Presets
Playback
Engine and load
A higher compression ratio raises efficiency; closing the throttle lowers the pressure and adds pumping loss.
Spark, burn and geometry
Spark timing shifts where the pressure peaks. Too late and the push on the piston is wasted.
Model checks
The science
The four strokes
Intake (0 to 180 degrees of crank angle), compression, power and exhaust. The cylinder volume follows the slider-crank geometry V(θ) = Vc [1 + ½(r - 1)(R + 1 - cosθ - √(R2 - sin2θ))] with R = l/a the rod length over the crank radius and r the compression ratio.
Pressure from the first law
With air-standard gas, dp/dθ = (γ - 1)/V · dQ/dθ - γ p/V · dV/dθ, integrated with RK4. Heat release follows a Wiebe function x = 1 - exp(-5 ((θ - θs)/Δθ)3). The ideal Otto efficiency is η = 1 - r1-γ; the simulated efficiency is lower because heat is released over a finite angle.
Work and power
The area of the loop is the work, IMEP = ∮ p dV / Vd. Brake power is (IMEP - FMEP) Vd N / 120 where the friction mean pressure FMEP uses an empirical rising function of speed.
Honest simplifications
- Constant gamma and no heat loss to the walls, so the efficiencies are higher than in a real engine; knock, flame speed physics, residual gas and valve timing details are not modelled.
- The exhaust blowdown is drawn as a step to the exhaust pressure.
- Friction is an empirical fit, not derived. Fuel energy is 2.8 MJ per kg of stoichiometric mixture with 95 % combustion efficiency.
What to try
- Raise the compression ratio from 8 to 14 and watch the efficiency curve follow the ideal Otto line below it.
- Load Late spark (retarded): the peak pressure moves after TDC and the loop shrinks.
- Close the throttle and see the negative pumping loop appear in the intake and exhaust strokes.
- In the last graph find the engine speed where torque peaks and power peaks.