vehicles frequently fly at very high altitudes and therefore encounter low-density conditions. Hence, the design and analysis of hypersonic vehicles sometimes require consideration of low-density flow. New generations of hypersonic airplanes may spend a considerable portion of their mission at high altitudes, and for these vehicles, low-density effects will become more significant. Thin shock layer The flow field between the shock wave and the body surface is called the shock layer. As the Mach number M increases, the angle of the resulting shock wave decreases. This Mach angle is described by the equation where a is the speed of the sound wave and v is the flow velocity. Since M=v/a, the equation becomes . Higher Mach numbers position the shock wave closer to the body surface, thus at hypersonic speeds, the shock wave lies extremely close to the body surface, resulting in a thin shock layer. At low Reynolds number, the boundary layer grows quite thick and merges with the shock wave, leading to a fully viscous shock layer. Viscous interaction The compressible flow boundary layer increases proportionately to the square of the Mach number, and inversely to the square root of the Reynolds number. At hypersonic speeds, this effect becomes much more pronounced, due to the exponential reliance on the Mach number. Since the boundary layer becomes so large, it interacts more viscously with the surrounding flow. The overall effect of this interaction is to create a much higher skin friction than normal, causing greater surface heat flow. Additionally, the surface pressure spikes, which results in a much larger aerodynamic drag coefficient. This effect is extreme at the leading edge and decreases as a function of length along the surface. Entropy layer The entropy layer is a region of large velocity gradients caused by the strong curvature of the shock wave. The entropy layer begins at the nose of the aircraft and extends downstream close to the body surface. Downstream of the nose, the entropy layer interacts with the boundary layer which causes an increase in aerodynamic heating at the body surface. Although the shock wave at the nose at supersonic speeds is also curved, the entropy layer is only observed at hypersonic speeds because the magnitude of the curve is far greater at hypersonic speeds. Applications Controlled detonation Researchers in China have used shock waves in a detonation chamber to compress ionized argon plasma waves moving at Mach