Machmeter

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 M_MO.

For example, if the M_MO is Mach 0.83, then at {{cvt|30000|ft|m|sigfig=2|order=flip}} where the speed of sound under standard conditions is {{convert|590|kn|km/h|0|order=flip}}, the true airspeed at M_MO is {{convert|489|kn|km/h|0|order=flip}}. The speed of sound increases with air temperature, so at Mach 0.83 at {{cvt|10000|ft|m|sigfig=1|order=flip}} where the air is much warmer than at {{cvt|30000|ft|m|sigfig=2|order=flip}}, the true airspeed at M_MO would be {{cvt|530|kn|km/h|0|order=flip}}.

Modern electronic Machmeters use information from an air data computer system which makes calculations using inputs from a pitot-static system. Some older mechanical Machmeters use an altitude aneroid and an airspeed capsule which together convert pitot-static pressure into Mach number. The Machmeter suffers from instrument and position errors.

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

:$$

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

or,

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

where:

:$\backslash \; M\backslash ,$ is Mach number

:q_c is impact pressure (dynamic pressure)

:$\backslash \; p$ 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:

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

where:

:$\backslash \; p\_t$ is now total pressure measured behind the normal shock.

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

• ICAO recommendations on use of the International System of Units
• Airspeed indicator
• Mach number
• Pitot-static system

• {{cite book

| title = Instrument Flying Handbook

| date = 2005-11-25

| publisher = U.S. Federal Aviation Administration

| location = U.S. Government Printing Office, Washington D.C.

| id = FAA-H-8083-15

| pages = 3–8

}}

• {{cite book

|title = Instrument Flying Handbook

|date = 2007

|publisher = U.S. Federal Aviation Administration

|location = U.S. Government Printing Office, Washington D.C.

|id = FAA-H-8083-15A

|pages = 3–10

|url = http://www.faa.gov/library/manuals/aviation/instrument_flying_handbook/

|url-status = dead

|archive-url = https://web.archive.org/web/20080422015034/http://www.faa.gov/library/manuals/aviation/instrument_flying_handbook/

|archive-date = 2008-04-22

}}

{{USGovernment|url=http://www.faa.gov/library/manuals/aviation/instrument_flying_handbook/|title=Instrument Flying Handbook}}

{{Flight instruments}}

Category:Aircraft instruments

Category:Measuring instruments

Category:Speed sensors

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