62.24
%
953.3
K
2,097.3
K
904.7
K
5,795,596
Pa
5,795,596
Pa
1,464.76
J
553.07
J
911.69
J
891,209
Pa
62.24
%
953.3
K
2,097.3
K
904.7
K
5,795,596
Pa
5,795,596
Pa
1,464.76
J
553.07
J
911.69
J
891,209
Pa
The Diesel Cycle Calculator analyzes the idealized thermodynamic cycle that models compression-ignition (diesel) engines. Invented by Rudolf Diesel in the 1890s, diesel engines compress air to such high temperatures that injected fuel ignites spontaneously, eliminating the need for spark plugs. The Diesel cycle differs from the Otto cycle in that heat addition occurs at constant pressure rather than constant volume.
The thermal efficiency of the ideal Diesel cycle depends on three parameters — the compression ratio $$r$$, the cutoff ratio $$r_c$$, and the heat capacity ratio $$\gamma$$:
$$\eta_{\text{Diesel}} = 1 - \frac{1}{r^{\gamma-1}} \cdot \frac{r_c^{\gamma} - 1}{\gamma(r_c - 1)}$$
The cutoff ratio $$r_c = V_3/V_2$$ represents how much the gas expands during the constant-pressure combustion phase. A lower cutoff ratio (less fuel burned) gives higher efficiency. Diesel engines operate at higher compression ratios (14:1 to 25:1) than gasoline engines because they compress air only, avoiding the knock limitation.
This calculator traces all four state points of the cycle, computing temperatures, pressures, heat flows, net work, and thermal efficiency. The results help engineers understand why diesel engines are more efficient than gasoline engines for the same compression ratio, and how the amount of fuel injected (reflected in the cutoff ratio) affects performance.
Diesel cycle analysis is essential for automotive and marine engineers, power plant designers, and mechanical engineering students studying internal combustion engines and thermodynamic cycles.
The calculator traces four processes of the Diesel cycle:
Process 1→2 (Isentropic Compression): $$T_2 = T_1 r^{\gamma-1}, \quad P_2 = P_1 r^{\gamma}$$
Process 2→3 (Isobaric Heat Addition): $$T_3 = T_2 \cdot r_c, \quad Q_{\text{in}} = nC_p(T_3 - T_2)$$
Process 3→4 (Isentropic Expansion): $$T_4 = T_3\left(\frac{r_c}{r}\right)^{\gamma-1}$$
Process 4→1 (Isochoric Heat Rejection): $$Q_{\text{out}} = nC_v(T_4 - T_1)$$
Net Work: $$W_{\text{net}} = Q_{\text{in}} - Q_{\text{out}}$$
Efficiency: $$\eta = 1 - \frac{1}{r^{\gamma-1}} \cdot \frac{r_c^\gamma - 1}{\gamma(r_c - 1)}$$
The factor $$\frac{r_c^\gamma - 1}{\gamma(r_c - 1)}$$ is always greater than 1, which means for the same compression ratio, the Diesel cycle is less efficient than the Otto cycle. However, diesel engines use much higher compression ratios, making them more efficient overall.
The thermal efficiency increases with higher compression ratio and lower cutoff ratio. At the limit $$r_c \to 1$$ (no combustion), the Diesel efficiency formula reduces to the Otto formula. Real diesel engines achieve 35–45% brake thermal efficiency. The peak pressure $$P_2$$ occurs at the end of compression and is much higher in diesel engines than gasoline engines. The cutoff ratio reflects engine loading: higher load means more fuel injected, higher $$r_c$$, and slightly lower efficiency — this is why diesel engines are most efficient at partial load.
Inputs
Results
At 18:1 compression with cutoff ratio 2.5, the Diesel cycle achieves ~57.2% ideal efficiency. Peak compression pressure reaches ~5.8 MPa and peak temperature is ~2383 K.
Inputs
Results
Raising compression to 22:1 with lower cutoff ratio 2.0 pushes efficiency to ~64.0%. Peak pressure climbs to 8.1 MPa, requiring robust engine construction.
The Diesel cycle is the idealized thermodynamic cycle for compression-ignition engines. It consists of: isentropic compression, isobaric (constant-pressure) heat addition, isentropic expansion, and isochoric (constant-volume) heat rejection. The key difference from the Otto cycle is that combustion is modeled at constant pressure rather than constant volume.
The cutoff ratio $$r_c = V_3/V_2$$ is the ratio of the volume at the end of combustion to the volume at the beginning. It reflects how much fuel is burned — more fuel means more expansion at constant pressure, higher $$r_c$$, and lower efficiency. Typical values range from 1.5 to 3.0 depending on engine load.
Diesel engines use much higher compression ratios (14–25:1 vs. 8–14:1) because they compress air only, avoiding knock. The higher compression ratio more than compensates for the Diesel cycle's inherently lower efficiency at equal compression ratio. Additionally, diesel fuel has higher energy density, and diesels run lean, further improving efficiency.
Diesel engines compress pure air, not a fuel-air mixture. Since air alone cannot pre-ignite or knock, compression can be much higher. Fuel is injected at the top of the compression stroke into the hot compressed air, where it auto-ignites. Gasoline engines must limit compression to prevent premature ignition of the fuel-air mixture.
Higher load requires more fuel injection, increasing the cutoff ratio $$r_c$$. Since the efficiency factor $$\frac{r_c^\gamma - 1}{\gamma(r_c - 1)}$$ increases with $$r_c$$, efficiency decreases at higher loads. This means diesel engines are most efficient at partial load — one reason they excel in variable-load applications like trucks, ships, and generators.
The dual (or mixed) cycle combines constant-volume and constant-pressure heat addition, more accurately modeling real diesel combustion. Part of the fuel burns rapidly at nearly constant volume (like Otto), and the rest burns at roughly constant pressure (like Diesel). The dual cycle efficiency falls between the Otto and Diesel values for the same compression ratio and total heat input.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
How helpful was this calculator?
Be the first to rate!
Carnot Efficiency Calculator
Thermodynamic Processes
Heat Engine Efficiency Calculator
Thermodynamic Processes
Coefficient of Performance Calculator
Thermodynamic Processes
Entropy Calculator
Thermodynamic Processes
Enthalpy Calculator
Thermodynamic Processes
Gibbs Free Energy Calculator
Thermodynamic Processes
