The combustion (thermodynamic) cycles used in internal combustion engines are the Otto, Diesel and Sabathe (dual/limited-pressure) cycles, which are idealised air-standard cycles.

1. Otto cycle (constant-volume combustion): The air is compressed adiabatically to a small volume, heat is added at constant volume (approximating a very fast burn), then the gas expands adiabatically, and heat is rejected at constant volume. It is the theoretical basis of spark-ignition engines. Since heat is added at constant volume, the peak pressure can be high. Application: petrol/gasoline engines and natural-gas SI engines; also the basis for gas engines used in marine applications (e.g. LNG-fuelled Otto cycle engines). Advantages: simple, high efficiency at moderate compression ratio, combustion fairly clean. Disadvantages: the compression ratio is limited by knocking (auto-ignition), so the thermal efficiency is limited; and a spark plug/ignition system is needed.

1. Diesel cycle (constant-pressure heat addition): Compression is adiabatic, heat is added at constant pressure (as in an idealised slow-burn diesel where the fuel burns progressively as the piston moves down), then adiabatic expansion. Application: diesel engines (compression-ignition) - all marine diesel engines when burning liquid fuel. Advantages: high compression ratio possible (no knocking limit as fuel is self-ignited), higher thermal efficiency, ability to burn heavier fuels, robust. Disadvantages: the constant-pressure idealisation is an approximation; the real engine burns a mixture, and pressure can rise.

1. Sabathe (dual / limited-pressure) cycle: heat is added partly at constant volume and partly at constant pressure - representing the real combustion which begins nearly at constant volume (as the burned portion at TDC) then continues at roughly constant pressure during the expansion. Application: the diesel engine in real operation approximates the dual cycle; it most closely models modern marine diesel engines. Advantages: more accurate representation, a compromise allowing a combination of high pressure rise and controlled pressure. Disadvantages: more complex to analyse; optimising between the constant volume (efficiency) and constant pressure phases is a balance.

Efficiency explanation: all air-standard cycles have efficiency η = 1 - 1/(r^(γ-1)) for Otto, and for the Diesel and Dual cycles the efficiency depends on the compression ratio and on the cut-off/ratio, with Otto being the most efficient at a given compression ratio, then dual, then diesel. The marine diesel is a compression-ignition engine best represented by the dual cycle, and the relevant design changes (e.g. increasing compression ratio) improve efficiency.

Each cycle's application: Ships use the Diesel/dual cycle in all marine main and auxiliary diesel engines (compression ignition) because of the high compression ratio, high efficiency, reliability and the ability to burn cheap fuels. The Otto cycle is used in gas engines (e.g. LNG-fuelled engines, gas-electric propulsion, and some dual-fuel low-speed engines running in gas mode) where the gaseous fuel forms a lean homogeneous charge ignited by a small pilot diesel or spark. Advantages of the Otto for gas: low NOx due to lean premixed combustion, no fuel pump/injector coking, clean exhaust. Disadvantages: risk of knocking and methane slip, need for gas handling and charge mixing.

The dual-fuel engine can run on diesel cycle when burning fuel oil and on Otto cycle when burning gas, combining the benefits.