Oblique Shock Calculator

Calculate oblique shock wave properties in supersonic flow. Determine the shock angle, downstream Mach number, pressure ratio, and temperature ratio from upstream conditions.

SHOCK ANGLE
--
Shock Angle β
--
Downstream Mach
--
Pressure Ratio
--
Temp Ratio
--

What Is an Oblique Shock?

An oblique shock wave is a shock wave that forms at an angle to the incoming supersonic flow, typically caused by a wedge, cone, or other deflecting surface. Unlike normal shocks (perpendicular to flow), oblique shocks allow the flow to remain supersonic downstream while changing direction. They are fundamental to supersonic aerodynamics and appear on aircraft wings, engine inlets, and around any body moving faster than sound.

The shock angle beta depends on the upstream Mach number and the deflection angle theta. For each combination, there are generally two solutions: a weak shock (smaller beta, flow remains supersonic) and a strong shock (larger beta, flow becomes subsonic). In practice, the weak shock solution almost always occurs.

Theta-Beta-Mach Relation

tan(θ) = 2 cot(β) × [M²sin²(β) - 1] / [M²(γ + cos(2β)) + 2]

Shock Properties

PropertyChange Across Shock
PressureIncreases
TemperatureIncreases
DensityIncreases
Mach numberDecreases
Total pressureDecreases (entropy rises)
Flow directionTurns toward shock

Frequently Asked Questions

When does a detached shock form?

When the deflection angle exceeds the maximum turning angle for a given Mach number, no attached oblique shock solution exists. A curved detached (bow) shock forms ahead of the body, with a subsonic region behind the shock near the nose. This maximum angle decreases as Mach number decreases toward 1.

What is the Mach angle?

The Mach angle is the minimum possible oblique shock angle, equal to arcsin(1/M). It represents an infinitesimally weak wave (Mach wave) with zero deflection. All oblique shock angles fall between the Mach angle and 90 degrees.