Oblique Shock Calculator

What Is an Oblique Shock?

An oblique shock forms when supersonic flow turns through a wedge or compression corner. Unlike a normal shock, the wave sits at an angle to the incoming flow. The flow deflection angle and upstream Mach number determine shock strength and downstream conditions.

Oblique Shock Relations

Given upstream Mach number $M_1$, deflection angle $\delta$, and heat capacity ratio $\gamma$, the shock angle $\beta$ satisfies:

$$\tan\delta = \frac{2\cot\beta\,(M_1^2\sin^2\beta - 1)}{M_1^2(\gamma + \cos 2\beta) + 2}$$

Normal shock relations then give pressure, density, and temperature ratios using $M_{1n} = M_1\sin\beta$. Tangential velocity is conserved across the shock.

Frequently Asked Questions

When does an oblique shock not exist?

For a given $M_1$, deflection has a maximum value. Beyond that, the shock detaches from the wedge and becomes curved (bow shock).

What is the weak shock solution?

For most wedge problems, two shock angles satisfy the deflection equation. The smaller angle (weak shock) is the physically typical attached solution calculated here.

What value of gamma should I use for air?

Use $\gamma = 1.4$ for dry air at moderate temperatures. Real gas effects matter at very high temperatures behind strong shocks.

Is downstream flow always supersonic?

After a weak oblique shock, downstream Mach number $M_2$ is usually still supersonic but lower than $M_1$. Strong shocks can produce subsonic downstream flow.

How is this different from a normal shock?

A normal shock has $\beta = 90°$ and stops all normal velocity. Oblique shocks turn the flow and generally produce weaker property jumps for the same upstream Mach number.

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What Is an Oblique Shock?

Oblique Shock Relations

Frequently Asked Questions

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