Sommer-Short Method
The Sommer-Short method maps compressible turbulent skin friction to the incompressible Karman-Schoenherr relation using an empirical reference temperature derived from free-flight drag measurements.1
The reference-temperature ratio is
\[
\frac{T'_{SS}}{T_e}
=
1 + 0.035M_e^2 + 0.45\left(\frac{T_w}{T_e} - 1\right).
\]
The transformation factors are
\[
F_c = \frac{T'_{SS}}{T_e},
\]
\[
F_\theta = \frac{\mu_e}{\mu'_{SS}},
\]
and, because these factors are constant along the plate,
\[
F_x = \frac{F_\theta}{F_c}.
\]
Here \(\mu'_{SS}=\mu(T'_{SS})\). The shared turbulent mapping from \(F_x\) and \(F_c\) to local compressible skin friction is documented in Turbulent Estimates.
References
-
Sommer, S.C. and Short, B.J. (1955). Free-flight measurements of turbulent boundary-layer skin friction in the presence of severe aerodynamic heating at Mach numbers from 2.8 to 7.0. NACA TN 3391. ↩