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Shock Polar Visualizer

Visualize the theta-beta-M curve, weak/strong oblique-shock solutions, and detachment limit from Mach and turn angle.

shock
visual calculatorCompressible Flow

Read the flow shape before trusting the number.

This page turns a CFD setup into regime, scale, and dominant-effect cues. Adjust the calculator below and compare the moving graphic with the computed result.

01
input scale
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model
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check
compressibleshock polaroblique shocktheta-beta-Mvisualization
formula
KaTeX rendered
tan(theta) = 2 cot(beta) (M1ˆ2 sinˆ2(beta) - 1) / [M1ˆ2 (gamma + cos(2 beta)) + 2]\begin{aligned}\text{tan(theta) = 2 cot(beta) (M1\^{}2 sin\^{}2(beta) - 1) / [M1\^{}2 (gamma + cos(2 beta)) + 2]}\end{aligned}
ASCII sourcetan(theta) = 2 cot(beta) (M1^2 sin^2(beta) - 1) / [M1^2 (gamma + cos(2 beta)) + 2]
Theta-beta-M shock mapweak and strong attached-shock branches081725332440577390beta (deg)theta (deg)detached regiontheta=12.0 degsupersonic inflowcompression cornerweakstrong
theta max (deg)
29.80
Mach angle (deg)
23.58
weak beta (deg)
33.80
strong beta (deg)
84.61
weak M2
2.002
strong M2
0.539
weak p2/p1
2.090
detachment margin
17.80 deg

The curve follows the theta-beta-M relation for attached oblique shocks. When the requested turn angle exceeds theta max, the attached solution disappears and a detached bow shock is expected.

compressibleshock polaroblique shocktheta-beta-Mvisualization