Was ist ein/eine Mach (M)?
The Mach number (symbol: M or Ma) is a dimensionless quantity representing the ratio of an object's speed to the local speed of sound. It is named after Austrian physicist Ernst Mach. An object traveling at Mach 1 moves at the speed of sound; Mach 2 is twice the speed of sound, and so on. Because the speed of sound varies with temperature, pressure, and the medium through which it travels, the Mach number is not a fixed speed but a ratio.
Variable Reference Speed
At sea level in standard atmospheric conditions (15 degrees Celsius / 59 degrees Fahrenheit), the speed of sound in air is approximately 343 m/s (1,235 km/h or 767 mph). Therefore, Mach 1 at sea level equals roughly 343 m/s. However, at 35,000 feet altitude where commercial jets cruise, the temperature drops to about -56.5 degrees Celsius, reducing the speed of sound to approximately 295 m/s (1,062 km/h or 660 mph). This means Mach 1 at cruising altitude represents a slower absolute speed than Mach 1 at sea level.
Flow Regime Classification
The Mach number classifies airflow into distinct regimes: subsonic (M < 0.8), transonic (0.8 < M < 1.2), supersonic (1.2 < M < 5), and hypersonic (M > 5). Each regime has fundamentally different aerodynamic characteristics, affecting aircraft design, shock wave formation, and heating effects. The transonic regime is particularly challenging because mixed subsonic and supersonic flow creates complex shock wave patterns.
Etymology
Ernst Mach (1838-1916)
The Mach number is named after Ernst Mach, an Austrian-Czech physicist and philosopher born in Moravia (now part of the Czech Republic) in 1838. Mach made pioneering contributions to the study of shock waves, supersonic motion, and the physics of sound. His experimental work in the 1870s and 1880s included photographing shock waves produced by supersonic projectiles — some of the first visual evidence of these phenomena.
Naming the Unit
The term "Mach number" was proposed by Swiss aeronautical engineer Jakob Ackeret in 1929, thirteen years after Mach's death. Ackeret introduced the notation during a lecture at the Eidgenossische Technische Hochschule (ETH) in Zurich. The usage rapidly spread through the aeronautics community during the 1930s and 1940s as aircraft speeds approached and exceeded the speed of sound.
Mach's Philosophical Legacy
Interestingly, Ernst Mach was as influential in philosophy as in physics. His positivist philosophy — which insisted that scientific concepts must be grounded in observable experience — profoundly influenced Albert Einstein during the development of relativity theory. Einstein credited Mach's critique of Newtonian absolute space as an important inspiration, though Mach himself never accepted relativity.
Precise Definition
The Mach number is formally defined as M = v / a, where v is the velocity of the object and a is the local speed of sound in the surrounding medium. It is a dimensionless quantity (it has no units) because it is a ratio of two speeds.
Speed of Sound in Air
The speed of sound in an ideal gas is given by a = sqrt(gamma * R * T / M_mol), where gamma is the heat capacity ratio (1.4 for air), R is the universal gas constant, T is the absolute temperature in Kelvin, and M_mol is the molar mass of the gas. For dry air at sea level and 15 degrees Celsius (288.15 K), this yields approximately 340.3 m/s.
International Standard Atmosphere
For aviation purposes, the Mach number is typically referenced to the International Standard Atmosphere (ISA). At sea level (ISA conditions: 15 degrees Celsius, 101,325 Pa), the speed of sound is 340.3 m/s. In the stratosphere (above approximately 11,000 m / 36,089 ft), ISA assumes a constant temperature of -56.5 degrees Celsius, giving a speed of sound of approximately 295.1 m/s. These standard values allow consistent Mach number reporting regardless of actual weather conditions.
Geschichte
Early Studies of Supersonic Motion
The scientific study of objects moving faster than sound began in the mid-19th century. Ernst Mach, working at the University of Prague in the 1870s-1880s, used schlieren photography to capture images of shock waves around supersonic bullets. His 1887 paper on projectiles moving through air showed the characteristic V-shaped shock wave (now called a Mach cone) that forms when an object exceeds the local speed of sound.
The Sound Barrier Era
During World War II, fighter aircraft in steep dives occasionally approached the speed of sound, encountering severe buffeting, loss of control, and structural failure — phenomena collectively known as the "sound barrier." Several pilots died attempting to fly faster than sound. The challenge drove intensive aerodynamic research in the US, UK, Germany, and Soviet Union.
On October 14, 1947, US Air Force Captain Chuck Yeager became the first person confirmed to have exceeded Mach 1 in level controlled flight, piloting the Bell X-1 rocket plane to Mach 1.06 (700 mph) at 43,000 feet altitude over the Mojave Desert. The achievement demonstrated that the sound barrier was an engineering challenge, not a physical impossibility.
Supersonic and Hypersonic Flight
The Cold War era saw rapid advances in supersonic flight. By 1953, the North American X-15 program was pushing boundaries further. The X-15 eventually reached Mach 6.7 (4,520 mph) in 1967, still the fastest speed achieved by a crewed, powered aircraft (excluding spacecraft). The Concorde entered commercial service in 1976, carrying passengers at Mach 2.04, and operated until 2003.
Modern military aircraft routinely operate at supersonic speeds: the F-22 Raptor can supercruise at Mach 1.5 without afterburner, and the SR-71 Blackbird held the record for the fastest air-breathing crewed aircraft at Mach 3.3 from 1976 until its retirement in 1998.
Hypersonic Research Today
The 21st century has seen renewed interest in hypersonic flight (above Mach 5). NASA's X-43A scramjet reached Mach 9.6 in 2004. Military programs in the US, Russia, and China are developing hypersonic weapons and vehicles. Commercial hypersonic travel concepts envision Mach 5+ aircraft that could fly from New York to London in under two hours.
Aktuelle Verwendung
Aviation
The Mach number is fundamental to modern aviation. Commercial airliners typically cruise at Mach 0.78-0.85 (about 470-530 knots or 540-610 mph). Aircraft speed indicators include a Machmeter that displays the current Mach number, essential because aerodynamic limits are defined in Mach numbers rather than absolute speeds. The critical Mach number (Mcrit) of an aircraft is the lowest Mach number at which airflow over the wing first reaches Mach 1 locally, causing drag to increase dramatically.
Military Applications
Military aviation uses Mach numbers to classify aircraft performance and weapon capabilities. Fighter jets are often described by their maximum Mach number: the F-16 reaches Mach 2.0, the F-15 reaches Mach 2.5, and the MiG-31 reaches Mach 2.83. Missiles are classified as subsonic, supersonic, or hypersonic based on their Mach numbers.
Aerospace Engineering
In aerospace engineering, the Mach number determines which physical models and equations apply to a given flow problem. Subsonic aerodynamics differs fundamentally from supersonic and hypersonic aerodynamics. Wind tunnel testing is classified by Mach number range, and computational fluid dynamics simulations must use appropriate solver methods for each Mach regime.
Space Reentry
Spacecraft reentering Earth's atmosphere experience extreme Mach numbers — the Space Shuttle reentered at approximately Mach 25. At these hypersonic speeds, air molecules dissociate and ionize, creating a plasma sheath around the vehicle and generating extreme heating that requires specialized thermal protection systems.
Everyday Use
For most people, the Mach number is encountered primarily in aviation news, military discussions, and popular science. The phrases "breaking the sound barrier" and "going supersonic" are widely understood cultural references even by those who rarely think about speed units.
Concorde Legacy
The Concorde supersonic airliner, which operated from 1976 to 2003, brought the Mach number into public consciousness. Passengers flying at Mach 2.04 could see the aircraft's Machmeter display and watch it climb past Mach 1. The Concorde crossed the Atlantic in about 3.5 hours compared to 7-8 hours for subsonic jets. Its retirement left a void in supersonic commercial travel that companies like Boom Supersonic aim to fill.
Sonic Booms
People living near military bases or supersonic test corridors are familiar with sonic booms — the thunder-like sound produced when an aircraft exceeds Mach 1. The boom is caused by the shock wave cone trailing behind the supersonic object. Sonic booms from Concorde over land were a significant factor in restricting supersonic commercial flights to overwater routes.
Speed Comparisons
The Mach number provides an intuitive way to compare speeds: Mach 2 is twice the speed of sound, Mach 3 is three times, and so on. This simplicity makes it a popular unit in science communication. Headlines about hypersonic missiles traveling at "Mach 8" or spacecraft at "Mach 25" immediately convey the extraordinary speeds involved.
In Science & Industry
Compressible Flow Dynamics
In fluid dynamics, the Mach number is the primary parameter determining whether compressibility effects must be considered. Below about Mach 0.3, air behaves as an essentially incompressible fluid, and simpler equations apply. Above Mach 0.3, density changes become significant, requiring the full compressible flow equations. This threshold affects everything from wind tunnel design to computational fluid dynamics.
Shock Wave Physics
The Mach number determines the geometry and strength of shock waves. The half-angle of a Mach cone is given by sin(theta) = 1/M, meaning higher Mach numbers produce narrower cones. Normal shock waves (perpendicular to the flow) cause abrupt pressure, temperature, and density increases described by the Rankine-Hugoniot equations, which are functions of the upstream Mach number.
Astrophysics
In astrophysics, Mach numbers describe the velocities of stellar winds, supernova blast waves, and accretion flows. Supernova remnants can expand at Mach 1,000 or more relative to the interstellar medium. The solar wind reaches the Earth at about Mach 8 relative to the ambient interstellar gas. Astrophysical jets from active galactic nuclei can have Mach numbers exceeding 10,000.
Aerodynamic Heating
The relationship between Mach number and aerodynamic heating is critical for high-speed vehicle design. Stagnation temperature increases with the square of the Mach number: at Mach 3, air stagnation temperature reaches about 330 degrees Celsius; at Mach 5, it exceeds 1,000 degrees Celsius; and at Mach 25 (orbital reentry speed), it reaches approximately 7,000 degrees Celsius. This drives the need for ablative heat shields and advanced thermal protection materials.
Interesting Facts
Chuck Yeager broke the sound barrier on October 14, 1947, reaching Mach 1.06 in the Bell X-1 — just two days before, he had cracked two ribs falling from a horse and almost could not close the cockpit door.
The fastest crewed aircraft ever was the X-15, which reached Mach 6.7 (4,520 mph) on October 3, 1967, piloted by William Knight. The aircraft's windshield was made of fused silica to withstand temperatures exceeding 600 degrees Celsius.
The Space Shuttle reentered Earth's atmosphere at approximately Mach 25 (about 17,500 mph), generating surface temperatures over 1,650 degrees Celsius on its heat shield tiles.
The SR-71 Blackbird cruised at Mach 3.3 and was so fast that its primary defense against missiles was simply to accelerate — no missile could catch it from behind.
The Concorde's nose drooped during takeoff and landing so pilots could see the runway, but was raised during supersonic cruise to reduce drag. The aircraft stretched 6-10 inches in length due to thermal expansion at Mach 2.
A bullwhip's crack is actually a miniature sonic boom — the tip of the whip exceeds Mach 1, making it one of the first human-made objects to break the sound barrier.
At Mach 1, the shock wave forms a flat disk perpendicular to the direction of travel. Above Mach 1, it forms a cone whose angle narrows as speed increases — at Mach 2, the half-angle is 30 degrees; at Mach 3, about 19.5 degrees.
Meteor entries into Earth's atmosphere typically occur at Mach 35-200. The Chelyabinsk meteor of 2013 entered at approximately Mach 55 (about 19,000 m/s), producing a shock wave that injured over 1,500 people.
Regional Variations
Universal Aviation Standard
The Mach number is used universally in aviation worldwide, regardless of whether a country uses metric or imperial units for other purposes. International Civil Aviation Organization (ICAO) standards reference Mach numbers for aircraft performance, and every commercial aircraft cockpit includes a Machmeter. This makes the Mach number one of the few speed measures with truly global and uniform usage.
Military Conventions
Military organizations worldwide use Mach numbers to describe aircraft and missile performance. NATO, Russian, and Chinese military documentation all reference Mach numbers in the same way. This universality stems from the Mach number being dimensionless — it requires no unit conversion between measurement systems.
Popular Culture
In popular culture, the Mach number is widely recognized across all countries and languages. Phrases like "Mach 2" or "breaking the sound barrier" are understood globally. Some languages adapt the term slightly — French uses "nombre de Mach," German uses "Machzahl," Russian uses "число Маха" — but the concept and numerical values remain identical.