Turbojet - Wikiparency

# Turbojet > [[PORTAL_Aviation|Aviation]] · [[PORTAL_Avionics|Avionics]] spine.  ## Microsims — three.js ### Turbojet (three.js) <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Turbojet.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Turbojet — three.js microsim"></iframe> </div> **Open it full-screen:** [Turbojet.html](https://wikitube-3d-microsims.netlify.app/Turbojet.html) · library `threejs` · route `microsim/threejs/` ### Related microsims Live sims on neighbouring articles: - [[Gas_turbine]] - [[Jet_engine]] - [[Aircraft_flight_dynamics]] - [[Sonic_boom]] - [[Fuel_economy_in_aircraft]] - [[Contrail]] *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4).*  ## Overview A **turbojet** is an airbreathing jet engine in which every kilogram of air that enters the intake passes through the compressor, the combustor and the turbine, and leaves as a single high-velocity jet. There is no bypass duct and no propeller. All of the thrust is produced by accelerating the core stream, which is what makes the turbojet the simplest complete realisation of the Brayton cycle in hardware, and also what eventually made it obsolete for subsonic transport. The machine is a loop. Air is compressed by a multi-stage axial compressor; fuel is burned in the compressed air at approximately constant pressure; the hot gas expands through a turbine; and whatever pressure the turbine leaves behind is converted to velocity in a nozzle. The turbine and the compressor are mounted on a single shaft, so the turbine's only job is to pay the compressor's bill. Everything the turbine does *not* need is surplus, and the surplus becomes thrust. This is not a design convenience but a hard constraint: if the gas arriving at the turbine cannot yield at least as much work as the compressor is drawing, the shaft decelerates, the pressure ratio falls, and the engine spools down until it reaches a speed the cycle can hold — or stops. The idea is old. George Brayton's constant-pressure "Ready Motor" of 1872 established the thermodynamic cycle, and the possibility of driving a compressor from a turbine in the same gas path was understood long before anyone could build one. What was missing was materials and compressor aerodynamics. Frank Whittle's British patent of January 1930 described the turbojet essentially in its modern form; his W.U. engine first ran in April 1937. Hans von Ohain's HeS 3 powered the Heinkel He 178 on 27 August 1939, the first flight of a turbojet aircraft. The Junkers **Jumo 004**, the first turbojet produced in quantity, ran with a compressor pressure ratio of only about 3.1 and a turbine inlet temperature near 1050 K, because wartime Germany had almost no nickel and its turbine blades were folded from hollow sheet steel with air blown through them. Service lives of 25 to 50 hours were normal. Every subsequent improvement in jet propulsion has been, in one way or another, an improvement in how hot the turbine is allowed to get and how efficiently the compressor can raise pressure. **A turbojet is not a turbofan.** In a turbofan, a large fan at the front is driven by extra turbine stages, and most of the air it moves — nine to twelve times the core flow in a modern high-bypass engine — goes *around* the core and is never burned. The core cycle is the same. What changes is how the thrust is produced: the turbojet throws a small mass of air very fast, the high-bypass turbofan throws a large mass of air gently. As explained below, that difference is worth roughly a factor of two in fuel burn at subsonic cruise, and it has nothing to do with thermal efficiency. It is entirely a matter of **propulsive efficiency**. Turbojets nevertheless remained the right answer for supersonic flight. Concorde's Rolls-Royce/SNECMA **Olympus 593** was a pure turbojet, and in Mach 2 cruise it reached an overall efficiency of roughly 43 per cent — among the highest ever achieved by an airbreathing engine — precisely because at that flight speed a turbojet's jet velocity is only modestly higher than the aircraft's own speed. ## The physics ### Stations Engine performance is written station by station, following the numbering of SAE ARP755 and used universally in the industry. The microsim labels the five that matter: | Station | Location | What happens upstream of it | | --- | --- | --- | | 0 | free stream | nothing; ambient *p*₀, *T*₀ | | 2 | compressor face | ram compression in the intake | | 3 | compressor exit | shaft work added | | 4 | turbine inlet | heat added at nearly constant pressure | | 5 | turbine exit | shaft work extracted | | 8 / 9 | nozzle throat / fully expanded exit | expansion to velocity | Quantities carrying a *t* subscript are **total** (stagnation) properties: the temperature and pressure the gas would reach if brought to rest adiabatically. Total properties are the natural currency of turbomachinery because work and heat change them while pure acceleration does not. ### The ideal cycle Strip away every loss and the turbojet becomes the air-standard Brayton cycle: isentropic compression, constant-pressure heat addition, isentropic expansion, constant-pressure heat rejection. For a perfect gas with constant *c*p and ratio of specific heats *γ*, a compression by pressure ratio *r* raises temperature by the factor *r*(γ−1)/γ, and so does the expansion back down the same pressure ratio. Because both isobars are traversed with the same temperature ratio, the heat rejected and the heat added are in that same fixed ratio, and the thermal efficiency collapses to a single expression: > **ηideal = 1 − 1 / r(γ−1)/γ** This is the equation shown live in the microsim's heads-up display. Three things follow immediately. Efficiency depends **only** on pressure ratio, not on how hot the flame is. It rises monotonically with *r*, but with diminishing returns — at *γ* = 1.4, a pressure ratio of 10 gives 48 per cent, 20 gives 58 per cent, and 40 gives 65 per cent. And the *work* the cycle produces does not behave like the efficiency at all: raising *r* at fixed turbine inlet temperature eventually squeezes the cycle flat, because the compressor delivery temperature climbs towards the turbine inlet temperature and there is no room left to add heat. The pressure ratio that maximises specific thrust in the ideal cycle is > *r*opt = (*T*t4 / *T*t2)γ/2(γ−1) which the microsim reports in its secondary readouts. Efficiency and work want different pressure ratios; every real engine is a compromise between them. ### The real cycle, as the microsim computes it The simulation carries the losses that matter and states its assumptions. Air is treated with *c*p = 1004.5 J kg⁻¹ K⁻¹ and *γ* = 1.40 up to the burner, combustion products with *c*p = 1148 J kg⁻¹ K⁻¹ and *γ* = 1.33 after it. Ambient conditions come from the ICAO Standard Atmosphere. **Intake (0 → 2).** No work is done, so *T*t2 = *T*t0 = *T*₀(1 + ½(γ−1)*M*₀²). Total pressure is only partly recovered: subsonic intakes achieve about 0.98, and above Mach 1 the reference schedule of MIL-E-5008B, πd = 1 − 0.075(*M*₀ − 1)1.35, charges for the shock system. Ram compression is free work the engine did not have to pay for, and by Mach 2 it exceeds the compressor's own contribution. **Compressor (2 → 3).** Euler's turbomachinery equation makes the work of a stage proportional to the square of blade speed, so to first order the compressor's total-temperature rise depends on physical shaft speed alone: Δ*T*t = Δ*T*t,design(*N*/100)². The delivered pressure ratio then follows from the polytropic (small-stage) relation πc = (*T*t3/*T*t2)γec/(γ−1), with a polytropic efficiency *e*c = 0.90. This is the simplest honest form of the "corrected speed" effect, and it has a consequence worth watching for in the microsim: the *same* engine at the *same* physical shaft speed delivers a **higher** pressure ratio in cold thin air at altitude than on a hot day at sea level, because Δ*T*t is fixed while *T*t2 has fallen. Push the Mach number up instead and the pressure ratio collapses, because ram heating has raised *T*t2. That is why supersonic engines use *low* compressor pressure ratios: the intake has already done the compressing. **Burner (3 → 4).** Heat is added at almost constant pressure; a real annular combustor loses three to five per cent of total pressure to the swirlers, the dilution holes and the flame itself. The fuel-to-air ratio follows from the energy balance, > *f* = (*c*p,h*T*t4 − *c*p,c*T*t3) / (ηb*Q*R − *c*p,h*T*t4) with *Q*R ≈ 43 MJ kg⁻¹ for Jet A and a combustion efficiency near 0.99. A burner can only add heat: if the commanded turbine inlet temperature is below what the compressor already delivers, the fuel valve simply shuts, *T*t4 = *T*t3 and *f* = 0. That is a fuel chop, and in the microsim it is the fastest way to break the shaft balance. **Turbine (4 → 5) — the coupling.** The turbine extracts exactly the compressor's demand and no more: > (1 + *f*) *c*p,h (*T*t4 − *T*t5) ηm = *c*p,c (*T*t3 − *T*t2) Solving for *T*t5 fixes the turbine exit state, and the polytropic relation then fixes *p*t5. The *maximum* work the turbine could ever take is the work of expanding all the way down to ambient static pressure — which would leave the nozzle nothing, and the aircraft no thrust. Comparing that ceiling with the compressor's demand gives the **work margin** displayed in the microsim. When the margin exceeds one, the surplus becomes jet velocity. When it falls below one, no shaft speed can be held and the engine winds down until, at some lower speed, the compressor demand has fallen enough for the balance to close again. That equilibrium-seeking behaviour is the self-sustaining loop made visible. **Nozzle (5 → 8/9).** The microsim reports the fully expanded case, *p*₉ = *p*₀, which is the standard cycle analysis: > *V*₉ = √( 2 *c*p,h *T*t5 [ 1 − (*p*₀/*p*t8)(γ−1)/γ ] ) A real turbojet's simple convergent nozzle chokes as soon as the nozzle pressure ratio exceeds ((γ+1)/2)γ/(γ−1) ≈ 1.85, after which the exit stays at Mach 1 and part of the thrust appears as a pressure term (*p*₉ − *p*₀)*A*₉. For the operating points in this sim the two answers differ by only two or three per cent, and the HUD reports the pressure ratio and whether the nozzle is choked so the reader can see when the approximation is working hardest. ### Thrust, and why the turbofan won Specific thrust — thrust per unit of air swallowed — is simply the momentum the engine adds: > *F*/*ṁ* = (1 + *f*) *V*₉ − *V*₀ Two efficiencies then divide the fuel's energy in two. **Thermal efficiency** is the fraction of fuel energy that appears as extra kinetic energy in the stream. **Propulsive (Froude) efficiency** is the fraction of *that* which ends up as useful work on the airframe rather than being left behind as a fast-moving wake. For a fully expanded nozzle, > ηp = 2 / (1 + *V*₉/*V*₀) and the overall efficiency is the product, ηo = ηth ηp. The algebra is brutal for a subsonic turbojet. At Mach 0.85 at 11 km with a pressure ratio of 20 and a turbine inlet temperature of 1550 K, the microsim's default settings, the core does well: thermal efficiency around 51 per cent. But the jet leaves at nearly 1100 m s⁻¹ while the aircraft is flying at 250 m s⁻¹, so *V*₉/*V*₀ ≈ 4.3 and propulsive efficiency is only about 38 per cent. Overall: about 19 per cent, and a thrust-specific fuel consumption near 30 g kN⁻¹ s⁻¹ (about 1.07 lb lbf⁻¹ h⁻¹) — a very recognisable 1960s turbojet number. Now hold the thrust *F* = *ṁ*Δ*V* fixed and ask where the waste goes. The kinetic energy dumped into the wake is roughly ½*ṁ*(Δ*V*)², so for a given thrust the wasted power scales with Δ*V* itself. Halve Δ*V* and double *ṁ*, and the thrust is unchanged while the waste halves. That is the entire argument for the high-bypass turbofan: the fan moves a much larger mass of air at a much smaller velocity increment, raising propulsive efficiency to 0.75–0.80 and roughly halving cruise fuel consumption — while doing **nothing whatever** to thermal efficiency, which is set by the core's pressure ratio and turbine temperature just as before. A modern high-bypass engine and a 1960s turbojet with the same core would have similar thermal efficiencies; the turbofan simply stops throwing the energy away. The limits are practical rather than thermodynamic. A larger fan means a larger, heavier, draggier nacelle and a ground-clearance problem, so bypass ratio is bounded by installation, not by the cycle. And the whole argument reverses at high flight speed: as *V*₀ rises towards *V*₉, ηp = 2/(1 + *V*₉/*V*₀) climbs on its own. Set the microsim to Mach 2.2 with a low pressure ratio and watch propulsive efficiency pass 65 per cent with no fan at all. That is why supersonic aircraft kept pure turbojets long after subsonic transports abandoned them. ### The material limit, told honestly Thermal efficiency wants pressure ratio; specific thrust wants turbine inlet temperature. The temperature is capped by metal. Nickel-based single-crystal superalloys begin to lose useful creep strength above roughly 1300 K of *metal* temperature, and incipient melting sets in near 1600 K. Yet modern engines run turbine entry gas temperatures of 1700–1900 K at take-off, several hundred kelvin above the melting point of the blade. They survive by three combined tricks: internal convective cooling through serpentine passages, film cooling that bleeds compressor air through hundreds of shaped holes to lay a cool blanket over the surface, and a thermal barrier coating of yttria-stabilised zirconia perhaps 100–300 µm thick. None of that is free. Turbine cooling air is taken from the compressor after it has been paid for and returned to the gas path without having passed through the burner, and in a modern high-pressure turbine it can amount to 15–20 per cent of core flow. The microsim does **not** account for it, which is the single largest optimism in its numbers. The control panel therefore names the honest bands — uncooled 1300 K, cooled and coated 1750 K, peak take-off 1900 K — and lets the slider run to 2100 K so the reader can see what the cycle *would* do, clearly flagged as beyond production practice. For reference, stoichiometric combustion of kerosene in air would reach roughly 2500 K; every engine ever built runs its burner lean of that for exactly this reason. ## Controls -> what each maps to | Control | Symbol | Range and units | Physical meaning | | --- | --- | --- | --- | | Compressor pressure ratio | πc | 4–45 : 1 (dimensionless), quoted at 100 % N1 on an ISA sea-level static day | Total-pressure ratio the compressor delivers at its design point. The slider sets the design value; the HUD reports the pressure ratio actually delivered at the current shaft speed and inlet temperature, which can be substantially different. Real turbojets ran 5–15; modern turbofan cores reach 30–45. | | Turbine inlet temperature | *T*t4 | 800–2100 K | Total temperature of the gas entering the first turbine stage; equivalently, the fuel flow. Sets specific thrust and, through the material limit, the whole engine's life. The design band is 1200–1900 K; below compressor delivery temperature the fuel valve shuts and *T*t4 falls back to *T*t3. | | Flight Mach number | *M*₀ | 0–3.0 (dimensionless) | Sets ram compression, *T*t2 = *T*₀(1 + 0.2*M*₀²), the intake total-pressure recovery, and the flight velocity *V*₀ against which propulsive efficiency is measured. Raising it lowers the compressor's delivered pressure ratio and raises propulsive efficiency. | | Altitude | *h* | 0–20 km | Selects ambient *p*₀ and *T*₀ from the ICAO Standard Atmosphere: −6.5 K km⁻¹ to 11 km, then isothermal at 216.65 K. Colder inlet air raises the delivered pressure ratio at fixed shaft speed. | | Shaft speed | *N1* | 20–105 % of design | Commanded physical speed of the single spool. Compressor temperature rise scales as *N*², so pressure ratio and thrust fall away quickly at part speed. If the cycle cannot sustain the commanded speed the engine spools down to the speed it can hold, and the HUD says so. | | T–s diagram | — | on / off (or the **T** key) | Shows the live temperature–entropy plot: stations 0, 2, 3, 4, 5 and 9, the ambient and compressor-delivery isobars, and the dashed constant-pressure heat rejection from 9 back to 0 that closes this open cycle. The shaded area is the net work. | | Pause | — | button, or **Space** | Freezes the flow and the rotor. Set automatically when the browser requests reduced motion. | | Reset | — | button, or the **R** key | Restores the default cruise point: pressure ratio 20, turbine inlet 1550 K, Mach 0.85, 11 km, 100 % N1. | ## Learning objective **After using this microsim, the learner should be able to explain why a turbojet's turbine and compressor must sit on one shaft and what happens when the turbine's available work falls below the compressor's demand — and to state, with numbers, why high-bypass turbofans replaced turbojets on subsonic airliners despite having essentially the same core thermal efficiency.** ## Limits and connections The model is a steady, one-dimensional cycle analysis with a very simple compressor characteristic, and several of its simplifications are worth naming. **Gas properties.** Two constant specific heats — cold air before the burner, combustion products after it — stand in for a real gas table. Above about 2000 K, dissociation absorbs energy that this model still counts as temperature, so the hottest settings flatter the cycle. The entropy axis of the T–s plot uses the same two-*c*p approximation, with a single continuous switch at 800 K; a proper chart would use NASA polynomial thermodynamic data. The entropy of mixing and the chemical entropy of combustion are ignored, so the 3 → 4 leg is drawn as if the working fluid merely got hotter. **Turbine cooling is not modelled.** This is the most important omission. Real engines running at 1800 K turbine entry divert a large fraction of compressor delivery air around the burner to cool the blades, and that air does no useful work in the burner while still costing compressor work. Including it would reduce specific thrust and thermal efficiency at high turbine temperature, and would make the high-temperature end of the slider considerably less attractive than it looks here. **Component efficiencies are fixed.** Polytropic efficiencies of 0.90 for compressor and turbine, a burner pressure ratio of 0.96 and a nozzle pressure ratio of 0.98 are held constant across the whole envelope. In reality they vary with stage loading, Reynolds number and, especially for the compressor, with distance from the surge line. **There is no compressor map.** The relation Δ*T*t ∝ *N*² is the first term of a real map and nothing more. It has no surge line, no choke, no variable-stator schedule, no bleed valves and no rotating stall. Real single-spool turbojets with high pressure ratios are difficult to start and to accelerate precisely because of the phenomena this model omits, and that is a large part of why high-pressure-ratio engines went to two and three spools. **The nozzle is fully expanded.** A convergent nozzle chokes above a pressure ratio of about 1.85 and produces pressure thrust; the microsim reports when this is happening but computes performance as if a perfectly matched convergent–divergent nozzle were fitted. It also has no afterburner, no thrust reverser and no variable area. **The spool-down is quasi-steady.** The simulation finds, by bisection, the highest speed at which the turbine work ceiling still covers the compressor demand, and then relaxes the shaft towards it with a first-order lag of a few seconds. It is not an integration of rotor polar inertia against instantaneous aerodynamic torque, and the criterion used — "could the turbine expand to ambient pressure?" — is an absolute floor. A real engine would surge, flame out or exceed a temperature limit long before reaching it. The shaft is also drawn turning about two hundred times slower than reality; 100 per cent N1 on a small turbojet is 12 000 to 17 000 rpm. **Atmosphere and installation.** The ISA is implemented only to 20 km, exactly where its next layer's inversion would begin, and there is no allowance for non-standard days, humidity, intake distortion, customer bleed, power offtake or nacelle drag. Installed thrust is always less than the uninstalled figure computed here. The turbojet sits at the centre of a family. Its core is the [[Gas_turbine]] that also drives ships, helicopters and electricity grids; the wider class of machines that turn it into aircraft thrust is covered in [[Jet_engine]]. What the resulting thrust does to an aeroplane is the subject of [[Aircraft_flight_dynamics]], and the fuel-burn consequences of the propulsive-efficiency argument above are developed in [[Fuel_economy_in_aircraft]]. The two flight regimes where turbojets remained competitive leave their own signatures: the pressure field of supersonic cruise in [[Sonic_boom]], and the water vapour and soot of the exhaust in [[Contrail]]. ## References - Brayton, G. B. "Ready Motor" constant-pressure engine, patented 1872. The cycle now named after him predates any practical gas turbine by six decades. - Cumpsty, N. A. *Compressor Aerodynamics*. Longman Scientific & Technical: Harlow, 1989. - Cumpsty, N. A. *Jet Propulsion: A Simple Guide to the Aerodynamic and Thermodynamic Design and Performance of Jet Engines*, 3rd ed. Cambridge University Press: Cambridge, 2015. - Han, J.-C.; Dutta, S.; Ekkad, S. *Gas Turbine Heat Transfer and Cooling Technology*, 2nd ed. CRC Press: Boca Raton, 2012. - Hill, P. G.; Peterson, C. R. *Mechanics and Thermodynamics of Propulsion*, 2nd ed. Addison-Wesley: Reading, MA, 1992. ISBN 978-0-201-14659-2. - International Civil Aviation Organization. *Manual of the ICAO Standard Atmosphere (extended to 80 kilometres / 262 500 feet)*, 3rd ed., Doc 7488. ICAO: Montreal, 1993. - Kerrebrock, J. L. *Aircraft Engines and Gas Turbines*, 2nd ed. MIT Press: Cambridge, MA, 1992. - Mattingly, J. D. *Elements of Propulsion: Gas Turbines and Rockets*. AIAA Education Series, American Institute of Aeronautics and Astronautics: Reston, VA, 2006. ISBN 978-1-56347-779-9. (Source of the station numbering, the MIL-E-5008B inlet recovery schedule and the cycle-analysis formulation used here.) - Padture, N. P.; Gell, M.; Jordan, E. H. "Thermal Barrier Coatings for Gas-Turbine Engine Applications." *Science* **2002**, *296* (5566), 280–284. DOI: 10.1126/science.1068609. - Reed, R. C. *The Superalloys: Fundamentals and Applications*. Cambridge University Press: Cambridge, 2006. ISBN 978-0-521-85904-2. - Rolls-Royce plc. *The Jet Engine*, 5th ed. Rolls-Royce: Derby, 1996; reissued Wiley: Chichester, 2015. ISBN 978-1-119-06599-9. - SAE International. *Gas Turbine Engine Performance Station Identification and Nomenclature*, Aerospace Recommended Practice ARP755. SAE International: Warrendale, PA. - Walsh, P. P.; Fletcher, P. *Gas Turbine Performance*, 2nd ed. Blackwell Science: Oxford, 2004. - Whittle, F. *Improvements Relating to the Propulsion of Aircraft and Other Vehicles*. British Patent 347,206, filed 16 January 1930. - Whittle, F. "The Early History of the Whittle Jet Propulsion Gas Turbine." *Proceedings of the Institution of Mechanical Engineers* **1945**, *152*, 419–435. **On the spine:** [[Aircraft]] · [[Aircraft_flight_dynamics]] · [[Fixed-wing_aircraft]] · [[Helicopter]] · [[Turbojet]] · [[Jet_engine]] · [[Sonic_boom]] · [[Contrail]] · [[Air_traffic_control]] · [[Avionics]] · [[Aviation]].  **Part of the [[Aviation]] hub** — main article for section A8, *The jet age*. Related sections: Turbofan · FADEC.  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Turbojet) : [Wikitube](https://en.wikitube.io/wiki/Turbojet) --- *PORTAL_Aviation three.js batch · 2026-08-05 · sim staged in `_3d_deploy_stage/`.*