Otto and Diesel Cycles
The same axes, and one line rotates from vertical to horizontal — which is the whole difference between petrol and diesel.
Skip to the animationOtto adds heat at constant volume and Diesel at constant pressure, and although Otto is more efficient at the same compression ratio, only Diesel is allowed to use a high one — because compressing air alone cannot knock.
Air-standard cycles
Carnot's isothermal heat addition is unachievable in a cylinder: combustion is fast and the piston never stops. Real cycles are analysed as air-standard cycles — air only, treated as an ideal gas, with combustion replaced by heat addition and exhaust by heat rejection.
The idealisation is severe and it still predicts the right trends, which is why it survives in every syllabus.
The Otto cycle
- 11→2 adiabatic compression.
- 22→3 constant volume heat addition — the spark fires and combustion is fast enough that the piston has barely moved.
- 33→4 adiabatic expansion, the power stroke.
- 44→1 constant volume heat rejection.
Efficiency is 1 − 1/r^(γ−1), depending on the compression ratio and nothing else — not on the heat added, not on the load.
Petrol engines are capped near r = 10. Compressing a fuel-air mixture heats it, and beyond that it ignites before the spark — knock, which destroys engines. The limit is chemical, not thermodynamic, and octane rating is what measures it.
The Diesel cycle
A diesel compresses air alone, so nothing can pre-ignite and r can reach 15–22. The air becomes hot enough to ignite fuel injected at the top, with no spark at all. Injection takes long enough that the piston is already moving, so heat addition is modelled at constant pressure.
Efficiency is 1 − (1/r^(γ−1))·[(ρᵞ − 1)/(γ(ρ − 1))], where ρ is the cut-off ratio. The bracket is always greater than one.
The comparison, both ways round
| Comparison | Winner | Why |
|---|---|---|
| Same compression ratio | Otto | Constant-volume heat addition raises T further before expansion; the cut-off term costs Diesel |
| Same peak pressure | Diesel | Diesel reaches its peak pressure at a much higher r |
| What each can actually reach | Diesel | r = 20 against r = 10 outweighs the worse heat-addition process |
The first row is the exam answer and the third is the engineering one. In practice diesels reach roughly 45% against petrol's 35% — and pay for it in weight, because those pressures need stronger components.
The dual cycle
Real combustion is neither instantaneous nor slow, so the dual (mixed) cycle adds some heat at constant volume and the rest at constant pressure. Otto and Diesel are its two limiting cases, and it is closer to what every real engine does.
All three ignore heat loss to the cylinder walls, friction, real gas behaviour, incomplete combustion and the fact that the working fluid changes composition. Measured efficiencies therefore fall well below all of them.
The numbers you will be asked for
- Compression ratio
r = V₁ / V₂
Total volume over clearance volume.
- Otto efficiency
η = 1 − 1/r^(γ−1)
Depends on r alone.
- Diesel efficiency
η = 1 − (1/r^(γ−1))·[(ρᵞ−1)/(γ(ρ−1))]
ρ is the cut-off ratio; the bracket always exceeds 1.
- Cut-off ratio
ρ = V₃ / V₂
How far into the stroke injection continues.
- Mean effective pressure
mep = W_net / V_swept
The comparison that accounts for engine size.
Advantages and disadvantages
Advantages
- Both are analysable in closed form with only r and γ.
- The trends they predict — more compression, more efficiency — are correct.
- They explain the real difference between petrol and diesel engines.
- The dual cycle covers the intermediate case with one extra parameter.
Disadvantages
- Air-standard ignores combustion chemistry entirely.
- Heat loss, friction and real gas behaviour are all excluded.
- Predicted efficiencies are well above measured ones.
- Constant-volume combustion is an idealisation no engine achieves.
Watch it work
Check yourself
question 1 / 4
One question at a time. Pick an answer to see why it is right or wrong, then move on — there is no score to keep and nothing is saved.