Oblique Shock Calculator

An oblique shock forms when a supersonic stream is turned into itself by a compression corner, wedge, or similar surface. Unlike a normal shock, its front stands at an angle to the incoming flow. The velocity component normal to that front experiences normal-shock changes, while the tangential component remains unchanged in the ideal inviscid model. This calculator solves the theta-beta-M relation for the weak attached-shock angle and then applies perfect-gas normal-shock equations to determine the downstream state. The three inputs describe the upstream condition and geometry. Upstream Mach number must exceed one because a stationary shock requires supersonic flow. Flow deflection is the angle through which the surface turns the stream. The specific heat ratio, conventionally called gamma, describes the gas; 1.4 is a common approximation for dry air near ordinary temperatures. The numerical solver searches above the Mach angle for the first valid root. That first root is the weak solution normally observed when the flow can adjust without a forced strong shock. Pressure, density, and temperature ratios compare downstream values with upstream values. Every ratio is dimensionless. A pressure ratio of 2 means static pressure has doubled across the shock. The downstream Mach number is reconstructed from the downstream normal component and the angle between the shock and deflected flow. Entropy rises across the shock, total pressure falls, and the flow slows even when its overall downstream Mach number remains supersonic. Increasing wedge angle generally strengthens these changes until the requested turning exceeds the maximum attached-shock angle. The equations assume steady, two-dimensional, adiabatic, inviscid flow of a calorically perfect gas with constant gamma. They do not model boundary layers, chemical reactions, high-temperature dissociation, three-dimensional effects, or curved shock structure. Near the attachment limit, small input changes can produce large differences and real shocks may detach ahead of the body. Use this tool for coursework, preliminary nozzle and inlet studies, and quick aerodynamic checks. Detailed vehicle design should rely on validated compressible-flow software, appropriate gas models, and experimental evidence.