We're starting a new chapter — Gas Turbines: Thrust — Page 310, Lesson 399

We're starting a new chapter — Gas Turbines: Thrust. This is where we finally get to the heart of what a jet engine actually produces, and more importantly, how we measure and predict it. Let's begin with the very foundation: thrust itself. Thrust is the force that moves an aircraft forward. For a gas turbine, it's generated by accelerating a mass of air backwards. Newton's third law — every action has an equal and opposite reaction — is the principle at work here. The engine throws air and exhaust gases out the back at high velocity, and the reaction pushes the engine, and the aircraft, forward. Now, the thrust formula. This is the mathematical heart of the chapter. Total thrust is made up of two elements: momentum thrust and pressure thrust. Let me give you the full formula as it appears in the book: F = ṁ(Vj - Va) + A(Pj - Pa) Let's break that down term by term, because every symbol matters. F is the total thrust, measured in Newtons. ṁ — that's the Greek letter "m-dot" — is the mass flow rate of air through the engine, in kilograms per second. It's the mass of air passing through the engine every second. Vj is the jet velocity — the velocity of the exhaust gases as they leave the nozzle, in metres per second. Va is the aircraft velocity — the speed of the aircraft through the air, also in metres per second. So the first part, ṁ(Vj - Va), is the momentum thrust. This is the thrust produced by the change in momentum of the air as it's accelerated from the aircraft's speed to the jet velocity. The faster you throw the air out the back relative to how fast you're already moving, the more momentum thrust you get. The second part, A(Pj - Pa), is the pressure thrust. A is the nozzle exit area, in square metres. Pj is the pressure of the exhaust gases at the nozzle exit, and Pa is the ambient atmospheric pressure. So this term accounts for the thrust produced when the exhaust pressure at the nozzle exit differs from the surrounding air pressure. If the jet pressure is higher than ambient, you get additional thrust from that pressure difference. Now, let's look at gross thrust, which we denote Fg. Gross thrust is the total thrust produced by the engine, and it's calculated as: Fg = ṁVj + A(Pj - Pa) Notice the difference from the total thrust formula. In gross thrust, we use the full jet velocity Vj — we don't subtract the aircraft velocity. So gross thrust is the thrust you'd measure if the engine were stationary, with the aircraft at rest. It's the raw thrust the engine produces from the momentum of the exhaust plus the pressure thrust. Then we have net thrust, Fn. Net thrust is what actually propels the aircraft, and it's calculated as: Fn = ṁ(Vj - Va) So net thrust is the momentum thrust — the mass flow rate times the difference between jet velocity and aircraft velocity. It's the gross thrust minus the momentum of the incoming air. When the aircraft is stationary on the ground, Va is zero, so net thrust equals gross thrust. But as the aircraft speeds up, the net thrust decreases because you're subtracting a larger incoming air velocity. Now, for fan engines — turbofans — the thrust calculation is a bit different. In a fan engine, some of the air bypasses the core and goes through the fan. The thrust is the sum of the thrust from the core and the thrust from the fan. The book gives us an example using the figures we've just discussed. Let me walk you through it. Let's say we have a fan engine. The core produces a certain amount of thrust, and the fan produces another amount. The total thrust is the sum of both. The example in the book uses specific numbers to show how you add the core thrust and the fan thrust together to get the total engine thrust. Now, there's a special case we need to consider: pressure thrust in a choked nozzle. When the nozzle is choked — meaning the exhaust gases reach the speed of sound at the nozzle throat — the pressure at the nozzle exit can be higher than ambient pressure. In this case, the pressure thrust term A(Pj - Pa) becomes significant. The book gives us a choked nozzle thrust example to illustrate this. When the nozzle is choked, you can't increase the mass flow rate any further by increasing the pressure upstream — the flow is limited by the speed of sound at the throat. But the pressure thrust can still contribute to the total thrust. Now let's talk about how we actually measure thrust in the cockpit. Thrust indications — how the pilot knows how much thrust the engine is producing. In modern engines, we use engine pressure ratio, or EPR, as the primary thrust indication. EPR is the ratio of the total pressure at the turbine outlet to the total pressure at the compressor inlet. It's a direct measure of the engine's thrust output. Some engines use fan speed, or N1, as the primary thrust indication instead. The book covers these thrust indications in detail. Then we have thrust ratings. These are the certified power settings for the engine. The main ratings are: - Take-off thrust — the maximum thrust the engine can produce for take-off, usually limited to a specific time, like five minutes. - Maximum continuous thrust — the maximum thrust the engine can produce indefinitely without damage. - Climb thrust — a thrust setting used for climbing, typically between take-off and cruise. - Cruise thrust — the thrust setting used for normal cruise, optimised for fuel efficiency. Now, for turboprop engines, we use a different measure: Equivalent Shaft Horsepower, or ESHP. This combines the shaft horsepower produced by the turbine driving the propeller with the residual jet thrust from the exhaust. The formula is: ESHP = SHP + (Jet Thrust × V) / 375 Where SHP is the shaft horsepower, Jet Thrust is the thrust from the exhaust gases, and V is the aircraft velocity. The factor 375 converts the thrust-velocity product into horsepower units. This gives us a single number that represents the total power output of a turboprop engine. Next, we have Specific Fuel Consumption, or SFC. This is a measure of the engine's fuel efficiency. For a jet engine, SFC is defined as the fuel flow in pounds per hour divided by the thrust in pounds: SFC = Fuel Flow (lb/hr) / Thrust (lb) So SFC tells us how much fuel the engine burns to produce one pound of thrust for one hour. Lower SFC means better fuel efficiency. For turboprops, we use a similar measure based on ESHP instead of thrust. Then we have the thrust-to-weight ratio. This is simply the thrust produced by the engine divided by the weight of the engine itself: Thrust-to-Weight Ratio = Thrust / Engine Weight A higher thrust-to-weight ratio means the engine produces more thrust for its weight, which is desirable for aircraft performance. Now let's look at how thrust varies with different conditions. First, variation of thrust with rpm. As the engine speed, or rpm, increases, the mass flow rate of air through the engine increases. Since thrust is proportional to mass flow rate, thrust increases with rpm. The relationship is roughly proportional — if you increase rpm, you increase thrust. Variation of thrust with altitude — as altitude increases, air density decreases. Since the mass flow rate depends on air density, thrust decreases with altitude. At higher altitudes, the engine produces less thrust because there's less air to accelerate. Variation of thrust with temperature — as the ambient temperature increases, air density decreases, so thrust also decreases. Hot days mean less thrust. This is why aircraft performance is often limited on hot days. Variation of thrust with aircraft speed — as the aircraft speed increases, the net thrust decreases, as we saw in the net thrust formula. The incoming air has more momentum, so the difference between jet velocity and aircraft velocity is smaller. Now, ram recovery. This is the recovery of the dynamic pressure of the incoming air as the aircraft speed increases. At high speeds, the air entering the engine is compressed by the ram effect — the forward motion of the aircraft compresses the air. This increases the pressure at the compressor inlet, which improves the engine's efficiency and can partially offset the thrust loss from increased aircraft speed. For turboprops, we also look at the effect of altitude on SHP. As altitude increases, air density decreases, so the shaft horsepower decreases. Similarly, the effect of aircraft speed on SHP — as speed increases, the ram effect can improve the efficiency of the propeller, but the overall effect is complex. That's the full scope of this chapter. We've covered the thrust formula, gross and net thrust, fan engine thrust, choked nozzle pressure thrust, thrust indications, thrust ratings, ESHP, SFC, thrust-to-weight ratio, and how thrust varies with rpm, altitude, temperature, and aircraft speed, plus ram recovery and the effects on SHP. That's a lot, but it's the foundation of understanding how a gas turbine produces and delivers thrust.