getting to grips with aircraft performance 如何掌握飞机性能 1(11)

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) and a compressibility correction (K).
TAS =
(ρo/ρ) K CAS
3.4. Ground Speed (GS)
The ground speed (GS) represents the aircraft speed in a fixed ground reference system. It is equal to the TAS corrected for the wind component (Figure A10).

 

GS = Ground Speed DA = Drift Angle TAS = True Air Speed
Figure A10: Ground Speed and Drift Angle
3.5. Mach Number
The Mach Number is a comparison between the TAS and the speed of sound.
TAS
M=
a
With TAS = True Air Speed a = The speed of sound at the flight altitude
The speed of sound in knots is:
a(kt) = 39
SAT(K)

With SAT = Static Air Temperature (ambient temperature)in Kelvin
The speed of sound is solely dependent on temperature. Consequently, the Mach number can be expressed as follows:
TAS (kt)

Flying at a given Mach number in the troposphere: When the pressure altitude increases, the SAT decreases and thus the True Air Speed (TAS). Or :
higher .
 slower

Pt and Ps, respectively measured by the aircraft pitot tube and static probes, are also used to compute the Mach number.  Therefore,
. Pt . Ps .. q .
M = f .. ..= f .. ..
P P
. s .. s.
The TAS indicated on the navigation display of modern aircraft is then obtained from the Mach number:
TAS(Kt) = 39M
273 + SAT (oC)
3.6. True Air Speed (TAS) Variations

The above graph (Figure A11) illustrates the TAS variations as a function of the pressure altitude for a climb at constant CAS (300 knots) and constant Mach (M0.78).
The altitude at which a given CAS is equal to a given Mach number is called the cross-over altitude.

4. FLIGHT MECHANICS
For a flight at constant speed in level flight, the drag force must balance the engine thrust.
As a general rule, when engine thrust is higher than drag, the aircraft can use this excess thrust to accelerate and/or climb. On the other hand, when the thrust is insufficient to compensate for drag, the aircraft is forced to decelerate and/or descend.
In flight, four forces are applied to an aircraft : Thrust, drag, lift and weight. If the aircraft is in steady level flight, the following balance is obtained (Figure A12):
.
The thrust for steady level flight (T) is equal to drag (D = . ρ S V2 CD),

.
Weight (mg) is equal to lift (L = . ρ S V2 CL).

 

4.1.1.1. Standard Lift Equation
Weight = mg = . ρ S (TAS)2 CL (1)
With  m = Aircraft mass g = Gravitational acceleration ρ = Air density S = Wing area CL = lift coefficient
The lift coefficient, CL, is a function of the angle of attack (α), the Mach number (M), and the aircraft configuration.

4.1.1.2. Standard Drag Equation
Thrust = . ρ S (TAS)2 CD (2) With CD = Drag coefficient The drag coefficient, CD, is a function of the angle of attack (α), the Mach number (M) and the aircraft configuration.
　
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