A statistical-mechanical model for surface pressure in hypersonic flows

Based on a statistical-mechanical model of gas molecules, a closed-form formula of the pressure coefficient of a surface is given as a function of the incident angle to the surface (or the surface inclination angle) and the Mach number, which is asymptotically accurate as the Mach number increases to the hypersonic regime. The classical Newtonian flow theory is a limiting case of this formula as the Mach number approaches to infinity. For validation, the lift and drag coefficients of a flat-plate airfoil and a sphere are calculated in a range of the Mach numbers from 2 to 30 in comparison with the shock-expansion-wave theory and the experimental data.