Gas Turbines - Thrust — Page 310, Lesson 401

Let's start with the very foundation of thrust, because everything in this chapter hangs off one idea. Back in Chapter 1, we established that thrust comes from a reaction — you accelerate a mass of air backwards, and by Newton's third law, for every action there is an equal and opposite reaction, so you get forward thrust. That's the core principle. Now, Newton's third law gives us a formula: F = ma, where F is force, m is mass, and a is acceleration. So force equals mass times acceleration. That's the mathematical backbone of everything we're about to do. Now, let's think about what a gas turbine engine actually is. I want you to picture it as a device that does two things in sequence. First, it manufactures potential pressure energy — that means it builds up pressure. Then it converts that pressure energy into kinetic velocity energy — that means it turns the pressure into speed of the airflow. Here's the key point: not all of that energy goes into thrust. Some of it performs work at the turbine — that's the work that keeps the compressor spinning. The remainder is what creates thrust. So the engine is a balance: some energy drives the turbine, the rest pushes the aircraft forward. Let me walk you through the physical picture. We have one unit of air entering the engine. That air gets increased in size — it expands — because of two things: combustion with fuel, and heat expansion. Because the air has expanded so much, it has to accelerate greatly in order to leave the exhaust nozzle. That acceleration is what produces the thrust. The air goes in relatively slowly, and it must come out very fast. Now, here's where we get precise about the thrust formula. There are two elements that make up total thrust. The first is momentum thrust. Momentum thrust is always present whenever the engine is running — it's derived directly from that F = ma equation we started with. The second element is pressure thrust. Pressure thrust is an extra source of thrust, and it only occurs when the airflow through the engine reaches the speed of sound. So it's not always there — it's a special condition. The total thrust formula is this: Thrust = Wa (Vo - Vi) + Pressure Thrust. Let me break down each symbol. Wa is the mass flow of air per second — that's how much air, in terms of mass, passes through the engine every second. Vo is the exit velocity of air — how fast the air leaves the engine. Vi is the inlet velocity of air — how fast the air enters the engine. So the momentum thrust part is Wa times (Vo minus Vi). That's mass flow times the change in velocity. And then we add pressure thrust on top of that. We'll deal with the calculation of pressure thrust shortly — for now, just know it's the second component of total thrust. Let me show you the thrust formula visually. That figure shows the two elements that make up total thrust — momentum thrust and pressure thrust. So when you look at an engine and ask "where does the thrust come from?", the answer is: it comes from accelerating the air (momentum thrust), plus, under certain conditions, from the pressure difference (pressure thrust). So to summarize what we've covered: thrust is a reaction to accelerating air backwards. The engine builds pressure energy and converts it to velocity energy. Some energy drives the turbine, the rest makes thrust. Total thrust equals momentum thrust plus pressure thrust, where momentum thrust is mass flow per second times the change in velocity from inlet to exit, and pressure thrust appears only when airflow hits the speed of sound.