to small incidence and thickness ratio, so that quadratic terms in the perturbation velocities are neglected. The results are valid, if |1 - M²|.A² is small compared to 1, i.e., either for any Mach number M for wings of a small aspect ratio A, or for any aspect ratio for sonic speeds (M ≉ 1). The aerodynamic coefficients and stability derivatives l~ and m~ for a wing family which is described by the parameters aspect ratio A, taper ratio λ, and sweep ratio α (Fig. 8), are given in the form of charts. The calculation indicates, that the plan-form of the wing is of similar importance as regards the pressure distribution at sonic speeds as the chordwise section of a wing at subsonic speeds for wings of larger aspect ratios. Although the calculation is based on the assumption of an inviscid flbw without shock-waves, the results are thought to be useful for showing the main trends of the behaviour of a wing near the speed of sound. Plan-forms, which show rapid variations of the aerodynamic properties near Mach number M = 1 according to the potential theory, will have to be abandoned in favour of other planforms with more favourable characteristics.