A Simple Method of Applying the Compressibility Correction in the Determination of True Air Speed

Abstract

By reviewing the complete impact pressure equation, which describes the pressure exerted by an air stream upon coming to rest, it is shown that the approximating assumption that is involved in the customary method of determining the true air speed of an airplane at altitude is no longer satisfactory for high-speed airplanes. The compressibility error that is a result of this assumption is isolated, and a method is described whereby the necessary correction may be applied by constructing additional altitude curves of indicated air speed (V\/<r) on the conventional air-speed indicator calibration chart. The true air speed at any altitude is then determined by the usual method—from the known value of indicated air speed and atmospheric pressure and temperature. The error that results if the compressibility correction is not applied is shown to be + 1 1 m.p.h. for a 400-m.p.h. airplane at 25,000 ft. altitude. The method here presented for applying the compressibility correction is less cumbersome than other suggested methods and has the additional advantage of retaining the use of the customary air-speed indicator calibration chart. Finally, the possible effect of compressibility on the position error of a pitot-static head installation is briefly analyzed and discussed, and the difficulties encountered in determining true atmospheric pressure and temperature in high-speed flight are mentioned.