The forward model is fully determined once the two approach speeds are chosen: impact, then separation to rest. So the speeds are found by repeating that until the simulated rest positions and headings match the documented ones, each weighted by the uncertainty recorded for that document.
Linear and angular momentum are conserved exactly. The analysis refuses any solution whose normal impulse is not compressive, that leaves the vehicles still approaching after separation, or that would create kinetic energy.
| Vehicle | Position error | Heading error |
|---|---|---|
| A | 0.05 m | 0.4° |
| B | 0.06 m | 0.3° |
The threshold adopted for this work is 1.5 m and 15 degrees. This reconstruction is within that threshold.
Every uncertain input was moved to each end of its stated range with the others held at their adopted values, and the whole reconstruction re-solved each time. This is not an error bar drawn around a point answer — it is the answer, re-derived.
| Assumption | Swing in A (km/h) | Swing in B (km/h) |
|---|---|---|
| Tyre-road drag factor (post-impact) | 6.2 | 5.0 |
| Impact-plane normal bearing | 5.2 | 2.5 |
| Coefficient of restitution | 1.6 | 4.1 |
| Vehicle A yaw inertia factor | 1.8 | 0.8 |
| Contact point along the impact plane | 0.7 | 1.6 |
| Vehicle A kerb mass | 1.2 | 0.1 |
| Vehicle B kerb mass | 1.1 | 0.1 |
| Impact-plane impulse ratio | 1.0 | 0.4 |
| Vehicle B yaw inertia factor | 0.6 | 0.2 |
Every input was drawn from its range simultaneously by Latin hypercube and the entire inverse problem re-solved for each draw. Draws that failed to converge are counted and excluded, never replaced.
Whichever engine runs, the complete input deck — every parameter, its source and the range it is swept across — is written into the bundle, so the analysis can be re-run independently rather than taken on trust.