Oblique Shock Calculator

When a supersonic gas stream encounters an inclined wedge, it forms an oblique shock wave at a wave angle (beta). The incoming Mach number (M1) and specific heat ratio (gamma, denoted as G) govern the calculations. First, the normal component of the Mach number squared is calculated as ATerm = M1^2 * sin(beta)^2. From there, conservation of mass, momentum, and energy yield the deflection angle (theta), downstream Mach number (M2), and the property ratios across the shock. The static pressure ratio is given by p2/p1 = 1 + (2*gamma)/(gamma+1)*(ATerm - 1), while temperature and density ratios follow directly from the Rankine-Hugoniot jump conditions.

Consider an incoming supersonic airflow with an initial Mach number (M1) of 2.5 and a shock angle (beta) of 40 degrees through air, where the specific heat ratio (gamma) is 1.4. First, calculate the normal component term: ATerm = 2.5^2 * sin(40°)^2 = 6.25 * (0.6428)^2 = 2.583. Next, determine the static pressure ratio: p2/p1 = 1 + (2 * 1.4 / 2.4) * (2.583 - 1) = 1 + 1.1667 * 1.583 = 2.847. If the upstream pressure (p1) is 100 kPa, the downstream static pressure (p2) becomes 284.7 kPa. Similarly, the calculator utilizes these intermediate variables to determine the downstream Mach number (M2), deflection angle (theta), and density and temperature ratios.

Always verify that your selected shock angle (beta) is greater than the minimum shock angle (bmin = arcsin(1/M1)) for a given supersonic Mach number. Keep in mind that for every wedge deflection angle (theta) less than the maximum allowable angle, there are two potential shock solutions: the weak shock and the strong shock. Most supersonic applications naturally exhibit the weak shock solution due to downstream pressure conditions.