A Curve That Never Met Its Design Speed
A rural two-lane highway has a 55 mph design speed, 12 ft lanes, 4 ft shoulders, and level grade. A horizontal curve has R = 700 ft with e = 0.06. On the inside of the curve a rock outcrop sits 22 ft from the centerline of the inside lane; the outcrop cannot be moved without a major cut. The corridor has had three run-off-road crashes on this curve in the last three years, all on the inside. The agency asks whether posting a 45 mph advisory speed sign and adding chevrons will resolve the deficiency.
1. Compute the required stopping sight distance at the 55 mph design speed and the middle ordinate needed to provide it on this curve.
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Stopping sight distance (level grade, driver reaction 2.5 s, braking friction 0.35): SSD = 1.47 V t + V² / [30 (f ± G)] SSD = 1.47 × 55 × 2.5 + 55² / (30 × 0.35) SSD = 202.1 + 288.1 = 490 ft
Middle ordinate required: M = R [1 − cos(28.65 S / R)] 28.65 × 490 / 700 = 20.06° M = 700 (1 − cos 20.06°) = 700 (1 − 0.9394) = 42.4 ft
The obstruction must be at least ~42 ft from the centerline of the inside lane. The outcrop is at 22 ft - a shortfall of roughly 20 ft, more than the entire lane-plus-shoulder width. The curve is deficient for sight distance at the design speed even before the guardrail and ditch are considered.
2. Is the curve otherwise adequate for 55 mph? What does that imply about the proposed signage fix?
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Check the curve for the design speed. The AASHTO minimum radius relationship is R = V² / [15(e + f)], with side friction f ≈ 0.12 at 55 mph: Rmin = 55² / [15(0.06 + 0.12)] = 3,025 / 2.70 ≈ 1,120 ft
The curve is R = 700 ft - far below the minimum for 55 mph at e = 0.06, and it cannot be brought into compliance by superelevation alone at a defensible e_max. So the curve is under-designed for the corridor's design speed on two independent counts: sight distance and radius.
Implication for the signage proposal: advisory speed and chevrons are appropriate interim measures - they are exactly what the crash pattern calls for - but they do not "resolve" the deficiency.
- Design speed is a property of the alignment, not of the sign; posting a lower speed does not make the geometric criteria pass.
- The real question is whether a reduced posted/design speed for this segment is defensible under the agency's speed-transition policy. A single low-speed curve in an otherwise 55 mph corridor creates a speed differential that itself generates crashes, so it needs advance warning, a transition, and consistency review.
- The outcrop removal or realignment is the permanent fix; a guardrail on the inside would not help sight distance and would add a fixed object in the clear zone.
3. Rank the candidate countermeasures and state what field data you would collect before committing to one.
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Ranking:
- Remove or bench the outcrop to achieve ~42 ft of clear sight distance on the inside. Permanent, addresses the root cause, eliminates the fixed object. Cost and rock excavation are the constraints.
- Realign or flatten the curve - the only fix that also corrects the radius. Expensive; justified only if the corridor is being reconstructed.
- Reduce the design/posted speed through the curve with an engineered speed transition and advisory signing. Lowest cost, and the right interim answer given three inside run-off-road crashes.
- Chevrons plus advance warning, delineation, and shoulder rumble strips - do these now regardless; they mitigate the crash pattern but not the sight distance.
Field data needed first:
- A measured, not computed, as-built radius and superelevation (as-builts of rural curves are frequently wrong).
- Actual 85th-percentile speeds, not the posted speed - the deficiency is judged against driver behavior.
- A sight-line survey from the inside lane at driver eye height (3.5 ft) to a 2.0 ft object, over the full curve, to confirm the 22 ft obstruction is the controlling one and check for others.
- Crash-collision diagrams and wet/dry and night conditions.
Without the 85th-percentile speed and the measured geometry, either the fix will be over-built or the speed reduction will be ignored by drivers.