General Principles - Take-off — Page 155, Lesson 177

Let's get straight into the heart of take-off performance. I want to walk you through how we actually calculate the take-off distance, and then we'll dig into the forces that make it happen. Here we have two formulae that work together. The upper one is the key: it calculates the distance required, which we call s, to reach a specified speed, V, given a certain acceleration, a. So the formula is s = V² / a. Read that as: distance equals speed squared divided by acceleration. Now, beneath that is the formula to calculate that acceleration. For an aircraft taking off, the acceleration is thrust minus drag. That's the net force driving you forward. But here's the crucial catch: both thrust and drag change as the speed changes. So the acceleration is not constant during the take-off. It's a moving target. Also, once you become airborne, the laws of motion are somewhat different. The upper formula will change a bit in its form, but the principle holds: the distance required still depends on the speed to be achieved and the acceleration. So the core idea is that take-off distance is governed by how quickly you can build speed, and that depends on the balance of thrust and drag. Now, because thrust and drag play such a crucial part, let's add some detail on these two forces. Let's start with thrust. The engine thrust will vary during take-off, and the variation with speed is different for jet and propeller engines. Let's look at the jet engine first. For a jet engine, the net thrust is the difference between the gross thrust and the intake momentum drag. Gross thrust is the total thrust produced by the engine's exhaust. Intake momentum drag is the resistance caused by the air being pulled into the engine. As speed increases, the intake momentum drag increases, which reduces the thrust. However, at higher speeds, the increased intake pressure due to the ram effect helps to reduce this loss of thrust. The ram effect is the pressure build-up from air being forced into the intake at high speed. Eventually, at very high speeds, it will cause the net thrust to increase again. But here's the important part for take-off: during the take-off, the aeroplane speed is still low. So the ram effect is insufficient to counteract the loss of thrust due to intake momentum drag. Therefore, during the take-off, there will be a decrease of thrust. Now, a note for later: in later chapters and in some performance graphs, you'll notice the assumption is made that jet thrust is constant with speed. That's done purely to simplify some teaching points. In reality, as we've just seen, it decreases during take-off. Now let's talk about flat rated engines. This is a key concept. The thrust produced by an engine at a given rpm will depend on the air density, and hence on air pressure and temperature. At a given pressure altitude, decreasing temperature will give increasing thrust. So colder air means denser air, which means more thrust. However, many jet engines are "flat rated". That means they are restricted to a maximum thrust even though the engine is capable of producing higher thrust. Why? Because at lower temperatures, too much thrust may be generated, and the pressures within the compressors may be exceeded. That's a structural limit you must not exceed. So the consequence is this: at temperatures below the flat rating cut off, which is typically about ISA + 15°C, engine thrust is not affected by temperature. In other words, below that cut-off, the engine is held back to its maximum rated thrust, so temperature changes don't change the thrust. Above that cut-off, the thrust will start to drop as temperature increases. So to tie it together: take-off distance depends on speed squared over acceleration, acceleration is thrust minus drag, and thrust itself is a variable — it decreases with speed during take-off for a jet, and it's capped by flat rating at low temperatures. That's the foundation we'll build on.