Going deeper10 min read5 / 9

Turbofans & bypass

The momentum article proved that gentle pushes on huge airflows beat hard pushes on small ones. The turbofan is that theorem built in titanium: a turbojet core whose turbine is enlarged to also drive a giant fan, which throws ten times the core’s airflow rearward at barely more than flight speed. It is why modern airliners burn half the fuel of their 1960s ancestors.

Two streams, one machine

Fig. 1. The bypass architecture. The core works exactly like the last article's turbojet; the fan stream skips combustion entirely — cold thrust, paid for by the turbine through the shaft.

Define the bypass ratio: for every kilogram through the core, $\alpha$ kilograms go around it. The fan raises the bypass stream’s pressure by the fan pressure ratio $\pi_f$ (a gentle 1.4–1.7, one stage), giving it temperature ratio $\tau_f = \pi_f^{(\gamma-1)/\gamma}$ , and the bypass nozzle expands that straight back to a modest exit velocity:

\frac{V_{19}^2}{2} = c_p T_0\,\tau_r \tau_f \left(1 - \frac{1}{\tau_r \tau_f}\right)

(1)

The turbine now feeds two customers

The only structural change to the turbojet analysis is the shaft work balance. The turbine must drive the compressor and the fan — and the fan pumps $\alpha$ times the core flow:

\tau_t = 1 - \frac{\tau_r}{\tau_\lambda}\Bigl[(\tau_c - 1) + \alpha\,(\tau_f - 1)\Bigr]

(2)

That $\alpha(\tau_f - 1)$ term is the whole turbofan, mathematically. Crank $\alpha$ up and the turbine bleeds the core jet harder and harder to power the fan — energy is being moved from the fast core jet to the slow bypass jet. Total thrust averages the two streams:

\frac{F}{\dot m_{\text{total}}} = \frac{(V_9 - V_0) + \alpha\,(V_{19} - V_0)}{1 + \alpha}

(3)

$\alpha$: bypass ratio: 0 = pure turbojet, 9–12 = modern airliner engine [–]
$\pi_f,\ \tau_f$: fan pressure / temperature ratio (single fan stage) [–]
$V_{19}$: bypass exit velocity — typically only 1.1–1.3 × V₀ [m/s]

Push $\alpha$ around a real solved cycle (this runs the demo’s own turbofan solver):

Bypass ratio

\alpha

8.0

M_0 = 0.85,\ 11\,\text{km},\ \pi_c = 32,\ \pi_f = 1.6

\tfrac{F}{\dot m} = 167\ \tfrac{\text{N}}{\text{kg/s}},\ \text{TSFC} = 13.7,\ \eta_p = 63\,\%

Computed live by the same solver as the turbofan demo. Raising α trades specific thrust (a bigger, heavier engine per newton) for propulsive efficiency and TSFC (g of fuel per kN·s) — until the turbine runs out of work to feed the fan.

Why not α = 25?

The turbine runs dry. Equation (2): with fixed $\tau_\lambda$ , there is an α beyond which $\tau_t$ leaves too little core jet — the slider’s infeasible zone.
The nacelle grows. Specific thrust falls as α rises (equation 3’s denominator), so the same thrust needs a fatter engine: more weight, more drag. Past a point the nacelle drag eats the TSFC gain.
The fan tips go supersonic. A bigger fan at the same rpm has faster tips; shocks on the blades cost efficiency and make noise. The newest engines insert a gearbox between turbine and fan so each can spin at its own best speed — that is the “geared turbofan”, and it bought the industry another few points of α.