Critical Mach number
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In
aerodynamics Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dy ...
, the critical Mach number (Mcr or M*) of an
aircraft An aircraft is a vehicle that is able to fly by gaining support from the air. It counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engine ...
is the lowest Mach number at which the airflow over some point of the aircraft reaches the speed of sound, but does not exceed it.Clancy, L.J. ''Aerodynamics'', Section 11.6 At the lower critical Mach number, airflow around the entire aircraft is subsonic. Supersonic aircraft such as
Concorde The Aérospatiale/BAC Concorde () is a retired Franco-British supersonic airliner jointly developed and manufactured by Sud Aviation (later Aérospatiale) and the British Aircraft Corporation (BAC). Studies started in 1954, and France an ...
and combat aircraft also have an upper critical Mach number at which the airflow around the entire aircraft is supersonic.


Aircraft flight

For an aircraft in flight, the speed of the airflow around the aircraft differs considerably in places from the airspeed of the aircraft; this is due to the airflow having to speed up and slow down as it travels around the aircraft's structure. When the aircraft's airspeed reaches the critical Mach number, the speed of the airflow in some areas near the airframe reaches the speed of sound, even though the aircraft itself has an airspeed lower than Mach 1.0. This creates a weak
shock wave In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a me ...
. As the aircraft exceeds the critical Mach number, its
drag coefficient In fluid dynamics, the drag coefficient (commonly denoted as: c_\mathrm, c_x or c_) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag e ...
increases suddenly, causing dramatically increased drag,Clancy, L.J., ''Aerodynamics'', Chapter 11 and, in an aircraft not designed for
transonic Transonic (or transsonic) flow is air flowing around an object at a speed that generates regions of both subsonic and supersonic airflow around that object. The exact range of speeds depends on the object's critical Mach number, but transoni ...
or supersonic speeds, changes to the airflow over the
flight control surfaces Aircraft flight control surfaces are aerodynamic devices allowing a pilot to adjust and control the aircraft's flight attitude. Development of an effective set of flight control surfaces was a critical advance in the development of aircraft. Ea ...
lead to deterioration in control of the aircraft. In aircraft not designed to fly at or above the critical Mach number, the shock waves that form in the airflow over the wing and tailplane are sufficient to stall the wing, render the control surfaces ineffective, or lead to loss of control of the aircraft (such as
Mach tuck Mach tuck is an aerodynamic effect whereby the nose of an aircraft tends to pitch downward as the airflow around the wing reaches supersonic speeds. This diving tendency is also known as tuck under. The aircraft will first experience this effect ...
, when shock waves in the airflow over the elevator send the aircraft into an uncontrollable dive). These problematic phenomena appearing at or above the critical Mach number became known as
compressibility In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a measure of the instantaneous relative volume change of a f ...
. Compressibility led to a number of accidents involving high-speed military and experimental aircraft in the 1930s and 1940s. Although unknown at the time, compressibility was the cause of the phenomenon known as the
sound barrier The sound barrier or sonic barrier is the large increase in aerodynamic drag and other undesirable effects experienced by an aircraft or other object when it approaches the speed of sound. When aircraft first approached the speed of sound, th ...
. 1940s-era military
subsonic aircraft A subsonic aircraft is an aircraft with a maximum speed less than the speed of sound (Mach 1). The term technically describes an aircraft that flies below its critical Mach number, typically around Mach 0.8. All current civil aircraft, including ...
, such as the Supermarine Spitfire, Bf 109, P-51 Mustang,
Gloster Meteor The Gloster Meteor was the first British jet fighter and the Allies of World War II, Allies' only jet aircraft to engage in combat operations during the Second World War. The Meteor's development was heavily reliant on its ground-breaking turb ...
,
He 162 The Heinkel He 162 ''Volksjäger'' ( German, "People's Fighter") was a German single-engine, jet-powered fighter aircraft fielded by the Luftwaffe in World War II. Developed under the Emergency Fighter Program, it was designed and built quickl ...
, and
P-80 The Lockheed P-80 Shooting Star was the first jet fighter used operationally by the United States Army Air Forces (USAAF) during World War II. Designed and built by Lockheed in 1943 and delivered just 143 days from the start of design, prod ...
, have relatively thick, unswept wings, and are incapable of reaching Mach 1.0 in controlled flight. In 1947,
Chuck Yeager Brigadier General Charles Elwood Yeager ( , February 13, 1923December 7, 2020) was a United States Air Force officer, flying ace, and record-setting test pilot who in October 1947 became the first pilot in history confirmed to have exceeded the ...
flew the Bell X-1 (also with an unswept wing, but a much thinner one), reaching Mach 1.06 and beyond, and the sound barrier was finally broken. Early
transonic Transonic (or transsonic) flow is air flowing around an object at a speed that generates regions of both subsonic and supersonic airflow around that object. The exact range of speeds depends on the object's critical Mach number, but transoni ...
military aircraft, such as the Hawker Hunter and
F-86 Sabre The North American F-86 Sabre, sometimes called the Sabrejet, is a transonic jet fighter aircraft. Produced by North American Aviation, the Sabre is best known as the United States' first swept-wing fighter that could counter the swept-wing Sov ...
, were designed to fly satisfactorily even at speeds greater than their critical Mach number. They did not possess sufficient engine thrust to break the sound barrier in level flight, but could exceed Mach 1.0 in a dive while remaining controllable. Modern
jet airliner A jet airliner or jetliner is an airliner powered by jet engines (passenger jet aircraft). Airliners usually have two or four jet engines; three-engined designs were popular in the 1970s but are less common today. Airliners are commonly clas ...
s, such as
Airbus Airbus SE (; ; ; ) is a European multinational aerospace corporation. Airbus designs, manufactures and sells civil and military aerospace products worldwide and manufactures aircraft throughout the world. The company has three divisions: ' ...
and
Boeing The Boeing Company () is an American multinational corporation that designs, manufactures, and sells airplanes, rotorcraft, rockets, satellites, telecommunications equipment, and missiles worldwide. The company also provides leasing and p ...
aircraft, have maximum operating Mach numbers slower than Mach 1.0. Supersonic aircraft, such as
Concorde The Aérospatiale/BAC Concorde () is a retired Franco-British supersonic airliner jointly developed and manufactured by Sud Aviation (later Aérospatiale) and the British Aircraft Corporation (BAC). Studies started in 1954, and France an ...
,
Tu-144 The Tupolev Tu-144 (russian: Tyполев Ту-144; NATO reporting name: Charger) is a Soviet supersonic passenger airliner designed by Tupolev in operation from 1968 to 1999. The Tu-144 was the world's first commercial supersonic transport ...
, the
English Electric Lightning The English Electric Lightning is a British fighter aircraft that served as an interceptor during the 1960s, the 1970s and into the late 1980s. It was capable of a top speed of above Mach 2. The Lightning was designed, developed, and manufa ...
,
Lockheed F-104 The Lockheed F-104 Starfighter is an American single-engine, supersonic air superiority fighter which was extensively deployed as a fighter-bomber during the Cold War. Created as a day fighter by Lockheed as one of the "Century Series" of fig ...
,
Dassault Mirage III The Dassault Mirage III () is a family of single/dual-seat, single-engine, fighter aircraft developed and manufactured by French aircraft company Dassault Aviation. It was the first Western European combat aircraft to exceed Mach number, Mach 2 ...
, and
MiG 21 The Mikoyan-Gurevich MiG-21 (russian: Микоян и Гуревич МиГ-21; NATO reporting name: Fishbed) is a supersonic jet fighter and interceptor aircraft, designed by the Mikoyan-Gurevich Design Bureau in the Soviet Union. Its nickna ...
, are designed to exceed Mach 1.0 in level flight, and are therefore designed with very thin wings. Their critical Mach numbers are higher than those of subsonic and transonic aircraft, but are still less than Mach 1.0. The actual critical Mach number varies from wing to wing. In general, a thicker wing will have a lower critical Mach number, because a thicker wing deflects the airflow passing around it more than a thinner wing does, and thus accelerates the airflow to a faster speed. For instance, the fairly-thick wing on the
P-38 Lightning The Lockheed P-38 Lightning is an American single-seat, twin piston-engined fighter aircraft that was used during World War II. Developed for the United States Army Air Corps by the Lockheed Corporation, the P-38 incorporated a distinctive tw ...
has a critical Mach number of about .69. The aircraft could occasionally reach this speed in dives, leading to a number of crashes. The Supermarine Spitfire's much thinner wing gave it a considerably higher critical Mach number (about 0.89).


See also

*
Drag divergence Mach number The drag-divergence Mach number (not to be confused with critical Mach number) is the Mach number at which the aerodynamic drag on an airfoil or airframe begins to increase rapidly as the Mach number continues to increase. This increase can caus ...


References

*
L. J. Clancy Laurence Joseph Clancy (15 March 1929 - 16 October 2014) was an Education Officer in aerodynamics at Royal Air Force College Cranwell whose textbook ''Aerodynamics'' became standard. He was born in Egypt to Alfred Joseph Clancy and Agnes Hunter. I ...
(1975) ''Aerodynamics'', Pitman Publishing Limited, London


Notes

{{reflist Aerodynamics