# Machmeter

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Illustration showing the face of a Machmeter reading a Mach number of 0.83

A Machmeter is an aircraft pitot-static system flight instrument that shows the ratio of the true airspeed to the speed of sound, a dimensionless quantity called Mach number. This is shown on a Machmeter as a decimal fraction. An aircraft flying at the speed of sound is flying at a Mach number of one, expressed as Mach 1.

## Use

As an aircraft in transonic flight approaches the speed of sound, it first reaches its critical mach number, where air flowing over low-pressure areas of its surface locally reaches the speed of sound, forming shock waves. The indicated airspeed for this condition changes with ambient temperature, which in turn changes with altitude. Therefore, indicated airspeed is not entirely adequate to warn the pilot of the impending problems. Mach number is more useful, and most high-speed aircraft are limited to a maximum operating Mach number, also known as MMO.

For example, if the MMO is Mach 0.83, then at 30,000 feet (9,144 m) where the speed of sound under standard conditions is 590 knots (1,093 km/h; 679 mph), the true airspeed at MMO is 489 knots (906 km/h; 563 mph). The speed of sound increases with air temperature, so at Mach 0.83 at 10,000 feet (3,048 m) where the air is much warmer than at 30,000 feet (9,144 m), the true airspeed at MMO would be 530 knots (982 km/h; 610 mph).

## Operation

Some older mechanical Machmeters use an altitude aneroid and an airspeed capsule which together convert pitot-static pressure into Mach number. Modern electronic Machmeters use information from an air data computer system.

## Calibration

In subsonic flow the Mach meter can be calibrated according to:

${M}=\sqrt{5\left[\left(\frac{p_t}{p}\right)^\frac{2}{7}-1\right]}\,$

where:

$\ M\,$ is Mach number
$\ p_t\,$ is total pressure and
$\ p$ is static pressure
and assuming the ratio of specific heats is 1.4

When a shock wave forms across the pitot tube the required formula is derived from the Rayleigh Supersonic Pitot equation, and is solved iteratively:

${M}=0.88128485\sqrt{\left[\left(\frac{p_t}{p}+1\right)\left(1-\frac{1}{[7M^2]}\right)^\frac{5}{2}\right]}$

where:

$\ p_t$ is now impact pressure measured behind a normal shock.

Note that the inputs required are impact pressure (or total pressure) and static pressure. Air temperature input is not required.

## References

• Instrument Flying Handbook. U.S. Government Printing Office, Washington D.C.: U.S. Federal Aviation Administration. 2005-11-25. p. 3–8. FAA-H-8083-15.
• Instrument Flying Handbook. U.S. Government Printing Office, Washington D.C.: U.S. Federal Aviation Administration. 2007. p. 3–10. FAA-H-8083-15A.

This article incorporates public domain material from the United States Government document "Instrument Flying Handbook".