An Existing Curve That Cannot Meet Its Posted Speed or Its Sight Distance
A 1.8-mi rural two-lane highway (12-ft lanes, 6-ft shoulders) contains a horizontal curve on an 800-ft radius with 4 percent superelevation. Agency policy allows up to 8 percent maximum superelevation. The posted speed is 55 mph. The inside of the curve is bounded 20 ft from the centerline of the inside lane by a stone retaining wall and dense vegetation; the district describes right-of-way acquisition as 'very difficult.' Annual average daily traffic is 6,400 with 12 percent trucks. There have been four run-off-road crashes in the curve in three years, all in wet weather. Resurfacing is programmed in 18 months and is the only construction window available for a decade.
1. Determine whether the curve can support the 55-mph posting with its existing superelevation, and what the maximum supportable speed would be if superelevation were raised to policy maximum.
Read the worked answer
Required side friction. Use the point-mass relationship and solve for the friction the driver must supply: e + f = V^2/(15R)
- At 55 mph, R = 800 ft: e + f = 3,025/(15 x 800) = 0.252
- With e = 0.04, f required = 0.212, versus about 0.12 available at 55 mph. The curve is deficient by a wide margin - it is not a marginal case.
Pushing superelevation to the limit. At e = 0.08, f required = 0.172, still well above 0.12. Maximum superelevation alone does not rescue the 55-mph posting.
Maximum supportable speed.
- With e = 0.08 and f = 0.12: V = sqrt(15 x 800 x 0.20) = 49 mph
- With the existing e = 0.04: V = sqrt(15 x 800 x 0.16) = 44 mph
Judgment. Two things follow. First, the 55-mph posting is not defensible and is a contributing factor in the wet-weather run-off-road pattern. Second, rebuilding to a 55-mph radius (roughly 1,120 ft at e = 0.06, f = 0.12) is not achievable against the wall, so the design decision is not 'realign' - it is 'raise e to the policy maximum during the resurfacing and re-post at 45 mph with an advisory speed of 40 on the approach.' Note the residual: at 49 mph of geometric capability a 45-mph posting is consistent, but the 45-mph posting must be supported by enforcement credibility and sequencing, not by a single sign.
2. Check stopping sight distance in the curve against the 20-ft lateral clearance to the wall and vegetation, and explain the relationship between the two speeds you developed.
Read the worked answer
Approximation for lateral clearance on a horizontal curve: m = R [1 - cos(28.65 S / R)]
At 55 mph (SSD = 495 ft, AASHTO, 2.5-s PRT):
- 28.65 x 495/800 = 17.7 degrees; cos = 0.9525
- m = 800 x (1 - 0.9525) = 38 ft required; 20 ft available -> roughly 18 ft short
At 45 mph (SSD = 360 ft):
- 28.65 x 360/800 = 12.9 degrees; cos = 0.9748
- m = 800 x (1 - 0.9748) = 20.2 ft required; 20 ft available -> essentially satisfied
Why this matters. The two checks agree, which is the point. The wall and vegetation are adequate only for a driver traveling at the lower speed; at 55 mph the driver cannot see through the curve even with dry friction. In wet weather the friction margin collapses further, which is exactly the observed crash pattern. The vegetation is removable within the existing right-of-way and should be cleared to restore at least 20 ft (preferably a few extra feet as maintenance tolerance) regardless of what happens to the wall.
Judgment. Never present the radius check and the sight-distance check as separate findings. Here they converge on one conclusion - the operating speed must come down to about 45 mph - and that conclusion is what makes the countermeasure package defensible.
3. Recommend a countermeasure package to be built during the 18-month resurfacing window. Rank the measures and explain any you would reject.
Read the worked answer
What the diagnosis supports. A wet-weather run-off-road pattern on a curve that is over-driven for its geometry, with limited sight distance and no room to realign.
Recommended, in priority order
- High-friction surface treatment through the curve - directly addresses the wet-friction failure mode; relatively inexpensive and can be placed during the resurfacing. Highest benefit per dollar here.
- Raise superelevation to 0.08 during the overlay, within the pavement reconstruction already funded. Cheap because the project is happening anyway; improves the friction margin at any speed.
- Speed management: re-post 55 -> 45 with an advisory 40 plaque, plus advance curve warning with sequential signage and chevrons on the outside of the curve. This is the measure that makes items 1 and 2 sufficient rather than partial.
- Clear vegetation to restore 20+ ft of sight line inside the curve; add object markers on the wall face.
- Shoulder rumble strips on the approaches if shoulder width permits; delineators through the curve for night guidance.
Rejected or deferred
- Full realignment to a 55-mph radius: right-of-way is described as very difficult and the cost is not justifiable when a 45-mph curve with high friction performs acceptably.
- Relocating the stone wall: only if vegetation clearing proves insufficient; the wall is a fixed object but moving it is a major structural and right-of-way undertaking.
- Signing alone: warning signs do not change the friction demand, and the crash history shows drivers are already exceeding the geometry.
Judgment. The package is deliberately built around the funded window. Committing to a realignment means a decade of nothing being done, which is the worst outcome. Document the 45-mph posting decision and the friction treatment so the next resurfacing cycle does not silently revert to 55.