Turbojet vs Turbofan Efficiency: A Second-Law Comparison
Every airliner today flies with turbofans, and every first-course gas turbine is a turbojet. Both burn fuel the same way — compress, heat, expand — yet at subsonic cruise a modern turbofan burns roughly half the fuel per unit of thrust. First-law bookkeeping alone never quite explains why. The exergy balance does.
The propulsive problem: thrust is cheap, kinetic energy is expensive
Thrust is momentum flux: F = ṁ·(Ve − V₀). You can produce the same thrust with a small mass flow accelerated hard, or a large mass flow accelerated gently. But the kinetic energy thrown away in the exhaust scales with the square of the velocity increment:
Ėwaste ≈ ½·ṁ·(Ve − V₀)²Double the airflow, halve the velocity increment, and you keep the same thrust while halving the wasted kinetic power. That is the entire turbofan idea in one line — and in the exergy balance, that wasted jet kinetic energy appears as exhaust-stream exergy loss.
What the exergy balance sees
Run a station-by-station exergy budget on both cycles at the same flight condition and a consistent picture emerges:
- Turbojet: the combustor is the largest destroyer, but the exhaust stream is the second great loss — high-velocity gas leaving at high temperature carries exergy that never becomes thrust.
- Turbofan: the fan moves exergy out of the exhaust and into thrust power. Exhaust-stream loss shrinks dramatically; the core's combustor destruction remains, essentially unchanged per unit of core airflow.
In other words: the turbofan does not fix the combustor — it fixes the plume. Propulsive efficiency is where the gain lives, and the second law quantifies it exactly.
Typical numbers at Mach 0.85 cruise
| Turbojet | Low-bypass (BPR≈1) | High-bypass (BPR 5–12) | |
|---|---|---|---|
| Propulsive efficiency | ~35–45% | ~50–60% | ~70–80% |
| TSFC (relative) | ~1.0 (reference) | ~0.75–0.85 | ~0.5–0.55 |
| Exhaust exergy waste | Large — dominant after combustor | Moderate | Small |
| Exhaust velocity | Far above flight speed | Closer | Closest to flight speed |
| Best regime | Supersonic | Transonic / military | Subsonic cruise |
Values are typical textbook ranges, not guarantees for any specific engine — but the ordering never changes: more bypass, less exhaust waste, lower fuel burn per unit thrust.
Rule of thumb: propulsive efficiency peaks when exhaust velocity equals flight velocity. A turbojet's exhaust is several times faster than the aircraft; a high-bypass turbofan's fan stream is barely faster. The exergy statement and the design conclusion are the same sentence.
Where the turbojet still wins
- Supersonic cruise: at Mach 2+, thrust requires high exhaust velocity, and inlet ram does much of the compressor's work. A big fan adds frontal area and drag without buying propulsive efficiency.
- Simplicity and cost: one spool, no fan duct — for expendable or compact applications the turbojet remains attractive.
- Afterburning: military low-bypass engines reheat the exhaust for thrust bursts. An exergy balance shows exactly what that costs: afterburners destroy exergy at a rate that makes the main combustor look gentle.
Second-law efficiency closes the loop
ηII — thrust-power exergy out over fuel exergy in — rises strongly with bypass ratio at subsonic speeds, almost entirely through the exhaust-stream term. Compressor and turbine efficiencies improve the core; bypass fixes the plume. A complete design study needs both, which is why modern engine optimization is really a second-law exercise.
Frequently asked questions
Why are turbofans more fuel efficient than turbojets?
Because they produce thrust by accelerating a large mass of air by a small amount instead of a small mass by a large amount. The kinetic energy carried away by the exhaust grows with the square of the velocity increment, so the slower, larger airflow of a turbofan wastes far less energy — and less exergy — in the jet plume.
What is bypass ratio and why does it matter?
Bypass ratio (BPR) is the mass flow through the fan duct divided by the mass flow through the core. A turbojet has BPR 0; modern airliner engines run BPR 5–12. Higher BPR lowers exhaust velocity, raises propulsive efficiency, and cuts the exhaust-stream exergy waste that dominates a turbojet's second-law balance.
When is a turbojet better than a turbofan?
At supersonic flight. Around Mach 2 and above, a high exhaust velocity is required for thrust, the intake already provides much of the compression, and a large fan adds drag and frontal area. This is why military fighters use low-bypass turbofans or turbojets, usually with an afterburner.
What is propulsive efficiency?
Propulsive efficiency is the fraction of the jet's kinetic power that becomes useful thrust power; it peaks when exhaust velocity approaches flight velocity. At Mach 0.85 cruise, a pure turbojet typically achieves roughly 35–45%, while a high-bypass turbofan reaches roughly 70–80%.
Can I compare a turbojet and a turbofan numerically?
Yes. ExergyJet models both cycles: turbojet analysis is available on the free tier, and turbofan analysis with full exergy breakdown is included in the Pro plan, including station-by-station results and Sankey diagrams.
See the difference yourself
The fastest way to internalize this is to run both cycles at the same Mach and altitude and compare the exergy Sankeys side by side. The turbojet's exhaust bar will do the talking.
Configure an engine, run the analysis, and watch where the exergy goes.
Run a free exergy analysis →