ICE calculation
Engine Templates:
What this engine simulator actually calculates
Most engine calculators on the web are formula sheets. You type in bore, stroke and compression ratio, and they return displacement and an ideal-cycle efficiency that no real engine has ever achieved. This one works differently: it integrates the real cycle one crank degree at a time, solving the mass and energy balance for the gas inside the cylinder at every step.
That means the valve timing you enter changes the answer. So does the port diameter, the valve lift, the ignition advance and the burn duration. If a change would matter on a real engine, it moves the numbers here — and if it would not, it does not.
The cycle it walks through
The simulation starts at exhaust valve opening and steps through a full cycle in one-degree increments, switching models as the engine passes through each phase:
- Blowdown and exhaust — the cylinder is above manifold pressure and gas flows out through the exhaust valve or port.
- Valve overlap — both valves are open. Gas can move in either direction depending on the pressure difference, and the model tracks fresh charge escaping into the exhaust as well as burnt gas pushed back into the intake.
- Intake — the descending piston draws in fresh charge through the intake valve, limited by the flow area that valve actually offers at each degree of lift.
- Compression — both valves closed, gas compressed with heat loss to the cylinder walls.
- Combustion — heat release follows a Wiebe function across the burn duration you specify, starting at your ignition angle.
- Expansion — the burnt gas pushes the piston down until the exhaust valve opens again and the cycle closes.
Why it runs the cycle more than once
To start the cycle the model has to assume a pressure and temperature at exhaust valve opening — but those are what the cycle is supposed to produce. So it runs the whole cycle, compares the state it ends with against the state it assumed, adjusts, and runs again. It repeats until the two agree to within 500 Pa and 10 K.
This is not a technicality. What converges is the residual gas left in the cylinder at the end of exhaust, and residual fraction drives everything downstream: it dilutes the fresh charge, raises the temperature at the start of compression, and changes how much air the engine can actually swallow. A calculator that skips this step cannot tell you what a valve timing change does, because the effect of valve timing is mostly an effect on residuals.
The models inside
- Combustion — a Wiebe function, the standard empirical description of how fuel burns over crank angle. You control when it starts (ignition angle) and how long it lasts (burn duration); the shape in between comes from the function.
- Heat transfer — a Woschni-type correlation, where the gas velocity that drives wall heat loss scales with mean piston speed and rises during combustion.
- Gas exchange — flow through each valve is computed from its effective flow area at the current lift, and through each port from the area the piston has uncovered. This is why valve diameter, stem diameter, seat angle, seat width and the number of valves per cylinder are all separate inputs rather than one lumped coefficient.
What you need to enter
Atmosphere
Intake pressure and temperature, and cylinder wall temperature. Intake pressure is where boost goes: enter the absolute pressure in the intake manifold, not the gauge reading. Wall temperature sets how much heat the charge loses, and a plausible value for a warmed-up engine is around 400 to 450 K.
Engine geometry
Bore, stroke, connecting rod length and compression ratio, plus whether the engine is two-stroke or four-stroke. Rod length is not decoration: it sets how fast the piston moves away from top dead centre, which changes how much of the burn happens near peak volume. Two engines with the same bore, stroke and compression ratio but different rods do not make the same power.
Valve timing and port geometry
Opening and closing angles for both valves, the opening ramp, dwell and closing ramp that make up the lift profile, then the physical valve data: head diameter, stem diameter, maximum lift, seat face width, seat angle and how many valves of each type the cylinder has. For a two-stroke with port scavenging you enter port heights, widths and entry angles instead.
All angles are absolute crank angles on the model's own 0 to 720 degree frame, not the degrees-before-top-dead-centre convention printed on a cam card. An intake opening 20 degrees before top dead centre is entered as 700, not as 20. This trips people up constantly, and the engine presets in the dropdown are the quickest way to see what a correct set looks like.
Operation
Fuel type, air-fuel ratio, excess air coefficient, ignition angle, burn duration and engine speed. Excess air near 1.0 means a stoichiometric mixture; a diesel runs lean, typically 1.4 to 1.8. Burn duration is the one most people guess at — 40 to 60 crank degrees covers most spark-ignition engines at moderate speed.
Dynamic
Piston and rod masses, crankpin and main journal dimensions, web geometry and material density. These do not affect the thermodynamics at all — they feed the second calculation, which turns the cylinder pressure trace into the forces and torque acting on the crank train.
Reading the results
| Symbol | What it is |
|---|---|
| pc, Tc | Pressure and temperature at the end of compression, taken at the ignition point. A low pc against the compression ratio you entered usually means the intake valve is closing too late for this engine speed. |
| pz, Tz | Peak pressure and temperature reached during combustion — the numbers that decide whether the engine detonates and what the bearings have to survive. |
| pe, TE | Pressure and temperature in the cylinder at the end of the cycle, where the iteration converged. |
| ps, Ts | Intake conditions the gas exchange model settled on. |
| Li | Indicated work for one cycle — the area enclosed by the P-V loop, in joules. |
| imep | Indicated mean effective pressure: indicated work divided by swept volume. The single best number for comparing engines of different sizes, because it strips displacement out. |
| bmep | Brake mean effective pressure — the same quantity after mechanical losses, so what actually reaches the crankshaft. |
| Ne, Me | Effective power and torque at the engine speed you entered. One point on the curve, not the curve: to get a curve, run the calculation at several speeds. |
| mf | Fuel mass burnt per cycle, in kilograms. |
| ηe | Effective efficiency — the fraction of the fuel's heating value that leaves as useful work. Around 0.25 to 0.35 for a petrol engine, 0.35 to 0.45 for a diesel. |
| ge | Specific fuel consumption, derived from the efficiency above. |
The charts
Pressure, temperature, mass and volume are plotted against crank angle, and the valve timing chart shows the effective flow area of each valve through the cycle. The mass trace is the one worth studying: it shows exactly where charge enters the cylinder, where it leaves during overlap, and how much never makes it in. Export CSV gives you every step of every trace if you would rather work in a spreadsheet.
Two-stroke and four-stroke
Switching to two-stroke changes the cycle the model runs and the geometry it asks for. Three scavenging arrangements are supported: loop scavenging through transfer ports, uniflow through inlet ports with an exhaust port, and uniflow through inlet ports with exhaust valves in the head. The last of these is what large marine two-strokes use, and it is the only two-stroke configuration where the valve inputs still matter.
Is my result believable?
Before trusting a number, check it against what engines of that type actually do. Naturally aspirated petrol engines land around 9 to 11 bar bmep; a turbocharged one can reach 15 to 25. A naturally aspirated diesel sits near 7 to 9 bar, a modern turbodiesel 18 to 24. If your result is far outside the range for the engine you are modelling, the inputs are wrong somewhere, and valve timing entered in the wrong convention is the most common cause.
The fastest way to build confidence is to load a preset for an engine whose published output you already know, confirm the model lands near it, and only then change one thing at a time. The presets carry real geometry and timing for a range of engines, from small motorcycle singles to large marine diesels.
What the model does not do
Every simulation is a set of choices about what to leave out, and being clear about them is more useful than pretending they are not there.
- Pressure waves in the intake and exhaust pipes are not modelled here. Manifold pressures are treated as steady. On a four-stroke at high speed, tuned-length effects are real and this model will not show them; for a two-stroke exhaust, use the dedicated expansion chamber calculator.
- Mechanical efficiency is applied as a fixed factor rather than computed from friction, so brake figures carry that assumption rather than a friction model.
- There is no knock model, no emissions model, and no in-cylinder turbulence or flame propagation. Combustion follows the Wiebe curve you specify; the model will not tell you that the mixture would actually have detonated.
- Gas exchange is quasi-steady: flow at each step is computed from the pressure difference and the open area at that instant, with no gas inertia.
Within those limits the model is a good tool for comparing designs: it will tell you reliably whether closing the intake valve later helps at 6000 rpm, or what a longer rod does to peak pressure. Treat the absolute numbers as close, and the differences between two runs as meaningful.