Stopping Distance Outside a School Gate
The road outside a school gate in a small town is straight and level. The posted limit is 30 km/h, but a survey finds most cars approach at 54 km/h. The gate is 24 m from the point at which a driver first has a clear view of a child stepping onto the road. An engineer measures braking deceleration as 5.0 m/s² on dry tar and 3.0 m/s² on wet tar. The average driver reaction time is 0.8 s. The school wants a defensible argument to present to the district road-safety committee. A councillor proposes only a larger 'SCHOOL' board and a speed bump at the gate. A parent proposes shifting the gate 15 m back from the road. A teacher proposes teaching children to raise a hand before crossing.
1. Calculate the total stopping distance at 54 km/h on dry and wet tar, and at 30 km/h on wet tar. Show each step.
Read the worked answer
54 km/h = 15 m/s.
Reaction distance = speed × reaction time = 15 × 0.8 = 12 m in every case.
- Dry tar, a = 5.0 m/s²: braking distance = v²/(2a) = 15²/(2×5.0) = 225/10 = 22.5 m. Total = 12 + 22.5 = 34.5 m.
- Wet tar, a = 3.0 m/s²: braking distance = 225/(2×3.0) = 225/6 = 37.5 m. Total = 12 + 37.5 = 49.5 m.
30 km/h = 8.33 m/s. Reaction distance = 8.33 × 0.8 = 6.7 m. Wet braking distance = 8.33²/(2×3.0) = 69.4/6 = 11.6 m. Total ≈ 18.3 m.
Comparison with the 24 m sight distance: at 54 km/h the total is 34.5 m dry and 49.5 m wet, both greater than 24 m. Only at 30 km/h on wet tar (18.3 m) is there a margin. The current approach speed is therefore incompatible with the available sight distance.
2. The councillor says the sign and bump are enough. Assess this against your figures and the 24 m sight distance.
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A sign does not change speed by itself, and the figures show that at 54 km/h a driver needs 34.5 m dry and 49.5 m wet - far more than the 24 m available. A bump placed at the gate is also too late: the driver must already have slowed before reaching the bump, and a child stepping out 24 m ahead can be struck before the bump is reached.
The measure can only be defended if it actually reduces approach speed to 30 km/h. At 30 km/h wet, 18.3 m is less than 24 m, so the sight distance is adequate with a margin of about 5.7 m. That makes speed reduction the controlling requirement, not the sign. A larger board plus a single bump is therefore not sufficient on its own; it needs advance warning, a gateway or rumble-strip treatment before the gate, and enforcement so that the design speed is actually achieved.
3. The parent's proposal to move the gate 15 m back would make the sight distance 39 m. Does that make 54 km/h safe in wet conditions? What does this show about choosing measures?
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No. At 54 km/h on wet tar the total stopping distance is 49.5 m, which is still greater than 39 m. At 54 km/h on dry tar it is 34.5 m, so 39 m would be adequate only in dry conditions. Wet weather is a credible condition, not an extreme one, so the design should not rely on dry-road braking.
This shows that an engineering measure must be matched to the design speed and the worst credible condition, not to the best one. Moving the gate back helps - it turns an inadequate 24 m into an adequate dry-condition distance - but it does not by itself justify 54 km/h. The defensible combination is to reduce the approach speed to 30 km/h and use the setback as an additional margin. The teacher's hand-raising instruction is useful education but cannot substitute for speed and sight-distance control.