Gas Turbines - Thrust — Page 310, Lesson 402

Let's get into the heart of gas turbine thrust. I want to walk you through the two elements that make up total thrust, starting with momentum thrust. Momentum thrust depends on the relationship between the inlet velocity and the exit velocity of the air passing through the engine. Because of that, it's directly dependent on the aircraft's speed through the air. It will be greatest when the aircraft is stationary on the ground before take-off, and it will reduce as the airspeed—and therefore the inlet speed—increases. It's considered to be maximum when the aircraft is stationary at sea level, under conditions of high pressure, low temperature, and low humidity. Let me unpack that: high pressure and low temperature give you high air density, and low humidity means the air is dry. All of those conditions pack more air mass into the engine, which maximizes the thrust. Now, there's a critical distinction here. When the engine is stationary and developing its maximum thrust, that's known as gross thrust. When there's airflow passing through it, as when the aircraft is airborne, the thrust developed is known as net thrust. So gross thrust is the static, on-the-ground case; net thrust is the in-flight case. Let's formalize gross thrust. Gross thrust, denoted Fg, is the thrust produced when the engine is not moving through the air. The acceleration given to the gas is the difference in velocity between the unit of air entering the intake, which we call Vi, and the unit of air exiting the nozzle, which we call Vo. Substituting into Newton's second law, F = ma, we get the momentum thrust equation: Fg = Wa(Vo - Vi) / g Let me define each symbol precisely. Wa is the weight of air per second. Vo is the exit velocity of air in feet per second. Vi is the inlet velocity of air in feet per second. And g is the gravitational force, which is 32.2 feet per second squared. Now, here's a crucial unit consideration. If the mass flow and velocities are given in Imperial units—that is, pounds per second and feet per second—it's necessary to convert from force to mass by dividing by g, as we do in that equation. But if they're given in SI units—kilograms per second and metres per second—the conversion is already factored into the units, and it is incorrect to divide by g. That's a common trap, so remember it. Most gas turbine engine manufacturers express their engine outputs in pounds, with a kilonewton equivalent in brackets alongside. Let me walk you through a worked example to make this concrete. A small business jet is at rest before take-off, at take-off power. The mass airflow is 60 pounds per second, and the exhaust velocity, Vo, is 1600 feet per second. Since the aircraft is at rest, the inlet velocity, Vi, is zero. Substituting into the momentum thrust equation: Fg = 60(1600 - 0) / 32.2 That gives us 2981 pounds, which is 13.26 kilonewtons. So you can see how the equation works in practice. The key takeaway is that gross thrust is the static case, and the difference between Vo and Vi drives the thrust. When the aircraft is moving, Vi increases, so the difference shrinks, and net thrust is less than gross thrust. That's the fundamental relationship you need to hold onto.