Safe-Route Lighting for Children Walking Roads: A Detection-Distance Design Bound for Solar LED Route Lamps

Children walking to school at dawn or dusk on unlit roads are visible to a driver only as far as headlights can make them visible, and that distance is often shorter than the distance the vehicle needs to stop. This paper models both distances for a reference child pedestrian (height 1.25 m) and derives a placement rule for solar LED route lamps. Under low-beam headlights alone (15,000 cd toward the pedestrian), the modelled detection distance is 19.9 m for dark clothing (reflectance 0.05), 34.5 m for a typical clothing mix (0.15), and 56.4 m for light clothing (0.40). Wet-road stopping distance at a 1.5 s perception-response time is 21.3 m at 30 km/h, 32.4 m at 40 km/h, 45.4 m at 50 km/h, and 60.4 m at 60 km/h. A dark-clothed child is therefore not detectable in time at any speed of 30 km/h or above, and a typically clothed child is not detectable in time at 50 km/h or above. Solar LED lamps (1,200 lm, 3.5 m mounting height) raise the worst-case (mid-span) detection distance for typical clothing to 43.1 m at 8 m spacing, which clears the 40 km/h wet stopping distance with the 1.25 safety factor applied in this paper (required 40.5 m; maximum admissible spacing 8.5 m). The adopted design — 8 m spacing, lamps at both corners of every crossing, and halved spacing with a lamp at the apex on bends — costs $2,832.21 per kilometre per year annualised, or $70.81 per child per year for a 1 km route used by 40 children. The design fails, and is printed here as failing, for dark clothing at 30 km/h and above, for any clothing at speeds above the 40 km/h design speed, in fog, and wherever lamp outages open a gap.