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True Airspeed

In der Luftfahrt unterscheidet man verschiedene Fluggeschwindigkeiten:

 Siehe Fluggeschwindigkeit für eine Übersicht

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True airspeed (TAS) is the physical speed of the aircraft relative to the air surrounding the aircraft. The true airspeed is a vector quantity. The relationship between the true airspeed and the speed with respect to the ground vgs is:

(1)
v_\mathrm{tas} = v_\mathrm{gs} - v_\mathrm{w}
wobei'
v_\mathrm{tas} ' =' 'True Air Speed TAS
v_\mathrm{gs} ' =' 'Ground Speed GS
v_\mathrm{w} ' =' 'Wind Speed 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. Basically, true airspeed is calibrated airspeed that is corrected for pressure altitude and temperature. The result is the true physical speed of the aircraft plus or minus the wind component. True Airspeed is equal to calibrated airspeed at standard sea level conditions.

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

(2)
v_\mathrm{tas} = a_0 \cdot Ma \cdot \sqrt{ T / T_0 }
wobei'
v_\mathrm{tas} ' =' 'True Air Speed TAS
a_0 ' =' 'Speed of sound at standard sea level (661,4788 knots)
Ma ' =' 'Mach number
T ' =' 'Temperature (Kelvins)
T_0 ' =' 'Standard sea level temperature (288,15 Kelvin)

Or if Mach number is not known:

(3)
v_\mathrm{tas} = a_0 \cdot \sqrt{ 5 \cdot \left[ \left( {q_\mathrm{c} \over p_\mathrm{s}} + 1 \right)^{(2/7)} - 1 \right] \cdot { T \over T_0 } }
wobei'
v_\mathrm{tas} ' =' 'True Air Speed TAS
a_0 ' =' 'Speed of sound at standard sea level (661,4788 knots)
q_\mathrm{c} ' =' 'Impact pressure (inHg)
p_\mathrm{s} ' =' 'Static pressure (inHg)
T ' =' 'Temperature (Kelvins)
T_0 ' =' '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.

(4)
\frac{1}{2} \cdot \rho \cdot v^2 = q = \frac{1}{2} \cdot \rho_0 \cdot v_\mathrm{e}^2

Thus

(5)
\frac{v}{v_\mathrm{e}} = \sqrt{ \frac{\rho_0 }{ \rho}}
wobei'
\rho ' =' 'is the air density at the flight condition.

The air density may be calculated from:

(6)
\frac{\rho}{\rho_0} = \frac{p \cdot T_0}{p_0 \cdot T}
wobei'
p ' =' 'air pressure at the flight condition
p_0 ' =' 'air pressure at sea level = 1013,2 hPa
T ' =' 'air temperature at the flight condition
T_0 ' =' 'air temperature at sea level, ISA = 288,15 K

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

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