It is always possible to convert an oblique shock into a normal shock by a Galilean transformation.
For a given Mach number, M1, and corner angle, θ, the oblique shock angle, β, and the downstream Mach number, M2, can be calculated. M2 is always less than M1. Unlike after a normal shock, M2 can still be supersonic. Discontinuous changes also occur in the pressure, density and temperature, which all rise downstream of the oblique shock wave.
Using the continuity equation and the fact that the tangential velocity component does not change across the shock, trigonometric relations eventually lead to the θ-β-M equation which shows θ as a function of M1 and β. 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 an applet.
Within the θ-β-M equation, a maximum corner angle, θMAX, exists for any upstream Mach number. When θ > θMAX, the oblique shock wave is no longer attached to the corner and is replaced by a detached bow shock. A θ-β-M diagram, common in most compressible flow textbooks, shows a series of curves that will indicate θMAX for each Mach number. The θ-β-M relationship will produce two β angles for a given θ and M1, with the larger angle called a strong shock and the smaller called a weak shock. The weak shock is almost always seen experimentally.
The rise in pressure, density, and temperature after an oblique shock can be calculated as follows:
M2 is solved for as follows:
Many supersonic aircraft wings are designed around a thin diamond shape. 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. When correctly designed, this generates lift.
For a perfect atmospheric gas approximation using γ = 1.4, the hypersonic limit for the density ratio is 6. However, hypersonic post-shock dissociation of O2 and N2 into O and N lowers γ, allowing for higher density ratios in nature. The hypersonic temperature ratio is:
US Patent Issued to National Research Council of Canada on Jan. 4 for "Super Compressed Detonation Method and Device to Effect Such Detonation" (Canadian Inventors)
Jan 08, 2011; ALEXANDRIA, Va., Jan. 8 -- United States Patent no. 7,861,655, issued on Jan. 4, was assigned to National Research Council of...