Calibrated airspeed
Encyclopedia
Calibrated airspeed is the speed shown by a conventional airspeed indicator
after correction for instrument error and position error
. Most civilian EFIS displays also show CAS. At high speeds and altitudes, calibrated airspeed is further corrected for compressibility errors and becomes equivalent airspeed
(EAS).
When flying at sea level under International Standard Atmosphere conditions (15°C, 1013 hPa, 0% humidity) calibrated airspeed is the same as equivalent airspeed and true airspeed
(TAS). If there is no wind it is also the same as ground speed
(GS). Under any other conditions, CAS may differ from the aircraft's TAS and GS.
Calibrated airspeed in knots is usually abbreviated as KCAS, while indicated airspeed is abbreviated as KIAS.
With the widespread use of GPS
and other advanced navigation systems in cockpits, the first application is rapidly decreasing in importance – pilots are able to read groundspeed (and often true airspeed)
directly, without calculating calibrated airspeed as an intermediate step. The second application remains critical, however – for example, at the same weight, an aircraft will rotate and climb at approximately the same calibrated airspeed at any elevation, even though the true airspeed and groundspeed may differ significantly. These V speeds
are usually given as IAS rather than CAS, so that a pilot can read them directly from the airspeed indicator.
, CAS is defined as a function of impact pressure alone. Static pressure and temperature appear as fixed coefficients defined by convention as standard sea level values. It so happens that the speed of sound
is a direct function of temperature, so instead of a standard temperature, we can define a standard speed of sound.
For subsonic
speeds, CAS is calculated as:
where:
For supersonic
airspeeds, where a normal shock forms in front of the pitot probe, the Rayleigh formula applies:
The supersonic formula must be solved iteratively, by assuming an initial value for
equal to 
.
These formulae work in any units provided the appropriate values for
and 
are selected. For example 
= 1013.25 hPa, 
= 661.48 knots. The ratio of specific heats for air is assumed to be 1.4.
These formulae can then be used to calibrate an airspeed indicator when impact pressure (
) is measured using a water manometer or accurate pressure gauge. If using a water manometer to measure millimeters of water the reference pressure (
) may be entered as 10333 mm 
.
At higher altitudes CAS can be corrected for compressibility error to give equivalent airspeed
(EAS). In practice compressibility error is negligible below about 10,000 feet and 200 knots.
Airspeed indicator
The airspeed indicator or airspeed gauge is an instrument used in an aircraft to display the craft's airspeed, typically in knots, to the pilot.- Use :...
after correction for instrument error and position error
Position error
Position error is one of the errors affecting the systems in an aircraft for measuring airspeed and altitude. It is not practical or necessary for an aircraft to have an airspeed indicating system and an altitude indicating system that are exactly accurate...
. Most civilian EFIS displays also show CAS. At high speeds and altitudes, calibrated airspeed is further corrected for compressibility errors and becomes equivalent airspeed
Equivalent airspeed
Equivalent airspeed is the airspeed at sea level in the International Standard Atmosphere at which the dynamic pressure is the same as the dynamic pressure at the true airspeed and altitude at which the aircraft is flying. In low-speed flight, it is the speed which would be shown by an airspeed...
(EAS).
When flying at sea level under International Standard Atmosphere conditions (15°C, 1013 hPa, 0% humidity) calibrated airspeed is the same as equivalent airspeed and true airspeed
True airspeed
True airspeed of an aircraft is the speed of the aircraft relative to the airmass in which it is flying. True airspeed is important information for accurate navigation of an aircraft.-Performance:...
(TAS). If there is no wind it is also the same as ground speed
Ground speed
Ground speed is the speed of an aircraft relative to the ground. Information displayed to passengers through the entertainment system often gives the aircraft groundspeed rather than airspeed....
(GS). Under any other conditions, CAS may differ from the aircraft's TAS and GS.
Calibrated airspeed in knots is usually abbreviated as KCAS, while indicated airspeed is abbreviated as KIAS.
Practical applications of CAS
CAS has two primary applications in aviation:- for navigation, CAS is traditionally calculated as one of the steps between indicated airspeed and true airspeed;
- for aircraft control, CAS (and EAS) are the primary reference points, since they describe the dynamic pressure acting on aircraft surfaces regardless of density altitude, wind, and other conditions. EAS is used as a reference by aircraft designers, but EAS cannot be displayed correctly at varying altitudes by a simple (single capsule) airspeed indicator. CAS is therefore a standard for calibrating the airspeed indicator such that CAS equals EAS at sea level pressure and approximates EAS at higher altitudes.
With the widespread use of GPS
Global Positioning System
The Global Positioning System is a space-based global navigation satellite system that provides location and time information in all weather, anywhere on or near the Earth, where there is an unobstructed line of sight to four or more GPS satellites...
and other advanced navigation systems in cockpits, the first application is rapidly decreasing in importance – pilots are able to read groundspeed (and often true airspeed)
directly, without calculating calibrated airspeed as an intermediate step. The second application remains critical, however – for example, at the same weight, an aircraft will rotate and climb at approximately the same calibrated airspeed at any elevation, even though the true airspeed and groundspeed may differ significantly. These V speeds
V speeds
In aviation, V-speeds are standard terms used to define airspeeds important or useful to the operation of all aircraft including fixed-wing aircraft, gliders, autogiros, helicopters, and dirigibles...
are usually given as IAS rather than CAS, so that a pilot can read them directly from the airspeed indicator.
Calculation from impact pressure
Since the airspeed indicator capsule responds to impact pressureImpact pressure
In compressible fluid dynamics, impact pressure is the difference between total pressure and static pressure. In aerodynamics notation, this quantity is denoted as q_c or Q_c....
, CAS is defined as a function of impact pressure alone. Static pressure and temperature appear as fixed coefficients defined by convention as standard sea level values. It so happens that the speed of sound
Speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
is a direct function of temperature, so instead of a standard temperature, we can define a standard speed of sound.
For subsonic
Speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
speeds, CAS is calculated as:
where:
= impact pressure
= standard pressure at sea level
is the standard speed of sound at 15 °C
For supersonic
Supersonic
Supersonic speed is a rate of travel of an object that exceeds the speed of sound . For objects traveling in dry air of a temperature of 20 °C this speed is approximately 343 m/s, 1,125 ft/s, 768 mph or 1,235 km/h. Speeds greater than five times the speed of sound are often...
airspeeds, where a normal shock forms in front of the pitot probe, the Rayleigh formula applies:
The supersonic formula must be solved iteratively, by assuming an initial value for
equal to .These formulae work in any units provided the appropriate values for
and are selected. For example = 1013.25 hPa, = 661.48 knots. The ratio of specific heats for air is assumed to be 1.4.These formulae can then be used to calibrate an airspeed indicator when impact pressure (
) is measured using a water manometer or accurate pressure gauge. If using a water manometer to measure millimeters of water the reference pressure () may be entered as 10333 mm .At higher altitudes CAS can be corrected for compressibility error to give equivalent airspeed
Equivalent airspeed
Equivalent airspeed is the airspeed at sea level in the International Standard Atmosphere at which the dynamic pressure is the same as the dynamic pressure at the true airspeed and altitude at which the aircraft is flying. In low-speed flight, it is the speed which would be shown by an airspeed...
(EAS). In practice compressibility error is negligible below about 10,000 feet and 200 knots.