Library / Thermodynamics / THE-13
Thermodynamics
Otto cycle efficiency
Ideal efficiency of a spark-ignition engine.
- Ref
- THE-13
- Rev
- v1
- Field
- Thermodynamics
- Result
- η
r is the compression ratio, the cylinder volume at the start of compression divided by the volume at the end, and γ the ratio of specific heats (1.4 for air). η is the ideal fraction of the heat added that becomes work in the air-standard Otto cycle: compression, constant-volume heat addition, expansion, constant-volume heat rejection.
Ideal efficiency of a spark-ignition engine. It rises with compression ratio, but with diminishing returns.
Calculator
- Efficiency at a compression ratio two higher0.6019
- Temperature ratio across compression rγ−12.297
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- At r = 8 the ideal efficiency is 56 %. Raising r to 10 gives 60 %, a gain of 3.7 points; the next two units gain only about 2 points. Real petrol engines reach roughly 25 to 35 %.
- Knock (uncontrolled ignition) limits petrol engines to compression ratios of about 10 to 12. A diesel compresses air alone, so it can use 15 to 20.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| γ Ratio of specific heats | 1.1 to 1.67 | 0.1877 | 0.7517 | 0.564 | +10% | +19.5 % |
| r Compression ratio | 2 to 20 | 0.2421 | 0.6983 | 0.4561 | +10% | +2.88 % |
Sweep of Compression ratio
| Compression ratio | Ideal efficiency |
|---|---|
| 2 | 0.2421 |
| 4.25 | 0.4394 |
| 6.5 | 0.527 |
| 8.75 | 0.5801 |
| 11 | 0.6168 |
| 13.25 | 0.6443 |
| 15.5 | 0.6659 |
| 17.75 | 0.6835 |
| 20 | 0.6983 |
Sweep one variable
Variables and how each one contributes
Ideal efficiency
What the equation gives you. Everything else feeds it.
Compression ratio
The compression ratio. Rises with diminishing returns: at r = 8 a 10 % rise in r raises η by about 3 %, and each further unit gains less.
Ratio of specific heats
The ratio of specific heats of the working gas. Strong: a higher γ gives more efficiency. Real hot combustion gas has a lower γ than cold air, which is one reason real engines fall short.
Worked example with the values above
- Exponent: γ − 1 = 0.4.
- Temperature ratio: rγ−1 = 80.4 = 2.2974.
- η = 1 − 1/2.2974 = 0.5647, or 56.47 %.
Assumptions and limits
- Air-standard cycle: a fixed mass of ideal gas with constant γ.
- Reversible processes, instantaneous combustion at constant volume and no heat loss to the walls.
Common mistakes
- Confusing it with the Carnot efficiency. The Otto efficiency depends on the compression ratio, not on the temperature limits.
- Using the pressure ratio or the swept volume in place of r.
Statistics and uncertainty
The ideal efficiency depends only on r and γ. Its sensitivity to r is (γ−1) r−(γ−1) / η near the default (about 0.3 for each 1 % in r), so measurement error in r matters little. The large gap to real engines comes from heat loss, friction and finite combustion time, not from input uncertainty.
Where it is used
- Estimating the effect of compression ratio on petrol engine efficiency.
- A benchmark against which a measured engine efficiency is compared.
Maths you need
- Isentropic compression: T₂ = T₁ rγ−1
- Powers: r to a decimal exponent