General Principles - Landing — Page 284, Lesson 350

Let’s pick this up right where the drag picture leaves off, because that graph on Figure 6.4 is the key to everything that follows. I want you to see the landing roll as a battle between two very different drag forces, and the graph shows how their roles swap as the aeroplane slows down. The first force is aerodynamic drag. As the speed decreases during the landing run, aerodynamic drag — which is made up of parasite drag and induced drag — decreases. That makes sense: drag from the airflow is proportional to speed, so as you bleed off speed, the air does less and less of the stopping work. The second force is brake drag. This one does the opposite. Brake drag increases during the landing roll, because more and more load is placed on the wheels as the aeroplane decelerates. So early in the landing roll, aerodynamic drag provides the majority of the total drag. But once the speed has dropped below 70% of the landing speed, brake drag takes over and provides the majority. That 70% figure is a real threshold you should remember — it’s the crossover point where the brakes become the dominant stopping force. The last line on the graph is total drag. From that line you can see that during the landing roll, total drag actually increases. That’s the important takeaway: even though aerodynamic drag is falling off, brake drag is rising fast enough that the sum keeps climbing. And that shows you just how important brake drag is. If the brakes were to fail, or if the landing surface is very slippery, the loss of braking would cause the landing performance to massively deteriorate, which means the landing distance increases. So the brakes aren’t just a convenience — they’re the primary stopping mechanism for most of the roll. Now let’s move to the landing distance formula, because this is what ties all the forces together. In Figure 6.5 you can see the expanded landing distance formula. The letter “s” is the displacement, or the distance required to stop from a specified speed, which is “V”, with a given deceleration “d”. So s is what we’re trying to find — the landing distance — and it depends on the speed you start from and how hard you can decelerate. Deceleration, “d”, is force divided by mass. And here’s where the four forces come in. The force in that equation is 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 sign convention, because it’s easy to get tangled. Aerodynamic drag and brake drag are both resisting motion, so they add to the decelerating force. Thrust is normally pushing the aeroplane forward, so it subtracts from the decelerating force — that’s the minus thrust. But if you’re using reverse thrust, that thrust is now opposing motion, so it adds to the decelerating force — that’s the plus thrust. So the formula is really just a balance of everything pushing you forward versus everything holding you back. Expanding the formula this way lets you see how a change in one variable has a knock-on effect on the landing distance. That’s the whole point of the analysis we’re about to do — we’ll look at each factor and see how it ripples through this equation. Let’s start with the first factor: 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 each one plays out. Increased mass increases stalling speed, and it reduces the deceleration for a given decelerating force. Both of those effects increase the landing distance. Why? A higher stalling speed means you start the landing roll at a higher speed, so you have more energy to dissipate. And for a given decelerating force, more mass means less deceleration — that’s Newton’s second law, force equals mass times acceleration, so more mass with the same force gives you less deceleration. Both push the landing distance up. But there’s a counteracting effect. Increased mass increases the brake drag available — if not torque limited. More weight on the wheels means more friction available for braking, and that decreases the landing distance. The qualifier “if not torque limited” is important: if the brakes are already at their torque limit, adding more weight won’t give you more braking force. 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 classic comparison you’ll see again and again in performance work — weight hurts take-off distance more than it hurts landing distance, because on take-off you’re fighting to accelerate a heavier aeroplane, while on landing the extra weight actually helps you by adding brake drag. That’s the weight effect. Next we’ll go through the other variable factors that affect landing distance — things like wind, runway slope, and surface condition — each one feeding into that same formula.