What is an Oblique Shock Wave?

An oblique shock wave is a type of shock wave that occurs when a supersonic flow is turned into itself by a concave corner or a wedge. Unlike a normal shock wave, which is perpendicular to the flow direction, an oblique shock is inclined at an angle. These shocks are critical in supersonic aerodynamics, appearing on aircraft wings, engine inlets, and rocket nozzles.

How to Use the Oblique Shock Calculator

To calculate the flow properties across an oblique shock, you need three primary inputs: the initial Mach number (M₁), the deflection angle of the wedge (θ), and the ratio of specific heats (γ), which is typically 1.4 for air.

Once you input these values, the tool solves the θ-β-M relation to find the shock wave angle (β). It then calculates the downstream Mach number (M₂), pressure increase, temperature rise, and density changes across the shock. Please note that for every combination of Mach number and deflection angle, there are typically two solutions (Weak and Strong), though in most practical aerodynamic cases, the weak shock solution is observed.

Understanding the Limits: Detached Shocks

For a given Mach number, there is a maximum deflection angle (θ_max). If the wedge angle exceeds this value, a straight oblique shock cannot stay attached to the tip of the wedge. Instead, it becomes a curved, detached shock (bow shock). This calculator will notify you if your inputs result in a detached shock condition, where the standard θ-β-M equations no longer provide a real solution.

Frequently Asked Questions

What is the difference between a normal and oblique shock?
A normal shock is a special case of an oblique shock where the shock angle is 90 degrees. Normal shocks result in the greatest loss of stagnation pressure and always lead to subsonic flow, whereas oblique shocks can result in either supersonic or subsonic downstream flow.

Why is the weak shock solution preferred?
In external aerodynamics (like flight over a wing), the downstream pressure is generally lower, allowing the flow to follow the weak shock solution. The strong shock solution is typically only seen in confined internal flows or under specific laboratory conditions.