Breaking the Sound Barrier
Below the speed of sound, pressure disturbances propagate ahead of an aircraft, allowing air to 'prepare' for its arrival. Above Mach 1, the aircraft outruns these signals — air encounters the vehicle with no warning and must adjust through shock waves, sudden discontinuities where pressure, temperature, and density spike. Chuck Yeager first exceeded Mach 1 in the Bell X-1 in 1947, proving that controlled flight beyond the sound barrier was possible despite violent buffeting in the transonic regime.
Oblique Shock Geometry
When supersonic flow encounters a wedge or cone, an oblique shock wave forms at a specific angle that depends on the Mach number and deflection angle. The θ-β-M relation — one of the most important equations in compressible flow — connects these three quantities. For a given Mach number, there is a maximum deflection angle beyond which an attached oblique shock cannot exist, and a curved detached bow shock forms instead. This simulation solves the θ-β-M relation numerically to find the shock geometry.
Across the Shock
Crossing an oblique shock, the flow changes abruptly. Pressure and temperature increase while velocity decreases. The normal component of Mach number drops below 1, but the tangential component is preserved — so the total downstream Mach number can remain supersonic. Engineers exploit this by using multiple weak oblique shocks (in supersonic inlets) rather than a single strong normal shock, dramatically reducing total pressure losses.
Expansion and Compression
Supersonic flow turning away from itself (around a convex corner) accelerates through a Prandtl-Meyer expansion fan — a continuous, isentropic process that is the opposite of a shock. By combining oblique shocks (compression) and expansion fans (acceleration), supersonic aerodynamicists can design efficient engine inlets, nozzles, and waverider vehicles that surf their own shock waves for maximum lift-to-drag ratio at hypersonic speeds.