ThrustLab

Input Parameters

Engine Model

Textbook examples

A. F. El-Sayed, Aircraft Propulsion & Gas Turbine Engines, Ch. 7 · static sea level ()

Load a case to populate every input and compare against the published answer.

Flight Conditions

Flight Mach Number : —

Altitude : m

Override ISA atmosphere

Air Mass Flow : kg/s

Cycle Parameters

Compressor Pressure Ratio : —

Turbine Inlet Temp : K

Real Cycle Inputs

Inlet efficiency :—

Compressor efficiency :—

Turbine efficiency :—

Nozzle efficiency :—

Combustor efficiency :—

Mechanical efficiency :—

Combustor pressure loss :frac.

Provide known stagnation temperatures/pressures. Leave fields blank to derive from efficiency defaults. Efficiencies will be back-calculated from the values you provide.

inlet exit (K) :K

inlet exit (kPa) :kPa

compressor exit (K) :K

compressor exit (kPa) :kPa

combustor exit (kPa) :kPa

turbine exit (K) :K

turbine exit (kPa) :kPa

Afterburner (Reheat)

Enable Afterburner

Gas Properties

cold (inlet to comp exit) :—

hot (turbine to nozzle exit) :—

cold :kJ/kg·K

hot :kJ/kg·K

afterburner :—

afterburner :kJ/kg·K

Fuel LHV :kJ/kg

Enter parameters and click Calculate.

Engine Schematic · Annular Cross-Section · Live Heat Field Click any station to drill in

Station 4 · TIT

— K — kPa T— K P— kPa

→ → → → →

T-s Diagram Temperature [K] vs Entropy [J/(kg·K)]

Ideal reference

Solved cycle

Afterburner add.

Figure 0.1 — Live T-s path of the solved cycle. Station dots are stagnation states; the nozzle-exit point is static.

P-v Diagram Pressure [kPa] vs Specific Volume [m³/kg]

Ideal reference

Solved cycle

Afterburner add.

Figure 0.2 — P-v projection of the same cycle. Compression climbs the left limb; expansion through turbine and nozzle returns down the right.

Results

Result Summary · edit driving parameters inline

(kg/s)

(K)

Spec. Thrust — N·s / kg

TSFC — kg / h·N

Thrust — kN

Primary Performance Outputs

Specific Thrust

—

N·s / kg

TSFC

—

kg / h·N

Thrust=—kN

Air mass flow=—kg/s

Fuel mass flow (actual)=—kg/s

Fuel mass flow (ideal, )=—kg/s

Fuel / air ratio =——

AB fuel/air ratio =——

Total fuel/air ratio =——

Nozzle exit velocity =—m/s

Nozzle exit temperature =—K

Nozzle exit area =—m²

Nozzle state=—

Thermal efficiency =—%

Propulsive efficiency =—%

Overall efficiency =—%

Station Properties

Convention (station number = station letter): 1(a) ambient · 2 inlet exit · 3 compressor exit · 4 turbine inlet · 5 turbine exit · 6 afterburner exit (shown only with reheat) · 7(e) nozzle exit.

Station	(K)	(kPa)	(K)	(kPa)
1(a) — Ambient / free stream	—	—	—	—
2 — Inlet exit	—	—	—	—
3 — Compressor exit	—	—	—	—
4 — Turbine inlet (TIT)	—	—	—	—
5 — Turbine exit	—	—	—	—
6 — Afterburner exit	—	—	—	—
7(e) — Nozzle exit	—	—	—	—

Section 1.0 · Exploration

Parametric Study

Single points answer questions; sweeps reveal structure. Vary one driving parameter across its range — flight Mach number or compressor pressure ratio — while every other input holds the value set in the dashboard, and the four trade curves of turbojet design appear.

Sweep Configuration

Sweep Parameter

Start Value

End Value

Points

Configure the sweep and click Run Sweep. The sweep reuses the current engine model, afterburner state, and all other dashboard inputs.

Specific Thrust

Figure 5.1 — Specific thrust across the swept range.

TSFC

Figure 5.2 — Fuel cost of thrust across the swept range.

Thrust

Figure 5.3 — Total thrust at the dashboard mass flow.

Efficiencies ()

Figure 5.4 — The efficiency chain. Overall efficiency is the product of the other two.

Method and limitations of the parametric sweep

The sweep varies a single independent variable — flight Mach number or compressor pressure ratio — in uniform increments between the specified bounds. At each increment the remaining inputs are held at their dashboard values and the complete cycle is solved from intake to nozzle, including the afterburner when it is enabled. Each plotted point is an independent converged solution of the same governing equations used for the single-point analysis; no values are interpolated between points.

A single operating point gives one performance figure; a sweep resolves the trade-offs between figures. Raising the compressor pressure ratio, for example, increases thermal efficiency while reducing specific thrust, and the curves locate the resulting compromise. In parametric cycle analysis the trend across the range is the primary result rather than any individual value.

Limitations

Single-variable variation. Only the swept parameter changes; all other quantities are fixed. An operating engine re-matches — shaft speed, bleed and nozzle area adjust together — so the curves are a controlled section through the design space, not measured engine behaviour.
Model assumptions. The working fluid is treated as calorically perfect, with separate constant values of cₚ and γ for the cold and hot sections, and the flow as quasi-one-dimensional and steady. These assumptions lose accuracy toward the extremes of the range (high Mach number, very high pressure ratio) even where a curve is still drawn.
Non-convergent points are omitted. Where a parameter value yields a non-physical cycle — for instance, insufficient turbine work to drive the compressor — the solver returns no result and the point is left blank rather than assigned an arbitrary value. A gap in a curve marks the boundary of the feasible cycle.
Resolution. The number of points sets the resolution of the curve; too few may miss a local extremum. The 200-point limit bounds computation time.
Intended use. Results are suitable for instruction and coursework. Trends are representative; absolute magnitudes are approximate and do not replace validated design tools.

Section 2.0 · Verification

Textbook Validation

A calculator is only as trustworthy as the published answers it can reproduce. The three preset buttons in the dashboard load worked examples 7.1 and 7.2 from El-Sayed — every input, every component efficiency, the book's own rounded sea-level atmosphere — so the solver's output can be laid directly against the printed result.^[6]

Below, the full station-by-station derivation of the current dashboard state, rendered live. Every line is the exact expression the solver evaluated, with the numbers it produced. Change any input above and this ledger rewrites itself.

Step-by-step Worked Solution · live

Calculate the cycle first to see the worked solution.

+ Assumptions

Steady, one-dimensional flow throughout the engine.
Calorically semi-perfect gas: three constant-property zones — cold (a→comp exit), hot (turbine inlet→turbine exit), and afterburner (post-AB→nozzle exit when the afterburner is active).
Mach correction applied at free stream: , .
Diffuser (inlet): adiabatic — stagnation temperature conserved. Real mode: stagnation pressure recovery via .
Compressor: isentropic efficiency on stagnation enthalpy basis.
Combustor: constant total pressure (ideal) or with fractional drop (real). Energy balance yields fuel/air ratio .
Single-spool shaft power balance: (compressor work equals turbine work divided by mechanical efficiency).
Turbine: isentropic efficiency ; exit stagnation pressure derived from shaft-balance exit temperature.
Nozzle: fully expanded to ambient () unless choked — if critical ratio, , pressure-thrust term added.
ISA standard atmosphere used for and from altitude input.
No afterburner, no cooling bleed, no inlet distortion.

+ Input Constraints & Validity Checks

Flight Mach number: 0 – 5
Altitude: 0 – 40 000 m (ISA model)
Air mass flow: 0.1 – 1000 kg/s
Compressor pressure ratio : 1 – 60
Turbine inlet temperature : 800 – 2200 K; must exceed compressor exit temperature
All component efficiencies : 0.5 – 1.0; combustor pressure loss : 0 – 0.3
Specific heat ratio : 1.2 – 1.5; : 0.8 – 1.5 kJ/kg·K; LHV: 20 000 – 120 000 kJ/kg
Computed fuel/air ratio must lie in (0, 0.10]
Nozzle exit temperature must exceed ambient temperature

PRECISION · The solver never rounds between stations. Where it disagrees with the book past the third significant figure, the solver is the more accurate of the two.

If comes out negative, the combustor is being asked to cool the flow. Raise .

Section 3.0 · Theory

The Physics
of Thrust

A turbojet is a momentum machine. It swallows a river of still air, pays for it in fuel, and throws it backwards faster than it arrived. Newton settles the account: the reaction to that rearward acceleration of gas is the forward push on the airframe.^[1]

Drawing a control volume around the whole engine and applying the integral momentum theorem gives the uninstalled thrust of a single-stream engine. Two terms appear: a momentum-flux term, and a pressure term that survives only when the nozzle cannot expand the flow all the way down to ambient pressure.^[2]

Eq. 1.1 — momentum theorem

Dividing by the air mass flow yields specific thrust — the figure of merit ThrustLab reports first, because it separates the thermodynamic quality of the cycle from the sheer size of the engine. A second figure, thrust-specific fuel consumption, measures what the thrust costs in fuel per hour.^[3]

Eq. 1.2 — figures of merit

Here is the total fuel-to-air ratio — the main-burner fuel-air ratio plus the afterburner fuel-air ratio, . With the afterburner off, so .

“The engine does not push against the air behind it. It pushes against the air it carries within.” — folklore of the propulsion lab

The deepest tension in jet propulsion lives inside Eq. 1.2. A large velocity excess buys thrust, but the kinetic energy left in the jet is wasted. Propulsive efficiency — the fraction of mechanical power that actually propels the aircraft — falls as the jet gets hotter and faster:

Eq. 1.3 — the efficiency chain

Everything the dashboard above computes — every station temperature, every pressure ratio — exists to evaluate these three numbers honestly. Change the compressor ratio in Section 0 and watch climb while specific thrust eventually sags: the trade is structural, not accidental.^[4]

CONTROL VOLUME · The momentum theorem is applied between the free-stream capture plane and the nozzle exit plane. Internal details cancel; only boundary fluxes survive.

Note: TIT here refers to Turbine Inlet Temperature, not the other thing. — Ed.

UNITS · Specific thrust in N·s/kg equals m/s — it is literally the effective velocity increment imparted per kilogram of air.

Section 4.0 · Thermodynamics

The Cycle,
Read on a T-s Plane

The turbojet runs an open Brayton cycle: compress, burn at nearly constant pressure, expand. On temperature–entropy axes the ideal cycle is a clean quadrilateral bounded by two isentropes and two isobars. The real cycle — the gold curve in Figure 0.1 — leans to the right, because every component manufactures entropy.^[5]

Read the live diagram station by station. From a to 2 the inlet recovers ram pressure; adiabatic, so stagnation temperature is conserved while a real diffuser loses some stagnation pressure. From 2 to 3 the compressor climbs steeply — a real machine needs more temperature rise than the isentropic minimum to reach the same pressure:

Eq. 2.1 — compressor exit

From 3 to 4 the combustor adds heat at essentially constant pressure; the great rightward sweep of entropy on the diagram is this heat addition. From 4 to 5 the turbine extracts exactly the shaft work the compressor demands — the single-spool power balance that closes the cycle algebraically. Whatever stagnation enthalpy remains above ambient is spent in the nozzle as kinetic energy.

+ Show full derivation — ideal-cycle thermal efficiency

2.1

Start from heat in minus heat out over heat in; isentropic relations collapse the four corner temperatures into two ratios.

2.2

Define the ram temperature ratio and the compressor temperature ratio. Flight speed itself acts as a free pre-compressor.

2.3

Thermal efficiency rises monotonically with both flight Mach number and pressure ratio — but approaching starves the combustor, which is exactly the validity check the solver enforces.

2.4

The combustor energy balance — the same expression evaluated live in the worked solution of the Validation chapter.

With the afterburner lit, a second constant-pressure heat addition appears after the turbine — the red segment from 5 to 6. It is thermodynamically crude (heat added at low pressure converts poorly to work) but operationally decisive: thrust rises steeply while TSFC roughly doubles. Toggle it in the dashboard and watch both diagrams restructure.^[6]

SIGN CONVENTION · Entropy on the live chart is plotted relative to the free-stream state: . The reference cancels in every difference that matters.

Babu uses where Mattingly uses . Same thing.

ISOBARS · On a T-s plane, constant-pressure lines are exponentials; the vertical gap between them grows with temperature. That widening gap is where the net work of the cycle lives.

Section 5.0 · Anatomy

Station Analysis

The solver walks the gas path in the canonical station numbering of Babu Ch. 7 — the same sequence the schematic above wears as numbered chips. Each station is a bookkeeping plane: a place where stagnation temperature and stagnation pressure are tallied before the next component takes its cut.^[2]

a

Free stream. Ambient static state from the ISA model (or your override), plus the ram state: .

2

Inlet / diffuser exit. Adiabatic, so ; the real diffuser surrenders stagnation pressure through .

3

Compressor exit. Pressure multiplied by ; temperature rise inflated by (Eq. 2.1). The hottest cold-section state.

4

Combustor exit — turbine inlet. Temperature pinned at the metallurgical limit T₀₄; pressure loses the fraction ; fuel/air ratio f from the energy balance.

5

Turbine exit. Set by the shaft power balance — the turbine takes exactly what the compressor needs, divided by mechanical efficiency.

6

Afterburner exit (when lit). A second energy balance gives ; pressure pays the duct loss .

e

Nozzle exit. The solver first tests choking: if the throat runs at M = 1 and a pressure-thrust term is added; otherwise the jet expands fully to ambient.

Hover any station chip in the dashboard and the probe reports all four properties — stagnation and static — straight from the last solve. The colour field inside the annulus is the same data, rendered as temperature.

NUMBERING · Some texts insert station 1 at the inlet lip. ThrustLab follows Babu: a → 2 → 3 → 4 → 5 → (6) → e. Nothing physical changes, only labels.

This equation only holds for ideal gas. See §7.3.

THREE-ZONE GAS · cold () up to compressor exit · hot () through turbine · afterburner gas () when reheat is lit.

Section 6.0 · Bibliography

References

J. D. Anderson, 2016

Introduction to Flight, 8th ed. — McGraw-Hill

Ch. 9 · Propulsion fundamentals and the momentum theorem

V. Babu, 2022

Fundamentals of Propulsion — Springer

Ch. 7 · Turbojet station numbering and cycle methodology used by this solver

J. D. Mattingly & K. M. Boyer, 2016

Elements of Propulsion: Gas Turbines and Rockets, 2nd ed. — AIAA Education Series

Ch. 5–7 · Parametric cycle analysis; specific thrust and TSFC definitions

S. Farokhi, 2014

Aircraft Propulsion, 2nd ed. — Wiley

Ch. 4 · Engine thrust and performance parameters; efficiency trades

P. Hill & C. Peterson, 1992

Mechanics and Thermodynamics of Propulsion, 2nd ed. — Addison-Wesley

Ch. 5–6 · Brayton cycle on T-s coordinates; component irreversibility

A. F. El-Sayed, 2017

Aircraft Propulsion and Gas Turbine Engines, 2nd ed. — CRC Press

Ch. 7 · Worked examples 7.1 and 7.2 reproduced by the validation presets

ICAO, 1993

Manual of the ICAO Standard Atmosphere — Doc 7488/3

Troposphere lapse-rate and stratosphere models implemented in isa(h)

Section 7.0 · Feedback

Feedback and Problem Reports

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