How wrong is the stopping distance of a twin that models friction as purely viscous?

What it found

With Coulomb friction c the real coast-down stops in finite time with exact distance (m/b)[v₀−(c/b)ln(1+b v₀/c)] (RK4 agreement 9×10⁻⁹), while the viscous twin only decays exponentially (6.5 s to reach 10⁻³ vs 1.95 s real). The least-squares gain b+cE[v]/E[v²] depends on the logged speed range (1.23 on [1,3], 3.44 on [0.05,0.3]); fitted on [1,3] the twin overestimates stopping distance ×1.8 at v₀=1 and ×17 at 0.05, is exact at 7.34 and underestimates above. Negative result: no single viscous gain does better than 0.87 worst relative error over [0.05,3], while an affine fit recovers (b,c) exactly. Stylised: one mass, noiseless logs.

A figure from its own output

Paper, code and results

• README and method
• White paper
• Experiments and results
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More in Digital twins & sim-to-real

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• A fixed-step twin of a bouncing ball: how wrong are its restitution and time to rest, and does calibrating on the first bounce fix it?A fixed-step twin of a bouncing ball: the true rest time (v1/g)(1+e)/(1−e) is hypersensitive to e (2/(1−e²)), the twin's apparent restitution and settling time are off by O(dt) with scheme-dependent sign (−20% to +4% at dt=10⁻², e=0.9), and calibrating e on the first bounce is not a reliable fix.

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.