How a jet engine makes thrust

Newton’s third law does all the work. If an engine takes in ṁ kilograms of air every second at the aircraft’s speed V₀ and throws it out of the back at a jet speed V₉, the push on the engine is

plus a small correction for the fuel’s own mass and for any pressure left in the jet. That’s it. Everything else in this page is about how to make V₉ bigger than V₀, and how to do it without wasting fuel.

There are two obvious ways to get more thrust: accelerate a little air a lot, or a lot of air a little. Hold on to that thought; it decides the shape of every modern airliner engine, and we’ll come back to it.

Here is the simplest engine there is: a turbojet, on a test bed, standing still.

The dots are air. They come in on the left cool and blue, turn yellow as the compressor squeezes them, glow red through the combustor, and leave on the right still hot. The circled numbers are the station numbers every engine maker uses, so that "T₄" means the same thing at Rolls-Royce and at Pratt & Whitney:

Try this. Scroll down to the station table. With this little engine (pressure ratio 8, turbine inlet 1,200 K, 20 kg of air a second) the compressor takes air at 288 K and 101 kPa and delivers it at about 558 K and 794 kPa. Nobody added any heat there — that 270 K rise is purely the work of squeezing it, the same reason a bicycle pump gets warm. The combustor then takes it to 1,200 K at almost the same pressure (a few per cent is lost to turbulence). The turbine drops it back to about 968 K and 289 kPa, and the nozzle turns what is left into a jet.

What to notice. The turbine takes out roughly 230 K of temperature, almost exactly what the compressor put in (270 K of cold air needs a bit less hot gas to pay for it, because hot gas carries more energy per kelvin). That is the deal at the heart of a gas turbine: the turbine exists to drive the compressor. Whatever energy is left after paying that bill is the engine’s profit, and it leaves as the jet.

Click the compressor, then the turbine, and compare what the tool says about each.

Strip the engine down to thermodynamics and it does four things to the air, over and over:

That loop is the Brayton cycle, and it is the same cycle as a power station’s gas turbine, just with the output taken as a jet instead of a spinning shaft. Here it is for an idealised turbojet cruising at Mach 0.8 and 10 km, with perfect components:

On the T–s diagram (temperature against entropy) an ideal compressor and an ideal turbine are vertical lines — no losses means no entropy made. Heating from 3 to 4 is the long curve along the top; the dashed line along the bottom is heat thrown away to the atmosphere. The area enclosed is the useful work. On the P–v diagram the same loop looks like a cartoon of the engine: squeeze the volume down from 0 to 3, swell it at constant pressure from 3 to 4, and let it expand all the way out to 9.

Try this. Note the thermal efficiency, about 54 %. For the ideal cycle it depends on one thing only: how much the air is squeezed before it is heated, counting the free squeeze it gets from ramming into the intake at Mach 0.8. Put the pressure ratio up to 30, then 40. The efficiency climbs every time.

What to notice. Now look at the other two efficiencies. Thermal efficiency is how well the engine turns fuel into jet kinetic energy. Propulsive efficiency is how much of that kinetic energy actually becomes useful push on the aeroplane — and at 35 % it is poor, because this jet leaves at over 1,100 m/s while the aeroplane flies at 240. All the energy in a jet that is much faster than the aircraft goes into stirring the air behind it. Multiply the two and you get overall efficiency: here 19 %. Hold on to that too.

Switch Cycle to With losses. The compressor and turbine lines on the T–s diagram lean to the right, every efficiency drops, and the engine is suddenly a real one.

If more pressure ratio always helps efficiency, why did early engines stop at 5 or 8? Partly because building compressors is hard (more on that below), but there is a subtler reason, and the trade-study tab shows it.

The left-hand chart is specific thrust — thrust per kilogram of air per second, which decides how big an engine has to be for a given thrust. It rises steeply, peaks around a pressure ratio of 10 for this engine, and then falls away. The reason is the ceiling on turbine inlet temperature. Squeeze the air harder and it leaves the compressor hotter, so there is less room left to add heat before you hit the 1,200 K the turbine blades can survive. Less heat added means less energy for the jet.

The right-hand chart is TSFC, thrust-specific fuel consumption: grams of fuel per second per kilonewton of thrust, the airline’s favourite number. Lower is better. The ideal curve keeps falling forever; the real one flattens out and eventually turns up, because each extra stage of compression costs a little more in losses than it gains.

Try this. Switch the swept input to Turbine inlet temperature. Specific thrust rises steadily with it: hotter turbines mean smaller, lighter engines for the same thrust. This is why turbine blades are single crystals of nickel superalloy, threaded with cooling passages and coated in ceramic, running in gas hotter than their own melting point. Half the history of jet engines is metallurgists buying another 50 K.

What to notice. On a turbojet, TSFC gets worse as the turbine gets hotter. More heat makes a faster jet, and a faster jet has worse propulsive efficiency. Keep that in mind for the turbofan.

A compressor is the hardest part of the engine to get right, because it is pushing air from low pressure to high — uphill, against the flow’s own wish to go backwards. A turbine has it easy: gas falling from high pressure to low pressure is happy to push blades round. That asymmetry is why a modern engine might have ten or more compressor stages driven by just one or two turbine stages.

The top table estimates how many stages a compressor needs for the core engine’s pressure ratio, using different rules of thumb. Older subsonic stages managed a pressure ratio of about 1.15 each; transonic front stages manage 1.4 or more. Because the ratios multiply, a few better stages save a lot of length and weight.

The velocity triangles show what one stage does. The rotor blade moves at speed U; the air arrives with velocity V1, which the blade sees as W1 relative to itself. The blade turns the relative flow, the air leaves with more swirl, and that swirl — handed on to a stationary row of stator vanes and slowed down — becomes pressure. The work done per kilogram is simply U times the change in swirl.

Try this. Drag the tip of W2 to turn the flow more. Stage work and stage pressure ratio go up. Keep going until the de Haller number goes below 0.72. That is the warning that the relative flow is being slowed down too much: the boundary layer on the blade can’t cope and separates, the blade stalls like an aeroplane wing at too high an angle, and the stage stops pumping.

Now scroll to the compressor map. Pressure ratio is up the side, mass flow along the bottom, and the curved grey lines are speeds. The red line on the top-left is the surge line: try to make more pressure than that at too little flow and the whole compressor stalls at once. The high-pressure air rushes back out of the front, often with a bang and a flame out of the intake. The orange running line is where this simple engine actually operates at each speed.

What to notice. Pull the operating speed down. The surge margin changes as the point slides down the running line. Slam the throttle open and the combustor gets more fuel before the spool has sped up: the operating point jumps upwards, towards surge. That is why engines have bleed valves, variable stator vanes and fuel controls that are deliberately slow to answer the throttle.

Between stations 3 and 4, fuel is sprayed into the compressed air and burned. The combustor is remarkable mostly for what it doesn’t do: it has to keep a stable flame in air rushing through at tens of metres a second, without letting the flame touch the walls or the turbine, and it uses only about a quarter of the air for burning. The rest goes round the outside of the flame tube and is mixed back in to cool the gas down to something the turbine can survive. Overall, a jet engine runs very lean: a fuel–air ratio around 0.02, where a car engine runs near 0.068.

The energy all comes from chemistry. Kerosene isn’t in the thermochemistry tool’s table, but natural gas is, and natural gas is what the gas turbines in power stations actually burn:

Try this. The tool says burning one mole of methane releases about 891 kJ. Now edit the equation so the water is H2O(g) and the figure drops to about 803 kJ. The difference is the latent heat of the water. In an engine the water leaves as steam in the exhaust, so engineers use the lower figure — the lower heating value. Divide 803 kJ by methane’s 16 g per mole and you get about 50 MJ/kg. Kerosene gives about 43 MJ/kg, and that 43 is built into the jet engine tool’s burner sums.

What to notice. A modern airliner engine at cruise turns only around a third of that 43 MJ/kg into useful work on the aircraft. Where does the rest go? Mostly out of the back as heat, the dashed line on the T–s diagram — the price the second law of thermodynamics charges any heat engine.

After the combustor, the gas passes through the turbine, which takes out just enough energy to drive the compressor (and in a turbofan, the fan). In our test-bed turbojet that left about 289 kPa and 968 K at the turbine exit — gas that is still under pressure and still hot, which is exactly what the nozzle needs.

The nozzle turns pressure into speed. A simple convergent nozzle like the one on our test-bed engine can only accelerate the gas to the speed of sound; past that the flow chokes. That’s what the tool reports on its Cycle tab — a core jet of 563 m/s at Mach 1.00, "choked (pressure thrust)" — with the gas leaving at about 153 kPa, well above the 101 kPa around it. The extra pressure pushing on the nozzle exit area is counted as pressure thrust. A convergent–divergent nozzle (the "Con-di" option on the Cycle tab) expands the gas fully and turns that pressure into extra velocity instead, which is why supersonic aircraft have nozzles whose shape changes in flight.

Another trick in the nozzle is the afterburner, or reheat: spraying fuel into the hot exhaust after the turbine and burning it again. With no turbine downstream to melt, the gas can go far hotter. Thrust jumps by something like half, and fuel consumption by far more, which is why fighters use it for take-off and combat and not to get anywhere. Open the afterburning turbojet on the cutaway to see where it sits: a second burner between the turbine exit (5) and the nozzle (7 to 9).

Back to the choice we put off: accelerate a little air a lot, or a lot of air a little. Our turbojet chose the first, and its propulsive efficiency suffered. A turbofan does the second. It puts a large fan at the front, driven by an extra turbine, and blows most of the air around the core in a bypass duct, accelerating it only gently.

This is a modern geared turbofan at cruise: for every kilogram of air that goes through the core, twelve go around it. That is the bypass ratio. The bypass stream has its own station numbers, 13 after the fan and 19 at its own nozzle, and you can see the blue, cool bypass air flowing round the outside while the core burns down the middle.

Try this. Open the Cycle tab. Propulsive efficiency is now about 70 %, against about 40 % for our little turbojet flying at the same speed and height. Overall efficiency roughly doubles, from around 15 % to around 31 %, and TSFC falls from about 35 to 17 g/(kN·s). Half the fuel for the same thrust — that’s the whole story of airliner engines since the 1960s.

What to notice. Specific thrust has collapsed, to about 113 N·s/kg. The engine moves so much air so gently that it needs an enormous fan to make useful thrust, which is why the engines on a modern twin look like they barely fit under the wing. Switch the engine to Turbofan (mixed exhaust) to see the low-bypass fighter arrangement, where the two streams merge before a single nozzle.

How far can you push it? The trade study answers:

As bypass ratio rises, TSFC falls and so does specific thrust — the engine gets more economical and bigger. Keep going and something odd happens around a bypass ratio of 12: the curves kink. The core can only supply so much power, and past that point the fan is asking for more than the turbine can give at this fan pressure ratio. The tool’s note says it plainly: "Past a point the fan asks more than the core can give."

Try this. Sweep Fan pressure ratio instead. A lower fan pressure ratio means a gentler, more efficient bypass jet, but you need even more air (and an even bigger fan) for the same thrust.

What to notice. The fan tip can’t go much faster than the speed of sound, and a huge fan has to turn slowly while the turbine that drives it wants to spin fast. Squaring that is why the newest engines put a gearbox between the fan and its turbine. The limit after that is the aircraft itself: a fan four metres across has to fit under a wing and clear the ground. Open rotors, with no duct at all, are the next step in the same direction.

A turbocharger is a gas turbine with one important substitution: the car’s engine is the combustor. Exhaust gas from the cylinders spins a small turbine, the turbine spins a compressor on the same shaft, and the compressor pushes extra air into the cylinders, so they can burn more fuel per stroke. It has stations, a pressure ratio, a turbine paying for a compressor, and the same kind of compressor map with the same surge line.

This is a 2-litre four-cylinder engine with a compressor that is too big for it. Each dot on the map is the engine at full throttle at one rpm, from where boost begins to peak power. At high rpm the points sit in the middle of the efficiency islands, which is where you want them. But while the boost is building, between about 1,800 and 3,000 rpm, the engine isn’t swallowing much air yet and the compressor is being asked for a high pressure ratio at a low flow — up and to the left, past the surge line. The tool flags it in red.

Try this. Raise Boost starts and Full boost from so the boost arrives later. The points slide right and clear the surge line. Or lower the target boost. Either way you’re doing what a jet engine’s fuel control does when it refuses to let you slam the throttle open: keeping the compressor on the safe side of the map.

What to notice. Look at the compressor outlet temperature, about 135 °C at a pressure ratio of 2.3. That’s the same heat of compression as station 3 in the turbojet, and it is why turbo cars have an intercooler, to cool the air back down before it reaches the cylinders. The Turbine & wastegate tab balances the turbine against the compressor, exactly as the jet engine balances station 4 to 5 against 2 to 3.

Follow a parcel of air through a jet engine and every step makes sense. The compressor squeezes it and heats it up doing so. The combustor heats it more. The turbine takes back just enough to keep the compressor turning, and the nozzle turns the rest into speed. The Brayton cycle says squeezing harder makes the engine more efficient, and hot turbines make it smaller. Propulsive efficiency says that the best way to push an aeroplane is a lot of air, a little faster. That last idea grew the fan from nothing to four metres across.