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1.2. Descent Equations 

While climb is due to excess thrust, descent is, on the other hand, caused by a lack of thrust. Therefore, the descent gradient and the rate of descent, which depend on the difference (Thrust – Drag), are negative. 

1.2.1. Descent Gradient (γ) 

As seen in the “Climb” chapter, the gradient can be expressed as: 

1 In order to simplify, the thrust vector is represented parallel to the aircraft longitudinal axis. 

(1) Descent is carried out at the Flight Idle thrust (i.e. at a thrust close to zero). Consequently: 

Drag

(2) By introducing L/D (the Lift to Drag ratio), and as the weight value is close to the lift one (Lift = Weight.cosγ), the descent angle becomes: 

(3) Which gives, in percent: 

(4) Conclusion: At a given weight, the magnitude of the descent gradient is minimum when the drag is minimum, or when the lift-to-drag ratio is maximum. The minimum descent angle speed is, therefore, green dot speed. 

1.2.2. Rate of Descent (RD) 

The Rate of Descent (RD) corresponds to the vertical component of the TAS. 

(5) RD = TAS sinγ ≈ TAS γ (sinγ≈γrad as γ is small) 

Hence: 

Conclusion: At a given aircraft weight, the rate of descent is minimum, when TASxDrag is minimum. 

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. 

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: 

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. 

As a conclusion, in the standard descent speed range: 

1.3.4. Wind Effect 

As shown in Figure H5 below, the air descent gradient (γa) remains unchanged, whatever the wind component. So, the fuel and time necessary to descend from the Top Of Descent (T/D) to the final level remain unchanged. 

2. DESCENT IN OPERATION 

2.1. Thrust Setting 

The standard engine rating for descent is “Flight Idle Thrust”. For fly-by-wire aircraft, the thrust throttle position doesn’t change when autothrust is engaged. The throttles remain on the “CL” (climb) gate for the entire flight (Figure H6). The engine-monitoring computer, or FADEC (Full Authority Digital Engine Control), adjusts the thrust level to the required value.