Seeing the Pedestrian in Time: A Detection-Distance Model and a Lighting Specification for Night Crossings

Most pedestrian deaths in road traffic occur in darkness, and at a crossing the binding question is whether the driver detects the pedestrian farther away than the vehicle needs to stop. This paper builds a stated-input detection-distance model - pedestrian luminance from vertical illuminance, spectrum and clothing reflectance, against the luminance of the road background beyond the crossing, reduced by glare veiling luminance and atmospheric extinction, against a threshold for a 65-year-old driver - and converts it into a lighting specification. On a dry road in clear air with no glare, a pedestrian in dark clothing (reflectance 0.08) is detected at 72 m on headlights alone, 103 m at 10 lux vertical illuminance, and at the 150 m scan limit at 30 lux; the wet stopping distance at 50 km/h is 55.9 m. Oncoming LED glare cuts detection at 10 lux to 48 m, below that stopping distance; 30 lux (70 m under LED glare) restores a margin at 50 km/h, and 50 lux (102 m) is required at 60 km/h (wet stopping distance 73.8 m). The specification is: luminaires 6 m upstream of the crossing at 6 m mounting height on each approach, cut-off optics holding background spill to a factor of 0.15, neutral-white spectrum, at least 30 lux vertical (50 lux at 60 km/h). Raising a crossing from the 10 lux baseline to this specification costs an additional $8,076 over 20 years, at most $171.8 per additional metre of detection distance for dark clothing. The failures are printed at full size: near-black clothing (reflectance 0.04) is below the critical reflectance of 0.0539 for positive contrast, and added light reduces dry-road detection from 52 m to 24 m at 50 lux, below the 50 km/h wet stopping distance at every level; in fog of 39 m visibility, detection is 20-24 m at every level, below even the 30 km/h wet stopping distance of 26.8 m. In those regimes lighting cannot buy enough detection, and only lower speed or retroreflective clothing can close the gap. SIMULATED, NOT MEASURED: all numbers are reproducible from the deposited compute.py.