Gas Turbines - Introduction — Page 212, Lesson 284

Let’s start with the idea of thrust, because everything here hangs off it. Thrust is the product of mass times acceleration. That’s the definition we’re working with: you take a mass of air, you accelerate it, and the reaction to that acceleration is your thrust. Now here’s the key insight. The same amount of thrust can be produced in two very different ways. You can take a large mass of air and give it only a small acceleration, or you can take a small mass of air and give it a large acceleration. Both can give you the same thrust, but they are not equal in practice. The preferred method is the first one — a large mass of air with a low acceleration. Why? Because the losses due to turbulence are much lower, and the propulsive efficiency is higher. That’s a fundamental design choice that runs through every gas turbine engine we’ll look at. So let’s define propulsive efficiency properly. It’s also called external efficiency. It is the efficiency of conversion of kinetic energy to propulsive work. In other words, how well the engine turns the kinetic energy it creates into useful work that moves the aircraft. And it’s affected by the amount of kinetic energy wasted by the propelling mechanism — the energy that goes into the exhaust and does nothing useful for you. The formula is written as a ratio: Propulsive Efficiency = Work Done on Aircraft, divided by Work Done on Airflow plus Work Wasted in Exhaust. That’s the conceptual form. Then we have the working form of the same formula, written as: PE = 2V divided by (V + VJ). Here, V is the aircraft speed, and VJ is the jet velocity. So the numerator is twice the aircraft speed, and the denominator is the aircraft speed plus the jet velocity. Let’s work through the two examples so you can see how this behaves. Example 1: a low bypass turbojet engine with a forward velocity V of 200 mph and a jet velocity VJ of 1000 mph. Plug it in: 2 times 200 is 400, over 200 plus 1000 which is 1200. That gives 400 over 1200, which simplifies to one third. Multiply by 100, and you get 33 percent. Example 2: same engine type, but now the forward velocity V is 600 mph, and the jet velocity VJ is still 1000 mph. So 2 times 600 is 1200, over 600 plus 1000 which is 1600. That gives 1200 over 1600, which simplifies to three quarters. Multiply by 100, and you get 75 percent. Now look at what happened. The jet velocity stayed the same at 1000 mph in both cases. The only thing that changed was the aircraft speed, and the efficiency jumped from 33 percent to 75 percent. The lesson is this: the closer the aircraft speed comes to the speed of the jet efflux — that is, the speed of the exhaust jet — the more efficient the propulsion unit becomes. When the aircraft is slow compared to the jet, you’re throwing a lot of kinetic energy away in the exhaust. As the aircraft speeds up and approaches the jet velocity, that wasted energy shrinks, and your propulsive efficiency climbs. And that’s the whole story of propulsive efficiency in one piece: it’s about how much of your kinetic energy actually does work on the aircraft, versus how much is wasted in the exhaust, and it improves as aircraft speed approaches jet velocity.