| Compression ratio r | Heat capacity ratio γ | Ideal efficiency η (%) | Notes |
|---|---|---|---|
| 8 | 1.40 | 56.47 | Conservative gasoline-like case |
| 10 | 1.40 | 60.19 | Higher r increases ideal efficiency |
| 12 | 1.35 | 58.85 | Lower γ reduces the improvement |
| 14 | 1.38 | 62.08 | Illustrative high-r scenario |
The ideal air‑standard Otto cycle thermal efficiency depends on the compression ratio and the heat capacity ratio:
- η is thermal efficiency (dimensionless).
- r is compression ratio, r = V1/V2.
- γ is heat capacity ratio, γ = Cp/Cv.
- Enter the compression ratio r for your case.
- Either enter γ directly, or switch to Cp/Cv mode.
- Optionally enable step-by-step output or sensitivity.
- Press Calculate Efficiency to view results above.
- Use Download CSV or Download PDF for reports.
1) What the efficiency number represents
The value reported here is the ideal thermal efficiency of the air-standard Otto cycle. It compares net work output to heat added during combustion under reversible compression and expansion with constant specific heats. It supports quick screening.
2) Compression ratio drives the trend
For a fixed heat capacity ratio, efficiency increases as the compression ratio rises because the cycle extracts more work during expansion. Typical spark-ignition engines operate around r = 8 to 12, while high-compression variants can exceed 12 with careful knock control.
3) Why γ matters and how to choose it
The parameter γ = Cp/Cv reflects how a working gas stores energy as temperature changes. Dry air near room temperature is often approximated with γ ≈ 1.4. Using the Cp/Cv option lets you compute γ from your chosen property data, keeping units consistent and γ greater than 1.
4) Example comparison using realistic inputs
With γ = 1.40, increasing r from 8 to 10 raises ideal efficiency from about 56.47% to 60.19%. If γ drops to 1.35 at higher temperatures, the same r = 12 case can produce a smaller gain than expected, which is why the calculator highlights both r and γ.
5) Interpreting the sensitivity table
The optional ±5% sensitivity check quantifies how much η changes when r or γ shifts slightly. It is useful when r has tolerance, or when γ is estimated from temperature-dependent property tables. If the r rows move more than the γ rows, compression dominates your uncertainty.
6) Real engines always underperform the ideal cycle
Friction, finite combustion duration, heat transfer to cylinder walls, pumping losses, and non-constant specific heats reduce real efficiency below the air-standard value. Spark timing, mixture strength, and exhaust residuals also alter effective γ. Modern spark-ignition engines often deliver roughly 20–35% brake thermal efficiency, depending on load and technology.
7) Design insights for spark-ignition systems
Raising r improves the ideal cycle, but knock limits set practical boundaries. Higher-octane fuel, cooled EGR, direct injection, and better charge cooling can permit higher r without detonation.
8) Using exports for documentation and reporting
After you calculate, export results to CSV for spreadsheets or to PDF for lab notes and design reviews. Keeping r, γ, and η together supports traceability when comparing variants. For multi-scenario work, record fuel grade, intake conditions, and the property source used to justify γ.
1) Is this the same as real engine efficiency?
No. This is the air-standard Otto thermal efficiency, a theoretical upper bound. Real brake thermal efficiency is lower due to heat loss, friction, pumping work, non-ideal combustion, and temperature-dependent properties.
2) What compression ratio values are typical?
Many gasoline engines fall between r = 8 and 12. High-efficiency designs may go higher when knock is controlled. Always use the actual geometric compression ratio for a fair comparison.
3) What γ should I use for air?
A common approximation is γ ≈ 1.4 near room temperature. At higher temperatures, γ can decrease. If you have Cp and Cv data, use the calculator’s Cp/Cv mode to compute γ directly.
4) Why must γ be greater than 1?
For gases, Cp is greater than Cv, so γ = Cp/Cv exceeds 1. Values at or below 1 would be nonphysical for this model and lead to invalid efficiency results.
5) Why does higher r increase ideal efficiency?
Higher r raises the temperature after compression and increases the expansion work fraction for the same heat addition. In the Otto model, this shifts more of the added heat into useful work during expansion.
6) How accurate is the sensitivity option?
It is a quick, local check. It recalculates efficiency after changing r or γ by ±5%. It does not model correlated changes, combustion effects, or real losses, but it is helpful for comparing assumptions.
7) Can I use Cp and Cv in any units?
Yes, as long as Cp and Cv share the same units because only their ratio is used. Common choices are kJ/kg·K or J/mol·K. Ensure Cp > Cv to keep γ valid.