Oblique Shock Calculator
Calculate oblique shock wave properties from Mach number and wave angle. Get turn angle, downstream Mach, pressure, density, temperature, and stagnation ratios.
About This Calculator
The Oblique Shock Calculator computes the fluid flow properties across an oblique shock wave using the θ-β-M relation and standard compressible flow equations. It is designed for aerospace engineers, mechanical engineers, and students working with supersonic aerodynamics, aircraft intake design, and compressible fluid dynamics.
An oblique shock wave forms when a supersonic flow is turned by a wedge or corner. The calculator takes the upstream Mach number (M₁), the shock wave angle (β), and the specific heat ratio (γ) to determine the flow deflection angle (θ), downstream Mach number (M₂), and the ratios of pressure (p₂/p₁), temperature (T₂/T₁), density (ρ₂/ρ₁), and stagnation pressure (p₀₂/p₀₁) across the shock. The normal shock components Mₓ = M₁ sin β and M_y are also computed.
The governing equations are derived from the conservation of mass, momentum, and energy across an oblique discontinuity. For dry air, the specific heat ratio is 1.4. The calculator also validates input constraints — the Mach number must be supersonic (M₁ > 1) and the wave angle must exceed the Mach angle μ = arcsin(1/M₁) to ensure an attached shock solution.
Frequently Asked Questions
What is an oblique shock wave?
An oblique shock wave is a shock wave that is inclined at an angle to the upstream flow direction. It occurs when a supersonic flow encounters a wedge or a corner, causing an abrupt change in fluid pressure, temperature, density, and velocity across the shock.
What is the θ-β-M relation in oblique shock theory?
The θ-β-M relation (theta-beta-Mach) relates the flow deflection angle (θ), shock wave angle (β), and upstream Mach number (M₁). It is given by tan(θ) = 2 cot(β)(M₁²sin²β − 1) / [M₁²(γ + cos(2β)) + 2], where γ is the specific heat ratio.
What is the difference between a normal shock and an oblique shock?
A normal shock wave is perpendicular to the flow direction, while an oblique shock wave is inclined at an angle. Oblique shocks are generally weaker than normal shocks for the same upstream Mach number, resulting in lower total pressure losses.
What causes an oblique shock wave to form?
An oblique shock forms when supersonic flow is forced to turn due to a geometric obstruction like a wedge, cone, or corner in an aircraft intake. The flow abruptly changes direction and compresses, creating an inclined discontinuity.
What is the Mach angle and how does it relate to shock waves?
The Mach angle (μ) is the minimum possible shock angle, given by μ = arcsin(1/M₁). For an attached oblique shock, the wave angle β must be greater than the Mach angle. If β ≤ μ, the shock becomes detached and a bow shock forms ahead of the body.
How do oblique shocks affect aircraft design?
Oblique shocks are used in supersonic aircraft intake design to slow down incoming air before it reaches the engine. Aircraft such as the Concorde, F-22 Raptor, and MiG-21 use inlet ramps or cones to generate controlled oblique shocks for efficient engine operation.
Can an oblique shock exist for subsonic flow?
No, oblique shocks only form when the upstream flow is supersonic (Mach number greater than 1). For subsonic flow, the disturbances propagate ahead of the object and no shock discontinuity forms.
What is the specific heat ratio and what value is used for air?
The specific heat ratio (γ) is the ratio of specific heat at constant pressure (Cp) to specific heat at constant volume (Cv). For dry air at standard conditions, γ = 1.4. The calculator allows adjusting this value for other gases.