Normal Shock Wave Approximations for Flight at Hypersonic Mach Numbers

Normal shock pressure ratios in equilibrium air for Mach numbers up to 30 and altitudes to 300,000 feet are shown to be correlated by a simple power law which provides an accuracy of ±2%, thereby permitting direct calculation of corresponding enthalpy ratios accurate to ±1% without iteration; a slight change in power-law coefficients extends this capability to Mach 65. Temperature, density, and compressibility may be then found directly from tables for high temperature air. For Mach numbers up to at least 6, a linear approximation for specific heat provides direct solutions for post-shock state variables, while a complementary logarithmic model of the equation of state enables direct solutions for Mach numbers up to about 12. This approach, which provides accuracy within ±3% for all relevant variables in the practical flight corridor of vehicles at these low to moderate hypersonic Mach numbers, should prove useful in design and analysis because the algebraic solutions obtained need neither iteration or interpolation.