Gas Turbines - Thrust — Page 310, Lesson 404

Let’s pick up right where we left off — we’ve just finished the momentum thrust calculation in imperial units, and now I want to walk you through the same calculation in SI units, because in professional aviation you’ll need to work in both. So, we had 60 lb of air per second, and an exhaust velocity of 1600 ft/sec. In SI units, 60 lb is 27.211 kg, and 1600 ft is 487.68 metres. The thrust formula is Fg = W(Vo – Vi), where W is the mass flow rate, Vo is the exit velocity, and Vi is the inlet velocity. So we get Fg = 27.211 × (487.68 – 0) = 13.27 kN. And just so you have the conversion in your head: 1 pound equals 4.448 newtons. Now, here’s a critical concept: net thrust. Thrust reduces as aircraft speed increases. Why? Because as the aircraft flies faster, the inlet velocity Vi increases, while the exit velocity Vo stays constant. That means the acceleration of the mass flow through the engine — the (Vo – Vi) term — decreases. And since F = ma, if the acceleration decreases, the thrust decreases. This reduced value is what we call net thrust, Fn. Let me show you with the same aircraft now flying at 300 knots TAS, which is 506 ft/sec. The formula becomes Fn = Wa(Vo – Vi)/g = 60 × (1600 – 506) / 32.2 = 2038 lb, which is 9.07 kN. Notice we divide by g, the acceleration due to gravity, because we’re working with weight flow rather than mass flow. Now let’s move to fan engine thrust. A fan engine produces two streams: a core engine stream, also called the hot stream, at high velocity, and a fan stream, also called the cold stream, at lower velocity. We deal with these two streams separately and then add them together. Look at Figure 20.2 for the example. For the fan: Thrust = Wa(Vo – Vi)/g = 1200 × 800 / 32.2 = 29,814 lb, which is 132.6 kN. For the core engine: Thrust = 300 × 1000 / 32.2 = 9,317 lb, which is 41.5 kN. The total is the sum: 29,814 + 9,317 = 39,131 lb, which is 175 kN. And here’s a key number to remember: the fan accounts for 75% to 90% of the total thrust. Now, there’s another type of thrust we need to cover: pressure thrust from a choked nozzle. Although the momentum change of the gas stream produces most of the thrust, additional thrust is produced under high thrust conditions when the gas velocity reaches the speed of sound and cannot be accelerated any further. When this happens, the nozzle is choked, and the pressure of the gases in the nozzle increases above atmospheric pressure. The pressure difference across the nozzle produces what we call pressure thrust, which is effective over the nozzle area and is additional to momentum thrust. Most turbojet engines operate a choked nozzle during high power conditions, and on these engines, pressure thrust is added to the calculated momentum thrust. Engines operating with a non-choked nozzle would use calculated momentum thrust only. Let me walk you through the choked nozzle thrust example. The choked nozzle thrust is caused by the difference between the pressure at the nozzle — which is atmospheric — and the pressure within the engine, which has increased because of supersonic airflow. For instance, at 32,000 feet, atmospheric pressure is about 4 lb/in², or psi. This is called ambient pressure, which we label as Po. If the pressure inside the engine were 10 psi, which we label as P, then the differential is 6 psi. The general expression for force is: FORCE = PRESSURE × AREA. This is expressed as Pf = (P – Po) × A. So suppose the area of the nozzle A is 332 in², P is 10 psi, and Po is 4 psi. Then pressure thrust Pf = (10 – 4) × 332 = 1,992 lb, which is 8.86 kN. Finally, let’s talk about thrust indications. The power of a turbojet is measured in thrust and displayed by a P7 or EPR gauge, which are thrust meters. A turbopropeller’s output is measured in shaft horsepower, or SHP, and displayed by a torque meter. In modern fan engines, N1 and sometimes EPR are indications of thrust. N1, P7, EPR, and torque meters are covered in detail in the Powerplant and Systems Monitoring Instruments section. So to tie it all together: momentum thrust comes from accelerating the air, pressure thrust comes from the choked nozzle pressure differential, and the total thrust of a fan engine is the sum of the fan and core streams. And the way we read that thrust depends on the engine type — P7 or EPR for turbojets, torque for turboprops, and N1 or EPR for modern fan engines.