In brief

The Mach number is the ratio between an aircraft's true airspeed and the speed of sound in the same atmospheric conditions; at Mach 1.0 an aircraft flies exactly as fast as sound. Critical Mach is the speed at which the airflow over some part of the aircraft, for example the top of the wing, first reaches exactly Mach 1.0 without exceeding it. Above critical Mach, shock waves form that can lead to Mach buffet, Mach tuck and extra drag; this is why Mmo, the maximum operating Mach number, is a hard operational limit.1

Definition and speed ranges

According to the FAA, at high speed and high altitude speed is expressed as a Mach number: the ratio of the aircraft's true airspeed to the speed of sound in the same atmospheric conditions. The FAA classifies Mach numbers below 0.75 as subsonic, 0.75 to 1.20 as transonic, 1.20 to 5.00 as supersonic and above 5.00 as hypersonic. The speed of sound depends on temperature: at sea level at 15 °C it is 661 kt according to the FAA, while at 40,000 ft, at minus 55 °C, it drops to 574 kt. Because the wing accelerates the air over its upper surface, the local airflow can already become sonic while the aircraft itself is still flying subsonically; at some moments, subsonic and supersonic airflow can therefore exist over the same aircraft at the same time.1

Critical Mach and drag divergence

The FAA describes critical Mach, also called Mach Crit, as the speed at which the airflow over any part of the aircraft first reaches, but does not exceed, Mach 1.0; this is the boundary between subsonic and transonic flight and depends strongly on wing and aerofoil design. Above critical Mach, shock waves form that can cause airflow separation, buffet and control problems; according to the FAA, a jet aircraft is usually most economical close to its critical Mach. According to the FAA, five to ten per cent above critical Mach, compressibility effects begin and drag rises sharply; this point is called drag divergence and is accompanied by buffet, trim and stability changes. According to the FAA, a swept wing raises the critical Mach number and the force divergence Mach number, the Mach number that produces a sharp change in the drag coefficient, delaying the onset of compressibility effects, although such wings tend to stall at the tip before the root.1

Vmo and Mmo

According to the FAA, Vmo/Mmo is the maximum operating speed limit: Vmo is expressed in knots calibrated airspeed (KCAS), Mmo as a Mach number. According to the FAA, the Vmo limit applies mainly at lower altitude and concerns structural loads and flutter; the Mmo limit applies mainly at higher altitude and concerns compressibility effects and flutter. As an example, the FAA cites an early civil jet with a Vmo of 306 KCAS up to about FL310, where an Mmo of 0.82 at FL310 was roughly equal to that 306 KCAS and at FL380 corresponded to 261 KCAS.1

Mach tuck, Mach buffet and coffin corner

According to the FAA, when the wing's centre of pressure moves aft because of airflow separation, a nose-down pitching moment results that is called 'Mach tuck' or 'tuck under'. According to the FAA, the buffet caused by airflow separation after shock wave formation is called Mach buffet; it is accompanied by trim and stability changes and reduced control effectiveness. According to the FAA, Mach buffet can also occur at low speed, at a high angle of attack: high altitude, high weight and high G loading all increase the angle of attack and with it the likelihood of this low-speed Mach buffet. At high altitude, the lowest (stall) and highest (Mmo) safe speeds of an aircraft in Mach number can creep towards each other; the FAA calls the situation in which a pilot can then neither slow down without stalling nor speed up without exceeding Mmo the 'coffin corner'.1

Frequently asked questions

Is a fixed Mach number also a fixed speed in knots?: No: the Mach number is the ratio between true airspeed and the speed of sound, and the speed of sound falls with temperature; the same Mach number therefore corresponds to a lower true airspeed at high altitude than at sea level. Is critical Mach the same as Mmo?: The FAA distinguishes critical Mach, the point at which local airflow first reaches Mach 1.0, from Mmo, the maximum operating speed in Mach number set by the manufacturer; in practice Mmo is higher than critical Mach.1