Sonic boom

A sonic boom is a sound associated with shock waves created when an object travels through the air faster than the speed of sound. Sonic booms generate enormous amounts of sound energy, sounding similar to an explosion or a thunderclap to the human ear.

The crack of a supersonic bullet passing overhead or the crack of a bullwhip are examples of a sonic boom in miniature.^[2]

Sonic booms due to large supersonic aircraft can be particularly loud and startling, tend to awaken people, and may cause minor damage to some structures. This led to the prohibition of routine supersonic flight overland. Although they cannot be completely prevented, research suggests that with careful shaping of the vehicle, the nuisance due to the sonic booms may be reduced to the point that overland supersonic flight may become a feasible option.^[3][4]

A sonic boom does not occur only at the moment an object crosses the sound barrier and neither is it heard in all directions emanating from the supersonic object. Rather, the boom is a continuous effect that occurs while the object is traveling at supersonic speeds and affects only observers that are positioned at a point that intersects a region in the shape of a geometrical cone behind the object. As the object moves, this conical region also moves behind it and when the cone passes over the observer, they will briefly experience the "boom".

Causes

When an aircraft passes through the air, it creates a series of

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

vapour cone

, with the aircraft at its tip. The half-angle ${\displaystyle \alpha }$ between the direction of flight and the shock wave is given by:

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

where ${\displaystyle {\tfrac {v_{\text{sound}}}{v_{\text{object}}}}}$ is the inverse ${\displaystyle {\tfrac {1}{\mathrm {Ma} }}}$ of the plane's Mach number ${\displaystyle \mathrm {Ma} ={\tfrac {v_{\text{object}}}{v_{\text{sound}}}}}$. Thus the faster the plane travels, the finer and more pointed the cone is.

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; therefore, an N-wave causes two booms – one when the initial pressure rise reaches an observer, and another when the pressure returns to normal. This leads to a distinctive "double boom" from a supersonic aircraft. When the aircraft is 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 ${\displaystyle \alpha }$.

For today's supersonic aircraft in normal operating conditions, the peak overpressure varies from less than 50 to 500

The power, or volume, of the shock wave, depends 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 depends 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.[7]

Several smaller shock waves can and usually do form at other points on the aircraft, primarily at 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 aircraft 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.

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 Mach than the speed of sound, or Mach 5." (Dunbar, 2015) The top mileage per hour 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. A typical model found in United States military use ranges from an average of $13 million to $35 million U.S. dollars.

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

This remained untested for decades, until

Some theoretical designs do not appear to create sonic booms at all, such as the Busemann biplane. However, creating a shockwave is inescapable if it generates aerodynamic lift.^[7]

In 2018, NASA awarded

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

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 flight path of Concorde. Windows would rattle and in some cases, the "torching" (pointing 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 

Depending on the aircraft's altitude, sonic booms reach the ground 2 to 60  seconds after flyover. However, not all booms are heard at ground level. The speed of sound at any altitude is a function of air temperature. A decrease or increase in temperature results in a corresponding decrease or increase in sound speed. Under standard atmospheric conditions, air temperature decreases with increased altitude. For example, when the sea-level temperature is 59 degrees Fahrenheit (15 °C), the temperature at 30,000 feet (9,100 m) drops to minus 49 degrees Fahrenheit (−45 °C). This temperature gradient helps bend the sound waves upward. Therefore, for a boom to reach the ground, the aircraft's speed relative to the ground must be greater than the speed of sound at the ground. For example, the speed of sound at 30,000 feet (9,100 m) is about 670 miles per hour (1,080 km/h), but an aircraft must travel at least 750 miles per hour (1,210 km/h) (Mach 1.12) for a boom to be heard on the ground.[6]

The composition of the atmosphere is also a factor. Temperature variations,

Currently, there are no industry-accepted standards for the acceptability of a sonic boom. However, work is underway to create metrics that will help in understanding how humans respond to the noise generated by sonic booms.^[15] Until such metrics can be established, either through further study or supersonic overflight testing, it is doubtful that legislation will be enacted to remove the current prohibition on supersonic overflight in place in several countries, including the United States.

Bullwhip

The cracking sound a bullwhip makes when properly wielded is, in fact, 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.^[2]

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.^[16]

See also

• Shockwave
• Cherenkov radiation
• Hypersonic
• Supershear earthquake
• Ground vibration boom
• Christine Darden

References

• Banse, Tom. "Supersonic Jets Could Return To Inland Northwest Skies". OPB. Oregon Public Broadcasting. Retrieved 8 February 2022.
• Vázquez, M.; Dervieux, A.; Koobus, B. (September 2004). "Multilevel optimization of a supersonic aircraft". Finite Elements in Analysis and Design. 40 (15): 2101–2124.
  doi:10.1016/j.finel.2004.01.010
  .
• Fox, Chris (4 June 2021). "United plans supersonic passenger flights by 2029". BBC News. Retrieved 30 November 2022.
• Cooper, J.E. (2001), "Aeroelastic Response", Encyclopedia of Vibration, Elsevier, pp. 87–97,
  ISBN 978-0-12-227085-7
  , retrieved 30 November 2022
• Smith, Heather R. (7 August 2017). May, Sandra (ed.). "What Is Supersonic Flight?". NASA.
• F.S., Billig (August 1993). "Research on Supersonic Combustion". Journal of Propulsion and Power. 9 (4). Johns Hopkins University: John Hopkin University: 4.
  doi:10.2514/3.23652
  . Retrieved 6 February 2022.

External links

Wikimedia Commons has media related to Sonic boom.

• Archived at Ghostarchive and the Wayback Machine: "Audio Recording of SR-71 Blackbird Sonic Booms – YouTube". YouTube. Retrieved 12 February 2015.
• Boston Globe profile of Spike Aerospace planned S-521 supersonic jet Archived 22 June 2016 at the Wayback Machine