In the design of contraction cones for wind tunnels little account appears to have been taken of the influence of compressibility on the performance; the rules of thumb resulting from experience in low-speed wind tunnels are applied regardless of the speed range being considered. This is not surprising in view of the lack of understanding of the complex processes in the development of the stream turbulence through a contraction cone. In addition to the dominant process of the distortion of the vortex lines, the flow is influenced by decay, by the interchange of energy between components both because of the tendency to isotropy and because of the curvature of the flow, and by the apparent turbulence created by turbulent wall boundary layers. Eventually methods of turbulence modelling should be able to calculate the flow but meanwhile it is worth examining the predictions of rapid distortion theory.