A Machmeter is an
aircraft
An aircraft is a vehicle that is able to flight, fly by gaining support from the Atmosphere of Earth, air. It counters the force of gravity by using either Buoyancy, static lift or by using the Lift (force), dynamic lift of an airfoil, or in ...
pitot-static system
A pitot-static system is a system of pressure-sensitive instruments that is most often used in aviation to determine an aircraft's airspeed, Mach number, altitude, and altitude trend. A pitot-static system generally consists of a pitot tube, a s ...
flight instrument that
shows the
ratio
In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
of the
true airspeed to the
speed of sound
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as we ...
,
a
dimensionless quantity
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1 ...
called
Mach number
Mach number (M or Ma) (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.
It is named after the Moravian physicist and philosopher Ernst Mach.
: \mathrm = \f ...
. This is shown on a Machmeter as a
decimal fraction
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic num ...
.
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
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 ...
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 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 ...
s. The
indicated airspeed
for this condition changes with ambient temperature,
which in turn changes with
altitude
Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...
.
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 where the speed of sound under
standard conditions
Standard temperature and pressure (STP) are standard sets of conditions for experimental measurements to be established to allow comparisons to be made between different sets of data. The most used standards are those of the International Union ...
is , the
true airspeed at M
MO is . The speed of sound increases with air temperature, so at Mach 0.83 at where the air is much warmer than at , the true airspeed at M
MO would be .
Operation
Modern electronic Machmeters use information from an
air data computer system which makes calculations using inputs from a
pitot-static system
A pitot-static system is a system of pressure-sensitive instruments that is most often used in aviation to determine an aircraft's airspeed, Mach number, altitude, and altitude trend. A pitot-static system generally consists of a pitot tube, a s ...
. Some older mechanical Machmeters use an altitude
aneroid and an
airspeed
In aviation, airspeed is the speed of an aircraft relative to the air. Among the common conventions for qualifying airspeed are:
* Indicated airspeed ("IAS"), what is read on an airspeed gauge connected to a Pitot-static system;
* Calibrated ...
capsule which together convert pitot-static pressure into Mach number. The Machmeter suffers from instrument and position errors.
Calibration
In subsonic flow the Mach meter can be calibrated according to:
:
where:
:
is Mach number
:''q
c'' is
impact pressure (dynamic pressure)
:
is
static pressure
In fluid mechanics the term static pressure has several uses:
* In the design and operation of aircraft, ''static pressure'' is the air pressure in the aircraft's static pressure system.
* In fluid dynamics, many authors use the term ''static pres ...
: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:
:
where:
:
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.
See also
*
ICAO recommendations on use of the International System of Units
*
Airspeed indicator
The airspeed indicator (ASI) or airspeed gauge is a flight instrument indicating the airspeed of an aircraft in kilometers per hour (km/h), knots (kn), miles per hour (MPH) and/or meters per second (m/s). The recommendation by ICAO is to use km ...
*
Mach number
Mach number (M or Ma) (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.
It is named after the Moravian physicist and philosopher Ernst Mach.
: \mathrm = \f ...
*
Pitot-static system
A pitot-static system is a system of pressure-sensitive instruments that is most often used in aviation to determine an aircraft's airspeed, Mach number, altitude, and altitude trend. A pitot-static system generally consists of a pitot tube, a s ...
References
*
*
Aircraft instruments
Measuring instruments
Speed sensors
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