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Publication Number: FHWA-HRT-05-042
Date: October 2005

Safety Effects of Differential Speed Limits

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FOREWORD

The Surface Transportation and Uniform Relocation Assistance Act, (STURAA) enacted on April 2, 1987, permitted individual States to raise rural interstate speed limits from the previously mandated national speed limit of 89 kilometers per hour (km/h) (55 miles per hour (mi/h)) to 105 km/h (65 mi/h) on rural interstate highways. Of those that changed their speed limits, some States raised the limits for passenger cars but not trucks while other States raised the limits for both passenger cars and trucks. The former category, with different speed limits for cars and trucks, is known as differential speed limits (DSL). The latter category, which mandates the same speed limits for cars and trucks, is known as uniform speed limits (USL). The 1995 repeal of the national maximum speed limit gave States additional flexibility in setting their limits, such that by 2002 several States had experimented with both DSL and USL.

This report compares the safety effects of USL for all vehicles as opposed to DSL for cars and heavy trucks. Detailed crash data, speed monitoring data, and traffic volumes were sought for rural interstate highways in 17 States for the period 1991 to 2000. The information and results of the study will be of particular interest to State traffic managers in making decisions about the application of USL or DSL in their highway systems.

Michael Trentacoste,

Director, Office of Safety Research and Development

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 high-quality information to serve Government, industry, and the public in a manner that promotes public understanding. Standards and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its information. FHWA periodically reviews quality issues and adjusts its programs and processes to ensure continuous quality improvement.

Technical Report Documentation Page

1. Report No. 
FHWA-HRT-05-042
2. Government Accession No. 
N/A
3. Recipient's Catalog No. 
N/A
4. Title and Subtitle 
THE SAFETY IMPACTS OF DIFFERENTIAL SPEED LIMITS ON RURAL INTERSTATE HIGHWAYS
5. Report Date 
October 2005
6. Performing Organization Code 
N/A
7. Authors(s) 
Nicholas J. Garber, John S. Miller, Bo Yuan and Xin Sun
8. Performing Organization Report No. 
N/A
9. Performing Organization Name and Address 
Virginia Transportation Research Council
530 Edgemont Road
Charlottesville, VA 22903
10. Work Unit No. (TRAIS) 
N/A
11. Contract or Grant No. 
VRC-000S(007)
12. Sponsoring Agency Name and Address 
Office of Safety
Federal Highway Administration
6300 Georgetown Pike
McLean, VA 22101
13. Type of Report and Period Covered 

14. Sponsoring Agency Code 
15. Supplementary Notes 
Contracting Officer's Technical Representative: A. J. Nedzesky, HRDS-05
16. Abstract 

To compare the safety effects of a uniform speed limit (USL) for all vehicles as opposed to a differential speed limit (DSL) for cars and heavy trucks, detailed crash data, speed monitoring data, and traffic volumes were sought for rural interstate highways in 17 States for the period 1991 to 2000. Conventional statistical tests (analysis of variance, Tukey's test, and Dunnett's test) were used to study speed and crash rate changes in the four policy groups. A modified empirical Bayes formation was used to evaluate crash frequency changes without presuming a constant relationship between crashes and traffic volume.

No consistent safety effects of DSL as opposed to USL were observed within the scope of the study. The mean speed, 85th percentile speed, median speed, and crash rates tended to increase over the 10-year period, regardless of whether a DSL or USL limit was employed. When all sites within a State were included in the analysis, temporal differences in these variables were often not significant. Further examination suggests that while these data do not show a distinction between DSL and USL safety impacts, the relationship between crashes and traffic volume cannot be generalized but instead varies by site within a single State. Because application of the modified empirical Bayes methodology suggested that crash risk increased for all four policy groups, a mathematical model that predicts sharp changes in crash rates based only on ADT does not appear valid at the statewide level.

17. Key Words 
Differential Speed Limit, Universal Speed Limit, Truck Speed Limit, Speed Limit
18. Distribution Statement 
No restrictions. This document is available to the Public through the National Technical Information Service; Springfield, VA 22161
19. Security Classif. (of this report) 
Unclassified
20. Security Classif. (of this page) 
Unclassified
21. No. of Pages 
99
22. Price 

Form DOT F 1700.7 (8-72)    Reproduction of completed page authorized

SI* (Modern Metric) Conversion Factors


TABLE OF CONTENTS

INTRODUCTION

PURPOSE AND SCOPE

APPENDIX A. EXAMPLES OF DATA COLLECTION LETTERS AND PROCESSING

APPENDIX B. EXAMPLE OF A CLARIFYING DATA REQUEST LETTER

APPENDIX F. THEORETICAL CONSIDERATIONS IN THE COMPUTATION OF CONFIDENCE INTERVALS FOR THE 85th PERCENTILE SPEED

ACKNOWLEDGMENTS

REFERENCES

LIST OF TABLES

     Table 1. Accident proportions by speed limit, collision type, and vehicle involvement

     Table 2. Overview of data availability for rural interstates from the various States

     Table 3. Available speed data

     Table 4. Available crash data for all sites

     Table 5. Five potential models for total number of crashes for Virginia rural interstate highways

     Table 6. Five models for total number of crashes on Arizona rural interstates

     Table 7. Before/after mean speed comparisons from the ANOVA test

     Table 8. Annual mean speed comparisons

     Table 9. Longitudinal comparison of speed variables within the States

     Table 10. Idaho speed limits

     Table 11. ANOVA results of mean speed and 85th percentile speed in Idaho

     Table 12. Statistical Tests for Significance in Crash Rates

     Table 13. Virginia data for the before and after periods

     Table 14. Crash estimation model parameters for Virginia data

     Table 15. Total crashes for Virginia

     Table 16. Virginia total fatal crashes

     Table 17. Crash data for Arkansas

     Table 18. Crash estimation model parameters for Arkansas data

     Table 19. Arkansas rear-end crashes

     Table 20. Total crashes for Arkansas

     Table 21. Fatal crashes for Arkansas

     Table 22. Crash data for Idaho

     Table 23. Total crashes for Idaho

     Table 24. Impact of speed limit changes according to the empirical Bayes formulation

     Table 25. Crash increases and confidence intervals according to the empirical Bayes formulation

     Table 26. T-Statistics for the empirical Bayes crash estimation models (before data)

     Table 27. Poisson validation description and results using the total crashes at four test sites

     Table 28. Negative binomial validation description and results

     Table 29. Estimation of expected crashes using 1991 data as a base in the Ci,y ratio

     Table 30. Estimation of expected crashes using 1993 data as a base in the Ci,y ratio

     Table 31. Summary Idaho data from speed sampling sites

     Table 32. Sample sizes required to achieve significant differences

     Table 33. 95 Percent confidence intervals for the 85th percentile speed.*

     Table 34. ANOVA variable definitions

     Table 35. ANOVA Arizona results

     Table 36. ANOVA Virginia results

     Table 37. Before and after crash data for a single site

     Table 38. Estimation results for the before years

     Table 39. Prediction results for the after years

     Table 40. Evaluation of the treatment for the example site

LIST OF FIGURES

     Figure 1. Chart. Speed limits throughout the 1990s on rural interstate highways

     Figure 2. Chart. Data analysis process flowchart

     Figure 3. Equation. Crash rate

     Figure 4. Chart. Fundamental steps of the empirical Bayes approach

     Figure 5. Equation. Crash models for Virginia

     Figure 6. Equation. Crash models for Washington

     Figure 7. Chart. Comparison of crash estimation models for Virginia and Washington State based on 1991-1993 data

     Figure 8. Equation. Expected mean value of crashes

     Figure 9. Chart. Plot of goodness of fit for the crash estimation model versus ADT

     Figure 10. Chart. Plot of goodness of fit for the crash estimation model versus length

     Figure 11. Equation. Alternative crash estimation model

     Figure 12. Equation. CEM for before years

     Figure 13. Equation. Expected crash frequency m for period 1

     Figure 14. Equation. Variance of expected crash frequency m for period 1

     Figure 15. Equation. Expected crash frequency m for period y

     Figure 16. Equation. Variance of expected crash frequency m for period y

     Figure 17. Equation. Would-have-been crashes, had there been no speed limit change

     Figure 18. Equation. Actual crashes, given that the speed limit did change

     Figure 19. Equation. The difference between would-have-been and actual crashes

     Figure 20. Equation. Variance for δ

     Figure 21. Equation. Confidence intervals for δ

     Figure 22. Equation. Reduction in the expected number of crashes

     Figure 23. Equation. Ratio of actual to would-have-been crashes

     Figure 24. Equation. Variance of ratio of actual to would-have-been crashes

     Figure 25. Equation. Confidence intervals for θ

     Figure 26. Chart. Mean speed for all vehicles

     Figure 27. Chart. 85th Percentile speeds and median speeds

     Figure 28. Chart. Median speed trends

     Figure 29. Chart. Speed variance rates

     Figure 30. Chart. Noncompliance rates

     Figure 31. Chart. Total crash rates

     Figure 32: Chart. Total truck-involved crash rates in Virginia interstate highways

     Figure 33. Chart. Relationship between the Poisson and negative binomial distributions for crash frequencies

     Figure 34. Chart. Comparison of Poisson distribution and actual crash distribution

     Figure 35. Chart. comparison of negative binomial distribution and actual crash distribution (probability density function)

     Figure 36. Equation. Crash frequency for year 1 as base year

     Figure 37. Equation. Crash frequency for year 3 as base year

     Figure 38. Equation. Expected value of crash count for year 1

     Figure 39. Equation. Variance of expected value of crash count for year 1

     Figure 40. Equation. Estimation of estimated values of crash counts for year 1

     Figure 41. Equation. Variance of estimation of estimated values of crash counts for year 1

     Figure 42. Equation. Expected value of crash count for year 3

     Figure 43. Equation. Expected value of crash count, year 3 as base year

     Figure 44. Equation. Variance of expected value of crash count, year 3 as base year

     Figure 45. Equation. Statistically significant difference in mean speeds

     Figure 46. Chart. Histogram based on random numbers

     Figure 47. Equation. Formula to determine confidence intervals associated with mean speed

     Figure 48. Equation. Example of formula in figure 47

     Figure 49. Equation. Confidence interval for 85th percentile speed

     Figure 50. Equation. Binomial distribution

     Figure 51. Chart. Arizona total crash rate versus ADT

     Figure 52. Chart. Virginia total crash rate versus ADT

     Figure 53. Chart. Virginia total crash rate versus ADT

     Figure 54. Equation. Crash estimation model

     Figure 55. Equation. Mean of the estimate for 1991

     Figure 56. Equation. Mean of the estimate for 1992

     Figure 57. Equation. Mean of the estimate for 1993

     Figure 58. Equation. Calculation for ratio before year y

     Figure 59. Equation. Ratio before year 1991

     Figure 60. Equation. Ratio before year 1992

     Figure 61. Equation. Ratio before year 1993

     Figure 62. Equation. Expected crash counts

     Figure 63. Equation. Variance of the expected crash counts for year 1

     Figure 64. Equation. Expected crash counts

     Figure 65. Equation. Variance of expected crash counts

     Figure 66. Equation. Application for 1991

     Figure 67. Equation. Application for variance 1991

     Figure 68. Equation. Application for 1992

     Figure 69. Equation. Application for variance 1992

     Figure 70. Equation. Application for 1993

     Figure 71. Equation. Application for variance for 1993

     Figure 72. Equation. Computation of E(m1,1995)

     Figure 73. Equation. Computation of E(m1,1996)

     Figure 74. Equation. Computation of C1,1995

     Figure 75. Equation. Computation of C1,1996

     Figure 76. Expected crash counts, year y

     Figure 77. Variance of expected crash counts, year y

     Figure 78. Equation. Expected crash counts, year 1995

     Figure 79. Variance of expected crash counts, year 1995

     Figure 80. Expected crash counts, year 1996

     Figure 81. Variance of expected crash counts, year 1996

     Figure 82. Equation. Total would-have-been crashes for a particular site

     Figure 83. Equation. Total actual crashes for a particular site

     Figure 84. Equation. Safety impact for a particular site

     Figure 85. Equation. Ratio of actual to would-have-been crashes

     Figure 86. Chart. Cumulative differences, by year, at the example site

     Figure 87. Total would-have-been crashes

     Figure 88. Total actual crashes

     Figure 89. Safety impact

     Figure 90. Variance of the difference between would-have-been crashes and actual crashes

     Figure 91. Standard deviation of the difference between would-have-been crashes and actual crashes

     Figure 92. Equation. Computation of the index of effectiveness

     Figure 93. Equation. Variance of θ

     Figure 94. Equation. Empirical confidence bounds

ABSTRACT

To compare the safety effects of a uniform speed limit (USL) for all vehicles as opposed to a differential speed limit (DSL) for cars and heavy trucks, detailed crash data, speed monitoring data, and traffic volumes were sought for rural interstate highways in 17 States for the period 1991 to 2000. Data from nine of those States were used such that they could be divided into four policy groups based on the type of speed limit employed during the period. These were maintenance of a uniform limit only, maintenance of a differential limit only, a change from a uniform to a differential limit, and a change from a differential to a uniform limit. Conventional statistical tests (analysis of variance, Tukey's test, and Dunnett's test) were used to study speed and crash rate changes in the four policy groups. A modified empirical Bayes formation was used to evaluate crash frequency changes without presuming a constant relationship between crashes and traffic volume.

No consistent safety effects of DSL as opposed to USL were observed within the scope of the study. The mean speed, 85th percentile speed, median speed, and crash rates tended to increase over the 10-year period, regardless of whether a DSL or USL limit was employed. When all sites within a State were included in the analysis, temporal differences in these variables were often not significant. Further examination suggests that while these data do not show a distinction between DSL and USL safety impacts, the relationship between crashes and traffic volume cannot be generalized but instead varies by site within a single State. Because application of the modified empirical Bayes methodology suggested that crash risk increased for all four policy groups, a mathematical model that predicts sharp changes in crash rates based only on ADT does not appear valid at the statewide level.

Any study that relies on historical data will be subject to the limitations of incomplete data sets, and to that extent, additional data collection may shed insights not available from an examination of 1990s data alone. Because the investigators believe that accurate mathematical models may require extensive calibration data, a future effort may be more productive if resources are focused on a small group of States over a period of several years, so that speed variance information and crash information may be obtained by individual roadway segment.

 

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