Ernst Mach (1838-1916), an Austrian physicist and philosopher, was the first to understand the fundamental principles that govern supersonic flows and their impact on aerodynamics (1887). He recognized that one of the most important variables affecting aerodynamic behavior is the speed of the airflow over a body (V) relative to the speed of sound (a). The ratio of a body's speed to the speed of sound is known as the Mach number (M). Subsonic conditions occur for Mach numbers less than one, M < 1; transonic conditions when M ~ 1; supersonic conditions when 1 < M < 5; and hypersonic conditions when M > 5. Space shuttles re-enter the Earth's atmosphere at high hypersonic speeds, at M ~ 25. Under these conditions, the heated air becomes an ionized plasma of gas and the spacecraft must be insulated to protect it from these high external temperatures.