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Mach number, named after Austrian physicist and philosopher Ernst Mach, is the ratio of an object's speed in a given medium to the speed of sound in that medium. Mach 1, the speed of sound, is approximately 761 mph at sea level. Mach numbers less than one indicate subsonic flow, while those greater than one indicate supersonic flow. The speed of sound is not constant; it increases proportionally to the square root of the absolute temperature, and as atmospheric temperature generally decreases with increasing altitude, the speed of sound also decreases.
| Characteristics | Values |
|---|---|
| Definition | The ratio of an object's speed in a given medium to the speed of sound in that medium |
| Named After | Austrian philosopher and physicist Ernst Mach |
| Speed of Sound | 340.3 meters per second (1,116.5 ft/s; 761.23 mph; 1,225.1 km/h; 661.49 kn) at sea level, standard temperature of 15 °C |
| Speed of Sound at Altitude | Decreases with increasing altitude; at 11,000 meters (36,089 ft), the speed of sound is 295.0 meters per second (967.8 ft/s; 659.9 mph; 1,062 km/h; 573.4 kn) |
| Mach 1 | Speed of sound; around 761 mph at sea level |
| Mach Number Below 0.8 | Commercial aircraft with aerodynamic features like rounded noses and leading edges |
| Mach Number 0.8-2.1 | Aircraft with swept wings |
| Mach Number 1.2-5.0 | Aircraft designed for supersonic speed, with features like cooled nickel-titanium skin and small wings |
| Mach Number Above 5.0 | Hypersonic flow |
| Mach Number Above 10.0 | Thermal controls become crucial in design; above 25.0, the design does not require wings |
| Mach Number = 1 | Subsonic flow |
| Mach Number > 1 | Supersonic flow |
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What You'll Learn
Mach number and speed of sound ratio
Mach number is a dimensionless quantity named after Austrian physicist and philosopher Ernst Mach. It is a measure of the compressibility characteristics of fluid flow. The Mach number is defined as the ratio of two speeds and is primarily used to determine the approximation with which a flow can be treated as an incompressible flow. The medium can be a gas or a liquid.
The speed of sound is not a constant; it increases proportionally to the square root of the absolute temperature. Since atmospheric temperature generally decreases with increasing altitude between sea level and 11,000 meters, the speed of sound also decreases. For example, at 11,000 meters (36,089 ft) altitude, the speed of sound is 295.0 meters per second (967.8 ft/s; 659.9 mph; 1,062 km/h; 573.4 kn), 86.7% of the sea level value.
The terms subsonic and supersonic are used to refer to speeds below and above the local speed of sound, respectively. When an aircraft exceeds Mach 1 (i.e., the speed of sound), a large pressure difference is created just in front of the aircraft. This abrupt pressure difference, called a shock wave, spreads backward and outward from the aircraft in a cone shape. As the speed increases, the zone of M > 1 flow increases towards both the leading and trailing edges.
When the speed of sound is known, the Mach number at which an aircraft is flying can be calculated. Conversely, if the speed of sound is not known, the Mach number can be determined by measuring the various air pressures (static and dynamic) and using a formula derived from Bernoulli's equation for Mach numbers less than 1.0.
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Transonic and supersonic speeds
Transonic speeds occur when an object is travelling at speeds close to the speed of sound, typically between Mach 0.8 and 1.2. At these speeds, the airflow around an object includes regions of both subsonic and supersonic airflow. Transonic speeds can cause issues for aircraft, as the airflow can cause the aircraft to become unsteady, increasing drag, asymmetry and unsteadiness. This issue, which first appeared during World War II, led to the development of dive flaps, which helped to stabilise the plane by slowing it down and preventing shock waves.
The speed of sound is not a constant, and it increases with the square root of the absolute temperature. Therefore, the speed of sound decreases with increasing altitude, as the atmospheric temperature generally decreases. At sea level, the speed of sound is around 340-343 m/s or 761-768 mph.
Transonic speeds can be achieved by modern jet-powered aircraft, which are engineered to operate at these speeds. To overcome the challenges of transonic flight, aircraft have been designed with swept wings, which reduce the thickness and chord ratio of the wings.
Supersonic speeds refer to speeds exceeding the local speed of sound (Mach 1). At these speeds, a large pressure difference is created in front of the aircraft, causing a shock wave known as a sonic boom. Supersonic speeds usually range from Mach 1.2 to Mach 5, with speeds greater than Mach 5 considered hypersonic.
Most modern fighter aircraft are supersonic, and historically, the Concorde and Tupolev Tu-144 were supersonic passenger aircraft. Supersonic flight is generally prohibited over land due to the potential impact of sonic booms, which can cause structural damage.
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Shock waves and sonic booms
Mach number is a measure of the compressibility characteristics of fluid flow. It is dependent on the speed of sound in a gas. The speed of sound in the air depends on temperature, which in turn depends on altitude. The speed of sound is not a constant; it increases proportionally to the square root of the absolute temperature.
When an aircraft exceeds Mach 1, it surpasses the speed of sound, creating a large pressure difference just in front of the aircraft. This abrupt pressure difference is called a shock wave, which spreads backward and outward from the aircraft in a cone shape (a so-called Mach cone). This shock wave creates a sonic boom, which sounds like an explosion or a thunderclap to the human ear. The power or volume of the shock wave depends on the quantity of air being accelerated and the size and shape of the aircraft.
Sonic booms generate enormous amounts of sound energy. They can be caused by objects as small as bullets and whips, but they are most commonly associated with aircraft. When an aircraft travels at supersonic speeds, it creates ripples of air molecules and sound that radiate outward in every direction. As the aircraft speeds up, the waves at the nose of the aircraft start to pile up and compress rather than ripple outward. The pressure from sonic booms caused by large supersonic aircraft can be particularly loud, startling people and causing minor damage to some structures.
The strongest sonic boom ever recorded was 7,000 Pa (144 psf), produced by an F-4 flying just above the speed of sound at an altitude of 100 feet (30 m). In more realistic flight conditions, the maximum boom measured was 1,010 Pa (21 psf). Buildings in good condition should not suffer any damage at pressures of 530 Pa (11 psf) or less. Community exposure to sonic booms is typically below 100 Pa (2 psf). Ground motion resulting from sonic booms is rare and is well below structural damage thresholds.
The Jones-Seebass-George-Darden theory of sonic boom minimization suggests that the N-wave can be spread out laterally and temporally by producing a strong and downwards-focused shock at a sharp, wide-angle nose cone. This theory aims to reduce the nuisance caused by sonic booms to make overland supersonic flight a feasible option.
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Compressibility and fluid flow
Mach number is a dimensionless quantity in fluid dynamics that represents the ratio of flow velocity past a boundary to the local speed of sound. It is a measure of the compressibility characteristics of fluid flow. Compressible flow, or gas dynamics, is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are technically compressible, flows are treated as incompressible when the Mach number is smaller than 0.3, as the density change due to velocity is minimal in this case.
The speed of sound is not constant; it increases proportionally with the square root of the absolute temperature. Therefore, the speed of sound decreases with increasing altitude. At sea level, the speed of sound is approximately 340 m/s, while at 11,000 meters above sea level, it decreases to about 295 m/s.
As an object accelerates towards supersonic speed, different wave phenomena occur. At transonic speeds, the flow field around the object includes both subsonic and supersonic parts. When an aircraft exceeds Mach 1, it creates a large pressure difference just in front of it, known as a shock wave. This shock wave spreads backward and outward in a cone shape, causing the sonic boom heard when a fast-moving aircraft travels overhead.
The study of compressible flow is crucial for understanding high-speed aircraft, jet engines, rocket motors, and atmospheric reentry. Compressibility effects become significant in transonic flows, leading to increased drag. Supersonic conditions occur for Mach numbers greater than one, and shock waves are generated by the object's surface. At hypersonic speeds (Mach > 5), a different mathematical approach is required due to the small wave angles.
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Mach number in popular culture
The term "Mach" is named after Ernst Mach, a renowned 19th-century Austrian scientist. Mach made significant contributions across various fields, including physics, fluid mechanics, and philosophy. He is particularly known for his groundbreaking work in supersonic aerodynamics, being the first to understand the fundamental principles governing supersonic flow and their impact on aerodynamics. Mach numbers are used to classify flight into six categories, with transonic speeds including both subsonic and supersonic parts, and supersonic flow creating shock waves.
In popular culture, the term "Mach" and the concept of breaking the sound barrier are often associated with speed and power. It is commonly used in aviation and aerospace contexts, with aircraft speeds often expressed in terms of Mach numbers. For example, the Concorde aircraft is known for its ability to cruise at Mach 2, twice the speed of sound.
In military contexts, Mach numbers are used to describe the speed of missiles, aircraft, and other projectiles. This is particularly prevalent in action films and video games, where Mach-level speeds are often a selling point for viewers or players seeking thrilling, high-speed experiences.
The concept of Mach speed has also found its way into automotive culture, with some high-performance cars being described as capable of achieving speeds in the Mach range. While these vehicles are not technically breaking the sound barrier, the use of Mach numbers emphasizes their extraordinary speed capabilities.
Additionally, the term "Mach" has been adopted in various brands and product names, often implying speed, efficiency, or a cutting-edge nature. For example, the Mach-E variant of the Ford Mustang is named to evoke a sense of speed and performance, even though it is an electric vehicle. Similarly, the Mach-III guitar amplifier from Peavey Electronics is named to suggest power and performance.
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Frequently asked questions
Mach speed is the speed of sound, which is around 761 mph at sea level. The speed of sound is not a constant and changes with altitude.
Mach 1 is the speed of sound. Mach numbers less than one indicate subsonic flow, and those greater than one indicate supersonic flow.
The term Mach is named after Austrian physicist and philosopher Ernst Mach.
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