Airspeed - True Airspeed

True Airspeed

True airspeed (TAS) is the speed of the aircraft relative to the atmosphere. The true airspeed and heading of an aircraft constitute its velocity relative to the atmosphere. The vector relationship between the true airspeed and the speed with respect to the ground is:

where:

= Windspeed vector

Aircraft flight instruments, however, don't compute true airspeed as a function of groundspeed and windspeed. They use impact and static pressures as well as a temperature input. True airspeed is equivalent airspeed that is corrected for pressure altitude and temperature (which define density). The result is the true physical speed of the aircraft plus or minus the wind component. True Airspeed is equal to calibrated airspeed and equivalent airspeed at standard sea level conditions.

The simplest way to compute true airspeed is using a function of Mach number:

Where:

= Speed of sound at standard sea level (661.4788 knots)

= Mach number

= Temperature (kelvins)

= Standard sea level temperature (288.15 kelvins)

Or if Mach number is not known:

Where:

= Speed of sound at standard sea level (661.4788 knots)

= Impact pressure (inHg)

= Static pressure (inHg)

= Temperature (kelvins)

= Standard sea level temperature (288.15 kelvin)

The above equation is only for Mach numbers less than 1.0.

True airspeed differs from the equivalent airspeed because the airspeed indicator is calibrated at SL, ISA conditions, where the air density is 1.225 kg/m³, whereas the air density in flight normally differs from this value.

Thus

Where

is the air density at the flight condition.

The air density may be calculated from:

Where

is the air pressure at the flight condition,

is the air pressure at sea level = 1013.2 hPa,

is the air temperature at the flight condition,

is the air temperature at sea level, ISA = 288.15 K.

Source: Aerodynamics of a Compressible Fluid. Liepmann and Puckett 1947. Publishers John Wiley & Sons Inc.