Let me walk you through this part of the take-off performance chapter — Page 155, Lesson 181

Let me walk you through this part of the take-off performance chapter. We're looking at the forces acting on the aeroplane during the take-off run, and I want to start with the term "excess thrust." Excess thrust is what is needed to accelerate the aeroplane. Think of it this way: the engines produce thrust, but the aeroplane also experiences drag as it moves. The difference between the thrust and the drag is the excess thrust — that's the portion left over that actually goes into accelerating the machine. If you look at the graph of forces against speed during the take-off, you'll see that the excess thrust, and therefore the acceleration of the aeroplane, decreases as the take-off progresses. That's an important trend to hold onto, because the term "excess thrust" will come back again when we introduce climb theory later. Now let's move to take-off speed. The speed V in the take-off distance formula is True Ground Speed. That's a specific distinction. When we calculate the take-off run required, we have to account for two effects: the effect of density on TAS for a given IAS, and the effect of wind on TGS for a given TAS. Let me unpack those. IAS is indicated airspeed — what the instruments show. TAS is true airspeed — the actual speed of the aeroplane through the air. Density affects the relationship between them because at higher altitude or higher temperature, the air is less dense, so for the same indicated airspeed the true airspeed is higher. Then TGS is true ground speed — the speed over the ground. Wind affects that: with a headwind, your ground speed is lower than your true airspeed; with a tailwind, it's higher. So the take-off distance formula uses true ground speed, and you must correct for both density and wind to get it right. Next, the speed to be reached at the screen — that's the Take-off Safety Speed. The screen is the imaginary obstacle height at the end of the take-off distance that the aeroplane must clear. This speed is determined by the Regulations, and it's required to be a safe margin above two things: the stall speed and the minimum control speed. It also must be a speed that gives adequate climb performance, and it must take account of the acceleration that will occur after lift-off. It is very important to ensure this speed is achieved by the screen height — that's a regulatory requirement, not a suggestion. Now let's look at the effect of variable factors on take-off distance, starting with mass. The mass of the aeroplane affects take-off distance in four distinct ways. First, the acceleration for a given accelerating force. This is the effect of inertia. An aeroplane with higher mass has more inertia, so as mass increases, acceleration decreases, which increases the take-off distance. Newton's second law in action — more mass, same force, less acceleration. Second, the wheel drag. Increased mass increases the load placed on the wheels, and therefore increases the wheel friction. Because of that increased wheel friction, wheel drag increases. So again, acceleration is reduced and the take-off distance increases. Third, the take-off safety speed. An aeroplane with a higher mass has a greater force of weight. That weight must be overcome by greater lift. To gain that extra lift, the aeroplane must be accelerated to a higher speed — and of course, that increases the take-off distance. Fourth, the angle of initial climb to the screen height. This effect will be better understood in the next chapter, but nonetheless, a higher mass reduces the angle of the initial climb. That means the aeroplane will use more distance to reach the screen height — the passage cuts off there, but the principle is that a shallower climb angle means you travel further horizontally before you clear the screen. So to summarise the mass effects: higher mass means more inertia, more wheel drag, a higher required safety speed, and a shallower climb angle — and every one of those four effects lengthens the take-off distance. That's why mass is such a central factor in take-off performance calculations.