Spark Timing & Pressure–Crank Angle Curve

Ignition & Combustion

Spark advance (° BTDC) 20°

Combustion duration 50°

Compression ratio 10.0:1

Engine speed 2000 RPM

Timing Status

Optimal

Live pressure

1.0 bar

Peak pressure

— bar

Peak location

— ° ATDC

Crank angle

−180°

How it works

The piston position is not a plain sine wave of crank angle θ — the connecting rod's finite length bends it. With crank radius r and rod length L, the slider-crank equation gives piston displacement from TDC:

s(θ) = (r+L) − [ r·cosθ + √(L² − r²sin²θ) ]
V(θ) = V_c + A·s(θ)

Cylinder pressure follows from the first law of thermodynamics for a polytropic process (exponent n ≈ 1.3) with heat released by a spreading flame front. Fraction of charge burned is modelled with the Wiebe function, the standard empirical combustion model used in engine simulation:

x_b(θ) = 1 − exp[ −a·((θ−θ₀)/Δθ)^(m+1) ]   (a=5, m=2)
dP/dθ = −n·(P/V)·(dV/dθ) + (n−1)·(Q_in/V)·(dx_b/dθ)

θ₀ is the spark timing (negative = before TDC), Δθ is the combustion-duration slider. Both curves — piston kinematics and the pressure ODE — are integrated numerically (RK4) every time you move a slider, then re-plotted live as the crank rotates.

Spark advance — fire too late and peak pressure lands deep in the expansion stroke, losing leverage on the crank; fire too early and peak pressure lands before TDC, fighting the piston's own compression.
Combustion duration — a slower-burning charge (more crank degrees to complete) needs more advance to centre its peak the same way.
Compression ratio — raises the theoretical Otto-cycle efficiency ceiling, but also raises pre-spark pressure and temperature, shrinking the advance margin before end-gas auto-ignites (knock).
Timing status — a simplified heuristic combining peak-pressure crank angle and CR×advance, mirroring why real engine control units retard timing when a knock sensor detects detonation.

This model covers only the compression + power strokes (360° of crank rotation); the intake and exhaust strokes are shown at roughly atmospheric pressure, as a real indicator diagram's induction/exhaust loop is.

Compression

Flame front Piston / rod / crank

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Spark Timing and the Pressure–Crank Angle Curve