Otto Cycle (Constant-Volume Spark Ignition)

Idealized thermodynamic cycle of spark-ignition piston engines with constant-volume heat addition at top dead center.

Specifications & Metrics

type: Internal Combustion Gas Cycle
processes: Isentropic compression (1→2), isochoric (constant-volume) combustion (2→3), isentropic expansion (3→4), isochoric heat rejection (4→1)
working fluid: Air–fuel vapor mixture (modeled as ideal gas with heat capacity ratio γ ≈ 1.3–1.4)
efficiency formula: η = 1 − 1 / r^(γ − 1), where r = V₁ / V₂ is the compression ratio
originator: Alphonse Beau de Rochas (patented 1861) & Nicolaus Otto (built 1876)
applications: Four-stroke and two-stroke spark-ignition gasoline and natural-gas piston engines

Patented theoretically by Alphonse Beau de Rochas in 1861 and first built as a working four-stroke engine by German engineer Nicolaus Otto in 1876, the Otto cycle adds heat at constant volume while the piston is momentarily at top dead center.
Ideal Otto cycle thermal efficiency η = 1 − r^(1−γ) depends strictly on the volumetric compression ratio r = V_max / V_min and the gas specific heat ratio γ.
In practical gasoline engines, the compression ratio is typically capped around 9:1 to 12:1 because higher compression temperatures cause premature autoignition ('engine knocking') ahead of the spark-ignited flame front.