Chris Collins

Tools · aviation

Jet engines and gas turbines

How jet engines work and what their numbers mean: an animated cutaway of turbojet, turbofan, turboprop, turboshaft, ramjet and afterburning engines with numbered stations; ideal and real Brayton cycle analysis at any Mach and altitude — thrust, TSFC, efficiencies, T–s and P–v diagrams and trade studies; compressor stages, draggable velocity triangles and a compressor map with surge margin; approximate figures for real engine families; and fuel, run time and start-up for model turbojets.

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How to use it

A gas turbine squeezes air, burns fuel in it, and lets the hot gas run a turbine that drives the compressor; what is left over makes a jet, turns a propeller, or drives a shaft. This page shows the engine, works through the cycle the way the textbooks do, and puts numbers on why airliner fans keep growing.

How to use it

The six tabs share one engine: pick a type and its numbers on Cycle and the cutaway, trade studies and compressor tab follow.

  • Cutaway draws the chosen engine in section — turbojet, afterburning turbojet, turbofan with separate or mixed exhausts (with or without afterburner), turboprop, turboshaft or ramjet — with the standard station numbers (0 free stream, 2 compressor face, 13 fan exit, 25 HP compressor inlet, 3 compressor exit, 4 turbine inlet, 45 between turbines, 5 turbine exit, 6 mixer, 7 afterburner, 9 and 19 nozzle exits). Dots of air flow through it, coloured by the temperatures the Cycle tab works out. Click or tap a part (fan, compressor, combustor, turbines, nozzle, bypass duct, afterburner, propeller…) to read what it does and its inlet and exit conditions. The table lists every station’s total and static temperature and pressure.

  • Cycle is an on-design (parametric) cycle analysis. Choose Ideal (perfect components, constant gas properties) or With losses (polytropic compressor, fan and turbine efficiencies, burner and nozzle pressure losses, mechanical efficiency, separate hot-gas properties, the fuel’s mass, inlet shock losses above Mach 1, and a convergent or fully expanding nozzle). Set the flight Mach number, altitude and ISA deviation, the overall pressure ratio, turbine inlet temperature Tt4, bypass and fan pressure ratios, the afterburner temperature and the air mass flow. Out come thrust, specific thrust, TSFC, fuel flow, fuel–air ratio, thermal, propulsive and overall efficiency, compressor powers, jet velocities, and the cycle on T–s and P–v diagrams. Turboprops and turboshafts give shaft power, specific fuel consumption, propeller thrust and equivalent shaft power. A mixed turbofan’s Match the core pressure button finds the fan ratio that makes the two streams meet at equal pressure.

  • Trade studies sweeps one input — pressure ratio, Tt4, bypass ratio, fan pressure ratio, Mach number or altitude — and plots specific thrust, TSFC and the three efficiencies, ideal and with losses, with a note on the trend.

  • Compressor & turbine estimates the number of compressor and turbine stages from the pressure ratio and from blade loading; draws a compressor stage’s velocity triangles, which you change by dragging the tips of V1 and W2, giving the work, temperature rise, stage pressure ratio, reaction and de Haller number; plots an illustrative compressor map with speed lines, efficiency islands, surge and choke lines and the running line, with the surge margin at the speed you choose; and works out spool speeds from tip speed and diameter.

  • Real engines lists engine families with approximate public figures (thrust or power class, bypass ratio, pressure ratio), plots them, and loads any of them into the Cycle tab.

  • Model jets works out fuel flow, run time and the oil to add for a small turbojet such as a 66 mm KJ66-class engine, with a table of typical classes, the start-up sequence and safety notes.

How it works

Atmosphere. The International Standard Atmosphere (ICAO Doc 7488): 288.15 K and 101,325 Pa at sea level, −6.5 K/km to the tropopause at 11 km, isothermal to 20 km, +1 K/km above.

The cycle follows the parametric (on-design) method of J. D. Mattingly, Elements of Propulsion: Gas Turbines and Rockets (AIAA), station by station in my own implementation, with the explanations of NASA Glenn Research Center’s Beginner’s Guide to Propulsion. Ram: Tt0 = T0(1 + (γ−1)/2·M0²). Compression with polytropic efficiency e: Tt3/Tt2 = π^γ−1)/(γe. The burner’s fuel–air ratio closes its energy balance: f = (cp,t·Tt4 − cp,c·Tt3)/(η_b·h − cp,t·Tt4), with h = 42.8 MJ/kg. The turbine supplies the compressor and fan work: (1+f)·η_m·cp,t·(Tt4 − Tt5) = cp,c[(Tt3 − Tt2) + α(Tt13 − Tt2)]. Nozzles expand to ambient pressure or, when convergent, choke at Mach 1 and add the pressure thrust (P9 − P0)·A9. Net thrust is the momentum leaving minus the ram drag ṁ·V0. A mixed turbofan mixes the streams by energy and averages their total pressures; an afterburner heats the gas again to Tt7. A turboprop’s power turbine expands the gas to the exhaust pressure you set and drives the propeller through a gearbox; propeller thrust is η_prop·P/V0 in flight and, at low speed, the momentum-theory static thrust (2ρAP²)^⅓ × a figure of merit of 0.75. Inlet shock losses above Mach 1 use the MIL-E-5007D recovery curve.

Efficiencies. Thermal efficiency is the kinetic energy added to the streams (plus shaft power) over the fuel’s heat; propulsive efficiency is thrust power over that kinetic energy; overall is their product, F·V0 over the fuel’s heat. A jet that leaves under-expanded is counted at the velocity it would reach fully expanded, so its pressure thrust is not lost from the energy.

Compressors. Velocity triangles and the Euler work ΔH = U·(Cw2 − Cw1) = U·Ca·(tan β1 − tan β2), the degree of reaction (Ca/2U)(tan β1 + tan β2) and the de Haller limit W2/W1 ≥ 0.72 follow H. I. H. Saravanamuttoo, G. F. C. Rogers and H. Cohen, Gas Turbine Theory (Pearson), chapter 5; the running line of a simple jet with a choked turbine and nozzle (corrected flow ∝ PR/√(PR^0.286 − 1)) follows chapter 9. The compressor map’s shape is generic — speed lines, surge line and efficiency islands drawn from a simple formula scaled through your design point — and is not any real compressor’s map.

The tests check the ideal turbojet, turbofan and ramjet against Mattingly’s closed-form results to machine precision, the ideal thermal efficiency of every engine type against the Brayton result 1 − 1/(τr·τc), the afterburning turbojet’s jet velocity, the burner and turbine energy balances, the choking nozzle, the textbook trends (an optimum pressure ratio for specific thrust; TSFC and specific thrust falling with bypass ratio), the velocity-triangle identities, and the ISA table.

Limits

  • On-design only: each answer is the engine designed for that point. A real engine flown off its design point (off-design or "engine deck" performance) needs component maps and matching, which this does not do — the compressor tab’s running line is the simple textbook version.

  • Constant specific heats (one set cold, one hot), no turbine cooling air, bleed or power offtake, and no installation losses (inlet spillage, nacelle drag). Real engines lose several per cent of thrust and TSFC to each.

  • The real-engine figures are approximate, rounded public numbers; turbine temperatures for them are guesses for the era. Nothing here is proprietary or suitable for engineering use.

  • The cutaway is schematic, not to scale, and the particle speeds are only indicative.

  • Model turbine figures are class averages; follow your engine maker’s manual for fuel, oil, start-up and maintenance, and your national model flying association’s turbine rules.

Linking to an example

Share link copies a link to the engine you have set up. Links can be written by hand: the parameters below are in SI units (altitude in metres, temperatures in kelvin, mass flow in kg/s), whatever the page shows. Add the tab after #: cutaway, cycle, sweeps, compressor, engines or model.

Parameter Meaning Example

type

turbojet, abjet (afterburning turbojet), turbofan, mixed (mixed-exhaust turbofan), turboprop, turboshaft, ramjet

type=turbofan

ideal

true for the ideal cycle, false with component losses

ideal=true

M0, alt, dT

Flight Mach number, altitude (m), ISA deviation (K)

M0=0.8&alt=10700

opr, tt4

Overall pressure ratio, turbine inlet temperature (K)

opr=40&tt4=1600

bpr, fpr

Bypass ratio, fan pressure ratio

bpr=10&fpr=1.45

ab, tt7

Afterburner on a mixed turbofan (true), afterburner exit temperature (K)

ab=true&tt7=2100

mdot, noz

Air mass flow (kg/s), nozzle (conv or ideal)

mdot=250&noz=conv

pid, ec, ef, et, etab, pib, pin, etam

Inlet pressure recovery, compressor, fan and turbine polytropic efficiencies, burner efficiency and pressure ratio, nozzle pressure ratio, mechanical efficiency

ec=0.92&et=0.91

pt9, etaprop, dprop

Turboprop/turboshaft exhaust Pt9/P0, propeller efficiency, propeller diameter (m)

pt9=1.1&dprop=2.6

sweep

Trade-study input: opr, tt4, bpr, fpr, M0, alt

sweep=bpr

U, Ca, a1, b2

Compressor stage: blade speed and axial velocity (m/s), α1 and β2 (°)

U=300&Ca=180&a1=30&b2=30

mapPR, mapN

Compressor map design pressure ratio (0 = from the cycle), operating speed (%)

mapPR=8&mapN=90

Dfan, Ufan, Dhpc, Uhpc

Fan and HP compressor tip diameters (m) and tip speeds (m/s)

Dfan=3&Ufan=400

thrust, tsfcm, tank, avg, idle, res, oil

Model turbine thrust (N), TSFC (kg/(N·h)), tank (mL), average power, idle flow, reserve and oil (%)

thrust=160&tank=4000

example

A preset below; parameters given with it override it

example=geared-fan

example= Opens

turbojet-static

A simple turbojet on the ground: pressure ratio 8, 1,200 K (open)

ideal-turbojet

The ideal turbojet at Mach 0.8 and 10 km, to compare with the textbook closed form (open)

j79-ab

An afterburning turbojet like the J79 at Mach 2 and 11 km (open)

cfm56-cruise

A medium-bypass turbofan at cruise (open)

geared-fan

A high-bypass geared turbofan at cruise: bypass 12, fan 1.4 (open)

fighter-ab

A low-bypass mixed turbofan with afterburner at Mach 1.6 (open)

turboprop

A PT6-class turboprop climbing at Mach 0.4 (open)

ramjet-m3

A ramjet at Mach 3 and 18 km (open)

bypass-trade

Turbofan trade study against bypass ratio (open)

stage-50

A 50 % reaction compressor stage (open)

kj66

A KJ66-class model turbojet with a 2.5 L tank (open)

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