Ignition / Lab

4.0 L · cross-plane

Firing sequence · select a cylinder

Assembly

0180360540720°
IntakeCompressionPowerExhaust

Inside the simulation

From fuel to work.

One cycle. Four connected ideas. The motion, pressure trace, and sound all start with the same engine geometry.

01

Geometry gives us volume

The crank and connecting rod determine each piston’s position. That position sets the volume of its cylinder.

V(θ)=Vc+A[r(1−cosθ)+l−l2−r2sin2θ]

A piston area · r crank radius · l rod length · Vc clearance volume

86 mm bore & stroke143 mm connecting rod4.00 L eight cylinders
02

Burning fuel raises pressure

A smooth burn curve releases fuel energy. Piston work and heat lost to the walls reduce the gas’s internal energy.

dUdθ=dQburndθ−pdVdθ−dQwalldθp=(γ−1)UV

Integrated with fourth-order Runge-Kutta at 0.5° crank steps.

03

The loop encloses work

Expansion adds work; compression and pumping subtract it. The signed area of the complete pressure-volume loop is the work of one cylinder over 720°.

W=∮pdV≈∑pi+pi+12(Vi+1−Vi)Pind=8W×RPM120

Indicated power is gas work before mechanical losses.

04

Exhaust events become sound

Each exhaust opening excites a damped resonator in its cylinder bank. Modeled blowdown pressure controls the pulse strength.

fevents=8×RPM120

Sound follows engine RPM. Study speed slows only the visible motion.

Assumptions & constants +

This is a steady-cycle educational model. Changing a control solves a new cycle. RPM is prescribed; the simulation does not solve crank acceleration, mechanical loading, friction, knock, fluid flow, or chemical kinetics. The 3D assembly is illustrative, not manufacturing CAD.

Gas & mixture
Ideal gas, γ = 1.35, air/fuel = 14.7
Fuel heat
44 MJ/kg × 0.93 efficiency
Temperatures
Inlet 310 K · wall 450 K
Wall heat transfer
130 W/(m² K), assumed constant
Intake / exhaust
(0.30 + 0.70 × throttle) bar / 1.06 bar
Valve timing
Ideal boundaries at dead centers; no overlap
Burn fraction
xb = (1 − exp(−6.9u³)) / (1 − exp(−6.9)), u ∈ [0,1]
Burn duration
55° + RPM × 0.002°
Firing order
1 · 8 · 4 · 3 · 6 · 5 · 7 · 2, one event every 90°
Acoustics
Pulse resonators; no exhaust-pipe fluid solver or recording

Background: NASA cycle thermodynamics · Work done by a gas