As an object moves through the air it creates a series of pressure waves in front 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 aircraft increases the waves are forced together 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 740 miles per hour at sea level.
In smooth flight, the shock wave starts at the nose of the aircraft and ends at the tail. There is a sudden rise in pressure at the nose, decreasing steadily to a negative pressure at the tail, where it suddenly returns to normal. This "overpressure profile" is known as the N-wave due to it's shape. We experience the "boom" when there is a sudden rise 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 manuvering the pressure distribution changes into different forms, with a characteristic U-wave shape.
The power, or volume, of the shock wave is dependant on the amount of air that is being sped up, and thus the size and weight of the aircraft. As the aircraft increases speed the shocks grow "tighter" around the craft, and do not become much "louder". At very high speeds and altitudes the cone does not intersect the ground, and no boom will be heard. The "length" of the boom from front to back is dependant on the length of the aircraft, although to a factor of 3:2 not 1:1. Longer aircraft therefore "spread out" their booms more than smaller ones, which leads to a less powerful boom.
Several smaller shock waves form at other points on the aircraft, primarily any convex points or curves. After travelling some distance these smaller shocks blend together with the main shocks to create a much more defined N-wave shape, which maximizes both the magnetude and the "rise time" of the shock, which makes it seem louder. On most designs the characteristic distance is about 40,000ft, meaning that below this altitude the sonic boom will be "softer". However the drag at this altitude or below makes supersonic travel particularily ineffecient, which poses a serious problem.
In the late 1950s when SST designs were being actively pursued it was thought that although the boom would be very large, they could avoid problems by flying higher. This premise was proven false when the North American B-70 Valkyrie started flying and it was found that the boom was a very real problem even at 70,000ft (21,000m), leading to the characterization of the N-wave. Seebass-George defined a "figure of merit", FM, to characterize the sonic boom levels of difference aircraft, proportional to the aircraft weight divided by the three-halves of the aircraft length, FM = W/L^(3/2). The lower this value, the less boom the aircraft generates, with figures of about 1 or lower being considered acceptable. Using this calculation they found FM's of 1.41 for the Concorde, and 1.9 for the Boeing 2707. This eventually doomed most SST projects as public resentment, somewhat blown out of proportion, mixed with politics and eventually resulted in laws that made any such aircraft impractical (flying only over water for instance).
At first it was thought there was little that could be done to address these issues, but theory at the time suggested that body shaping might be able to use the secondary shocks to either "spread out" the N-wave, or interfere with each other to the same end. Ideally this would raise the characteristic altitude from 40,000ft to 60,000, which is where most SST designs fly. The design required some fairly sophisticated shaping in order to achieve the dual needs of reducing the shock and still leaving an aerodynamically efficient shape, and therefore had to wait for the advent of computer aided design before being able to be built. This remained untested for decades, until DARPA started the Quiet Supersonic Platform project and funded the Shaped Sonic Boom Demonstration aircraft to test it. SSBD used a F-5 Freedom Fighter modified with a new body shape, and demonstrated dramatically reduced sound levels at the ground after the test series concluded in August 2003 and the data was analyzed. There is some hope that such shaping may make a future generation of SST designs more practical.
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