Oblique Shock Relations
Oblique shocks satisfy the theta-beta-Mach relation for a wedge or local turning angle in supersonic flow.
Theta-Beta-Mach Relation
For upstream Mach number \(M\), shock angle \(\beta\), deflection angle \(\theta\), and \(\gamma\):
\[
\tan\theta = \frac{2\cot\beta\,(M^2\sin^2\beta - 1)}{M^2(\gamma + \cos 2\beta)+2}
\]
The normal component is handled using normal-shock relations:
\[
M_{n1} = M\sin\beta
\]
Then \(M_{n2}\) is computed from normal-shock equations, and full downstream Mach is:
\[
M_2 = \frac{M_{n2}}{\sin(\beta-\theta)}
\]
References
Anderson, J. D. (2003). Modern Compressible Flow: With Historical Perspective, 3rd ed. McGraw-Hill, Chapter 4.