General Principles - Descent — Page 221, Lesson 256

Let’s pick this up right where the descent theory gets quantitative. We’ve already seen that in a normal powered descent the forces balance, and that the weight apparent thrust — that’s the component of weight acting along the flight path — is what pulls the aeroplane down the descent. Now I want to show you how we actually calculate that, and then how we turn it into a formula you can use. The weight apparent thrust is calculated by multiplying the weight by the sine of the angle gamma. Gamma is the Greek letter we use for the descent angle — the angle between the flight path and the horizontal. So weight apparent thrust equals W times sine gamma. If you reduce thrust even more, as Figure 4.2 shows, you create a greater amount of excess drag. Excess drag is simply drag minus thrust — the amount by which drag exceeds thrust. Now, to balance that greater excess drag, you need more weight apparent thrust. And to get more weight apparent thrust, you have to lower the nose even more. The result is an increase in the descent angle. And for the purposes of the examinations, lowering the nose is a decrease in pitch. So remember that distinction: pitch is the attitude of the aeroplane relative to the horizon, and lowering the nose is a decrease in pitch. From this demonstration, the key conclusion is that it is the excess drag which determines the angle of descent. Notice that the angle gamma is the same angle as the angle of descent — they’re identical. Now, we can rearrange the force balance equation. In Figures 4.1 and 4.2, the balance is written as DA equals T plus W sine gamma, where DA is the drag in the descent, T is thrust, W is weight, and gamma is the descent angle. Rearranging that to solve for gamma gives us the formula for the angle or gradient of descent. The gradient of descent, expressed as a percentage, is (D minus T) divided by W, all multiplied by 100. So gradient of descent in percent equals (D − T) over W times 100. Drag minus thrust gives you the excess drag. So in summary, the angle or gradient of descent is controlled by the excess drag. To visualize this excess drag, we need to go back to the thrust and drag graphs we used in the climbing lesson. Figure 4.3 shows the thrust and drag curves for a jet and for a propeller aeroplane. We’ve learnt that to descend, there has to be an excess of drag. On the graphs, excess drag is found by taking the area beneath the drag curve and subtracting from it the area beneath the thrust curve. The solid purple highlighted areas represent the excess drag. Notice that if thrust is reduced at any given speed, then excess drag increases, and therefore the descent angle increases. Now let’s consider the maximum angle of descent. If it were a performance priority to maximize the angle of descent, then from the theory we’ve seen, we would have to maximize excess drag. Figure 4.4 shows the situation with zero thrust. If thrust is reduced to zero, notice that the excess drag area is a maximum — but to obtain that maximum excess drag, the aeroplane needs to be accelerated to a very high speed, as shown in Figure 4.4. This is achieved by closing the throttles and continuously lowering the nose of the aeroplane, so that the increasing amount of weight apparent thrust accelerates the aeroplane. As speed rises even more, both the excess drag and the angle of descent will increase. So the angle of descent is a function of excess drag — the greater the excess drag, the steeper the angle of descent. This angle could be increased even more if it were possible to increase the excess drag further. That can be achieved by deploying drag devices such as the speed brakes and the undercarriage. But attention must be paid to their maximum deployment speeds — you can’t just throw them out at any speed. That’s the practical side of increasing the descent angle, and it’s where we’ll continue next.