Car Restoration Workshop — 2D Torque, Rust, Cleaning and Dyno Charts

The 2D companion of the 3D garage: the same equations, drawn as sections, curves and force balances the 3D view cannot show.

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Educational model with illustrative constants. A generic car, no brand. Not a repair or safety manual: follow the manufacturer's torque specifications for real work.

Scenarios

Controls: bolt

Joint (as in the 3D rebuild)

Applied torque

Oiled threads (K 0.15 instead of 0.20)

Controls: stuck fastener

Original tightening torque

Rust level r

Tool

Penetrating oil soak (rust x 0.45)

Controls: cleaning

Method

Initial grease G₀

Initial rust R₀

Cleaning time t

Controls: rolling road

Engine rebuild quality

Playback speed

Live readouts

Experiment: measured vs predicted

Runs the numerical models against closed-form hand calculations.

How to read the charts

Bolt preload: the top is a slice through two clamped plates; green arrows are the clamp force F. The curve shows F against torque for dry and oiled threads, with the proof load as a red line. Rust: the left chart is the torque needed to break a seized fastener free, the right shows the tool ramp and its overshoot; if the peak crosses the shear line the fastener snaps. Cleaning: grease and rust fall exponentially; the half-life is where a curve is half its start. Dyno: engine force in each gear against the resistance curve; where they cross is top speed, the gap is acceleration.

The science

Bolt torque and preload. A tightened bolt is a spring: torque T becomes clamp load F by T = K d F, with d the nominal diameter and K the nut factor (about 0.20 dry steel, about 0.15 oiled; typical values). Only about 10% of T becomes stretch, the rest fights thread and face friction, so oil raises preload by about 33% at the same torque. Past the proof load A_s S_p (for example 84.3 mm² × 830 MPa for an M12 class 10.9 bolt) the bolt stretches permanently.

Rust and breakaway. Oxide welds threads together. The model uses an illustrative law T_break = T_tight(1 + 3r), a shear limit of 3.2 T_tight and an overshoot of rate × 0.04 s after breakaway. Penetrating oil cuts r by 55%. Real fasteners vary widely; these numbers teach the trade-off.

Cleaning kinetics. Solvent on grease and brush on rust are first-order: dG/dt = −kG, so G(t) = G₀e^−kt, half-life ln 2 / k. The rate constants per method are made-up values chosen so each takes seconds.

Rolling road. m dv/dt = min(F_engine, μ m g w_r) − ½ρC_dA v² − C_rr m g with F_engine = T(rpm) G η / r, a parabolic torque curve peaking at 3800 rpm (480 N·m × power factor 0.75..1.0 from rebuild quality), 4-speed gearbox, final drive 3.2, explicit Euler at 2 ms.

Simplified: a generic car; the game's scores and timers are not used here. This page uses exactly the same physics module as the 3D lab (assets/physics.js), so the numbers agree.