getting to grips with aircraft performance 如何掌握飞机性能 2(22)

1.2.3. Speed Polar
The example below (Figure H2) illustrates both thrust and drag forces, as opposed to True Air Speed.
The above equations indicate that, for a given weight:
.  
The descent angle (γ) is proportional to the drag force, which is at its minimum at green dot speed.

.  
The rate of descent (RD) is proportional to the power of the drag force. As RD = TAS.γ, the minimum rate of descent is obtained for a TAS lower than green dot (when dRD/dTAS = 0).

1.3. Influencing Parameters
1.3.1. Altitude Effect
During the descent phase, air density increases, so that, for a given aircraft weight and a given true air speed, the drag force also increases. As the descent gradient and rate of descent are proportional to drag (Equations 2 and 6 above), an increase in their magnitude should be observed.

Nevertheless, as the descent is never performed at a given TAS, but at a given Mach or a given IAS, it is not possible to conclude. The following graph (Figure H3) represents the evolution of the descent gradient (γ) and rate of descent (RD), versus the altitude for a given descent profile M0.82 / 300 knots / 250 knots.
ALT (ft)
ALT (ft) ALT (ft)
39,000
36,089

31,800
10,000
TAS(kt)
Figure H3: A330 example - Descent Gradient (γ) and Rate of Descent (RD) versus Altitude and TAS
Unlike the climb phase, it is difficult to assess descent parameters (gradient and rate), as they only depend on drag and not on thrust (which is assumed to be set to idle).
1.3.2. Temperature Effect
As for pressure altitude, the temperature effect is difficult to assess. Indeed, at a given altitude, an increase in temperature causes a reduction in air density. As a result, drag also decreases, and it could be convenient to conclude that the magnitude of the gradient and rate of descent are thus reduced.
Nevertheless, the TAS is not constant during the descent. For a given Mach or IAS, TAS increases with temperature, thus compensating for drag reduction. This is why descent parameter variations versus temperature are not really significant.
1.3.3. Weight Effect
Green dot speed (minimum gradient) is a function of weight.  Figure H4 shows that, in the standard descent speed range (from green dot to VMO), the rate and gradient of descent magnitudes are reduced at higher weights.
Indeed, the balance of forces during descent indicates that:
Lift = Weight.cosγ = . ρ.S.TAS2.CL

At a given TAS, a higher weight means that a higher lift coefficient (CL) is needed to maintain the balance of forces. This is achieved by increasing the angle of attack (α) and reducing the descent gradient (γ). As RD = TAS.γ, the rate of descent is also reduced at higher weights.
　
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