Wet-Night Run-Off Crash Cluster on a 250 m Radius Curve
A two-lane rural arterial carries an AADT of 9,200 with 12 % heavy vehicles and a posted speed of 80 km/h. A 180 m long horizontal curve has a radius of 250 m, 4 % superelevation, 3.6 m lanes, 2.4 m shoulders and no transition spiral; both approaches are long tangents. Over three years there were 14 reported run-off-road crashes on the curve, 11 of them on wet pavement and 8 at night; the expected frequency for comparable segments is 3.5 crashes. The pavement is a polished crushed-stone asphalt with a locked-wheel skid number (SN40R) of 32. The local authority's draft response is to install chevron alignment signs and a 70 km/h advisory speed plate at a cost of about USD 25,000, because capital budget for reconstruction is unavailable for two years. The jurisdiction's design maximum superelevation is 6 %.
1. Calculate the side-friction demand at 80 km/h and at 70 km/h and compare with the friction that can reasonably be assumed.
Read the worked answer
Use the point-mass relation f = V²/(127R) − e, with V in km/h, R in metres and e as a decimal.
At 80 km/h, R = 250 m, e = 0.04:
- V²/(127R) = 6400 / (127 × 250) = 6400 / 31,750 = 0.202
- f = 0.202 − 0.04 = 0.162
At 70 km/h:
- 4900 / 31,750 = 0.154
- f = 0.154 − 0.04 = 0.114
Now compare with what may be assumed. At 80 km/h with the maximum superelevation of 6 %, the standard design value of side friction is about 0.14 (a 250 m radius at e = 6 % gives f ≈ 0.14). So the curve at 80 km/h demands 0.162 - above the maximum side friction any superelevation in this jurisdiction can justify. In other words, the curve cannot be made adequate for 80 km/h by reshaping it within the 6 % limit; it would need a larger radius.
At 70 km/h the demand falls to 0.114, which is within normal design assumptions - but only on a surface that can supply it. An SN40R of 32 on polished crushed stone indicates a wet friction supply that is marginal at highway speeds, and cornering demand is higher than the locked-wheel number suggests. The 11 wet crashes out of 14 confirm the shortfall is real, not theoretical.
2. Is the proposed chevron and advisory-speed package an adequate response? Justify your answer quantitatively.
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No. It treats the symptom and relies on compliance.
The package does not change the geometry, the superelevation or the pavement friction. It works only if drivers slow to 70 km/h or below, every time, in the wet, at night. The crash record says they are not doing so: 8 of 14 crashes were at night, when the curve is least legible, and the wet crashes dominate, which points to a friction deficiency rather than a signing deficiency. An advisory plate is also advisory - it carries no enforcement and no geometric consequence.
Quantitatively, at 80 km/h the demand of 0.162 exceeds the maximum justifiable friction of about 0.14 by roughly 16 %, and the margin is worse on a polished surface. Signing at best produces a partial speed reduction; it cannot close a 16 % deficit for the drivers who ignore it, and those are precisely the drivers in the crash sample.
The correct diagnosis is a friction-and-geometry problem: superelevation is at 4 % where 6 % is available, there is no spiral so the tangent-to-curve transition is abrupt, and the aggregate is polished. The proportionate response is a package, not a sign:
- high-friction surface treatment through the curve and 30 m of each approach (addresses the wet, night crashes directly);
- restore superelevation toward 6 % at the next resurfacing;
- add spiral or lengthen the transition, and widen the shoulders;
- keep the chevrons and advisory speed as a supplement, not as the intervention.
3. Reconstruction is two years away. What interim measures would you implement now, and how would you sequence them?
Read the worked answer
Sequence by how much friction or alignment each buys per dollar and per month of disruption.
Immediately (weeks, low cost):
- High-friction surface treatment is the single highest-value interim measure: it directly raises the available friction where the crashes are, and the quantity is small (about 180 m × 7.2 m plus tapers, roughly 1,500 m²), so it can be procured and placed well inside the two-year window. Budget order USD 40,000–70,000 depending on binder and aggregate.
- Refresh delineation: larger chevrons, retroreflective pavement markers on both edges through the curve, and post-mounted delineators on the outside of the bend so the geometry reads at night.
- Rumble strips on the tangent approach on the outside of the curve, to give a tactile warning before the driver is committed.
Within the year:
- Add shoulder widening or a paved shoulder on the outside of the curve where run-off vehicles are leaving the road, so an errant vehicle has recovery room rather than striking an embankment or fixed object. Verify the clear zone and relocate any non-yielding posts.
- Consider a temporary or permanent speed reduction backed by enforcement, and monitor before/after crash and speed data.
Sequencing rationale: fix the friction and the night-time legibility first because the crash pattern is wet and dark; defer the superelevation and spiral work to the reconstruction, where it belongs and where it can be built without a second closure.