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

Let's pick this up right where the forces on the aeroplane start to get interesting. We've already looked at how thrust behaves for a jet, and now I want to walk you through the two other big players in the take-off: the propeller-driven thrust and then the drag. First, the propeller. For a propeller-driven aircraft, thrust is produced by the propeller converting the shaft torque into propulsive force. So the engine turns the shaft, and the propeller turns that twisting force into a forward push. Now, here's the key behaviour. For a fixed pitch propeller, the angle of attack of the blades decreases as forward speed increases. Think of it this way: as the aircraft speeds up, the relative airflow over the blade changes, and the blade meets the air at a shallower angle. That means the thrust decreases with increasing speed. For a variable pitch propeller, the story is a little more refined. During take-off, the propeller is initially held in the fine pitch position. That's the low blade angle setting, which gives you maximum thrust at low speed. As speed builds, the propeller angle of attack will decrease with increasing speed, just like the fixed pitch. 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 curve flattens out a bit. In summary, though, for any propeller aeroplane, the thrust decreases with forward speed. That's the takeaway. Now, before we leave thrust, let's talk about supercharged engines. If the engine is un-supercharged, the power produced will decrease with decreasing density. And decreasing density means higher temperature or lower pressure. So on a hot day or at altitude, an un-supercharged engine loses power. 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 maintain sea-level power. Above that height, power starts to fall off again. Now let's move to drag, because this is where the take-off really gets interesting. The total drag, which we call D, of an aeroplane during take-off is a product of both aerodynamic drag, DA, and wheel drag, which is the wheel friction, mu. And the formula is this: D equals DA plus mu times (W minus L). Let me unpack that. W is the weight of the aeroplane, and L is the lift. So (W minus L) is the load on the wheels — the part of the weight that the wheels are actually carrying. Mu is the runway surface resistance, the friction coefficient. So wheel drag is the friction coefficient times the load on the wheels. Now, aerodynamic drag comes in two principal forms: parasite drag and induced drag. Parasite drag is increased by the square of the speed. So as the aircraft accelerates down the runway, parasite drag grows quickly. Induced drag is a function of the angle of attack. During the ground roll, the angle of attack is constant until the aeroplane rotates. At rotation, the angle of attack increases dramatically, and so induced drag increases during the take-off. Now for wheel drag. The wheel drag depends on the load on the wheel, which is (W minus L), and the runway surface resistance, mu. At the start of the take-off, the load on the wheels is the entire weight of the aeroplane. There's no lift yet, so W minus L is just W. Therefore wheel friction and wheel drag are high. But as forward speed increases, lift starts to counteract the weight force. That reduces the load on the wheels. So the wheel friction and the wheel drag reduce, and eventually they become zero at lift-off, because at that point the wheels are no longer touching the runway. Now here's the crucial comparison. The increase of aerodynamic drag is much higher than the decrease of wheel drag. So the total drag during the take-off increases. Even though wheel drag is falling, aerodynamic drag is rising faster, and the net effect is that total drag goes up. So let me summarise the forces for you, because this is the heart of the take-off. For all aeroplanes during the take-off, thrust decreases and drag increases. The acceleration force is determined by subtracting the total drag from the total thrust. So acceleration equals thrust minus drag. When thrust is more than drag, we use the term "excess thrust." Excess thrust is what is needed to accelerate the aeroplane. And you can see from the graph that the excess thrust — the area between the total drag line and the thrust line — is what drives the acceleration down the runway. So the picture you should hold in your mind is this: at the start of the roll, thrust is high and drag is low, so excess thrust is large and the aircraft accelerates briskly. As speed builds, thrust falls and drag rises, so excess thrust shrinks. But as long as there's excess thrust, the aircraft keeps accelerating. That's the fundamental balance of the take-off.