The speed of sound and the TAS factors [in the mach equation are both dependent on temperature AND since they are both composite functions of temperature the changes that occur in temperature are only required for determine local 'FREE -STREAM conditions'
meaning,...with out any influnce of an aerodyamnic body impinging on the local freesteam,...i.e nothing possesing a TAS [dependent on temperature],...so instrument for calibration i.e the machmeter there's no T
Further, ram rise could be thought of as equally affected both terms of the mach number realation,....therefore there's no temperature differential,...
However, when dealing with supersonic flows the ram rise contributes to a temperature differential and dyanmic heating has to be taken into account in both terms ....
the Karman-Tsien relationship derived about 1926 by Von Karman and Hsue-Tsien just happens to be the most comonly used [at least in the US
] for the subsonic regimes for correcting the q term in H,...H being Ps+q, for compressibility,... the relation fails miserably at supersonic speeds
PA
