Glossary term
Mach Number
A dimensionless ratio comparing object or flow speed with the local speed of sound in the surrounding medium.
Definition
quantityMach number is the ratio of an object's speed or flow speed to the local speed of sound in the surrounding medium.
Mach number indicates the importance of compressibility effects. It is written M = V/a, where V is flow speed relative to the medium and a is local speed of sound. As Mach number increases, density changes, shock waves, expansion waves, wave drag, choking, and temperature effects become important. It is central to aircraft design, nozzles, turbomachinery, wind-tunnel testing, missiles, re-entry vehicles, and high-speed internal flows.
Mach number compares a speed with the local speed of sound:
where V is the flow speed relative to the medium and a is the local speed of sound. For an ideal gas:
so speed of sound depends on gas composition and temperature, not directly on aircraft ground speed. The same true airspeed can therefore correspond to different Mach numbers at different altitude and temperature.
Flow regimes
At low Mach number, usually below about 0.3, density changes are often small enough for incompressible-flow assumptions. In subsonic compressible flow, pressure disturbances can propagate upstream. Near transonic conditions, local pockets of supersonic flow and shock waves can appear even if freestream Mach number is below 1. Supersonic flow has regions where disturbances cannot travel upstream through the flow. Hypersonic flow adds strong shock heating, high-temperature gas effects, and surface heating constraints.
These regime labels are useful but not absolute. Geometry, angle of attack, boundary-layer state, Reynolds number, and gas properties influence when compressibility effects become significant.
Engineering significance
Mach number affects lift, drag, stability, control effectiveness, inlet performance, nozzle choking, turbine blade aerodynamics, wind-tunnel similarity, and thermal loading. In aircraft design, drag rise near transonic Mach number can dominate cruise performance. In nozzles and ducts, Mach number determines whether flow can choke and limit mass flow rate. In propulsion, compressor and turbine blade sections may encounter local Mach effects that constrain efficiency and operability.
Common mistakes
A common mistake is treating Mach number as just another way to state speed. It is a ratio to local sound speed, so temperature and medium matter. Another mistake is applying low-speed aerodynamic coefficients at high Mach number without correction. Good aerodynamic data states Mach number, Reynolds number, reference geometry, angle convention, and whether the data comes from wind tunnel, CFD, flight test, or analytical model.