Wall corrections for wings oscillating in wind tunnels of closed rectangular section. Part I Theory and Tables. Part II Applications to a Delta Planform in a 9 x 7 Tunnel

Abstract

A method of calculating the tunnel interference due to oscillating loadings on wings in rectangular tunnels is described. This will apply to incompressible flow for all frequencies or to subsonic flow for small frequencies. The interference upwash due to a horse-shoe vortex of oscillating strength is derived from that for a steady horse-shoe vortex and hence the interference on wings with symmetrical or antisyminetrical loadings. An Appendix describes tables of a function basic to the theory for any rectangular section. Some other functions applicable in the particular case of a 9 x 7 tunnel are tabulated and their use is discussed. The effect of frequency variation on a typical interference upwash is illustrated. Part II contains an application of the method proposed in Part I to a cropped delta wing of aspect ratio 1.8. All the computation applies to incompressible flow in a 9 x 7 rectangular tunnel. In Section 2 the formulae necessary for the calculations are quoted or derived, and in Section 3 they are used for three ratios of wing span to tunnel breadth on the assumption that the frequency is small. The wing is assumed to be pitching or to have a full-span trailing-edge flap which is oscillating. Some calculations for the wing in pitching or heaving motion at a higher frequency are described in Section 4. In conclusion Section 5 contains a brief discussion of computability and accuracy.