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Compressibility Correction

The polynomial model described above is valid only for Mach numbers below about 0.3. Compressibility effects become important above Mach 0.3.

For subsonic flight, before the onset of drag divergence at about Mach 0.7, a simple correction is to divide each force coefficient by a compressibility correction factor $\beta$. For example, the equation to correct CZ is $C_Z = (C_{Z,incomp.})/\beta$.

The simplest correction is the Prandtl-Glauert factor (Reference 7, p. 212):

 \begin{displaymath}\beta = \sqrt{1-\mathbf{M}^2}
\end{displaymath} (60)

This relation is derived for isentropic flow. Most of the time, this is a reasonable assumption, as the flow around the streamlined aircraft is mostly isentropic. However, in conditions where isotropy is dubious (such as advanced stall, where there is substantial separation, and drag divergence, when shock waves appear), the correction is not valid.

Carl Banks