Causes
When an object passes through the air it creates a series of pressure waves in front of it and behind it, similar to the bow and stern waves created by a boat. These waves travel at the speed of sound, and as the speed of the object increases, the waves are forced together, or compressed, because they cannot get out of the way of each other, eventually merging into a single shock wave at the speed of sound. This critical speed is known as Mach 1 and is approximately 1,225 km/h (761 mph) at sea level and 20 °C (68 °F). In smooth flight, the shock wave starts at the nose of the aircraft and ends at the tail. Because radial directions around the aircraft's direction of travel are equivalent, the shock forms a Mach cone with the aircraft at its tip. The half-angle (between direction of flight and the shock wave) is given by
- ,
where is the plane's Mach number. So the faster it goes, the finer, (more pointed) the cone.
There is a rise in pressure at the nose, decreasing steadily to a negative pressure at the tail, followed by a sudden return to normal pressure after the object passes. This "overpressure profile" is known as an N-wave because of its shape. The "boom" is experienced when there is a sudden change in pressure, so the N-wave causes two booms, one when the initial pressure rise from the nose hits, and another when the tail passes and the pressure suddenly returns to normal. This leads to a distinctive "double boom" from supersonic aircraft. When maneuvering, the pressure distribution changes into different forms, with a characteristic U-wave shape.
Since the boom is being generated continually as long as the aircraft is supersonic, it fills out a narrow path on the ground following the aircraft's flight path, a bit like an unrolling red carpet and hence known as the boom carpet. Its width depends on the altitude of the aircraft. The distance from the point on the ground where the boom is heard to the aircraft depends on its altitude and the angle .
For today's supersonic aircraft in normal operating conditions, the peak overpressure varies from less than 50 to 500 Pa (about 1 to 10 psf (pound per square foot)) for a N-wave boom. Peak overpressures for U-waves are amplified two to five times the N-wave, but this amplified overpressure impacts only a very small area when compared to the area exposed to the rest of the sonic boom. The strongest sonic boom ever recorded was 7,000 Pa (144 psf) and it did not cause injury to the researchers who were exposed to it. The boom was produced by a F-4 flying just above the speed of sound at an altitude of 100 feet (30 m). In recent tests, the maximum boom measured during more realistic flight conditions was 1,010 Pa (21 psf). There is a probability that some damage — shattered glass for example — will result from a sonic boom. Buildings in good repair should suffer no damage by pressures of 11 psf (530 Pa) or less. And, typically, community exposure to sonic boom is below two psf (100 Pa). Ground motion resulting from sonic boom is rare and is well below structural damage thresholds accepted by the U.S. Bureau of Mines and other agencies.
The power, or volume, of the shock wave is dependent on the quantity of air that is being accelerated, and thus the size and shape of the aircraft. As the aircraft increases speed the shock cone gets tighter around the craft and becomes weaker to the point that at very high speeds and altitudes no boom is heard. The "length" of the boom from front to back is dependent on the length of the aircraft to a power of 3/2. Longer aircraft therefore "spread out" their booms more than smaller ones, which leads to a less powerful boom.
Several smaller shock waves can, and usually do, form at other points on the aircraft, primarily any convex points or curves, the leading wing edge and especially the inlet to engines. These secondary shockwaves are caused by the air being forced to turn around these convex points, which generates a shock wave in supersonic flow.
The later shock waves are somewhat faster than the first one, travel faster and add to the main shockwave at some distance away from the aircraft to create a much more defined N-wave shape. This maximizes both the magnitude and the "rise time" of the shock which makes the boom seem louder. On most designs the characteristic distance is about 40,000 feet (12,000 m), meaning that below this altitude the sonic boom will be "softer". However, the drag at this altitude or below makes supersonic travel particularly inefficient, which poses a serious problem.
Read more about this topic: Sonic Boom