getting to grips with aircraft performance 如何掌握飞机性能 2(17)

(4)
Lift = Weight

From equation (3), Thrust -Drag = Weight γ. Then:
Thrust -Drag
(5)
γ
rad =
Weight
Thrust Drag
γ
rad =.
(4)+(5)
Weight Lift
By introducing L/D (the Lift-to-Drag ratio), the climb angle becomes:
Thrust 1
γ
rad =.
(6)
Weight
Which gives, in percent:
. Thrust 1 .
γ
(%) = 100..
..

(7)
. Weight LD .
Conclusion: At a given weight and engine rating, the climb gradient is maximum when (Thrust – Drag) is maximum (i.e. when the drag is minimum or when the lift-to-drag ratio is maximum). The best lift-to-drag ratio speed is called Green Dot (or Drift-down) speed. In case of an engine failure, flying at green dot speed permits maximizing the aircraft’s aerodynamic efficiency and compensating for the power loss.

1.2.2. Rate of Climb (RC)
The Rate of Climb (RC) corresponds to the aircraft’s vertical speed. As a consequence:
(8) RC = TAS sinγ ≈ TAS γ (sinγ≈γrad as γ is small)
Thrust -Drag
From equation (5), γ= . Therefore:
Weight
Thrust -Drag
RC = TAS .
(9)
Weight
Conclusion: At a given aircraft weight, the rate of climb is maximum when TASx(Thrust – Drag) is maximum. In terms of power1, the rate of climb is maximum when (Pthrust – Pdrag) is maximum.
1.2.3. Speed Polar
The following Figure (G2) illustrates both the thrust and the drag forces versus the True Air Speed.
To fly at a constant level and speed, the thrust must balance the drag. As a result, drag can be considered as the thrust required to maintain a constant flight level and a constant speed. Climb is only possible when the available thrust is higher than the required thrust (excess of thrust).
The above equations indicate that, for a given weight:
.  
The climb angle (γ) is proportional to the difference between the available thrust and the required thrust.

.  
The rate of climb (RC) is proportional to the difference between the available power and the required power. Moreover, as RC = TAS γ, the maximum rate of climb is obtained for a TAS higher than green dot (when dRC/dTAS = 0).

1 The force power (Pforce) represents the force multiplied by the speed (TAS). The unit is watt (W).

It can be observed that it is not beneficial to climb at a speed lower than green dot, as it would require a longer distance and time to reach a given flight level.
1.3. Influencing Parameters
1.3.1. Altitude Effect
Due to air density reduction when pressure altitude increases, climb thrust and drag decrease. But, since the drag force decreases at a lower rate than the available thrust, the difference between thrust and drag decreases. Therefore, the climb gradient and the rate of climb decrease with pressure altitude, due to a lower excess of thrust.
　
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