The science

This is a compact, purpose-built educational model, not a certified vehicle dynamics solver. State is integrated with a fixed dt = 1/120 s and the simulation core is independent of Three.js.

• Longitudinal force: m·a = Fdrive − mg·sin(θ) − Fdrag − Frolling − Fbrake.
• Tyre grip: Fₓ,max = μN·√(1 − (Fᵧ/μN)²), a friction-circle approximation.
• Stopping distance: d = v²/(2 μ g cos θ) for a level-equivalent constant deceleration approximation. The graph displays the idealised analytic curve.
• Static tip threshold: θtip = atan(b / hCOM). The live model uses the smaller forward / lateral support margin after shifting the bucket payload centre of mass.
• Suspension: m·ẍ + c·ẋ + k·x = k·yroad. Four damped channels respond to a deterministic procedural gravel ripple.
• Motor: torque is approximated from T = 9550·P(kW)/rpm, shaped by a smooth RPM envelope and final-drive ratio.

Assumptions and simplifications: rigid chassis; no chassis articulation, wheel-by-wheel contact solver, differential, gear-shift lag, tire relaxation, hydraulic pressure dynamics, bucket-ground collision, or deformable soil. The point-load COM is a stability cue, not a certified overturning calculation. The grade slider applies a uniform slope to the whole yard. Water, rain and gravel are represented by friction coefficients rather than full fluid / granular physics.

Self-test: call window.__selfTest() in the browser console. It returns closed-form slope, tip-angle and spring-period checks.