A simple form of Rayleigh pitot tube formula
Rayleigh pitot tube formula is a very basic and commonly used formula in aerodynamics. It gives the rate of the total pressure behind a normal shock wave and the pressure of freestream at a given Mach number. Although the relation is rigorous in theory, it is difficult to understand the changing relationships between these variables due to its complexity as shown in the above formula. A numerically equivalent formula has been discovered. It is very simple while it still retains a high-precision. The coefficient of determination between the two formula is greater than 99.9% in a domain sufficient for practical applications. The new formula was detected by a special machine learning method, functional learning. The function blocks are limited to rational functions. A divide and conquer scheme is also applied during the learning process.
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