sonic boom

Causes

When an aircraft passes through the air, it creates a series of pressure waves in front of the aircraft 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 each other's way quickly enough. Eventually, they merge into a single shock wave, which travels at the speed of sound, a critical speed known as Mach 1, which is approximately 1,192 km/h (741 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 the different radial directions around the aircraft's direction of travel are equivalent (given the "smooth flight" condition), the shock wave forms a Mach cone, similar to a vapour cone, with the aircraft at its tip. The half-angle

α

{\displaystyle \alpha }

between the direction of flight and the shock wave is given by:

sin

⁡

α

=

v

sound

v

object

{\displaystyle \sin \alpha ={\frac {v_{\text{sound}}}{v_{\text{object}}}}}

,

where

v

sound

v

object

{\displaystyle {\tfrac {v_{\text{sound}}}{v_{\text{object}}}}}

Supersonic aircraft

Supersonic aircraft are any aircraft that can achieve flight faster than Mach 1, which refers to the speed of sound. "Supersonic includes speeds up to five times the speed of sound, or Mach 5." The top speed for a supersonic aircraft normally ranges from 700 to 1,500 miles per hour (1,100 to 2,400 km/h). Typically, most aircraft do not exceed 1,500 mph (2,414 km/h). There are many variations of supersonic aircraft. Some models of supersonic aircraft make use of better-engineered aerodynamics that allow a few sacrifices in the aerodynamics of the model for thruster power. Other models use the efficiency and power of the thruster to allow a less aerodynamic model to achieve greater speeds.

Measurement and examples

The pressure from sonic booms caused by aircraft is often a few pounds per square foot. A vehicle flying at greater altitude will generate lower pressures on the ground because the shock wave reduces in intensity as it spreads out away from the vehicle, but the sonic booms are less affected by vehicle speed.

Abatement

In the late 1950s when supersonic transport (SST) designs were being actively pursued, it was thought that although the boom would be very large, the problems could be avoided by flying higher. This assumption was proven false when the North American XB-70 Valkyrie first flew, and it was found that the boom was a problem even at 70,000 feet (21,000 m). It was during these tests that the N-wave was first characterized.

Richard Seebass and his colleague Albert George at Cornell University studied the problem extensively and eventually defined a "figure of merit" (FM) to characterize the sonic boom levels of different aircraft. FM is a function of the aircraft's weight and the aircraft length. 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 FMs of about 1.4 for Concorde and 1.9 for the Boeing 2707. This eventually doomed most SST projects as public resentment, mixed with politics, eventually resulted in laws that made any such aircraft less useful (flying supersonically only over water for instance). Small airplane designs like business jets are favored and tend to produce minimal to no audible booms.

Building on the earlier research of L. B. Jones, Seebass, and George identified conditions in which sonic boom shockwaves could be eliminated. This work was extended by Christine M. Darden and described as the Jones-Seebass-George-Darden theory of sonic boom minimization. This theory approached the problem from a different angle, trying to spread out the N-wave laterally and temporally (longitudinally), by producing a strong and downwards-focused (SR-71 Blackbird, Boeing X-43) shock at a sharp, but wide angle nose cone, which will travel at slightly supersonic speed (bow shock), and using a swept back flying wing or an oblique flying wing to smooth out this shock along the direction of flight (the tail of the shock travels at sonic speed). To adapt this principle to existing planes, which generate a shock at their nose cone and an even stronger one at their wing leading edge, the fuselage below the wing is shaped according to the area rule. Ideally, this would raise the characteristic altitude from 40,000 feet (12,000 m) to 60,000 feet (from 12,000 m to 18,000 m), which is where most SST aircraft were expected to fly.

This remained untested for decades, until DARPA started the Quiet Supersonic Platform project and funded the Shaped Sonic Boom Demonstration (SSBD) aircraft to test it. SSBD used an F-5 Freedom Fighter. The F-5E was modified with a highly refined shape which lengthened the nose to that of the F-5F model. The fairing extended from the nose back to the inlets on the underside of the aircraft. The SSBD was tested over two years culminating in 21 flights and was an extensive study on sonic boom characteristics. After measuring the 1,300 recordings, some taken inside the shock wave by a chase plane, the SSBD demonstrated a reduction in boom by about one-third. Although one-third is not a huge reduction, it could have reduced Concorde's boom to an acceptable level below FM = 1.

Perception, noise, and other concerns

The sound of a sonic boom depends largely on the distance between the observer and the aircraft shape producing the sonic boom. A sonic boom is usually heard as a deep double "boom" as the aircraft is usually some distance away. The sound is much like that of mortar bombs, commonly used in firework displays. It is a common misconception that only one boom is generated during the subsonic to supersonic transition; rather, the boom is continuous along the boom carpet for the entire supersonic flight. As a former Concorde pilot puts it, "You don't actually hear anything on board. All we see is the pressure wave moving down the airplane – it indicates the instruments. And that's what we see around Mach 1. But we don't hear the sonic boom or anything like that. That's rather like the wake of a ship – it's behind us."

In 1964, NASA and the Federal Aviation Administration began the Oklahoma City sonic boom tests, which caused eight sonic booms per day over six months. Valuable data was gathered from the experiment, but 15,000 complaints were generated and ultimately entangled the government in a class-action lawsuit, which it lost on appeal in 1969.

Sonic booms were also a nuisance in North Cornwall and North Devon in the UK as these areas were underneath the transatlantic flight path of Concorde. Windows would rattle and in some cases, the "torching" (masonry mortar underneath roof slates) would be dislodged with the vibration.

There has been recent work in this area, notably under DARPA's Quiet Supersonic Platform studies. Research by acoustics experts under this program began looking more closely at the composition of sonic booms, including the frequency content. Several characteristics of the traditional sonic boom "N" wave can influence how loud and irritating it can be perceived by listeners on the ground. Even strong N-waves such as those generated by Concorde or military aircraft can be far less objectionable if the rise time of the over-pressure is sufficiently long. A new metric has emerged, known as perceived loudness, measured in PLdB. This takes into account the frequency content, rise time, etc. A well-known example is the snapping of one's fingers in which the "perceived" sound is nothing more than an annoyance.

The energy range of sonic boom is concentrated in the 0.1–100 hertz frequency range that is considerably below that of subsonic aircraft, gunfire and most industrial noise. Duration of sonic boom is brief; less than a second, 100 milliseconds (0.1 second) for most fighter-sized aircraft and 500 milliseconds for the space shuttle or Concorde jetliner. The intensity and width of a sonic boom path depend on the physical characteristics of the aircraft and how it is operated. In general, the greater an aircraft's altitude, the lower the over-pressure on the ground. Greater altitude also increases the boom's lateral spread, exposing a wider area to the boom. Over-pressures in the sonic boom impact area, however, will not be uniform. Boom intensity is greatest directly under the flight path, progressively weakening with greater horizontal distance away from the aircraft flight track. Ground width of the boom exposure area is approximately 1 statute mile (1.6 km) for each 1,000 feet (300 m) of altitude (the width is about five times the altitude); that is, an aircraft flying supersonic at 30,000 feet (9,100 m) will create a lateral boom spread of about 30 miles (48 km). For steady supersonic flight, the boom is described as a carpet boom since it moves with the aircraft as it maintains supersonic speed and altitude. Some maneuvers, diving, acceleration, or turning, can cause the focus of the boom. Other maneuvers, such as deceleration and climbing, can reduce the strength of the shock. In some instances, weather conditions can distort sonic booms.

Bullwhip

The cracking sound of a bullwhip is a small sonic boom. The end of the whip, known as the "cracker", moves faster than the speed of sound, thus creating a sonic boom.

A bullwhip tapers down from the handle section to the cracker. The cracker has much less mass than the handle section. When the whip is sharply swung, the momentum is transferred down the length of the tapering whip, the declining mass being made up for with increasing speed. Goriely and McMillen showed that the physical explanation is complex, involving the way that a loop travels down a tapered filament under tension.