A diesel engine compresses air before injecting fuel into the hot compressed charge. It uses compression ignition rather than a spark plug. The four-stroke illustration shows intake, compression, expansion and exhaust, while the calculator estimates only the air state at the end of a selected polytropic compression.
Diesel Motor Interactive Calculator
Follow a four-stroke compression-ignition engine while calculating the air temperature and pressure ratio at the end of a specified polytropic compression. The crank, rod and piston remain connected. Fuel injection is shown separately from air intake; no spark plug is used.
Equation Used
- Ideal-gas relation and constant polytropic exponent during compression.
- Compression ratio is maximum cylinder volume divided by clearance volume.
- Illustrative crank radius 70 and connecting rod 250 give stroke 140 in arbitrary drawing units.
- Valve timing follows nominal stroke boundaries without overlap; real timing can differ.
- Temperature-reference difference is a comparison only, not a pass/fail ignition prediction.
- No fuel energy, combustion duration, torque, power, emissions or thermal-efficiency model.
n is an assumed compression exponent. The comparison temperature is not a complete autoignition criterion. Fuel properties, injection, mixing, heat transfer and ignition delay are outside this model.
Four strokes and two crank revolutions
During intake the piston descends with the inlet valve open, drawing in air. During compression it rises with both valves closed. Fuel is then injected into the compressed air; the following expansion drives the piston downward. On the final upward stroke the exhaust valve opens to release the spent gases.
The piston pin travels along the cylinder axis. A fixed-length connecting rod joins it to a pin on the rotating crank. This geometric closure is solved at every frame. The flywheel turns with the crank, and the cycle takes two revolutions rather than one.
The poppet motion follows simplified stroke boundaries. The brief spray marks fuel injection; the colours distinguish stages without claiming calculated flame temperatures. Real injection schedules and valve events depend on the engine. The page does not attempt to reproduce one named engine’s hardware or timing.
A compression model within an engine illustration
The mechanism explains how reciprocating piston motion relates to the crankshaft and how the four strokes differ. The calculator lets you compare compression ratio, starting air temperature and an assumed compression exponent.
It does not size an engine, select fuel or predict a starting condition. A two-stroke diesel uses a different gas-exchange sequence; it should not be treated as the four-stroke layout shown here.
Polytropic compression of ideal-gas air
Define compression ratio r = V₁/V₂, where V₁ is maximum cylinder volume and V₂ is clearance volume. Assuming pVⁿ remains constant gives p₂/p₁ = rⁿ. Combining that with pV proportional to absolute temperature gives T₂/T₁ = rⁿ⁻¹.
Temperature must be in kelvin for this ratio. The calculator adds 273.15 to the starting Celsius value, applies the ratio, and subtracts 273.15 afterward. Minimum volume as a percentage of maximum is 100/r.
The exponent n is a model input. An isentropic ideal-gas example uses the ratio of specific heats; a chosen polytropic exponent can describe another assumed compression path. Neither approach by itself models a complete real diesel combustion cycle.
The reference comparison subtracts the selected temperature from the predicted compressed-air temperature. A positive difference is not proof of ignition: the model includes no injection quality, chemical delay or local mixture conditions.
Compare one input at a time
Increasing compression ratio reduces clearance volume relative to maximum volume and raises both calculated temperature and pressure ratio. Increasing starting air temperature raises final temperature without changing the pressure ratio for fixed r and n.
Changing only the comparison temperature changes only the reported temperature difference. It does not change the piston motion, compression pressure or calculated air temperature. This separates a chosen reference from the state calculation.
Keep the model’s scope clear
Temperature and pressure rise during compression are useful parts of engine reasoning, but they are not brake thermal efficiency, power or emissions. Those require additional processes and measured or modeled losses.
The drawing preserves rod length and a positive clearance space at top dead centre. It does not determine a permissible mechanical compression ratio, structural load or real valve-to-piston clearance. The component proportions are illustrative.
Diesel motor questions
Why is there no spark plug?
The illustrated principle is compression ignition: fuel is introduced into hot compressed air.
Does the intake bring in fuel as well as air?
The sequence shown admits air, with fuel injection shown separately near the start of expansion.
Why does one complete cycle take 720°?
Four piston strokes require two crankshaft revolutions in this four-stroke arrangement.
Is the comparison temperature an ignition guarantee?
No. It is a reference value for comparing the compression result. Ignition also depends on processes that this calculator does not simulate.
Does the animation calculate temperature during combustion?
No. Live gas-state calculations are shown during compression only. Stage colours outside compression are illustrative.
References
U.S. Department of Energy, Internal Combustion Engine Basics: diesel air compression, fuel injection and four-stroke sequence. NASA Glenn, Isentropic Compression or Expansion: ideal-gas pressure, volume and absolute-temperature relations. The adjustable polytropic exponent is an explicitly stated extension of the compression assumption, not a measured engine calibration.
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