TWO STREAMS. ONE ENERGY ACCOUNT.

Turbofan Cycle & Bypass Ratio

Split the airflow between core and bypass. Trace the shaft work, nozzle states and two contributions to net thrust.

INTERACTIVE CALCULATED DIAGRAMB · LIVE

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A · no saved reference

01 / READ THE CHANGE

Keep both mass streams

The fan acts on core and bypass air. Fuel mass is added only to the core downstream of the burner.

02 / READ THE CHANGE

Pay for the fan

The turbine must supply both fan and compressor work. Some parameter combinations leave insufficient nozzle pressure and are rejected.

03 / READ THE CHANGE

A fair design comparison

Core air flow is fixed at 20 kg/s; total engine flow changes with bypass ratio. Exit areas are resized for each design, so this is not a fixed engine throttle simulation.

THE SAME MODEL, CONNECTED VIEWS

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B · solid turquoise A · dashed amber

Compare A and B

Quantity	A · saved	B · live	B − A	Unit

A remains fixed until saved again. Export includes the model version, settings and plotted data.

Equations, assumptions & sources

Read the balance, then connect each symbol to the model. Open a symbol key for definitions and units. Long equations can be scrolled sideways.

01 · Fuel adds energy

{\dot{m}}_{core} c_{p} T_{3} + η_{b} {\dot{m}}_{fuel} Q = ({\dot{m}}_{core} + {\dot{m}}_{fuel}) c_{p} T_{4}

Fuel changes both the gas mass flow and the energy entering the turbine.

Symbols & units

${\dot{m}}_{core}, {\dot{m}}_{fuel}$: Core air and fuel mass-flow rates, kg/s.
$T_{3}, T_{4}$: Compressor-delivery and turbine-entry stagnation temperatures, K.
$c_{p}, Q, η_{b}$: Specific heat, J/(kg K); fuel lower heating value, J/kg; burner efficiency, dimensionless.

02 · The turbine powers both compressors

η_{m} {\dot{m}}_{gas} c_{p} (T_{4} - T_{5}) = P_{fan} + P_{compressor}

Shaft power extracted from the gas must cover the fan and core-compressor demand.

Symbols & units

${\dot{m}}_{gas}, T_{5}$: Turbine gas mass flow including fuel, kg/s; turbine-exit stagnation temperature, K.
$P, η_{m}$: Shaft power, W; mechanical efficiency, dimensionless.

03 · Add momentum and pressure thrust

F = \sum_{j} [{\dot{m}}_{exit, j} V_{exit, j} - {\dot{m}}_{air, j} V_{0} + (p_{exit, j} - p_{a}) A_{exit, j}]

Sum the core and bypass streams. The core exhaust includes the added fuel mass.

Symbols & units

$F, j$: Net thrust, N; stream index j = core or bypass.
$V, p, A$: Speed, m/s; static pressure, Pa; nozzle exit area, m². V₀ is flight speed and pₐ is ambient pressure.

Constant γ = 1.4 and cₚ = 1004.675 J/(kg K), Q = 42.8 MJ/kg. Fan/compressor/turbine efficiencies 0.90/0.88/0.91; mechanical and combustion efficiencies 0.99. Inlet and burner pressure recoveries 0.98/0.95. Generic steady separate-flow design, convergent nozzles. No spool dynamics, cooling bleed or manufacturer maps.

NASA · turbofan thrust ↗

Physical relations and teaching sources support the stated concepts. Generic coefficients are explicitly illustrative; they are not measured manufacturer data. Numerical verification is separate from experimental validation. Model version: applied-labs-v1.1.

Turbofan Cycle & Bypass Ratio

Keep both mass streams

Pay for the fan

A fair design comparison

Follow the calculation

Compare A and B

01 · Fuel adds energy

02 · The turbine powers both compressors

03 · Add momentum and pressure thrust

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