TECHBRIEF Safety Evaluation of

Improved Curve Delineation

FHWA Publication No.: FHWA-HRT-09-046

FHWA Contact: Roya Amjadi, HRDS-06, (202) 493-3383, 

roya.amjadi@dot.gov

This document is a technical summary of the Federal Highway 

Administration report, Safety Evaluation of Improved Curve 

Delineation (FHWA-HRT-09-045), which will be available online 

at http://www.tfhrc.gov/safety.

Objective

The Federal Highway Administration (FHWA) organized 

26 States to participate in the FHWA Low Cost Safety 

Improvements Pooled Fund Study as part of its strategic highway safety plan support effort. The purpose of the pooled fund 

study is to estimate the safety effectiveness for several of the 

unproven low-cost safety strategies identified in the National 

Cooperative Highway Research Program (NCHRP) Report 

500 Series. One of the strategies chosen to be evaluated for 

this study is improved curve delineation. This strategy is 

intended to reduce the frequency of curve-related crashes by 

providing more conspicuous signing and lane markings. The 

safety effectiveness of this strategy has not been thoroughly 

documented, and this study is an attempt to provide a crashbased evaluation through scientifically rigorous procedures.

Introduction

Statistics from the Fatality Analysis Reporting System indicate 

that 42,642 people were killed in 38,588 fatal crashes on the 

U.S. highway system in 2006.(1) Approximately 27 percent of 

these fatal crashes occurred along horizontal curves.(1) These 

crashes occurred predominantly on two-lane rural highways 

that are often not part of the State system.(2) Approximately 

70 percent of curve-related fatal crashes were single-vehicle 

crashes in which the vehicle left the roadway and struck a 

fixed object or overturned, and 11 percent of curve-related fatal 

crashes were head-on crashes. Thus, run-off-road and head-on 

crashes accounted for 81 percent of the fatal crashes at horizontal curves.(1) Also, the average accident rate for horizontal 

curves is about three times the average accident rate for 

Research, Development, and 

Technology

Turner-Fairbank Highway 

Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

www.tfhrc.gov
2

highway tangents.(3) Hence, implementing strategies designed to improve the safety at horizontal curves will help achieve the overall goal 

of the American Association of State Highway 

and Transportation Officials (AASHTO) Strategic 

Highway Safety Plan.

One such strategy with potential for improving horizontal curve safety is enhancing delineation along curves. According to the NCHRP 

Report 500 Series Volume 7, "A Guide for 

Reducing Collisions on Horizontal Curves," 

enhancing delineation along a curve is currently a tried but not proven strategy that can 

be implemented on most curves as well as 

problem curves.(2) Enhanced curve delineation 

can serve multiple purposes. First, it allows for 

drivers of vehicles to have better visibility when 

approaching curves by increasing visual cues. 

In addition, enhanced curve delineation can 

provide positive guidance while navigating 

through a curve. Improved delineation can also 

encourage drivers to decrease their speed into 

and through a curve, which can reduce the frequency of run-off-road and head-on crashes. 

Last, improved delineation can be especially 

helpful under low-light or nighttime conditions.

Options for enhanced delineation include using 

better pavement markings such as higher durability, all-weather quality, and higher retroreflectivity. Other options include post-mounted 

delineators, chevrons, raised pavement markers, 

and wider edge lines.(2) An example of enhanced 

curve delineation is shown in figure 1.

Enhanced delineation is a potential treatment 

for curves that have some form of delineation or other safety treatment but continue to 

experience higher crash rates.(1) The installation or upgrade of any pavement marking 

should follow the guidelines in the Manual on 

Uniform Traffic Control Devices (MUTCD).

(4)

While the literature supports the use of 

improved curve delineation, this strategy cannot 

be considered a proven strategy because there 

are no truly valid estimates of effectiveness 

based on sound before-after crash-based studies in North America. More research is needed 

to substantiate the evidence for highway agencies implementing this strategy. The safety 

effectiveness of improved curve delineation is 

explored empirically in this study to provide 

better support to the States when selecting 

safety improvements at horizontal curves on 

two-lane rural roads.

Methodology

Data were collected from Connecticut and 

Washington. Both States have implemented 

delineation improvements for horizontal curves 

on two-lane rural roads. Study locations were 

selected from the two States based on the 

availability of installation data, including location and installation dates. Geometric, traffic, and crash data were obtained for a total 

before period sample of 188.8 kilometer-years 

(117.3 mile-years), including 73.7 kilometer-years 

(45.8 mile-years) from Connecticut and 

115.1 kilometer-years (71.5 mile-years) from 

Washington. A total of 187.6 kilometer-years 

(116.6 mile-years) was obtained for the after 

period, including 34.8 kilometer-years 

(21.6 mile-years) from Connecticut and 

152.9 kilometer-years (95.0 mile-years) from 

Washington. Kilometer-years are the number 

of kilometers where the strategy is applied 

multiplied by the number of years the strategy has been in place at each location. For 

example, if a strategy is applied along 9 km 

Figure 1. Example of a curve treated with enhanced 

delineations in Connecticut. 
3

(5.6 mi) of roadway and is in place for 3 years 

along all 9 km (5.6 mi), there is a total of 

27 kilometer-years (16.8 mile-years) available 

for the study. Geometric, traffic, and crash 

data were also obtained for reference curves 

with characteristics similar to the strategy sites 

in both States but without curve delineation 

improvements.

During the data collection process, the project 

team identified a variation in curve delineation improvements between the two States. 

Specifically, Connecticut improved signing 

by upgrading to fluorescent yellow sheeting. 

This included installing new signs or replacing existing signs. The signs in question were 

either warning signs (e.g., curve ahead or suggested speed limit) and/or curve delineation 

signs (e.g., chevrons or horizontal arrows). 

Figure 2 shows the types of signs used in the 

treatment. Signs W1-1 through W1-5 and W1-10 

were classified as warning signs in this study. 

Signs W1-6 and W1-8 were classified as curve 

delineation signs. Unlike Connecticut, the treatments in Washington only involved the installation of chevrons (W1-8 signs) on horizontal 

curves. This included locations where there 

were previously no chevrons and locations 

where the number of chevrons was increased.

Empirical Bayes (EB) methods were incorporated in a before-after analysis to determine 

the safety effectiveness of curve delineation 

improvements along two-lane rural roads. The 

EB methodology for observational before-after 

studies was used for the evaluation.(5) In order 

to account for site selection biases, the study 

analysis required the identification of reference 

sites. Reference sites were identified as curves 

that were similar to the treatment sites but did 

not receive the improved signing treatment.

Safety performance functions (SPFs) were calibrated separately for use in the EB methodology using the reference sites for each State. 

Generalized linear modeling (GLM) was used 

to estimate the model coefficients using the 

software package SAS®.

(6) A negative binomial 

error distribution was assumed for the GLM, 

which was consistent with the state of research 

in developing these models.

SPFs were estimated for the following crash 

classifications:

•	 Total non-intersection crashes (all severities and all crash types).

•	 Non-intersection injury and fatal crashes 

(all crash types).

•	 Non-intersection lane departure crashes 

(all severities).

•	 Non-intersection crashes during dark (all 

severities and all crash types where light 

condition was coded as "dark-not lighted" 

or "dark-lighted."

•	 Non-intersection lane departure crashes 

during dark (all severities where light condition was coded as "dark not-lighted" or 

"dark-lighted."

The full report includes a detailed explanation

of the methodology, including a description 

of how the estimate of percent reduction was 

calculated.

Results

Two sets of results were calculated and are 

presented in the following sections. One set 

contains aggregate results for each State as 

well as for the two States combined. The other 

set of results is a disaggregate analysis, which 

grouped sites by various characteristics to 

Figure 2. Sign types used in Connecticut horizontal 

curve treatments from MUTCD.

W1-1 W1-2 W1-3 W1-4

W1-5 W1-10 W1-6 W1-8
4

evaluate the impact of these variables on the 

safety effectiveness. The disaggregate analysis 

focused on the following factors: 

•	 Average annual daily traffic (AADT) before 

treatment. 

•	 Radius of curve.

•	 Roadside hazard rating (RHR).

•	 Number of signs in advance of the curve 

that were added or replaced.

•	 Number of signs within the curve that were 

added or replaced. 

AADT and curve radius were available from

both Washington and Connecticut. RHR and 

the number of signs were available only in 

Connecticut.

Aggregate Analysis

The aggregate results are shown in table 1

for Connecticut and Washington. The following 

points summarize the results for the individual 

State analyses:

•	 In Connecticut, there was a statistically 

significant reduction in all crash types 

that were evaluated. Total non-intersection and non-intersection lane departure 

crashes were reduced by approximately 

18 percent. Injury and fatal non-intersection crashes were reduced by about 

25 percent. The percentage reduction was 

larger (35 percent) for the crashes that 

occurred during dark conditions. 

•	 In Washington, there was a statistically 

significant reduction in crashes during dark 

conditions and lane departure crashes during dark conditions. The reduction for these 

two crash types exceeded 20 percent. 

•	 The combined results for the two 

States indicated a statistically significant reduction in injury and fatal crashes, 

crashes during dark conditions, and lane 

departure crashes during dark conditions. 

Results from the aggregate analyses indicated 

general safety benefits for improved curve 

delineation. The disaggregate analysis is presented in the following section, indicating 

specific situations where the strategy may be 

more effective.

Disaggregate Analysis

A disaggregate analysis was completed in an 

attempt to discern factors that may impact the 

safety effectiveness of delineation improvements for curves. The results of the disaggregate analysis are summarized below.

Curve Radius

In Connecticut, the treatments appeared to be 

more effective for sharper curves (radius less 

than 150 m (491.8 ft) or 0.15 km (0.093 mi)) 

compared to flatter curves (radius equal to 

or exceeding 150 m (491.8 ft) or 0.15 km 

(0.093 mi)). However, in Washington and for 

the two States combined, there were no clear 

trends regarding the differential effects of 

curve radius.

RHR

RHR was only available for Connecticut sites. 

The results indicated that the treatments were 

more effective at sites with more hazardous 

roadsides (RHR of 5 or 6) compared to less 

hazardous roadsides (RHR between 2 and 4) for 

total and lane departure crashes during dark 

conditions.

Number of Signs in Advance of Curve

The number of signs in advance of the curve 

was only examined for Connecticut. There was 

no clear trend in terms of differential safety 

effects.

Number of Signs Within Curve

The number of signs within the curve was only 

examined for Connecticut. The disaggregate 

analysis indicated that sites with more signs 

added or replaced (more than seven per curve) 

had a larger reduction in crashes compared to 
5

sites where fewer signs were added or replaced 

(less than or equal to seven per curve).

AADT

There were indications that the treatment 

was more effective for sites with higher AADT 

compared to sites with lower AADT in both 

Connecticut and Washington.

Economic Analysis

The purpose of the economic analysis was 

to evaluate the economic feasibility of delineation improvements for curves on two-lane 

rural roads. A combined economic analysis is 

provided, but separate analyses are also provided for each State due to the variation of 

the treatment. 

Life cycle costs and the discounted annual cost 

were estimated for the strategy based on input 

from the two States. Crash cost savings were 

estimated from the most recent FHWA unit 

crash cost data.(7) The benefit-cost ratio was 

estimated by comparing the cost of the strategy 

to the crash costs.

The annualized cost of the treatment was 

computed based on information provided 

by the Connecticut and Washington transportation departments. Connecticut provided costs based on the type of treatment 

ranging from $30 to $160 for a fluorescent 

yellow sign with a service life of 5 years. The 

unit cost varied depending on the size of the 

sign—smaller signs such as chevrons and 

advisory speed signs were less expensive 

Table 1. Results for Connecticut, Washington, and combined strategy sites.

Applicable Crash Types

EB Estimate 

of Crashes in 

After Period 

Without Strategy

Observed 

Crashes 

in After 

Period

Estimate 

of Percent 

Reduction

Standard 

Deviation 

of Percent 

Reduction

Connecticut—Non-intersection 188.1 155 17.8 7.7

Connecticut—Non-intersection lane departure 158.8 131 17.7 8.4

Connecticut—Injury and fatal (K, A, B, or C) 

non-intersection 55.9 42 25.2 12.7

Connecticut—Non-intersection during dark 

conditions 72.2 47 35.3 10.5

Connecticut—Non-intersection lane departure 

during dark conditions 60.4 40 34.2 11.5

Washington—Non-intersection 374.8 361 4.3 8.9

Washington—Non-intersection lane departure 308.6 292 5.9 8.8

Washington—Injury and fatal (K, A, B, or C) nonintersection 211.8 179 16.4 10.4

Washington—Non-intersection during dark 

conditions 169.5 129 24.5 9.5

Washington—Non-intersection lane departure 

during dark conditions 147.7 116 22.1 10.1

Combined—Non-intersection 562.9 516 8.6 6.4

Combined—Non-intersection lane departure 467.4 423 9.7 6.4

Combined—Injury and fatal 

(K, A, B, or C) non-intersection 267.7 221 18.0 8.6

Combined—Non-intersection during dark 

conditions 241.7 176 27.5 7.3

Combined—Non-intersection lane departure 

during dark conditions 562.9 516 8.6 6.4

Note: Bold denotes those safety effects that are significant at the 95-percent confidence level.
6

than larger signs such as curve warning signs. 

Washington provided an estimate of $100 for 

chevrons. The lower and upper cost limits from 

Connecticut were used to provide a range of 

cost estimates, but the cost may vary for other 

States depending on the size of the signs and 

installation and maintenance practices.

Based on information from the Office of

Management and Budget, a discount rate of 

2.4 percent was used to determine the annual 

cost of the strategy.(8) Although the number 

of signs per curve may have varied, it was 

assumed that 10 chevron signs were installed 

per curve. Assuming installation costs of $30 

per sign, this equated to an annualized cost of 

$6.44 per sign and an annual treatment cost of 

$64 per curve. Assuming installation costs of 

$160 per sign, the annualized cost was $34 per 

sign and $343 per curve.

Crash savings were computed based on the

results for non-intersection lane departure 

crashes during dark conditions. The most 

recent FHWA mean comprehensive crash costs 

were used to estimate the cost for a lane departure crash based on 2001 dollar values.(7) The 

FHWA crash cost document does not directly 

report the cost for a lane departure crash, so 

it was estimated based on the cost of lane 

departure-related crashes and the percentage of 

these crashes. Lane departure-related crashes 

include head-on, sideswipe, single-vehicle rollover, and single-vehicle fixed object crashes. 

Based on Washington crash data, these crashes 

represented 2.6, 1.6, 25.9, and 69.9 percent, 

respectively. The mean comprehensive crash 

costs for these crash types were $60,451;

$16,019; $147,629; and $67,353, respectively, 

assuming a speed limit less than 72.45 km/h 

(45 mi/h). A weighted average was computed by 

combining the crash costs with the percentage 

of each crash type, resulting in a cost of $87,143 

per lane departure crash.

The total crash reduction was calculated for 

each State by subtracting the actual crashes in 

the after period from the expected crashes in 

the after period had the treatment not been 

implemented. Crashes per site-year were calculated by dividing the total crash reduction by the 

number of site-years for each State. Site-years, 

which are computed similarly to kilometeryears, are the number of sites multiplied by the 

number of years of installation. The benefit (i.e., 

crash savings) is the product of the total crash 

reduction per site-year and the cost of a lane 

departure crash (i.e., $87,143). The benefit-cost 

ratios are presented in table 2. The lower and 

upper limits represent the assumed installation 

costs of $160 and $30 per sign, respectively.

Even with the conservative assumptions made, 

a very modest reduction in crashes is required 

to justify this strategy economically. The benefitcost ratios far exceeded 2:1. While the cost of 

the strategy may have varied by State, it is likely 

that the annualized costs will not exceed the 

annual crash savings. Therefore, this strategy 

was justified economically.

Summary

The objective of this study was to evaluate 

the safety effectiveness of improved delineation 

on horizontal curves through signing improvements. The study examined the effects of this 

strategy on specific non-intersection crash 

types including total, injury and fatal, lane 

Table 2. Summary of economic analysis results.

State Sites Years

Total Crash 

Reduction Per Year

Total Crash Reduction 

Per Site-Year

Crash Savings 

Per Site-Year

Benefit-Cost 

Ratio

All 228 4.58 11.373 0.050 $4,347 12.7–67.9

Connecticut 89 3.05 6.686 0.075 $6,546 19.1–102.3

Washington 139 6.76 4.687 0.034 $2,938 8.6–45.9
7

departure, total during dark, and lane departure 

during dark in a rigorous crash-based analysis. 

The evaluation was based on 89 sites in 

Connecticut and 139 sites in Washington, 

representing a total of 188.8 kilometer-years 

(117.3 mile-years) in the before period and 

187.6 kilometer-years (116.6 mile-years) in the 

after period. The specific strategies varied 

between the two States, but both strategies 

involved curve delineation improvements. 

Connecticut improved signing by upgrading 

to fluorescent yellow sheeting for new sign 

and replacement sign installations. Signs W1-1 

through W1-6, W1-8, and W1-10 were included 

in the upgrade. The treatments in Washington 

involved only the installation of chevrons (W1-8 

signs) on horizontal curves. This included locations where there were previously no chevrons 

and locations where the number of chevrons 

was increased.

From a practical standpoint, results presented

in table 3 support the conclusion that curve 

delineation improvements have the potential to 

reduce target crashes. This conclusion is based 

on the combined analysis from Connecticut and 

Washington. Table 3 presents the recommended crash reduction factors and standard errors.

The disaggregate analysis provided further 

insight into the circumstances where curve 

delineation improvements may have been 

more effective. In both States, the reductions 

appeared to be more prominent at locations 

with higher traffic volumes. Based on the limited 

data from Connecticut, the reductions in crashes 

were more prominent on sharper curves (curve 

radius less than 150 m (491.8 ft)) and in locations 

with more hazardous roadsides (RHR of 5 or 

higher) compared to locations with less hazardous roadsides (RHR of 4 or lower). In addition, 

curves where more signs were either added or 

replaced within the curve with a more retroreflective material experienced larger reductions 

in crashes.

Conclusion

The general conclusion from this research is

that delineation improvements for curves 

have the potential to reduce crashes and crash 

severity on two-lane rural roads. Based on the 

installations in Connecticut and Washington, 

the combined results indicate substantial 

and highly significant crash reductions—

injury and fatal (18 percent), dark conditions 

(27.5 percent), and dark condition lane departure (25.4 percent). In Connecticut, the effectiveness was greater for curves where more signs 

were either added or replaced within the curve. 

An economic analysis revealed that improving 

curve delineation with signing improvements 

is a very cost-effective treatment with the 

benefit-cost ratio exceeding 8:1. Given the 

potential to reduce crashes, the use of curve 

delineation improvements is justified as a safety 

improvement, particularly at curves with more 

hazardous roadsides, higher traffic volumes, 

and smaller curve radii.

References

1. National Center for Statistics and Analysis 

of the National Highway Traffic Safety 

Administration. (2006). Fatality Analysis 

Reporting System, Washington, DC. Obtained 

from: http://www-fars.nhtsa.dot.gov/Main/

index.aspx. Last accessed June 21, 2008. 

Table 3. Summary of crash reduction factors.

Crash Type

Recommended Crash Reduction 

Factors (Point Estimate) Standard Error

Injury and fatal curve crashes 18 8.6

Curve crashes during dark conditions 27.5 7.3

Lane departure crashes on curves during dark conditions 25.4 7.8
8

Researchers— This study was performed by Raghavan Srinivasan of HSRC with support from staff 

from HSRC, Persaud & Lyon, and Vanasse Hangen Brustlin, Inc. For more information about this research, contact Roya Amjadi, FHWA Project Manager, HRDS, at (202) 493-3383, roya.amjadi@dot.gov.

Distribution—This TechBrief is being distributed according to a standard distribution. Direct distribution is being made to the Divisions and Resource Center.

Availability—The TechBrief may be obtained from the FHWA Product Distribution Center by e-mail to 

report.center@dot.gov, fax to (814) 239-2156, phone to (814) 239-1160, or online at http://www.tfhrc.gov/

safety.

Key Words—Horizontal curve, curve delineation, low-cost, safety improvement, safety evaluation, 

Empirical Bayesian, chevrons, horizontal arrows, advance warning signs, sign upgrade, and fluorescent 

yellow sheeting.

Notice—This document is disseminated under the sponsorship of the U.S. Department of 

Transportation in the interest of information exchange. The U.S. Government assumes no liability 

for the use of the information contained in this document. The U.S. Government does not endorse 

products or manufacturers. Trademarks or manufacturers' names appear in this report only because 

they are considered essential to the objective of the document.

Quality Assurance Statement—The Federal Highway Administration (FHWA) provides highquality information to serve the Government, industry, and public in a manner that promotes public 

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processes to ensure continuous quality improvement.

2. Torbic, D.J., Harwood, D.W., Gilmore, D.K., 

Pfefer, R., Neuman, T.R., Slack, K.L., and Hardy, 

K.K. (2004). "Guidance for Implementation 

of the AASHTO Strategic Highway Safety 

Plan: A Guide for Reducing Collisions on 

Horizontal Curves," NCHRP Report 500 

Series, Vol. 7, Transportation Research 

Board, Washington, DC.

3. Glennon, J.C., Neuman, T.R., and Leisch, 

J.E. (1983). Safety and Operational 

Considerations for Design of Rural 

Highway Curves, FHWA/RD-86-035, Federal 

Highway Administration, Washington, DC.

4. Federal Highway Administration. (2003). The

Manual on Uniform Traffic Control Devices, 

Washington, DC. Obtained from: http://

mutcd.fhwa.dot.gov/pdfs/2003r1r2/pdf_

index.htm. Last accessed June 18, 2008.

5. Hauer, E. (1997). Observational Before-After 

Studies in Road Safety: Estimating the Effect 

of Highway and Traffic Engineering Measures 

on Road Safety, Pergamon Press, Elsevier 

Science Ltd, Oxford, U.K. 

6. SAS®. SAS Institute Inc., Cary, NC.

7. Council, F., Zaloshnja, E., Miller, T., and

Persaud, B. (2005). Crash Cost Estimates 

by Maximum Police-Reported Injury 

Severity within Selected Crash Geometries, 

FHWA-HRT-05-051, Federal Highway Administration, McLean, VA.

8. Office of Management and Budget. (2008). 

Discount Rates for Cost-Effectiveness, Lease 

Purchase, and Related Analyses, No. A-94. 

Obtained from: http://www.whitehouse.

gov/omb/circulars/a094/dischist.pdf. Last 

accessed March 7, 2009. 

august 2009 FHWA-HRT-09-046

HRDS-06/08-09(1M)E