Now let's move into take-off speed, because this is where the formula really… — Page 155, Lesson 181

Let me pick up right where we left off — we've just seen that excess thrust is what accelerates the aeroplane, and the graph shows it decreasing during the take-off run. Now I want to make sure you really understand what that means, because this term will come back when we do climb theory. Excess thrust is simply the difference between the thrust available and the drag at any given moment. It's the leftover thrust, the part that isn't being used just to overcome drag — and that leftover is what actually pushes the aeroplane forward and makes it accelerate. So when I say the excess thrust decreases during take-off, I mean the acceleration decreases too. The aeroplane is still speeding up, but the rate at which it speeds up is getting smaller as the run goes on. That's a key idea to hold onto. Now let's move into take-off speed, because this is where the formula really matters. The speed V in the take-off distance formula is True Ground Speed. That's a very precise statement, so let me unpack it. True Ground Speed is the actual speed of the aeroplane over the ground, and it's the speed that determines how much runway you physically cover. When you're calculating the take-off run required, you have to account for two separate effects. First, the effect of density on TAS for a given IAS — that's the difference between what your airspeed indicator reads and your true airspeed, which changes with altitude and temperature. Second, the effect of wind on TGS for a given TAS — that's the difference between your true airspeed through the air and your actual speed over the ground, which changes with headwind or tailwind. So both density and wind feed into that ground speed, and both must be considered. Then we have the speed to be reached at the screen — the Take-off Safety Speed. The screen is that imaginary vertical height you must clear at the end of the take-off distance, and the speed you must have when you reach it is determined by the Regulations. It's not a number you choose; it's a regulatory requirement. That speed must be a safe margin above the stall speed and above the minimum control speed. It must be a speed that gives adequate climb performance. And it must take account of the acceleration that will occur after lift-off. So it's a speed that's high enough to be safe, but it also recognises that the aeroplane will keep accelerating once it's airborne. It is very important to ensure this speed is achieved by the screen height — that's the whole point of the take-off distance calculation. Now let's look at the effect of variable factors on take-off distance, starting with mass. Mass affects the take-off distance in four distinct ways, and I want you to track each one. First, mass affects the acceleration for a given accelerating force. This is the effect of inertia. An aeroplane with higher mass has more inertia — it resists changes to its motion more. So as mass increases, acceleration decreases, and that increases the take-off distance. More mass, more inertia, less acceleration, longer run. Second, mass affects 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. This is a separate mechanism from inertia — it's about the tyres and the ground contact. Third, mass affects the take-off safety speed. An aeroplane with 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 a higher required speed means a longer take-off distance. So the heavier you are, the faster you must go to get airborne, and the more runway you need to reach that speed. Fourth, mass affects the angle of initial climb to the screen height. This effect will be better understood in the next chapter, but the principle is this: a higher mass reduces the angle of the initial climb. That means the aeroplane will use more distance to reach the screen height, because it's climbing at a shallower angle. So even after lift-off, the mass is still working against you in terms of the total take-off distance. So there you have it — four separate ways mass stretches out your take-off distance: inertia, wheel drag, the higher safety speed, and the shallower climb angle. Each one is a distinct physical mechanism, and in professional performance work you need to appreciate all four, because they all feed into the same final answer — how much runway you need.