KEVOS® MAKEOS · Engineering
Air-Standard Otto and Diesel Cycle Check (Efficiency, Net Work, Mean Effective Pressure, Peak Pressure)
What thermal efficiency, net work, mean effective pressure and peak cylinder pressure does the ideal Otto or Diesel cycle give for this compression ratio, and is the peak pressure within the limit?
Cold-air-standard analysis of the ideal Otto (constant-volume heat addition) or Diesel (constant-pressure heat addition) cycle: the pressure and temperature at each corner of the cycle, the heat added and rejected, the net work, the thermal efficiency, the mean effective pressure and the Carnot efficiency between the cycle’s lowest and highest temperatures, with the peak pressure checked against a limit you enter.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Ideal cycle | choice | Otto for spark-ignition engines, Diesel for compression-ignition engines. |
| Compression ratio (V₁ ÷ V₂) | :1 | Engine compression ratio from the maker’s data sheet (swept plus clearance volume ÷ clearance volume). |
| Heat added per kilogram of air (Otto) | kJ/kg | Heat released per kilogram of air in the cylinder (Otto only): roughly the fuel’s heating value ÷ the air–fuel ratio for a full charge. |
| Cutoff ratio (V₃ ÷ V₂, Diesel) | :1 | Cutoff ratio (Diesel only): the cylinder volume when fuel injection ends ÷ the volume at top dead centre. |
| State at the start of compression | ||
| Pressure at the start of compression (absolute) | kPa | Absolute pressure in the cylinder at the start of compression: about atmospheric for a naturally aspirated engine, boost pressure for a turbocharged one. |
| Temperature at the start of compression | °C | Air temperature at the start of compression: intake temperature, or after the intercooler for a turbocharged engine. |
| Specific heat ratio of the working gas (cp ÷ cv) | Ratio of specific heats of the working gas: 1.4 for air at room temperature; lower values allow for heating of the gas. | |
| Gas constant of the working gas | kJ/kg·K | Specific gas constant of the working gas: 0.287 kJ/kg·K for air. |
| Limit | ||
| Allowable peak cylinder pressure (absolute) | kPa | Allowable peak cylinder pressure from the engine maker or your design limit. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Ideal cycle
- What it is
- Which ideal cycle models the engine: Otto adds all the heat at constant volume at top dead centre (spark ignition); Diesel adds it at constant pressure while the piston moves down (compression ignition).
- Units and format
- Choose one of 2 options from the list: Otto (spark ignition, heat added at constant volume); Diesel (compression ignition, heat added at constant pressure).
- Example
- The form opens with “Otto (spark ignition, heat added at constant volume)” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Switches between the constant-volume and constant-pressure heat-addition formulas.
- Get it right
- Otto uses the heat-added input and ignores the cutoff ratio; Diesel uses the cutoff ratio and ignores the heat added.
What this means: Compression ratio (V₁ ÷ V₂)
- What it is
- The cylinder volume with the piston at bottom dead centre divided by the volume at top dead centre (the clearance volume), which sets how hard the air is squeezed before heat is added.
- Units and format
- Enter a number in :1: a ratio to one (type 3 for 3:1). The form accepts 1.5 :1 to 30 :1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 :1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher ratio raises the efficiency, the compression temperature and the peak pressure.
- Get it right
- Use the geometric ratio from the engine data sheet, not a pressure ratio.
What this means: Heat added per kilogram of air (Otto)
- What it is
- The heat released into each kilogram of air in the cylinder during combustion in the Otto model, standing in for the fuel energy burnt per charge.
- Units and format
- Enter a number in kJ/kg: kJ/kg. The form accepts 1 kJ/kg to 5000 kJ/kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1600 kJ/kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- In the Otto cycle more heat raises the peak temperature, peak pressure, net work and MEP but not the efficiency.
- Get it right
- Roughly the fuel’s heating value divided by the air–fuel ratio; it is per kilogram of air, not per kilogram of fuel.
What this means: Cutoff ratio (V₃ ÷ V₂, Diesel)
- What it is
- In the Diesel model, the cylinder volume when heat addition ends divided by the volume at top dead centre; it measures how long fuel keeps burning as the piston descends.
- Units and format
- Enter a number in :1: a ratio to one (type 3 for 3:1). The form accepts 1.01 :1 to 10 :1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 :1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- In the Diesel cycle a larger cutoff ratio adds more heat and work but lowers the efficiency.
- Get it right
- It must be below the compression ratio; typical ideal-cycle values are about 1.5 to 3.
State at the start of compression
What this means: Pressure at the start of compression (absolute)
- What it is
- The absolute pressure of the air trapped in the cylinder when compression begins, the starting point of the cycle.
- Units and format
- Enter a number in kPa: kilopascals. The form accepts 10 kPa to 1000 kPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 kPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Every pressure in the cycle scales with it, as do the MEP and the peak pressure; efficiency does not change.
- Get it right
- Absolute, not gauge: about 100 kPa for a naturally aspirated engine; add the boost for a turbocharged one.
What this means: Temperature at the start of compression
- What it is
- The temperature of the air in the cylinder when compression begins, from which every later temperature in the cycle follows.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -50 °C to 300 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A hotter start raises every cycle temperature but leaves the ideal Otto and Diesel efficiencies unchanged.
- Get it right
- Use the intake air temperature, or the temperature after the intercooler on a turbocharged engine.
What this means: Specific heat ratio of the working gas (cp ÷ cv)
- What it is
- The ratio of the specific heat at constant pressure to that at constant volume for the gas in the cylinder, which sets how temperature and pressure rise in isentropic compression.
- Units and format
- Enter a plain number with no unit. The form accepts 1.05 to 1.67. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.4 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher ratio raises the efficiency and the compression temperature and pressure.
- Get it right
- Use 1.4 for cold air; values nearer 1.3 represent hot combustion gases and give more realistic, lower results.
What this means: Gas constant of the working gas
- What it is
- The specific gas constant of the working gas, the universal gas constant divided by its molar mass, which links pressure, volume and temperature.
- Units and format
- Enter a number in kJ/kg·K: kilojoules per kilogram per kelvin. The form accepts 0.05 kJ/kg·K to 5 kJ/kg·K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.287 kJ/kg·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- In the Otto cycle it sets cv, so it moves the peak temperature, peak pressure and MEP; in the Diesel cycle it scales the heat and work per kilogram.
- Get it right
- Air is 0.287 kJ/kg·K; do not enter the universal constant 8.314.
Limit
What this means: Allowable peak cylinder pressure (absolute)
- What it is
- The highest absolute pressure the cylinder, head gasket and bearings are allowed to see, against which the ideal peak pressure of the cycle is checked.
- Units and format
- Enter a number in kPa: kilopascals. The form accepts 100 kPa to 100000 kPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12000 kPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line of the peak-pressure check.
- Get it right
- Take it from the engine maker; ideal-cycle peaks are high, so the check is a screen, not a strength calculation.
Method and formulas
- Isentropic compression: T₂ = T₁ r^(k−1) and P₂ = P₁ r^k, with temperatures in kelvin and cv = R ÷ (k − 1), cp = k cv.
- Otto: heat added at constant volume, T₃ = T₂ + q_in ÷ cv and P₃ = P₂ T₃ ÷ T₂; expansion T₄ = T₃ ÷ r^(k−1). Diesel: heat added at constant pressure, T₃ = r_c T₂, P₃ = P₂, q_in = cp (T₃ − T₂); expansion T₄ = T₃ (r_c ÷ r)^(k−1).
- Heat rejected at constant volume q_out = cv (T₄ − T₁); net work w = q_in − q_out; efficiency η = w ÷ q_in, which equals 1 − 1 ÷ r^(k−1) (Otto) or 1 − (r_c^k − 1) ÷ [k (r_c − 1) r^(k−1)] (Diesel).
- Mean effective pressure MEP = w ÷ (v₁ − v₂) with v₁ = R T₁ ÷ P₁ and v₂ = v₁ ÷ r.
- Example: an Otto cycle with r = 10, 1,600 kJ/kg added, starting at 100 kPa and 30 °C, gives 60.19 % efficiency, 963 kJ/kg of net work, an MEP of 1,230 kPa and a peak of 9,868 kPa, inside a 12,000 kPa limit.
Limitations
- Ideal cycles: no friction, heat loss to the walls, finite combustion time, valve timing, pumping work, residual gas or fuel mass. Real engines reach well under these efficiencies.
- Constant specific heats at the value of k you enter; at combustion temperatures specific heats rise and the gas dissociates, so the ideal peak temperature and pressure are overstated.
- This is a screening model of the thermodynamic cycle, not an engine design or a check of cylinder, head or bearing strength; qualified review governs real engine work.
- Example values are illustrations. Replace them with values for your actual engine.
Typical uses
- See how compression ratio, cutoff ratio and heat input change the ideal efficiency and peak pressure of an engine
- Set an upper bound on the efficiency a reciprocating engine can reach before comparing it with test data
- Explain why diesel engines need higher compression ratios and stronger cylinders than spark-ignition engines
Who it is for
- Mechanical engineers
- Engine and generator-set technicians
- Engineering students and trainers
What you get
- Temperatures and pressures at the four states of the cycle
- Heat added, heat rejected and net work per kilogram of air
- Thermal efficiency and the Carnot efficiency between T₁ and T₃
- Mean effective pressure
- Peak pressure against the limit
Interpreting the result
- Efficiency climbs steeply at low compression ratios and flattens above about 8 to 10, while peak pressure keeps rising, which is why gains from very high ratios are small.
- For the same compression ratio the Otto cycle is more efficient than the Diesel; diesels win in practice because they can run much higher compression ratios without knock.
Before relying on the result
- Compare the ideal efficiency with the engine’s measured brake thermal efficiency from fuel use and output.
- Check the allowable peak cylinder pressure with the engine maker before changing compression ratio, boost or timing.
References
- Çengel Y. A. and Boles M. A., Thermodynamics: An Engineering Approach, 5th edition (McGraw-Hill, 2006), chapter 9 (sections 9-3 to 9-6: air-standard assumptions, Otto and Diesel cycles, mean effective pressure). Method reference; no tables, figures or examples are reproduced.
- Heywood J. B., Internal Combustion Engine Fundamentals (McGraw-Hill): ideal cycle analysis and the difference between ideal and real engine cycles.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Method explained here · KEVOS® original book
The Otto cycle and the gas engine
In On-Site Power and Heat by the Numbers
What it covers: The air-standard Otto cycle step by step: compression ratio, efficiency, net work, mean effective and peak pressure, why the ideal overstates a gas engine, and how knock and lean burn set limits.
Worked example · Library collection
Engines after steam: internal combustion, diesel, gas turbines and matching technology to the duty
In How Engineering Shaped Industry: Power, Networks and the Modern Era
What it covers: Petrol, diesel and gas turbine engines each won where their strengths matched the work. How they developed, why efficiency depends on compression and temperature, and how to choose power.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.