A linear-drag twin of a quadratic-drag vehicle: what does it get wrong about braking, terminal speed and the safe speed under a stopping limit?

What it found

Real drag cv|v|, twin kv with k matched at one speed. Coast-down time to fall to v₀/10 is 9/(cv₀) for the truth and independent of v₀ in the twin (0.05×, 0.51×, 1.02× the truth at v₀=1, 10, 20 for a fit at 5); terminal speed is off by v_term/v_fit; a least-squares fit over [0, v_max] has k=3cv_max/4, exact only at 0.75v_max. The safe speed under a 10 m stopping limit is mis-stated by −20.8%, −8.9%, +7.0%, +41.1% for fits at 1, 5, 10, 20 m/s, so the error changes sign with the fit speed, and trace-fitted k falls from 0.382 to 0.223 as the coast-down lengthens because the slow tail dominates. Stylised: one dimension, pure quadratic drag, closed-form noiseless truth.

A figure from its own output

Paper, code and results

• README and method
• White paper
• Experiments and results
• Code
• Tests

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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.