General Principles - Take-off — Page 155, Lesson 179

Let’s pick this up right where the forces on the aeroplane start to get interesting — the propeller and the engine, then the drag picture. First, the propeller. For a propeller-driven aircraft, thrust is produced by the propeller converting the shaft torque — that’s the twisting force coming out of the engine — into a propulsive force, the forward push. Now, the key behaviour: for a fixed pitch propeller, the angle of attack of the blades decreases as forward speed increases. Think of the blade meeting the air at a shallower angle the faster you go. Because of that, thrust decreases with increasing speed. For a variable pitch propeller, during take-off the propeller is initially held in the fine pitch position — that’s the low blade angle setting. As speed builds, the propeller angle of attack will decrease with increasing speed, just like the fixed pitch case. But here’s the difference: above the selected rpm, the propeller governor comes into operation. The governor increases the propeller pitch, and that reduces the rate at which the thrust decreases. So the thrust falls off more gently. In summary, for any propeller aeroplane, thrust decreases with forward speed. Now the engine itself — supercharged engines. If the engine is un-supercharged, the power produced will decrease with decreasing density, which means higher temperature or lower pressure. For a supercharged engine, power may be maintained with increasing altitude, up to the Full Throttle Height. That’s the altitude where the throttle is fully open and the supercharger can no longer hold the power — beyond that, power starts to fall off. Now let’s move to drag. The total drag, D, of an aeroplane during take-off is a product of both aerodynamic drag, DA, and wheel drag, which is the wheel friction, µ. The formula is D = DA + μ(W − L). Let me unpack that. W is the weight of the aeroplane, L is the lift. So (W − L) is the load on the wheels — the weight not yet supported by lift. μ is the runway surface resistance, the friction coefficient. Multiply that by the wheel load and you get the wheel drag. Aerodynamic drag comes in two principal forms: parasite drag and induced drag. Parasite drag is increased by the square of the speed — so as speed builds during take-off, parasite drag increases. Induced drag is a function of the angle of attack. The angle of attack is constant until the aeroplane rotates — that’s the point where the pilot raises the nose — and at rotation the angle of attack increases dramatically. So induced drag will increase during the take-off as well. Now wheel drag. It depends on the load on the wheel, (W − L), and the runway surface resistance, µ. At the start of the take-off, the load on the wheels is the entire weight of the aeroplane — lift is zero — so wheel friction and wheel drag are high. But as forward speed increases, lift starts to counteract the weight force, reducing the load on the wheels. So wheel friction and wheel drag reduce, eventually becoming zero at lift-off, when the wheels leave the ground. Here’s the net effect: the increase of aerodynamic drag is much higher than the decrease of wheel drag. Therefore total drag during the take-off increases. So let me summarise the forces for you. For all aeroplanes during take-off, thrust decreases and drag increases. The acceleration force is determined by subtracting the total drag from the total thrust. When thrust is more than drag, we use the term “excess thrust.” Excess thrust is what is needed to accelerate the aeroplane. You can see from the graph that the excess thrust — the gap between the thrust line and the drag line — is what drives the acceleration down the runway.