At ordinary aeroplane speeds the effect of the compressibility of the air is very small, and there is complete justification for the usual assumption that the air may be regarded effectively as an incompressible medium. This assumption, however, ceases to be valid in the case of high tip-speed airscrews and is not really satisfactory even when the tip speed is no greater than 800 f. p. s. It is important, therefore, to examine, both theoretically and experimentally, the effect of compressibility at high speed on the characteristics of an aerofoil. Experimental investigations are in progress at the Royal Aircraft Establishment in which the aerofoil characteristics are derived by analysing the observed behaviour of high-speed model airscrews, but owing to the complexity both of the experiments and of the analysis it is impossible that the results should have the same accuracy as those obtained from direct tests of an aerofoil at low speed. An attempt has now been made to estimate theoretically the effect of compressibility on the lift of an aerofoil in two-dimensional motion and to indicate the nature of the variation which may be anticipated in the curve of lift coefficient against angle of incidence. It is unfortunately impossible at the present state of knowledge to make any similar calculation for the drag of the aerofoil, but on general grounds we may anticipate that the drag coefficient will rise at an increasing rate until the velocity of sound is reached, and that above this speed the drag coefficient will decrease again, remaining, however, higher than at low speeds.
Three optimization formulations for an inverse problem in saddle point problems with applications to elasticity imaging of locating tumor in incompressible medium
