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.
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Technical Report Documentation Page
1. Report No.
FHWAHRT05042 
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.
VRC000S(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, HRDS05 
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 10year 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 (872) Reproduction of completed page authorized
SI* (Modern Metric) Conversion Factors
TABLE OF CONTENTS
INTRODUCTION
PURPOSE AND SCOPE
RESULTS, DISCUSSION, AND LIMITATIONS
Vehicle Speeds
Mean Speeds: An Example of How the Data May Be Assessed
Graphical Overview of Changes in Speed Variance, 85th Percentile Speed, Median Speed, and Noncompliance Rates
Statistical Results of Changes in Speed Variance, 85th Percentile Speed, Median Speed, and Noncompliance Rates
Comparison of Six Interstate Highway Segments in Idaho
Discussion of Speed Impacts
Crash Rates (Analyzed by Conventional Methods)
Crashes (Analyzed by the Modified Empirical Bayes Method)
Virginia Crashes (DSL to USL)
Arkansas Crashes (USL to DSL)
Idaho Crashes (USL to DSL)
Crashes from the States of Arizona, Missouri, North Carolina, and Washington
Relating Speed and Crash Changes
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 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 19911993 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. Wouldhavebeen 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 wouldhavebeen 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 wouldhavebeen crashes
Figure 24. Equation. Variance of ratio of actual to wouldhavebeen 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 truckinvolved 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(m_{1,1995})
Figure 73. Equation. Computation of E(m_{1,1996})
Figure 74. Equation. Computation of C_{1,1995}
Figure 75. Equation. Computation of C_{1,1996}
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 wouldhavebeen 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 wouldhavebeen crashes
Figure 86. Chart. Cumulative differences, by year, at the example site
Figure 87. Total wouldhavebeen crashes
Figure 88. Total actual crashes
Figure 89. Safety impact
Figure 90. Variance of the difference between wouldhavebeen crashes and actual crashes
Figure 91. Standard deviation of the difference between wouldhavebeen 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 10year 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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