Otto Efficiency⚠ unverified
Physics / Thermodynamics · Compute the thermal efficiency of an ideal Otto cycle
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| r | r | — | 1.0 | Compression ratio (dimensionless) |
| gamma | γ | — | 1.4 | Ratio of specific heats (dimensionless). Default is 1.4 |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | η | — | Otto-cycle efficiency (dimensionless) |
The science & history
Understanding the Parameters
- $r$ — higher compression raises ideal Otto efficiency (knock limits real SI engines).
- $\gamma$ — larger $\gamma$ increases $\eta$ at fixed $r$.
- $\eta$ — air-standard ceiling; real indicated efficiency is lower (friction, timing, heat loss).
Derivation (Approaching a Proof)
Isentropic relations: $T_2/T_1 = r^{\gamma-1} = T_3/T_4$. With $q_{\mathrm{in}} = c_v(T_3-T_2)$ and $q_{\mathrm{out}} = c_v(T_4-T_1)$,
$$\eta = 1 - \frac{T_4-T_1}{T_3-T_2} = 1 - \frac{T_1}{T_2} = 1 - r^{1-\gamma}.$$
History
Nikolaus Otto’s four-stroke engine and the ideal Otto cycle model are foundational ICE thermodynamics (see also Diesel and dual cycles for CI engines).
Related Concepts: Brayton Efficiency, Carnot Efficiency, Thermal Efficiency, Rankine Efficiency
Notes: Registry calculator otto-efficiency (unverified). Ideal air-standard only.