What is the Diesel cycle?

The Diesel cycle is the ideal thermodynamic model for a compression-ignition (diesel) engine. It consists of two isentropic processes, one constant-pressure heat addition, and one constant-volume heat rejection. Fuel ignites from the heat of compression — no spark plug is needed.

What is the Diesel cycle efficiency formula?

Ideal Diesel cycle thermal efficiency is η = 1 − (1 / (γ · r^(γ−1))) · (r_c^γ − 1) / (r_c − 1), where r is the compression ratio, r_c is the cutoff ratio, and γ is the heat capacity ratio Cp/Cv.

What is the cutoff ratio?

The cutoff ratio r_c is the ratio of the cylinder volume at the end of constant-pressure heat addition to the volume at the start of that process. A value of 1 means instantaneous heat addition (degenerates to Otto cycle); higher values mean longer combustion at constant pressure, which reduces efficiency.

Why is Diesel cycle efficiency lower than Otto cycle efficiency at the same compression ratio?

For the same compression ratio, the Diesel cycle adds heat at constant pressure over a finite volume change (cutoff ratio > 1). This results in lower average temperature during heat addition compared to the Otto cycle (constant-volume), so a larger fraction of heat is rejected. As r_c → 1 the two efficiencies converge.

What compression ratios do diesel engines use?

Diesel engines typically operate between 14:1 and 23:1. Higher compression ratios raise ignition temperature and improve efficiency, but also increase mechanical stress and NOx emissions.

What value of γ should I use?

For air or diatomic gases at moderate temperatures, γ = 1.4 is standard. At higher temperatures γ drops toward 1.3 because vibrational degrees of freedom become active. Use 1.4 for air-standard analysis unless the problem specifies otherwise.

Diesel Cycle Efficiency Calculator

Name: Diesel Cycle Efficiency Calculator
Availability: InStock
Author: Nham Vu

Enter compression ratio, cutoff ratio, and heat capacity ratio to calculate the ideal Diesel cycle thermal efficiency and cycle performance metrics.

Cycle Parameters

Compression Ratio (r)

Typical diesel engines: 14 – 23

Cutoff Ratio (r_c)

Must be > 1 and < compression ratio

Heat Capacity Ratio γ (C_p/C_v)

Air (diatomic ideal gas): 1.4

Heat Input q_in (kJ/kg) (optional)

Used to compute net work output

Common Diesel Engine Ratios

Engine type	r	r_c
Light automotive diesel	14	2
Typical automotive diesel	18	2
Heavy-duty truck diesel	20	2.5
Large marine/industrial	22	3

Click a row to load its values.

Ideal Thermal Efficiency

—

Enter values and press Calculate

0%100%

Efficiency η

—

decimal

Net Work w_net

—

kJ/kg

Heat Rejected q_out

—

kJ/kg

Formula

η = 1 − (1 / (γ · r^(γ−1))) · (r_c^γ − 1) / (r_c − 1)

r = compression ratio

r_c = cutoff ratio

γ = heat capacity ratio C_p/C_v

w_net = η × q_in

Summary

Enter compression ratio, cutoff ratio, and heat capacity ratio to calculate the ideal Diesel cycle thermal efficiency and cycle performance metrics.

How it works

Enter the compression ratio (r) — the ratio of maximum to minimum cylinder volume; diesel engines typically use 14–23.
Enter the cutoff ratio (r_c) — the ratio of the volume at end of constant-pressure combustion to volume at start; must be less than the compression ratio.
Enter the heat capacity ratio γ (Cp/Cv); use 1.4 for standard air analysis.
The calculator applies η = 1 − (1/(γ·r^(γ−1))) · (r_c^γ − 1)/(r_c − 1) to compute ideal thermal efficiency.
Optionally enter heat input (kJ/kg) to see net work output and heat rejected.
Results update instantly when you press Calculate or hit Enter in any field.

Use cases

Estimate the theoretical efficiency ceiling of a diesel engine at a given compression and cutoff ratio.
Compare Diesel cycle efficiency with Otto cycle efficiency at the same compression ratio.
Solve thermodynamics homework problems on air-standard Diesel cycles.
Understand how increasing the cutoff ratio lowers efficiency at a fixed compression ratio.
Evaluate how compression ratio changes affect diesel engine performance.
Cross-check textbook Diesel cycle examples against known numerical results.
Study the effect of different γ values (mono-, di-, and polyatomic gases) on cycle efficiency.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu