Pedestrian Death Physics: A Survivable Speed Bound for Crossings from Stopping Distance, Fatality Risk, and Available Sight Distance

SIMULATED, NOT MEASURED. A pedestrian crossing is survivable at a given traffic speed only if a driver who first sees the pedestrian at the available sight distance can stop before reaching them, or can shed enough speed that a strike is unlikely to be fatal. Combining stopping-distance kinematics (reaction plus braking), a logistic fatality-risk curve for struck pedestrians, and available sight distance at crossings, this paper derives a design table mapping sight distance to the maximum traffic speed at which a full stop is still possible. On a wet surface (friction coefficient 0.40) with a 1.5 s reaction time, 10 m of sight distance supports only 17.1 km/h, 20 m supports 28.6 km/h, 30 m supports 38.0 km/h, and 50 m supports 53.2 km/h; with a conservative 2.5 s design reaction time the caps fall to 12.3 km/h at 10 m and 22.0 km/h at 20 m. The risk curve places a 10% fatality risk at an impact speed of 25.9 km/h and a 52.4% risk at 50 km/h; wet stopping distance at 50 km/h is 45.4 m. Under the stated sight-triangle geometry (ratio 2.33), clearing an obstruction back 6 m buys 14.0 m of sight distance, and holding 30 km/h on a wet surface requires about 9.1 m of clearing, while 50 km/h requires 19.5 m. Two regimes defeat the bound: approaches occluded to 5 m, where the survivable cap is 9.8 km/h wet and 10.5 km/h dry, below any normal traffic speed; and wet high-speed arterials, where stopping from 80 km/h needs 96.3 m and a strike at that speed carries a 0.950 fatality risk. In those regimes only removing the occlusion, moving the crossing, physical speed control, or separation makes the crossing survivable. All numbers are computed by the accompanying script from stated inputs; nothing was built or field-tested.