Discontinuous changes also occur in the pressure, density and temperature, which all rise downstream of the oblique shock wave.
[2] It is more intuitive to want to solve for β as a function of M1 and θ, but this approach is more complicated, the results of which are often contained in tables or calculated through a numerical method.
A θ-β-M diagram, common in most compressible flow textbooks, shows a series of curves that will indicate θMAX for each Mach number.
This can be attributed to the fact that using one or a combination of oblique shock waves results in more favourable post-shock conditions (smaller increase in entropy, less stagnation pressure loss, etc.)
Early supersonic aircraft jet engine intakes were designed using compression from a single normal shock, but this approach caps the maximum achievable Mach number to roughly 1.6.
Placing a diamond-shaped object at an angle of attack relative to the supersonic flow streamlines will result in two oblique shocks propagating from the front tip over the top and bottom of the wing, with Prandtl-Meyer expansion fans created at the two corners of the diamond closest to the front tip.
As the Mach number of the upstream flow becomes increasingly hypersonic, the equations for the pressure, density, and temperature after the oblique shock wave reach a mathematical limit.