General Principles - Landing — Page 284, Lesson 350

Let’s pick this up right where the drag discussion left off, because the graph in Figure 6.4 is the perfect bridge into the landing distance formula. I want you to picture the landing roll as a speed race that’s slowing down. As the aeroplane decelerates along the runway, we have three drag forces at work, and they behave very differently. The first is aerodynamic drag. This is the total of parasite drag and induced drag, and it decreases as speed decreases during the landing run. That makes sense — less speed means less air hitting the airframe, so less aerodynamic resistance. Now, brake drag is the opposite. It increases during the landing roll, because as the aeroplane slows, more and more of its weight is transferred onto the wheels, which means the tyres can grip harder and the brakes can do more work. Here’s the key crossover point: during the early part of the landing roll, aerodynamic drag provides the majority of the total drag. But once the speed drops below 70% of the landing speed, brake drag takes over and provides the majority. So at high speed, the air is doing most of the stopping; at low speed, the brakes are. The last line on that graph is total drag, and you can see that during the landing roll, total drag actually increases. That’s a really important takeaway — the overall stopping force grows as you slow down, largely because brake drag builds up so strongly. And this shows you just how critical brake drag is. If the brakes were to fail, or if the landing surface is very slippery, you lose that braking contribution, and the landing performance massively deteriorates — which means the landing distance increases dramatically. Now let’s move to the landing distance formula, because this is what ties all the forces together. In Figure 6.5 you’ll see the expanded formula. The letter “s” is the displacement, or the distance required to stop from a specified speed, which is “V”, given a deceleration “d”. So s is the stopping distance, V is the speed you’re starting from, and d is how hard you’re slowing down. Deceleration is force divided by mass. And here’s where the four forces come in. The force in that formula is made up of aerodynamic drag, plus the braking coefficient — which is a function of wheel load — minus thrust, or in the case of reverse thrust, plus thrust. Let me unpack that. Aerodynamic drag is helping you stop, so it adds to the decelerating force. The braking coefficient, which depends on how much load is on the wheels, also adds to it. Thrust is normally working against you — it’s trying to keep you moving — so you subtract it. But if you’re using reverse thrust, that thrust is now helping you stop, so you add it instead. Expanding the formula this way lets you see how a change in one variable has a knock-on effect on the landing distance. And that’s exactly what we’re going to analyse now — all the factors that affect the landing, with our principal concern being how they change the landing distance. Let’s start with weight. The mass of the aeroplane affects three things. First, it affects the stalling speed, and hence VREF — that’s the reference landing speed you fly on approach. Second, it affects the deceleration for a given decelerating force. Third, it affects the wheel drag. Here’s how it plays out. Increased mass increases the stalling speed, and it reduces the deceleration for a given decelerating force. Both of those effects increase the landing distance — you’re coming in faster, and for the same stopping force, a heavier aeroplane slows down less. But there’s a counteracting effect: increased mass increases the brake drag available, if the brakes are not torque limited. More weight on the wheels means more grip, so more braking force, and that decreases the landing distance. So what’s the net effect? The landing distance will increase with increasing mass, but to a lesser degree than the increase of take-off distance with increasing mass. That’s a really important contrast to remember — weight hurts your take-off performance more than it hurts your landing performance, because on landing, the extra weight actually gives you more braking capability to offset some of the penalty. So to summarise where we are: we’ve got the drag picture through the landing roll, we’ve got the formula that ties distance, speed, and deceleration together, and we’ve started with weight as the first variable factor. The next factors will build on this same framework.