Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges (2021)

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385 APPENDIX C: PROPOSED HSM FREEWAYS CHAPTER CHAPTER 18—PREDICTIVE METHOD FOR FREEWAYS TABLE OF CONTENTS List of Figures ................................................................................................................................ 387 List of Tables .................................................................................................................................. 388 18.1. Introduction ........................................................................................................................... 390 18.2. Overview of the Predictive Method ....................................................................................... 390 18.3. Freeways—Definitions and Predictive Models ...................................................................... 391 18.3.1. Definition of Freeway Facility and Site Types ................................................................ 391 18.3.2. Predictive Model for Freeway Segments ........................................................................ 393 18.3.3. Predictive Model for Freeway Speed-Change Lanes ..................................................... 395 18.4. Predictive Method for Freeways ........................................................................................... 396 18.4.1. Step-by-Step Description of the Predictive Method ........................................................ 396 18.4.2. Data Needed to Apply the Predictive Method ................................................................ 404 18.5. Roadway Segments and Speed-Change Lanes ................................................................... 412 18.5.1. Definition of Freeway Segment and Speed-Change Lane ............................................. 412 18.5.2 Segmentation Process .................................................................................................... 413 18.5.3. Crash Assignment to Sites ............................................................................................. 415 18.6. Safety Performance Functions .............................................................................................. 415 18.6.1. Safety Performance Functions for Roadway Segments ................................................. 416 18.6.2. Safety Performance Functions for Speed-Change Lanes .............................................. 422 18.7. Crash Modification Factors ................................................................................................... 429 18.7.1. Crash Modification Factors for Roadway Segments ...................................................... 430 18.7.2. Crash Modification Factors for Speed-Change Lanes ................................................... 441 18.7.3. Supplemental Calculations to Apply Crash Modification Factors ................................... 447 18.8. Severity Distribution Functions ............................................................................................. 450

386 18.9. Calibration of the SPFs and SDFs to Local Conditions ........................................................ 453 18.10. Limitations of Predictive Method ......................................................................................... 453 18.11. Application of Predictive Method ......................................................................................... 454 18.11.1. Freeways with Barrier-Separated Managed Lanes ...................................................... 454 18.11.2. Freeways with Toll Facilities ......................................................................................... 454 18.12. Summary ............................................................................................................................. 454 18.13. Sample Problems ................................................................................................................ 455 18.13.1. Sample Problem 1 ........................................................................................................ 455 18.13.2. Sample Problem 2 ........................................................................................................ 467 18.13.3. Sample Problem 3 ........................................................................................................ 481 18.13.4. Sample Problem 4 ........................................................................................................ 490 18.13.5. Sample Problem 5 ........................................................................................................ 499 18.13.6. Sample Problem 6 ........................................................................................................ 506 18.14. References .......................................................................................................................... 512 Appendix 18A—Worksheets for Predictive Method for Freeways ................................................. 513

387 LIST OF FIGURES Figure 18-1. The HSM Predictive Method ...................................................................................... 397 Figure 18-2. Through Lane Count in Segments with Lane Add or Lane Drop ............................... 405 Figure 18-3. Freeway Speed-Change Lane Length ....................................................................... 405 Figure 18-4. Curve Length and Radius Measurements ................................................................. 407 Figure 18-5. Measurement of Cross Section Data Elements ......................................................... 408 Figure 18-6. Barrier Variables ........................................................................................................ 409 Figure 18-7. Type B Weaving Section and Length ........................................................................ 410 Figure 18-8. Distance to Nearest Ramp ........................................................................................ 411 Figure 18-9. Clear Zone Width Considerations .............................................................................. 412 Figure 18-10. Illustrative Freeway Segments and Speed-Change Lanes ..................................... 413 Figure 18-11. Segmentation for Varying Median Width ................................................................. 415 Figure 18-12. Graphical Form of the SPFs for Multiple-Vehicle Crashes on Freeway Segments . 419 Figure 18-13. Graphical Form of the SPFs for Single-Vehicle Crashes on Freeway Segments .... 421 Figure 18-14. Graphical Form of the SPFs for Ramp Entrance Speed-Change Lanes ................. 424 Figure 18-15. Graphical Form of the SPFs for Ramp Exit Speed-Change Lanes ......................... 427

388 LIST OF TABLES Table 18-1. Urban Freeway Segment SPFs .................................................................................. 392 Table 18-2. Urban Freeway Speed-Change Lane SPFs ............................................................... 393 Table 18-3. Freeway Safety Performance Functions ..................................................................... 415 Table 18-4. Applicable AADT Volume Ranges for SPFs ............................................................... 416 Table 18-5. SPF Coefficients for Multiple-Vehicle Crashes on Freeway Segments ...................... 418 Table 18-6. Default Distribution of Multiple-Vehicle Crashes by Crash Type for Freeway Segments ....................................................................................................................................... 420 Table 18-7. SPF Coefficients for Single-Vehicle Crashes on Freeway Segments ........................ 421 Table 18-8. Default Distribution of Single-Vehicle Crashes by Crash Type for Freeway Segments ....................................................................................................................................... 422 Table 18-9. SPF Coefficients for Ramp-Entrance-Related Crashes in Speed-Change Lanes ...... 424 Table 18-10. Default Distribution of Ramp-Entrance-Related Crashes by Crash Type ................. 426 Table 18-11. SPF Coefficients for Ramp-Exit-Related Crashes in Speed-Change Lanes ............ 427 Table 18-12. Default Distribution of Ramp-Exit-Related Crashes by Crash Type ......................... 428 Table 18-13. Freeway Crash Modification Factors and their Corresponding SPFs ....................... 429 Table 18-14. Coefficients for Horizontal Curve CMF–Freeway Segments .................................... 431 Table 18-15. Coefficients for Lane Width CMF–Freeway Segments ............................................. 432 Table 18-16. Coefficients for Inside Shoulder Width CMF–Freeway Segments ............................ 432 Table 18-17. Coefficients for Median Width CMF–Freeway Segments ......................................... 433 Table 18-18. Coefficients for Median Barrier CMF–Freeway Segments........................................ 434 Table 18-19. Coefficients for High Volume CMF–Freeway Segments .......................................... 435 Table 18-20. Coefficients for Lane Change CMF–Freeway Segments ......................................... 437 Table 18-21. Coefficients for Outside Shoulder Width CMF–Freeway Segments ......................... 439 Table 18-22. Coefficients for Outside Barrier CMF–Freeway Segments ....................................... 441 Table 18-23. Coefficients for Horizontal Curve CMF–Speed-Change Lanes ................................ 442 Table 18-24. Coefficients for Inside Shoulder Width CMF–Speed-Change Lanes ........................ 443

389 Table 18-25. Coefficients for Median Width CMF–Speed-Change Lanes ..................................... 444 Table 18-26. Coefficients for Median Barrier CMF–Speed-Change Lanes.................................... 444 Table 18-27. Coefficients for High Volume CMF–Speed-Change Lanes ...................................... 445 Table 18-28. Coefficients for Ramp Entrance CMF–Speed-Change Lanes .................................. 446 Table 18-29. Coefficients for Ramp Exit CMF–Speed-Change Lanes .......................................... 447 Table 18-30. SDF Coefficients for Freeway Segments and Speed-Change Lanes ....................... 452 Table 18-31. List of Sample Problems ........................................................................................... 455 Table 18-32. Freeway Segment Worksheet (1 of 4)—Sample Problem 1 ..................................... 464 Table 18-33. Freeway Segment Worksheet (2 of 4)—Sample Problem 1 ..................................... 465 Table 18-34. Freeway Segment Worksheet (3 of 4)—Sample Problem 1 ..................................... 466 Table 18-35. Freeway Segment Worksheet (4 of 4)—Sample Problem 1 ..................................... 467 Table 18-36. Freeway Segment Worksheet (1 of 4)—Sample Problem 2 ..................................... 478 Table 18-37. Freeway Segment Worksheet (2 of 4)—Sample Problem 2 ..................................... 479 Table 18-38. Freeway Segment Worksheet (3 of 4)—Sample Problem 2 ..................................... 480 Table 18-39. Freeway Segment Worksheet (4 of 4)—Sample Problem 2 ..................................... 481 Table 18-40. Freeway Speed-Change Lane Worksheet (1 of 3)—Sample Problem 3 .................. 488 Table 18-41. Freeway Speed-Change Lane Worksheet (2 of 3)—Sample Problem 3 .................. 489 Table 18-42. Freeway Speed-Change Lane Worksheet (3 of 3)—Sample Problem 3 .................. 490 Table 18-43. Freeway Speed-Change Lane Worksheet (1 of 3)—Sample Problem 4 .................. 497 Table 18-44. Freeway Speed-Change Lane Worksheet (2 of 3)—Sample Problem 4 .................. 498 Table 18-45. Freeway Speed-Change Lane Worksheet (3 of 3)—Sample Problem 4 .................. 499 Table 18-46. Freeway Segment Worksheet (1 of 4)—Sample Problem 5 ..................................... 503 Table 18-47. Freeway Segment Worksheet (2 of 4)—Sample Problem 5 ..................................... 504 Table 18-48. Freeway Segment Worksheet (3 of 4)—Sample Problem 5 ..................................... 505 Table 18-49. Freeway Segment Worksheet (4 of 4)—Sample Problem 5 ..................................... 506 Table 18-50. Project-Level EB Method Worksheet (1 of 2)—Sample Problem 6 .......................... 511 Table 18-51. Project-Level EB Method Worksheet (2 of 2)—Sample Problem 6 .......................... 512

390 Chapter 18—Predictive Method for Freeways 18.1. INTRODUCTION This chapter presents the predictive method for freeways. A general introduction to the Highway Safety Manual (HSM) predictive method is provided in Part C—Introduction and Applications Guidance. The predictive method for freeways provides a structured methodology to estimate the expected average crash frequency (in total, or by crash type or severity) for a freeway with known characteristics. Crashes involving vehicles of all types are included in the estimate. The predictive method can be applied to an existing freeway, a design alternative for an existing freeway, a new freeway, or for alternative traffic volume projections. An estimate can be made of expected average crash frequency for a prior time period (i.e., what did or would have occurred) or a future time period (i.e., what is expected to occur). The development of the predictive method in this chapter is documented by Bonneson et al. (1). This chapter presents the following information about the predictive method for freeways:  A concise overview of the predictive method.  Definitions of the facility types and site types addressed by the predictive method.  A step-by-step description of the predictive method.  Details for dividing a freeway facility into individual evaluation sites.  Safety performance functions (SPFs) for freeways.  Crash modification factors (CMFs) for freeways.  Severity distribution functions (SDFs) for freeways.  Limitations of the predictive method.  Sample problems illustrating the application of the predictive method. 18.2. OVERVIEW OF THE PREDICTIVE METHOD The predictive method provides an 18-step procedure to estimate the expected average crash frequency (in total, or by crash type or severity) for a roadway network, facility, or site. A site is a freeway segment or a freeway speed-change lane. A freeway speed-change lane is an uncontrolled terminal between a ramp and a freeway. A facility consists of a contiguous set of individual sites. A facility is defined by the surrounding land use, roadway cross section, and degree of access. A roadway network consists of a number of contiguous facilities. The predictive method is used to estimate the expected number of crashes for an individual site. This estimate can be summed for all sites to compute the expected number of crashes for the entire facility or network. The estimate represents a given time period of interest (in years) during which the geometric design and traffic control features are unchanged and traffic volumes are known or forecasted. The expected average crash frequency is obtained by dividing the expected number of crashes by the number of years during the time period of interest. The estimate is obtained by combining the prediction from the predictive model with observed crash data using the empirical Bayes (EB) Method.

391 The predictive models used in this chapter are described in detail in Section 18.3. The variables that comprise the predictive models include a series of subscripts to describe precisely the conditions to which they apply. These subscripts are described in detail in later sections of this chapter. For this section, it is sufficient to use “place-holder” subscripts such as w, x, y, z, and m. The subscript w is a place-holder for specific site-type subscripts that define the equation’s application (e.g., it is replaced with “fs” when needed to indicate that the equation applies to a freeway segment). Similarly, x is a place-holder for segment cross-section subscripts, y is a place-holder for crash-type subscripts, z is a place holder for crash severity, and m is a place-holder for a specific geometric design or traffic control feature. The predictive models used in this chapter to determine the predicted average crash frequency are of the general form shown in Equation 18-1. ( ) z,y,x,wz,y,x,w,mz,y,x,w,z,y,x,w,z,y,x,w,spfz,y,x,w,p CCMFCMFCMFNN ×××××= 21 Where: Np, w, x, y, z = predicted average crash frequency for a specific year for site type w, cross section or control type x, crash type y, and severity z (crashes/yr); Nspf, w, x, y, z = predicted average crash frequency determined for base conditions of the SPF developed for site type w, cross section or control type x, crash type y, and severity z (crashes/yr); CMFm, w, x, y, z = crash modification factors specific to site type w, cross section or control type x, crash type y, and severity z for specific geometric design and traffic control feature m; and Cw, x y, z = calibration factor to adjust SPF for local conditions for site type w, cross section or control type x, crash type y, and severity z. The predictive models provide estimates of the predicted average crash frequency in total, or by crash type or severity. A default distribution of crash type is included in the predictive method. It is used with the predictive models to quantify the crash frequency for each of several crash types. The models predict fatal-and-injury crash frequency and property-damage-only crash frequency. A severity distribution function is available to further quantify the crash frequency by the following severity levels: fatal, incapacitating injury, non-incapacitating injury, and possible injury. 18.3. FREEWAYS—DEFINITIONS AND PREDICTIVE MODELS This section provides the definitions of the facility and site types discussed in this chapter. It also describes the predictive models for each of the site types. 18.3.1. Definition of Freeway Facility and Site Types The predictive method in this chapter applies to the following freeway facilities: rural freeway segment with four to eight lanes, urban freeway segment with four to ten lanes, and freeway speed-change lanes associated with entrance ramps and exit ramps. Freeways have fully-restricted access control and grade separation with all intersecting roadways. Freeways are accessed only through grade-separated interchanges. Roads having at-grade access should be analyzed as rural highways or urban or suburban arterials. These facility types are addressed in Chapters 10, 11, and 12. The terms “freeway” and “road” are used interchangeably in this chapter and apply to all freeways independent of official state designation or local roadway designation. Equation 18-1

392 Classifying an area as urban, suburban, or rural is subject to the roadway characteristics, surrounding population, and surrounding land uses, and is at the analyst’s discretion. In the HSM, the definition of “urban” and “rural” areas is based on Federal Highway Administration (FHWA) guidelines which classify “urban” areas as places inside urban boundaries where the population is greater than 5,000 persons. “Rural” areas are defined as places outside urban areas where the population is less than 5,000 persons. The HSM uses the term “suburban” to refer to outlying portions of an urban area; the predictive method does not distinguish between urban and suburban portions of a developed area. Table 18-1 identifies the urban freeway segment configurations for which SPFs have been developed. A second set of SPFs have been developed for rural freeway segments with four, six, or eight lanes (they are not shown in the table, but use the same nomenclature). The SPFs are used to estimate the predicted average crash frequency by crash type and crash severity. These estimates are added to yield the total predicted average crash frequency for an individual site. The predictions include both travel directions combined. Table 18-1. Urban Freeway Segment SPFs Site Type (w) Cross Section (x) a Crash Type (y) Crash Severity (z) SPF Freeway segments (fs) Four-lane divided (4) Multiple vehicle (mv) Fatal and injury (fi) Nspf, fs, 4, mv, fi Property damage only (pdo) Nspf, fs, 4, mv, pdo Single vehicle (sv) Fatal and injury (fi) Nspf, fs, 4, sv, fi Property damage only (pdo) Nspf, fs, 4, sv, pdo Six-lane divided (6) Multiple vehicle (mv) Fatal and injury (fi) Nspf, fs, 6, mv, fi Property damage only (pdo) Nspf, fs, 6, mv, pdo Single vehicle (sv) Fatal and injury (fi) Nspf, fs, 6, sv, fi Property damage only (pdo) Nspf, fs, 6, sv, pdo Eight-lane divided (8) Multiple vehicle (mv) Fatal and injury (fi) Nspf, fs, 8, mv, fi Property damage only (pdo) Nspf, fs, 8, mv, pdo Single vehicle (sv) Fatal and injury (fi) Nspf, fs, 8, sv, fi Property damage only (pdo) Nspf, fs, 8, sv, pdo Ten-lane divided (10) Multiple vehicle (mv) Fatal and injury (fi) Nspf, fs, 10, mv, fi Property damage only (pdo) Nspf, fs, 10, mv, pdo Single vehicle (sv) Fatal and injury (fi) Nspf, fs, 10, sv, fi Property damage only (pdo) Nspf, fs, 10, sv, pdo Note: a The term “divided” indicates that opposing directions of travel are separated by use of a non-traversable median (i.e., a depressed median, a depressed median with barrier, or a flush-paved median with barrier). The freeway segment is defined as follows:  Four-lane freeway segment (4)—a length of roadway consisting of four through lanes with a continuous cross section providing two directions of travel in which the opposing travel lanes are physically separated by either distance or a barrier.  Six-lane freeway segment (6)— a length of roadway consisting of six through lanes with a continuous cross section providing two directions of travel in which the opposing travel lanes are physically separated by either distance or a barrier.

393  Eight-lane freeway segment (8)— a length of roadway consisting of eight through lanes with a continuous cross section providing two directions of travel in which the opposing travel lanes are physically separated by either distance or a barrier.  Ten-lane freeway segment (10)— a length of roadway consisting of ten through lanes with a continuous cross section providing two directions of travel in which the opposing travel lanes are physically separated by either distance or a barrier. Table 18-2 identifies the urban speed-change lane configurations for which SPFs have been developed. A second set of SPFs have been developed for rural speed-change lanes with four, six, or eight lanes (they are not shown in the table, but use the same nomenclature). The SPFs are used to estimate the predicted average crash frequency by crash severity. These estimates are added to yield the total predicted average crash frequency for an individual site. Table 18-2. Urban Freeway Speed-Change Lane SPFs Site Type (w) Cross Section (x) Crash Type (y) Crash Severity (z) SPF Speed-change lanes (sc) Ramp entrance to four- lane divided (4EN) All types (at) Fatal and injury (fi) Nspf, sc, 4EN, at, fi Property damage only (pdo) Nspf, sc, 4EN, at, pdo Ramp entrance to six- lane divided (6EN) All types (at) Fatal and injury (fi) Nspf, sc, 6EN, at, fi Property damage only (pdo) Nspf, sc, 6EN, at, pdo Ramp entrance to eight-lane divided (8EN) All types (at) Fatal and injury (fi) Nspf, sc, 8EN, at, fi Property damage only (pdo) Nspf, sc, 8EN, at, pdo Ramp entrance to ten- lane divided (10EN) All types (at) Fatal and injury (fi) Nspf, sc, 10EN, at, fi Property damage only (pdo) Nspf, sc, 10EN, at, pdo Ramp exit from four- lane divided (4EX) All types (at) Fatal and injury (fi) Nspf, sc, 4EX, at, fi Property damage only (pdo) Nspf, sc, 4EX, at, pdo Ramp exit from six- lane divided (6EX) All types (at) Fatal and injury (fi) Nspf, sc, 6EX, at, fi Property damage only (pdo) Nspf, sc, 6EX, at, pdo Ramp exit from eight- lane divided (8EX) All types (at) Fatal and injury (fi) Nspf, sc, 8EX, at, fi Property damage only (pdo) Nspf, sc, 8EX, at, pdo Ramp exit from ten- lane divided (10EX) All types (at) Fatal and injury (fi) Nspf, sc, 10EX, at, fi Property damage only (pdo) Nspf, sc, 10EX, at, pdo The speed-change lane cross section is defined as a ramp entrance (nEN) or ramp exit (nEX) with n lanes. The variable n is used to describe the number of through lanes in the portion of freeway adjacent to the speed-change lane plus those freeway lanes in the opposing travel direction. This approach to describing the speed-change lane cross section is used for consistency with that used for freeway segment SPFs. The variable n is not intended to describe the number of lanes in the speed-change lane. 18.3.2. Predictive Model for Freeway Segments In general, a predictive model is used to compute the predicted average crash frequency for a site. It combines the SPF, CMFs, and a calibration factor. The predicted quantity can describe crash frequency in

394 total, or by crash type or severity. This section describes the predictive model for freeway segments. The next section describes the predictive model for speed-change lanes. The predictive model for freeway segments is used to estimate the predicted average frequency of segment crashes (i.e., the estimate does not include speed-change-lane-related crashes). Speed-change- related crashes are defined in Section 18.3.3 and estimated using the predictive method described in that section. The predictive model for freeway segments is presented in Equation 18-2. This equation consists of four terms, where each of Equation 18-3 to Equation 18-6 correspond to one term. pdosvnfsppdomvnfspfisvnfspfimvnfspasatnfsp NNNNN ,,,,,,,,,,,,,,,,,,,, +++= ( ) ( )fiatacfsmfiatacfs fimvacfsmfimvacfsfimvnfsspffimvacfsfimvnfsp CMFCMF CMFCMFNCN ,,,,,,,,1 ,,,,,,,,1,,,,,,,,,,, ××× ××××=   ( ) ( )fiatacfsmfiatacfs fisvacfsmfisvacfsfisvnfsspffisvacfsfisvnfsp CMFCMF CMFCMFNCN ,,,,,,,,1 ,,,,,,,,1,,,,,,,,,,, ××× ××××=   ( ) ( )pdoatacfsmpdoatacfs pdomvacfsmpdomvacfspdomvnfsspfpdomvacfspdomvnfsp CMFCMF CMFCMFNCN ,,,,,,,,1 ,,,,,,,,1,,,,,,,,,,, ××× ××××=   ( ) ( )pdoatacfsmpdoatacfs pdosvacfsmpdosvacfspdosvnfsspfpdosvacfspdosvnfsp CMFCMF CMFCMFNCN ,,,,,,,,1 ,,,,,,,,1,,,,,,,,,,, ××× ××××=   Where: Np, fs, n, y, z = predicted average crash frequency of a freeway segment with n lanes, crash type y (y = sv: single vehicle, mv: multiple vehicle, at: all types), and severity z (z = fi: fatal and injury, pdo: property damage only, as: all severities) (crashes/yr); Nspf, fs, n, y, z = predicted average crash frequency of a freeway segment with base conditions, n lanes, crash type y (y = sv: single vehicle, mv: multiple vehicle, at: all types), and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/yr); CMFm, fs, ac, y, z = crash modification factor for a freeway segment with any cross section ac, feature m, crash type y (y = sv: single vehicle, mv: multiple vehicle, at: all types), and severity z (z = fi: fatal and injury, pdo: property damage only); and Cfs, ac, y, z = calibration factor for freeway segments with any cross section ac, crash type y (y = sv: single vehicle, mv: multiple vehicle, at: all types), and severity z (z = fi: fatal and injury, pdo: property damage only). Equation 18-2 shows that freeway segment crash frequency is estimated as the sum of four components: fatal-and-injury multiple-vehicle crash frequency, fatal-and-injury single-vehicle crash frequency, property-damage-only multiple-vehicle crash frequency, and property-damage-only single-vehicle crash frequency. Equation 18-2 Equation 18-3 Equation 18-4 Equation 18-5 Equation 18-6

395 Different CMFs are used in Equation 18-3 to Equation 18-6. The first term in parentheses in each equation recognizes that the influence of some features is unique to each crash type. In contrast, the second term in parentheses in these equations recognizes that some features have a similar influence on all crash types. All CMFs are unique to crash severity. Equation 18-3 and Equation 18-4 are used to estimate the fatal-and-injury crash frequency. Equation 18-5 and Equation 18-6 are used to estimate the property-damage-only crash frequency. The SPFs for freeway segments are presented in Section 18.6.1. The associated CMFs are presented in Section 18.7.1. Similarly, the associated SDFs are presented in Section 18.8. A procedure for establishing the value of the calibration factor is described in Section B.1 of Appendix B to Part C. 18.3.3. Predictive Model for Freeway Speed-Change Lanes The predictive model for speed-change lanes is used to compute the predicted average crash frequency for a speed-change lane. Speed-change-related crashes include all crashes that are located between the gore point and the taper point of a speed-change lane and that involve vehicles (a) in the speed-change lane or (b) in the freeway lanes on the same side of the freeway as the speed-change lane. The predictive model for ramp entrance speed-change lanes is presented in Equation 18-7. This equation consists of two terms, where each of Equation 18-8 and Equation 18-9 correspond to one term. pdoatnENscpfiatnENscpasatnENscp NNN ,,,,,,,,,,,, += ( ) ( )fiatacscmfiatacsc fiatnENscmfiatnENscfiatnENscspffiatENscfiatnENscp CMFCMF CMFCMFNCN ,,,,,,,,1 ,,,,,,,,1,,,,,,,,,,, ××× ××××=   ( ) ( )pdoatacscmpdoatacsc pdoatnENscmpdoatnENscpdoatnENscspfpdoatENscpdoatnENscp CMFCMF CMFCMFNCN ,,,,,,,,1 ,,,,,,,,1,,,,,,,,,,, ××× ××××=   Where: Np, sc, nEN, at, z = predicted average crash frequency of ramp entrance speed-change lane on a freeway with n lanes, all crash types at, and severity z (z = fi: fatal and injury, pdo: property damage only, as: all severities) (crashes/yr); Nspf, sc, nEN, at, z = predicted average crash frequency of a ramp entrance speed-change lane on a freeway with base conditions, n lanes, all crash types at, and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/yr); CMFm, sc, x, at, z = crash modification factor for a speed-change lane with feature m, cross section x (x = nEN: ramp entrance adjacent to a freeway with n lanes, nEX: ramp exit adjacent to a freeway with n lanes, ac: any cross section), all crash types at, and severity z (z = fi: fatal and injury, pdo: property damage only); and Csc, EN, at, z = calibration factor for a ramp entrance speed-change lane with all crash types at and severity z (z = fi: fatal and injury, pdo: property damage only). The predictive model for ramp exit speed-change lanes is presented in Equation 18-10. This equation consists of two terms, where each of Equation 18-11 and Equation 18-12 correspond to one term. Equation 18-7 Equation 18-8 Equation 18-9

396 pdoatnEXscpfiatnEXscpasatnEXscp NNN ,,,,,,,,,,,, += ( ) ( )fiatacscmfiatacsc fiatnEXscmfiatnEXscfiatnEXscspffiatEXscfiatnEXscp CMFCMF CMFCMFNCN ,,,,,,,,1 ,,,,,,,,1,,,,,,,,,,, ××× ××××=   ( ) ( )pdoatacscmpdoatacsc pdoatnEXscmpdoatnEXscpdoatnEXscspfpdoatEXscpdoatnEXscp CMFCMF CMFCMFNCN ,,,,,,,,1 ,,,,,,,,1,,,,,,,,,,, ××× ××××=   Where: Np, sc, nEX, at, z = predicted average crash frequency of ramp exit speed-change lane on a freeway with n lanes, all crash types at, and severity z (z = fi: fatal and injury, pdo: property damage only, as: all severities) (crashes/yr); Nspf, sc, nEX, at, z = predicted average crash frequency of a ramp exit speed-change lane on a freeway with base conditions, n lanes, all crash types at, and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/yr); and Csc, EX, at, z = calibration factor for a ramp exit speed-change lane with all crash types at and severity z (z = fi: fatal and injury, pdo: property damage only). Equation 18-7 and Equation 18-10 show that speed-change lane crash frequency is estimated as the sum of two components: predicted average fatal-and-injury crash frequency and predicted average property- damage-only crash frequency. Different CMFs are used in Equation 18-8, Equation 18-9, Equation 18-11, and Equation 18-12. The first term in parentheses in each equation recognizes that the influence of some features is unique to each speed-change lane type. In contrast, the second term in parentheses in these equations recognizes that some features have a similar influence on both speed-change lane types. All CMFs are unique to crash severity. The SPFs for speed-change lanes are presented in Section 18.6.2. The associated CMFs are presented in Section 18.7.2. Similarly, the associated SDFs are presented in Section 18.8. A procedure for establishing the value of the calibration factor is described in Section B.1 of Appendix B to Part C. 18.4. PREDICTIVE METHOD FOR FREEWAYS This section describes the predictive method for freeways. It consists of two sections. The first section provides a step-by-step description of the predictive method. The second section describes the geometric design features, traffic control features, and traffic volume data needed to apply the predictive method. 18.4.1. Step-by-Step Description of the Predictive Method The predictive method for freeways is shown in Figure 18-1. Applying the predictive method yields an estimate of the expected average crash frequency (in total, or by crash type or severity) for a freeway facility or network. The predictive models described in this chapter are applied in Steps 9, 10, and 11 of the predictive method. The information needed to apply each step is provided in this section. Equation 18-10 Equation 18-11 Equation 18-12

397 Define roadway limits and facility type. Define the period of study. Determine AADT and availability of crash data for every year in the period of interest. Determine geometric conditions. Divide roadway into individual roadway segments and speed-change lanes Assign observed crashes to individual sites (if applicable). Select a roadway segment or speed-change lane. Select first or next year of the evaluation period. Select and apply SPF. Apply CMFs. Apply a calibration factor. Is there another year? Apply site-specific EB method (if applicable) and apply SDF. Sum all sites and years. Apply project-level EB method (if applicable). Compare and evaluate results. Is there another site? Is there an alternative design, treatment, or forecast AADT to be evaluated? YES YES YES Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 11 Step 12 Step 13 Step 14 Step 15 Step 16 Step 17 Step 18 NO NO NO Figure 18-1. The HSM Predictive Method

398 There are 18 steps in the predictive method. In some situations, certain steps will not be needed because data are not available or the step is not applicable to the situation at hand. In other situations, steps may be repeated if an estimate is desired for several sites or for a period of several years. In addition, the predictive method can be repeated as necessary to undertake crash estimation for each alternative design, traffic volume scenario, or proposed treatment option (within the same time period to allow for comparison). The following discussion explains the details of each step of the method, as applied to freeways. Step 1—Define the limits of the project. A project can be a freeway network, a freeway facility, or a site. A site is either a speed-change lane or a homogeneous freeway segment. A site is further categorized by its cross section. A description of the specific site types is provided in Section 18.3.1. The project limits are defined in this step. They will depend on the purpose of the study. The study may be limited to one specific site or, to a group of contiguous sites. Alternatively, the limits can be expanded to include a very long corridor for the purposes of network screening (as discussed in Chapter 4). For comparative analysis of design alternatives, the project limits should be the same for all alternatives. The analyst should identify (or establish) a reference line for the freeway. This line is defined as the inside edge of traveled way for the roadbed serving traffic moving in the increasing milepost direction. All lengths along the roadway are determined using this line. The location of the reference line is shown in subsequent figures (e.g., Figure 18-6). Locations along this line are specified using a linear referencing system, and are identified using the label “milepost X,” where the number for X has units of miles (e.g., milepost 1.4). Step 2—Define the period of interest. The study period is defined as the consecutive years for which an estimate of the expected average crash frequency is desired. The crash period is defined as the consecutive years for which observed crash data are available. The evaluation period is defined as the combined set of years represented by the study period and crash period. Every year in the evaluation period is evaluated using the predictive method. All periods are measured in years. If the EB Method is not used, then the study period is the same as the evaluation period. The EB Method is discussed in more detail in Step 3. If the EB Method is used and the crash period is not fully included in the study period, then the predictive models need to be applied to the study years plus each year of the crash period not represented in the study period. In this situation, the evaluation period includes the study period and any additional years represented by the crash data but not in the study period. For example, let the study period be defined as the years 2010, 2011, and 2012. If crash data are available for 2008, 2009, and 2010, then the evaluation period is 2008, 2009, 2010, 2011, and 2012. The study period can represent either a past time period or a future time period. Whether the predictive method is used for a past or future period depends upon the purpose of the study. The study period may be:  A past period for:  An existing roadway network, facility, or site. If observed crash data are available, the study period is the period of time for which the observed crash data are available and for which (during that period) the site geometric design features, traffic control features, and traffic volumes are known.

399  An existing roadway network, facility, or site for which alternative geometric design or traffic control features are proposed (for near-term conditions) and site traffic volumes are known.  A future period for:  An existing roadway network, facility, or site for a future period where forecast traffic volumes are available.  An existing roadway network, facility, or site for which alternative geometric design or traffic control features are proposed and forecast traffic volumes are available.  A new freeway network, facility, or site that does not currently exist but is proposed for construction and for which forecast traffic volumes are available. Step 3—For the study period, determine the availability of AADT volumes and, for an existing project, the availability of observed crash data (to determine whether the EB Method is applicable). Traffic volume data are acquired in this step. Also, a decision is made whether the EB Method will be applied. If it will be applied, then it must also be decided whether the site-specific or project-level EB Method will be applied. If the EB Method will be applied, then the observed crash data are also acquired in this step. Determining Traffic Volumes The SPFs used in Step 9 (and some CMFs in Step 10) include annual average daily traffic (AADT) volume as a variable. For a past period, the AADT volume may be determined by using automated recorder data, or estimated by a sample survey. For a future period, the AADT volume may be a forecast estimate based on appropriate land use planning and traffic volume forecasting models. For each freeway segment, five AADT values are required. They include: (1) the AADT volume of the freeway segment, (2) AADT volume of the nearest entrance ramp upstream of the segment for the increasing milepost travel direction, (3) AADT volume of the nearest entrance ramp upstream of the segment for the decreasing milepost travel direction, (4) AADT volume of the nearest exit ramp downstream of the segment for the increasing milepost travel direction, and (5) AADT volume of the nearest exit ramp downstream of the segment for the decreasing milepost travel direction. For each ramp entrance speed-change lane, two values are required. They include the AADT volume of the freeway segment and the AADT volume of the ramp. For each ramp exit speed-change lane, only the AADT volume of the freeway segment is required. The AADT volume of the ramp is not needed. The AADT volumes are needed for each year of the evaluation period. The AADT volume for a given year represents an annual average daily 24-hour traffic volume. The freeway segment AADT volume is a two-way volume (i.e., total of both travel directions). Each ramp AADT volume represents a one-way volume. In many cases, it is expected that AADT data will not be available for all years of the evaluation period. In that case, an estimate of AADT volume for each missing year is interpolated or extrapolated, as appropriate. If there is not an established procedure for doing this, the following rules may be applied within the predictive method to estimate the AADT volumes for years in which no data are available. If these rules are applied, the fact that some AADT volumes are estimated should be documented with the analysis results.

400  If AADT volume is available for only a single year, that same volume is assumed to apply to all years of the evaluation period.  If two or more years of AADT data are available, the AADT volumes for intervening years are computed by interpolation.  The AADT volumes for years before the first year for which data are available are assumed to be equal to the AADT volume for that first year.  The AADT volumes for years after the last year for which data are available are assumed to be equal to the AADT volume for that last year. Determining Availability of Observed Crash Data Where an existing site (or an alternative condition for an existing site) is being considered, the EB Method can be used to obtain a more reliable estimate of the expected average crash frequency. The EB Method is applicable when crash data are available for the entire project, or for its individual sites. Crash data may be obtained directly from the jurisdiction’s crash report system. At least two years of crash data are desirable to apply the EB Method. The EB Method (and criteria to determine whether the EB Method is applicable) is presented in Section B.2 in Appendix B to Part C. The EB Method can be applied at the site-specific level or at the project level. At the site-specific level, crash data are assigned to specific sites in Step 6. The site-specific EB Method is applied in Step 13. At the project level, crash data are assigned to a group of sites (typically because they cannot be assigned to individual sites). The project-level EB Method is applied in Step 15. In general, the best results will be obtained if the site-specific EB Method is used. Guidance to determine whether the site-specific or project-level EB Method is applicable is presented in Section B.2.2 in Appendix B to Part C. Step 4—Determine geometric design features, traffic control features, and site characteristics for all sites in the project limits. A range of data is needed to apply a predictive model. These data are used in the SPFs and CMFs to estimate the predicted average crash frequency for the selected site and year. These data represent the geometric design features, traffic control features, and traffic demand characteristics that have been found to have some relationship to safety. These data are needed for each site in the project limits. They are needed for the study period and, if applicable, the crash period. The specific data, and means by which they are measured or obtained, is described in Section 18.4.2. Step 5—Divide the roadway into sites. Using the information from Step 1 and Step 4, the freeway is divided into individual sites, consisting of individual homogeneous freeway segments and speed-change lanes. The procedure for dividing the freeway into individual segments is provided in Section 18.5. Step 6—Assign observed crashes to the individual sites (if applicable). Step 6 applies if it was determined in Step 3 that the site-specific EB Method is applicable. If the site- specific EB Method is not applicable, then proceed to Step 7. In this step, the observed crash data are assigned to the individual sites using the criteria outlined in the next paragraph. Specific criteria for assigning crashes to individual sites are presented in Section B.2.3 in Appendix B to Part C. Step 7—Select the first or next individual site in the project limits. If there are no more sites to be evaluated, proceed to Step 15. Steps 7 through 14 are repeated for each site within the project limits identified in Step 1.

401 Any site can be selected for evaluation because each site is considered to be independent of the other sites. However, good practice is to select the sites in an orderly manner, such as in the order of their physical occurrence in the direction of increasing milepost. Step 8—For the selected site, select the first or next year in the period of interest. If there are no more years to be evaluated for that site, proceed to Step 13. Steps 8 through 12 are repeated for each year in the evaluation period for the selected site. The individual years of the evaluation period are analyzed one year at a time because the SPFs and some CMFs are dependent on AADT volume, which may change from year to year. Step 9—For the selected site, determine and apply the appropriate SPF. The SPF determines the predicted average crash frequency for a site whose features match the SPF’s base conditions. The SPFs (and their base conditions) are described in Section 18.6. Determine the appropriate SPF for the selected site based on its site type and cross section (or traffic control). This SPF is then used to compute the crash frequency for the selected year using the AADT volume for that year, as determined in Step 3. Step 10—Multiply the result obtained in Step 9 by the appropriate CMFs. Collectively, the CMFs are used in the predictive model to adjust the SPF estimate from Step 9 such that the resulting predicted average crash frequency accurately reflects the geometric design and traffic control features of the selected site. The available CMFs are described in Section 18.7. All CMFs presented in this chapter have the same base conditions as the SPFs in this chapter. Only the CMFs presented in Section 18.7 may be used as part of the predictive method described in this chapter. For the selected site, determine the appropriate CMFs for the site type, geometric design features, and traffic control features present. The CMF’s designation by crash type and severity must match that of the SPF with which it is used (unless indicated otherwise in the CMF description). The CMFs for the selected site are calculated using (a) the AADT volume determined in Step 3 for the selected year and (b) the geometric design and traffic control features determined in Step 4. Multiply the result from Step 9 by the appropriate CMFs. Step 11—Multiply the result obtained in Step 10 by the appropriate calibration factor. The SPFs and CMFs in this chapter have each been developed with data from specific jurisdictions and time periods. Calibration to local conditions will account for any differences between these conditions and those present at the selected sites. A calibration factor is applied to each SPF in the predictive method. Detailed guidance for the development of calibration factors is included in Section B.1 of Appendix B to Part C. Multiply the result from Step 10 by the calibration factor to obtain the predicted average crash frequency. Step 12—If there is another year to be evaluated in the evaluation period for the selected site, return to Step 8. Otherwise, proceed to Step 13. This step creates a loop from Step 8 through Step 12 that is repeated for each year of the evaluation period for the selected site.

402 Step 13—Apply site-specific EB Method (if applicable) and apply SDFs. The site-specific EB Method combines the predicted average crash frequency computed in Step 11 with the observed crash frequency of the selected site. It produces a more statistically reliable estimate of the site’s expected average crash frequency. The procedure for applying the site-specific EB Method is provided in Section B.2.4 of Appendix B to Part C. The decision to apply the site-specific EB Method was determined in Step 3. If the EB Method is not used, then the estimate of expected average crash frequency for each year of the study period is limited to the predicted average crash frequency for that year, as computed in Step 11. If the EB Method is used, then the expected average crash frequency is equal to the estimate obtained from the EB Method. An estimate is obtained for each year of the crash period (i.e., the period for which the observed crash data are available). The individual years of the crash period are analyzed one year at a time because the SPFs and some CMFs are dependent on AADT volume, which may change from year to year. Apply the site-specific EB Method to a future time period, if appropriate. Section B.2.6 in Appendix B to Part C provides a procedure for converting the estimates from the EB Method to any years in the study period that are not represented in the crash period (e.g., future years). This approach gives consideration to any differences in traffic volume, geometry, or traffic control between the study period and the crash period. This procedure yields the expected average crash frequency for each year of the study period. Apply the severity distribution functions (SDFs), if desired. The SDFs can be used to compute the expected average crash frequency for each of the following severity levels: fatal, incapacitating injury, non-incapacitating injury, and possible injury. Each SDF includes variables that describe the geometric design and traffic control features of a site. In this manner, the computed distribution gives consideration to the features present at the selected site. The SDFs are described in Section 18.8. They can benefit from being updated based on local data as part of the calibration process. Detailed guidance for the development of the SDF calibration factor is included in Section B.1.4 of Appendix B to Part C. Apply the crash type distribution, if desired. Each predictive model includes a default distribution of crash type. This distribution can be used to compute the expected average crash frequency for each of ten crash types (e.g., head-on, fixed object). The distribution is presented in Section 18.6. It can benefit from being updated based on local data as part of the calibration process. Step 14—If there is another site to be evaluated, return to Step 7; otherwise, proceed to Step 15. This step creates a loop from Step 7 through Step 14 that is repeated for each site of interest. Step 15—Apply the project-level EB Method (if applicable) and apply SDFs. The activities undertaken during this step are the same as undertaken for Step 13 but they occur at the project level (i.e., network or facility). They are based on estimating the project-level predicted average crash frequency. This crash frequency is computed for each year during the crash period. It is computed as the sum of the predicted average crash frequency for all sites (as computed in Step 11). The project-level EB Method combines the project-level predicted average crash frequency with the observed crash frequency for all sites within the project limits. It produces a more statistically reliable estimate of the project-level expected average crash frequency. The procedure for applying the project- level EB Method is provided in Section B.2.5 of Appendix B to Part C.

403 The decision to apply the project-level EB Method was determined in Step 3. If this method is not used, then the project-level expected average crash frequency for each year of the study period is limited to the project-level predicted average crash frequency for that year, as computed in Step 11. If the EB Method is used, then the project-level expected average crash frequency is equal to the estimate obtained from the EB Method. An estimate is obtained for each year of the crash period (i.e., the period for which the observed crash data are available). The individual years of the crash period are analyzed one year at a time because the SPFs and some CMFs are dependent on AADT volume, which may change from year to year. Apply the project-level EB Method to a future time period, if appropriate. Follow the same guidance as provided in Step 13 using the estimate from the project-level EB Method. Apply the severity distribution functions, if desired. Follow the same guidance as provided in Step 13 using the estimate from the project-level EB Method. Apply the crash type distribution, if desired. Follow the same guidance as provided in Step 13 using the estimate from the project-level EB Method. Step 16—Sum all sites and years in the study to estimate the total crash frequency. One outcome of the predictive method is the total expected average crash frequency. The term “total” indicates that the estimate includes all crash types and severities. It is computed from an estimate of the total expected number of crashes, which represents the sum of the total expected average crash frequency for each site and for each year in the study period. The total expected number of crashes during the study period is calculated using Equation 18-13:   = ===         ++= sn j sitesall i jasatnEXisce sitesall i jasatnENisce sitesall i jasatnifseasatacaSe NNNN 1 1 ,,,),(, 1 ,,,),(, 1 ,,,),(, * ,,,, Where: N*e, aS, ac, at, as = total expected number of crashes for all sites aS and all years in the study period (includes all cross sections ac, all crash types at, and all severities as) (crashes); Ne, fs(i), n, at, as, j = expected average crash frequency of freeway segment i with n lanes for year j (includes all crash types at and all severities as) (crashes/yr); Ne, sc(i), nEN, at, as, j = expected average crash frequency of ramp entrance speed-change lane i on a freeway with n lanes for year j (includes all crash types at and all severities as) (crashes/yr); Ne, sc(i), nEX, at, as, j = expected average crash frequency of ramp exit speed-change lane i on a freeway with n lanes for year j (includes all crash types at and all severities as) (crashes/yr); and ns = number of years in the study period (yr). Equation 18-13 is used to compute the total expected number of crashes estimated to occur in the project limits during the study period. The summation of crashes by type and severity for each site and year is not shown in mathematic terms (but it is implied by the subscripts at and as). Equation 18-14 is used to estimate the overall expected average crash frequency within the project limits during the study period. Equation 18-13

404 s asatacaSe asatacaSe n N N * ,,,, ,,,, = Where: Ne, aS, ac, at, as = overall expected average crash frequency for all sites aS and all years in the study period (includes all cross sections ac, all crash types at, and all severities as) (crashes/yr). Step 17—Determine if there is an alternative design, treatment, or forecast AADT to be evaluated. Steps 3 through 17 are repeated as appropriate for the same project limits but for alternative conditions, treatments, periods of interest, or forecast AADT volumes. Step 18—Evaluate and compare results. The predictive method is used to provide a statistically reliable estimate of the expected average crash frequency (in total, or by crash type and severity) for the specified project limits, study period, geometric design and traffic control features, and known or estimated AADT volume. 18.4.2. Data Needed to Apply the Predictive Method The input data needed for the predictive models are identified in this section. These data represent the geometric design features, traffic control features, and traffic demand characteristics that have been found to have some relationship to safety. They are identified by bullet in this section, and are listed in Table B- 2 of Appendix B to Part C. The input data are needed for each site in the project limits. Criteria for defining site boundaries are described in Section 18.5. There are several data identified in this section that describe a length along the roadway (e.g., segment length, curve length, weaving section length, etc.). All of these lengths are measured along the reference line, which is the inside edge of traveled way in the increasing milepost direction of travel. Points that do not lie on the reference line must be projected onto the reference line (along a perpendicular line if the alignment is straight, or along a radial line if the alignment is curved) to facilitate length determination. These dimensions can be obtained from field measurements, a plan set, or aerial photographs.  Number of through lanes. For a freeway segment, use the total number of through lanes (in both directions of travel). For a speed-change lane, use the number of through lanes in the portion of freeway adjacent to the speed-change lane plus those freeway lanes in the opposing travel direction. Rural freeways are limited to eight lanes. Urban freeways are limited to ten lanes. A segment with a lane-add (or lane-drop) taper is considered to have the same number of through lanes as the roadway just downstream of the lane-add (or lane-drop) taper. This guidance is shown in Figure 18-2. Equation 18-14

405 Taper point Exit Ramp with Taper Design Entrance Ramp with Parallel Design Ramp Exit Length Ramp Entrance Length * * * Point where marked gore is 2 ft wide (gore point) Taper point Lane add Segment Median Begin segment at upstream start of taper Number of through lanes: 5 (= downstream lane count) Ladd,seg Lane drop Segment Median Segment length, L Number of through lanes: 4 (= downstream lane count) Ldrop,seg End segment at upstream start of taper Segment length, L Figure 18-2. Through Lane Count in Segments with Lane Add or Lane Drop Do not include any high-occupancy vehicle (HOV) lanes or managed lanes. Do not include any auxiliary lanes that are associated with a weaving section, unless the weaving section length exceeds 0.85 mi (4,500 ft). If this length is exceeded, then the auxiliary lane is counted as a through lane that starts as a lane-add ramp entrance and ends as a lane-drop ramp exit. Do not include the speed-change lane that is associated with a ramp that merges with (or diverges from) the freeway, unless its length exceeds 0.30 mi (1,600 ft). If this length is exceeded, then the speed-change lane is counted as a through lane that starts as a lane-add ramp entrance and ends as a lane drop by taper (or starts as a lane add by taper and ends as a lane-drop ramp exit).  Length of freeway segment, and length of speed-change lane (if present). Speed-change lane length is measured from the gore point to the taper point. Figure 18-3 illustrates these measurement points for a ramp entrance and a ramp exit speed-change lane with the parallel and taper design, respectively. Figure 18-3. Freeway Speed-Change Lane Length

406  Presence of a horizontal curve on one or both roadbeds. If a curve is present, then the three data elements in the following list are needed. Guidelines for obtaining these data are provided in Figure 18- 4.  Length of curve. Curve length is measured along the reference line from the point where the tangent ends and the curve begins (i.e., the PC) to the point where the curve ends and the tangent begins (PT). If the curve PC and PT do not lie on the reference line, then they must be projected onto this line and the curve length measured between these projected points along the reference line. If the curve has spiral transitions, then measure from the “effective” PC point to the “effective” PT point. The effective PC point is located midway between the TS and SC, where the TS is the point of change from tangent to spiral and the SC is the point of change from spiral to circular curve. The effective PT is located midway between the CS and ST.  Radius of curve. Radius is measured separately for each roadbed curve. The line used to define curve radius is the inside edge of the traveled way. This line is established separately on each roadbed. If the curve has spiral transitions, then use the radius of the central circular portion of the curve.  Length of curve in segment. The length of the curve within the boundaries of the segment (or speed- change lane). This length cannot exceed the segment length or the curve length.

407 Increasing milepost travel direction Curve in both directions (concentric) Rules 1. Roadbed in increasing milepost travel direction is basis of curve length measurement. 2. Curve length is measured along the inside edge of traveled way. 3. Radius is measured for both roadbeds. 4. Radius is measured to inside edge of traveled way. Note: curve is shown to be only partially in segment, but could also be fully in segment. Median Length of curve PC PT Length of curve in segment Segment PC PT Increasing milepost travel direction Rules 1. Roadbed in increasing milepost travel direction is basis of curve length measurement. 2. Curve length is measured along the inside edge of traveled way. 3. Radius is measured for curved roadbed. 4. Radius is measured to inside edge of traveled way. Note: curve is shown to be fully in segment, but could also be only partially in segment. Curve in one direction Length of curve = Length of curve in segment Segment Curve in both directions (not concentric) Median Length of curve 2 Increasing milepost travel direction Length of curve 3 Length of curve 1 Rules 1. Disaggregate into multiple curved pieces, where one or both roadbeds are curved in each piece. 2. If one roadbed is curved, use rules for "Curve in one direction." 3. If both roadbeds are curved, use rules for "Curve in both directions (concentric)." Note: roadbeds are shown to curve in same direction; however, these rules also apply when curves are in the opposite direction. Curve 1 is "Curve in one direction." Curve 2 is "Curve in both directions." Curve 3 is "Curve in one direction." Figure 18-4. Curve Length and Radius Measurements

408  Widths of lanes, outside shoulders, inside shoulders, and median. The first three elements represent an average for both roadbeds. These widths should be measured where the cross section is constant, such as along line A or B shown in Figure 18-5. They should not be measured where one or more edges are discontinuous or tapered. If a width varies along the segment or speed-change lane (but not enough to justify beginning a new segment), then compute the length-weighted average width. Rules for defining segment boundaries are provided in Section 18.5.2.  Lane width. This width is computed as an average for all through lanes.  Shoulder width. This width represents only the paved width.  Median width. This width is measured between the edges of the traveled way for the two roadways in the opposite direction of travel, including the width of the inside shoulders, if they are present. Gore point Taper point This barrier is on the ramp. This barrier is on the freew ay. Measure lane, shoulder, and median widths in areas with constant cross section. Measure along a line such as line A or line B. If necessary, move the line off the subject segment to the nearest point with constant cross section. A B Avoid measuring widths where one or more edges are discontinuous or tapered. Median width Figure 18-5. Measurement of Cross Section Data Elements  Length of rumble strips on the inside (or median) shoulder and on the outside (or roadside) shoulder. Measured separately for each shoulder type and travel direction.  Length of (and offset to) the barrier in the median and the barrier on the roadside. Measured for each short piece of barrier. Offset is also measured for barrier that continues for the length of the segment or speed-change lane (and beyond). Each piece is represented once for a site. Barrier length is measured along the reference line. Offset is measured from the nearest edge of traveled way to the barrier face. Figure 18-6 illustrates these measurements for two barrier elements protecting a sign support in a median with width Wm and adjacent to shoulders with width Wis. Each barrier element has a portion of its length that is parallel to the roadway and a portion of its length that is tapered from the roadway. One way to evaluate these elements is to separate them into four pieces, as shown in Figure 18-6. Each piece is represented by its average offset Woff, in, i and length Lib, i. Alternatively, the analyst may recognize that the offset is the same for pieces 1 and 4 and for pieces 2 and 3. In this case, each pair can be combined by adding the two lengths (e.g., Lib, 1 + Lib, 4) and using the common offset. A barrier is associated with the freeway if the offset from the near edge of traveled way is 30 ft or less. Barrier adjacent to a ramp but also within 30 ft of the freeway traveled way should also be associated with the freeway. The determination of whether a barrier is adjacent to a speed-change lane or a ramp is based on the gore and taper points, as shown in Figure 18-5.

409 Lib,1 Lib,2 Wof f ,in,1 Wof f ,in,2 Lib,4Lib,3 Wof f ,in,4 Wof f ,in,3 Wm WisReference line Increasing milepost Figure 18-6. Barrier Variables  Width of continuous median barrier, if present.  Presence and length of a Type B weaving section. This weaving section has the following characteristics: (a) one of the two weaving movements can be made without making any lane changes, (b) the other weaving movement requires at most one lane change, and (c) the ramp entrance and ramp exit associated with the weaving section are located on the right side of the freeway. Typical Type B weaving sections are shown in Figure 18-7. Other weaving section types are addressed directly by the predictive method.  Type B weaving section length. This length is measured along the edge of the freeway traveled way from the gore point of the ramp entrance to the gore point of the next ramp exit, as shown in Figure 18-7. The gore point is located where the pair of solid white pavement edge markings that separate the ramp from the freeway main lanes are 2.0 ft apart. If the markings do not extend to a point where they are 2.0 ft apart, then the gore point is found by extrapolating both markings until the extrapolated portion is 2.0 ft apart. If the measured gore-to-gore distance exceeds 0.85 mi (4,500 ft), then a weaving section is not considered to exist. Rather, the entrance ramp is a “lane add” and the exit ramp is a “lane drop.”  Length of weaving section located in the segment, between the segment’s begin and end points. This length cannot exceed the length of the segment. This length cannot exceed the length of the weaving section.

410 Lwev = w eaving section length 2' 2' Lwev Figure 18-7. Type B Weaving Section and Length  Distance to nearest upstream entrance ramp in each travel direction. Measure this distance from the segment boundary to the ramp gore point, along the freeway’s solid white pavement edge marking that intersects the gore point. The distance to the nearest upstream entrance ramp in each travel direction is shown in Figure 18-8 using the two variables Xb, ent and Xe, ent. If the ramp entrance is located in the segment, then the corresponding distance is equal to 0.0 mi. If the ramp does not exist or is located more than 0.5 mi from the segment, then this distance can be set to a large value (i.e., 999) in the predictive method to obtain the correct results. The gore point is located where the pair of solid white pavement edge markings that separate the ramp from the freeway main lanes are 2.0 ft apart. If the markings do not extend to a point where they are 2.0 ft apart, then the gore point is found by extrapolating both markings until the extrapolated portion is 2.0 ft apart. Upstream exit ramps are not of direct interest, and data are not needed for them if they exist in the vicinity of the segment. Figure 18-8a shows an upstream exit ramp serving travel in the decreasing milepost direction. This ramp is not of interest to the evaluation of the subject segment.  Distance to nearest downstream exit ramp in each travel direction. The measurement technique is the same as for upstream entrance ramps. This distance is shown in Figure 18-8 using the two variables Xb, ext and Xe, ext. Downstream entrance ramps are not of direct interest, and their data are not needed.

411 Segment Increasing mile post Begin milepost Xb,ent Xb,ext End milepost Xe,ext Xe,ent All measurements are to the marked gore point. AADTb,ent AADTb,ext AADTe,ent AADTe,ext a. All Ramps External to the Segment AADTb,ext Segment Increasing mile post Begin milepost Xb,ent = 0.0 Xb,ext End milepost Xe,ext Xe,ent All measurements are to the marked gore point. AADTb,ent AADTe,ent AADTe,ext b. Three Ramps External to the Segment and One Ramp in the Segment Figure 18-8. Distance to Nearest Ramp  Clear zone width. This width is measured from the edge of traveled way to typical limits of vertical obstruction (e.g., non-traversable slope, fence line, utility poles) along the roadway. The Roadside Design Guide (2) provides detailed information about roadside features that define this width. The clear zone width includes the outside shoulder. It is measured for both travel directions. If this width varies along the segment, then use the estimated length-weighted average clear zone width (excluding the portion of the segment with barrier). Do not consider roadside barrier when determining the clear zone width for the predictive method. Barrier location and influence is addressed in other CMFs. If the segment has roadside barrier on both sides for its entire length, then the clear zone width will not influence the model prediction, and any value can be used as a model input (e.g., 30 ft). This guidance is illustrated in Figure 18-9 where the clear zone is shown to be established by a fence line that varies in offset from the edge of traveled way. A length-weighted width is appropriate for this situation. The lone tree and the guardrail are not considered in the determination of clear zone width.

412 Tree Tree Tree Fence line Whc,1 Whc, 2 Increasing milepost Whc, 3 Lone tree not considered Guardrail not considered Median Reference line Whc = clear zone width Figure 18-9. Clear Zone Width Considerations  Proportion of freeway AADT volume that occurs during hours where the lane volume exceeds 1,000 vehicles per hour per lane (veh/h/ln). The lane volume for hour i LVi is computed as LVi = HVi/n where HVi is the volume during hour i (i = 1, 2, 3, ..., 24) and n is the number of through lanes. The desired proportion Phv is computed as Phv = (Σ HVi*)/AADT where Σ HVi* is the sum of the volume during each hour where the lane volume exceeds 1,000 veh/h/ln. The AADT, HV, and n variables include both freeway travel directions. These data will typically be obtained from the continuous traffic counting station that (1) is nearest to the subject freeway and (2) has similar traffic demand and peaking characteristics. A default value can be computed as Phv = 1.0 − exp(1.45 − 0.000124 × AADT/n). If the value computed is less than 0.0, then it is set to 0.0.  Freeway AADT volume, upstream entrance ramp AADT volume, downstream exit ramp AADT volume. 18.5. ROADWAY SEGMENTS AND SPEED-CHANGE LANES This section consists of three subsections. The first subsection defines freeway segments and speed- change lanes. The second subsection provides guidelines for segmenting the freeway facility. The assignment of crashes to sites is discussed in the last subsection. 18.5.1. Definition of Freeway Segment and Speed-Change Lane When using the predictive method, the freeway within the defined project limits is divided into individual sites. A site is either a homogeneous freeway segment or a speed-change lane. A facility consists of a contiguous set of individual sites. A roadway network consists of a number of contiguous facilities. A speed-change lane site is defined as the section of roadway area located (a) between the marked gore and taper points of a ramp merge or diverge area, and (b) on the same side of the freeway as the merge or diverge area. The location of the gore and taper points is identified in Figure 18-3. Three freeway segments are shown schematically in Figure 18-10. They are labeled Fr in the figure. The presence of a speed-change lane adjacent to a freeway segment requires a reduction in the effective length of the freeway segment. This reduction is used to account for the crashes assigned to the speed-change lane. The equation for computing the “effective” segment length is shown in the bottom of Figure 18-10 for a freeway segment with one ramp entrance and one ramp exit. Two speed-change lanes are shown schematically in Figure 18-10. The speed-change lane associated with an entrance ramp is labeled SCen and that associated with an exit ramp exit is labeled SCex.

413 PLAN VIEW COMPONENT PARTS Speed-Change Lane Speed-Change Lane Type: ramp entrance Type: ramp exit Seg. length = Len Seg. length = Lex Freeway Segment Effective segment length, L* = Lfs - Len/2 - Lex/2 (note: freeway segment length does not include the length of speed-change lanes, if these lanes are adjacent to the segment) Ramp Entrance Length, Len Ramp Exit Length, Lex SCen Fr2 Lfs2 SCen SCex SCex Fr1 Fr2 Lfs3Lfs1 Fr3 Fr3Fr1 Ramp Ramp Freeway Cross -road Figure 18-10. Illustrative Freeway Segments and Speed-Change Lanes 18.5.2 Segmentation Process A speed-change lane site begins at the gore (or taper) point and ends at the associated taper (or gore) point. These points are shown in Figure 18-3. The segmentation process produces a set of segments of varying length, each of which is homogeneous with respect to characteristics such as traffic volume, key geometric design features, and traffic control features. A new homogeneous freeway segment begins where there is a change in at least one of the following characteristics of the freeway:  Number of through lanes. Begin segment at the gore point if the lane is added or dropped at a ramp or C-D road. Begin segment at the upstream start of taper if the lane is added or dropped by taper. Guidance in this regard is described in the text accompanying Figure 18-2.  Lane width. Measure the lane width at successive points along the roadway. Compute an average lane width for each point and round this average to the nearest 0.5 ft. Begin a new segment if the rounded value for the current point changes from that of the previous point (e.g., from 11.5 to 12.0 ft).

414  Outside shoulder width. Measure the outside shoulder width at successive points along the roadway. Compute an average shoulder width for each point and round this average to the nearest 1.0 ft. Begin a new segment if the rounded value for the current point changes from that of the previous point (e.g., from 6 to 7 ft).  Inside shoulder width. Measure the inside shoulder width at successive points along the roadway. Compute an average shoulder width for each point and round this average to the nearest 1.0 ft. Begin a new segment if the rounded value for the current point changes from that of the previous point (e.g., from 6 to 5 ft).  Median width. Measure the median width at successive points along the roadway. Round the measured median width at each point to the nearest 10 ft. If the rounded value exceeds 90 ft, then set it to 90 ft. Begin a new segment if the rounded value for the current point changes from that of the previous point (e.g., from 30 to 20 ft).  Ramp presence. Begin segment at the ramp gore point.  Clear zone width. Measure the clear zone width at successive points along the roadway. Compute an average clear zone width for each point and round this average to the nearest 5 ft. Begin a new segment if the rounded value for the current point changes from that of the previous point (e.g., from 25 to 30 ft). The presence of a horizontal curve does not necessarily define segment boundaries. This approach represents a difference with the process described in Chaper 10, where a curve does define segment boundaries. Application of the “median width” segmentation criterion is shown in Figure 18-11. The freeway section in this figure is shown to consist of five segments. Segment 1 has a rounded median width of 70 ft. Segment 2 starts where the rounded median width first changes to 80 ft. Segment 3 begins at the point where the rounded median width first changes to 90 ft. Segment 4 begins where the rounded median width first changes to 80 ft. Segment 5 begins where the rounded median width first changes to 70 ft. Guidance regarding the location of the lane, shoulder, and median width measurement points is provided in the text associated with Figure 18-5. Each width represents an average for the segment. Similarly, guidance associated with Figure 18-9 is used to determine the clear zone width for the segment. The rounded lane, shoulder, median, and clear zone width values are used solely to determine segment boundaries. Once these boundaries are determined, the unrounded values for the segment are then used for all subsequent calculations in the predictive method.

415 Seg. 1 Seg. 2 Seg. 3 Seg. 4 Seg. 5 = point where median width is 85 ft = point where median width is 75 ft 65 ft 65 ft 70 ft 80 ft 90 ft 90 ft 80 ft 70 ft Figure 18-11. Segmentation for Varying Median Width 18.5.3. Crash Assignment to Sites Observed crash counts are assigned to the individual sites to apply the site-specific EB Method. Any crashes that occur on the freeway are classified as speed-change-lane-related or segment-related crashes. The speed-change-lane-related crashes are assigned to the corresponding speed-change lane. The speed- change lane predictive model estimates the frequency of these crashes. The segment-related crashes are assigned to the corresponding freeway segment. The freeway segment predictive model estimates the frequency of these crashes. The procedure for assignment of crashes to individual sites is presented in Section B.2.3 in Appendix B to Part C. 18.6. SAFETY PERFORMANCE FUNCTIONS When using the predictive method, the appropriate safety performance functions (SPFs) are used to estimate the predicted average crash frequency of a site with base conditions. Each SPF was developed as a regression model using observed crash data for a set of similar sites as the dependent variable. The SPFs, like all regression models, estimate the value of the dependent variable as a function of a set of independent variables. The independent variables for the freeway segment SPFs include the segment AADT volume, segment length, and area type (i.e., rural or urban). The independent variables for the speed-change lane SPFs include the AADT volume of the freeway, speed-change lane length, and area type. The SPFs in this chapter are summarized in Table 18-3. Table 18-3. Freeway Safety Performance Functions Site Type (w) Cross Section (x) Crash Type (y) SPF Equations Freeway segments (fs) n lanes (n) Multiple vehicle (mv) Equation 18-15 Single vehicle (sv) Equation 18-18 Speed-change lanes (sc) Ramp entrance, n lanes (nEN) All types (at) Equation 18-20 Ramp exit, n lanes (nEX) All types (at) Equation 18-22 A detailed discussion of SPFs and their use in the HSM is presented in Section 3.5.2 of Chapter 3, and in Section C.6.3 of Part C. Some transportation agencies may have performed statistically-sound studies to develop their own jurisdiction-specific SPFs. These SPFs may be substituted for the SPFs presented in this chapter. Criteria

416 for the development of SPFs for use in the predictive method are addressed in the calibration procedure presented in Section B.1.2 in Appendix B to Part C. Each SPF has an associated overdispersion parameter k. The overdispersion parameter provides an indication of the statistical reliability of the SPF. The closer the overdispersion parameter is to zero, the more statistically reliable the SPF. This parameter is used in the EB Method that is discussed in Section B.2 in Appendix B to Part C. 18.6.1. Safety Performance Functions for Roadway Segments The SPFs for freeway segments are presented in this section. Specifically, SPFs are provided for freeway segments with 4, 6, 8, or 10 through lanes (total of both travel directions). The range of AADT volume for which these SPFs are applicable is shown in Table 18-4. Application of the SPFs to sites with AADT volumes substantially outside these ranges may not provide reliable results. Table 18-4. Applicable AADT Volume Ranges for SPFs Area Type Cross Section (Through Lanes) (x) Applicable AADT Volume Range (veh/day) Rural 4 0 to 73,000 6 0 to 130,000 8 0 to 190,000 Urban 4 0 to 110,000 6 0 to 180,000 8 0 to 270,000 10 0 to 310,000 The SPFs described in this section are directly applicable to segments with an even number of through lanes. They can be extended to the evaluation of segments with 5, 7, or 9 lanes using the following procedure. If a freeway segment has X total lanes that represent Y lanes in one direction and Z lanes in the opposite direction (i.e., X = Y + Z) and Y is not equal to Z, then it is recommended that the segment be evaluated twice. One evaluation would be conducted where the number of lanes is equal to 2×Y and one evaluation would be conducted where the number of lanes is equal to 2×Z. All other inputs to the SPFs would be unchanged between evaluations. The two estimates of predicted average crash frequency obtained in this manner are then averaged to obtain the best estimate of the predicted average crash frequency for the subject segment. Other types of freeway segments may be found on freeways, but they are not addressed by the predictive model described in this chapter. Multiple-Vehicle Crashes The base conditions for the SPFs for multiple-vehicle crashes on freeway segments are presented in the following list. The variables are defined in Section 18.4.2.  Length of horizontal curve 0.0 mi (i.e., not present)  Lane width 12 ft

417  Inside shoulder width (paved) 6 ft  Median width 60 ft  Length of median barrier 0.0 mi (i.e., not present)  Number of hours where volume exceeds 1,000 veh/h/ln None  Distance to nearest upstream ramp entrances More than 0.5 mi from segment  Distance to nearest downstream ramp exits More than 0.5 mi from segment  Length of Type B weaving section 0.0 mi (i.e., not present) The SPFs for multiple-vehicle crashes on freeway segments are represented using the following equation. ])ln[exp(*,,,, fszmvnfsspf AADTcbaLN ××+×= with,       ×−      ×−=  == 2 1 ,, 2 1 ,, * 5.05.0 i isegex i isegenfs LLLL Where: Nspf, fs, n, mv, z = predicted average multiple-vehicle crash frequency of a freeway segment with base conditions, n lanes, and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/yr); L* = effective length of freeway segment (mi); Lfs = length of freeway segment (mi); Len, seg, i = length of ramp entrance i adjacent to subject freeway segment (mi); Lex, seg, i = length of ramp exit i adjacent to subject freeway segment (mi); AADTfs = AADT volume of freeway segment (veh/day); a, b = regression coefficients; and c = AADT scale coefficient. The calculation of the “effective length of freeway segment” was discussed in the text associated with Figure 18-10. The variable Len, seg, i represents the length of the speed-change lane located between the start and end points of the adjacent freeway segment. This length cannot exceed the length of the segment or the length of the ramp entrance speed-change lane. Similarly, the variable Lex, seg, i represents the length of the speed-change lane located between the start and end points of the adjacent freeway segment. The summation terms in Equation 18-16 recognize the potential for there to be as many as two ramp entrances (and two ramp exits) adjacent to a freeway segment. If there are two ramp entrances, then they Equation 18-15 Equation 18-16

418 will be serving opposing directions of travel. If there are two ramp exits, then they will be serving opposing directions of travel. The SPF coefficients and the inverse dispersion parameter are provided in Table 18-5. The SPFs are illustrated in Figure 18-12. Table 18-5. SPF Coefficients for Multiple-Vehicle Crashes on Freeway Segments Crash Severity (z) Area Type Number of Through Lanes (n) SPF Coefficient Inverse Dispersion Parameter Kfs, n, mv, z (mi-1) a b c Fatal and injury (fi) Rural 4 -5.975 1.492 0.001 17.6 6 -6.092 1.492 0.001 17.6 8 -6.140 1.492 0.001 17.6 Urban 4 -5.470 1.492 0.001 17.6 6 -5.587 1.492 0.001 17.6 8 -5.635 1.492 0.001 17.6 10 -5.842 1.492 0.001 17.6 Property damage only (pdo) Rural 4 -6.880 1.936 0.001 18.8 6 -7.141 1.936 0.001 18.8 8 -7.329 1.936 0.001 18.8 Urban 4 -6.548 1.936 0.001 18.8 6 -6.809 1.936 0.001 18.8 8 -6.997 1.936 0.001 18.8 10 -7.260 1.936 0.001 18.8

419 0 3 6 9 12 0 50 100 150 200 250 AADT (1000s of veh/day) FI M ul tip le -V eh ic le C ra sh Fr eq ue nc y (c ra sh es /y r) 1.0-mile segment length 4 lanes 6 8 Rural freeway Urban freeway 6 10 8 0 10 20 30 40 0 50 100 150 200 250 AADT (1000s of veh/day) PD O M ul tip le -V eh ic le C ra sh Fr eq ue nc y (c ra sh es /y r) 1.0-mile segment length 4 lanes 6 8Rural freeway Urban freeway 6 10 8 a. Fatal-and-Injury Crash Frequency b. Property-Damage-Only Crash Frequency Figure 18-12. Graphical Form of the SPFs for Multiple-Vehicle Crashes on Freeway Segments The value of the overdispersion parameter associated with the SPFs for freeway segments is determined as a function of the segment length. This value is computed using Equation 18-17. * ,,, ,,, 1 LK k zmvnfs zmvnfs × = Where: kfs, n, mv, z = overdispersion parameter for freeway segments with n lanes, multiple-vehicle crashes mv and severity z; and Kfs, n, mv, z = inverse dispersion parameter for freeway segments with n lanes, multiple-vehicle crashes mv and severity z (mi-1). The inverse dispersion parameter for segments with even numbers of lanes is provided in Table 18-5. A procedure is described in Section B.2.7 in Appendix B to Part C for using these parameters to estimate the overdispersion parameter for segments with an odd number of lanes. The crash frequency obtained from Equation 18-15 can be multiplied by the proportions in Table 18-6to estimate the predicted average multiple-vehicle crash frequency by crash type category. Equation 18-17

420 Table 18-6. Default Distribution of Multiple-Vehicle Crashes by Crash Type for Freeway Segments Area Type Crash Type Category Proportion of Crashes by Severity Fatal and Injury Property Damage Only Rural Head-on 0.018 0.004 Right-angle 0.056 0.030 Rear-end 0.630 0.508 Sideswipe 0.237 0.380 Other multiple-vehicle crashes 0.059 0.078 Urban Head-on 0.008 0.002 Right-angle 0.031 0.018 Rear-end 0.750 0.690 Sideswipe 0.180 0.266 Other multiple-vehicle crashes 0.031 0.024 Single-Vehicle Crashes The base conditions for the SPFs for single-vehicle crashes on freeway segments are presented in the following list. The variables are defined in Section 18.4.2.  Length of horizontal curve 0.0 mi (i.e., not present)  Lane width 12 ft  Inside shoulder width (paved) 6 ft  Median width 60 ft  Length of median barrier 0.0 mi (i.e., not present)  Number of hours where volume exceeds 1,000 veh/h/ln None  Outside shoulder width (paved) 10 ft  Length of shoulder rumble strip 0.0 mi (i.e., not present)  Clear zone width 30 ft  Length of outside barrier 0.0 mi (i.e., not present) The SPFs for single-vehicle crashes on freeway segments are represented with the following equation. ])ln[exp(*,,,, fszsvnfsspf AADTcbaLN ××+×= Where: Equation 18-18

421 0 1 2 3 4 5 0 50 100 150 200 250 AADT (1000s of veh/day) FI S in gl e- Ve hi cl e C ra sh Fr eq ue nc y (c ra sh es /y r) 1.0-mile segment length 4 lanes 6 8 Rural & urban freeway 10 0 2 4 6 8 10 12 0 50 100 150 200 250 AADT (1000s of veh/day) PD O S in gl e- Ve hi cl e C ra sh Fr eq ue nc y (c ra sh es /y r) 1.0-mile segment length 4 lanes 6 8 Rural & urban freeway 10 Nspf, fs, n, sv, z = predicted average single-vehicle crash frequency of a freeway segment with base conditions, n lanes, and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/yr). The SPF coefficients and the inverse dispersion parameter are provided in Table 18-7. The SPFs are illustrated in Figure 18-13. Table 18-7. SPF Coefficients for Single-Vehicle Crashes on Freeway Segments Crash Severity (z) Area Type Number of Through Lanes (n) SPF Coefficient Inverse Dispersion Parameter Kfs, n, sv, z (mi-1) a b c Fatal and injury (fi) Rural 4 -2.126 0.646 0.001 30.1 6 -2.055 0.646 0.001 30.1 8 -1.985 0.646 0.001 30.1 Urban 4 -2.126 0.646 0.001 30.1 6 -2.055 0.646 0.001 30.1 8 -1.985 0.646 0.001 30.1 10 -1.915 0.646 0.001 30.1 Property damage only (pdo) Rural 4 -2.235 0.876 0.001 20.7 6 -2.274 0.876 0.001 20.7 8 -2.312 0.876 0.001 20.7 Urban 4 -2.235 0.876 0.001 20.7 6 -2.274 0.876 0.001 20.7 8 -2.312 0.876 0.001 20.7 10 -2.351 0.876 0.001 20.7 a. Fatal-and-Injury Crash Frequency b. Property-Damage-Only Crash Frequency Figure 18-13. Graphical Form of the SPFs for Single-Vehicle Crashes on Freeway Segments

422 The value of the overdispersion parameter associated with the SPFs for freeway segments is determined as a function of the segment length. This value is computed using Equation 18-19. * ,,, ,,, 1 LK k zsvnfs zsvnfs × = Where: kfs, n, sv, z = overdispersion parameter for freeway segments with n lanes, single-vehicle crashes sv and severity z; and Kfs, n, sv, z = inverse dispersion parameter for freeway segments with n lanes, single-vehicle crashes sv and severity z (mi-1). The inverse dispersion parameter for segments with even numbers of lanes is provided in Table 18-7. A procedure is described in Section B.2.7 in Appendix B to Part C for using these parameters to estimate the overdispersion parameter for segments with odd numbers of lanes. The crash frequency obtained from Equation 18-18 can be multiplied by the proportions in Table 18-8 to estimate the predicted average single-vehicle crash frequency by crash type category. Table 18-8. Default Distribution of Single-Vehicle Crashes by Crash Type for Freeway Segments Area Type Crash Type Category Proportion of Crashes by Severity Fatal and Injury Property Damage Only Rural Crash with animal 0.010 0.065 Crash with fixed object 0.567 0.625 Crash with other object 0.031 0.125 Crash with parked vehicle 0.024 0.023 Other single-vehicle crashes 0.368 0.162 Urban Crash with animal 0.004 0.022 Crash with fixed object 0.722 0.716 Crash with other object 0.051 0.139 Crash with parked vehicle 0.015 0.016 Other single-vehicle crashes 0.208 0.107 18.6.2. Safety Performance Functions for Speed-Change Lanes The SPFs for freeway speed-change lanes are presented in this section. SPFs are provided for ramp entrances and ramp exits adjacent to freeways with 4, 6, 8, or 10 through lanes. The SPFs for speed- change lanes are applicable to the same freeway AADT volume ranges that are listed in Table 18-4. Application to sites with AADT volumes substantially outside these ranges may not provide reliable results. Equation 18-19

423 The SPFs described in this section are directly applicable to speed-change lanes adjacent to freeways with an even number of through lanes. They can be extended to the evaluation of speed-change lanes adjacent to freeways with 5, 7, and 9 lanes using the procedure described in Section 18.6.1. Ramp Entrance Speed-Change Lanes The base conditions for the SPFs for ramp-entrance speed-change lanes are presented in the following list. The variables are defined in Section 18.4.2.  Length of horizontal curve 0.0 mi (i.e., not present)  Lane width 12 ft  Inside shoulder width (paved) 6 ft  Median width 60 ft  Length of median barrier 0.0 mi (i.e., not present)  Number of hours where volume exceeds 1,000 veh/h/ln None The SPFs for ramp entrance speed-change lanes are represented using the following equation. ])ln[exp(,,,, fsenzatnENscspf AADTcbaLN ××+×= Where: Nspf, sc, nEN, at, z = predicted average crash frequency of a ramp entrance speed-change lane on a freeway with base conditions, n lanes, all crash types at, and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/yr); and Len = length of ramp entrance (mi). The SPF coefficients and the inverse dispersion parameter are provided in Table 18-9 The variable n is used in this table to describe the number of through lanes in the portion of freeway adjacent to the speed- change lane plus those freeway lanes in the opposing travel direction. This approach to describing the speed-change lane cross section is used for consistency with that used for freeway segment SPFs. The variable n is not intended to describe the number of lanes in the speed-change lane. Equation 18-20

424 0.0 0.2 0.4 0.6 0.8 1.0 0 50 100 150 200 250 AADT (1000s of veh/day) FI R am p En tra nc e C ra sh Fr eq ue nc y (c ra sh es /y r) 4 lanes 8 10 6 Ramp AADT = 0.1 x Directional AADT Ramp entrance length = 700 ft Rural freeway Urban freeway 0.0 0.5 1.0 1.5 2.0 0 50 100 150 200 250 AADT (1000s of veh/day) PD O R am p En tra nc e C ra sh Fr eq ue nc y (c ra sh es /y r) 4 lanes 8 10 6 Ramp entrance length = 700 ft Rural freeway Urban freeway Table 18-9. SPF Coefficients for Ramp-Entrance-Related Crashes in Speed-Change Lanes Crash Severity (z) Area Type Number of Through Lanes (n) SPF Coefficient Inverse Dispersion Parameter Ksc, nEN, at, z (mi-1) a b c Fatal and injury (fi) Rural 4 -3.894 1.173 0.0005 26.1 6 -4.154 1.173 0.0005 26.1 8 -4.414 1.173 0.0005 26.1 Urban 4 -3.714 1.173 0.0005 26.1 6 -3.974 1.173 0.0005 26.1 8 -4.234 1.173 0.0005 26.1 10 -4.494 1.173 0.0005 26.1 Property damage only (pdo) Rural 4 -2.895 1.215 0.0005 24.8 6 -3.097 1.215 0.0005 24.8 8 -3.299 1.215 0.0005 24.8 Urban 4 -2.796 1.215 0.0005 24.8 6 -2.998 1.215 0.0005 24.8 8 -3.200 1.215 0.0005 24.8 10 -3.402 1.215 0.0005 24.8 The SPFs are illustrated in Figure 18-14. The Ramp entrance CMF is combined with this SPF to create the trend lines shown in the figure. This CMF is a function of entrance ramp volume and the speed- change lane length. These variables in combination do not readily lend themselves to the specification of a representative base condition. For this reason, the CMF is combined with the SPF for the graphical presentation. The Ramp entrance CMF is described in Section 18.7.2. a. Fatal-and-Injury Crash Frequency b. Property-Damage-Only Crash Frequency Figure 18-14. Graphical Form of the SPFs for Ramp Entrance Speed-Change Lanes

425 The value of the overdispersion parameter associated with the SPFs for ramp-entrance speed-change lanes is determined as a function of the speed-change lane length. This value is computed as: enzatnENsc zatnENsc LK k × = ,,, ,,, 1 Where: ksc, nEN, at, z = overdispersion parameter for ramp entrance speed-change lane on a freeway with n lanes, all crash types at, and severity z; and Ksc, nEN, at, z = inverse dispersion parameter for ramp entrance speed-change lane on a freeway with n lanes, all crash types at, and severity z (mi-1). The inverse dispersion parameter for speed-change lanes adjacent to freeways with 4, 6, 8, or 10 through lanes is provided in Table 18-9. A procedure is described in Section B.2.7 in Appendix B to Part C for using these parameters to estimate the overdispersion parameter for speed-change lanes adjacent to freeways with 5, 7, or 9 lanes. The crash frequency obtained from Equation 18-20 can be multiplied by the proportions in Table 18-10 to estimate the predicted average ramp-entrance-related crash frequency by crash type or crash type category. These proportions are based on ramp-entrance speed-change lane crashes. They do not include crashes associated with a ramp entrance that adds a lane to the cross section. Equation 18-21

426 Table 18-10. Default Distribution of Ramp-Entrance-Related Crashes by Crash Type Area Type Crash Type Crash Type Category Proportion of Crashes by Severity Fatal and Injury Property Damage Only Rural Multiple vehicle Head-on 0.021 0.004 Right-angle 0.032 0.013 Rear-end 0.351 0.260 Sideswipe 0.128 0.242 Other multiple-vehicle crash 0.011 0.040 Single vehicle Crash with animal 0.000 0.009 Crash with fixed object 0.245 0.296 Crash with other object 0.021 0.070 Crash with parked vehicle 0.021 0.000 Other single-vehicle crashes 0.170 0.066 Urban Multiple vehicle Head-on 0.004 0.001 Right-angle 0.019 0.016 Rear-end 0.543 0.530 Sideswipe 0.133 0.252 Other multiple-vehicle crash 0.017 0.015 Single vehicle Crash with animal 0.000 0.002 Crash with fixed object 0.194 0.129 Crash with other object 0.019 0.036 Crash with parked vehicle 0.004 0.003 Other single-vehicle crashes 0.067 0.016 Ramp Exit Speed-Change Lanes The base conditions for the SPFs for ramp exit speed-change lanes are the same as those for ramp entrance speed-change lanes, as described in the preceding subsection. The SPFs for ramp exit speed-change lanes are represented using the following equation. ])ln[exp(,,,, fsexzatnEXscspf AADTcbaLN ××+×= Where: Nspf, sc, nEX, at, z = predicted average crash frequency of a ramp exit speed-change lane on a freeway with base conditions, n lanes, all crash types at, and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/yr); and Equation 18-22

427 0.0 0.1 0.2 0.3 0 40 80 120 AADT (1000s of veh/day) FI R am p Ex it C ra sh F re qu en cy (c ra sh es /y r) All lanes Ramp exit length = 350 ft Rural & urban freeway 0.0 0.2 0.4 0.6 0 40 80 120 AADT (1000s of veh/day) PD O R am p Ex it C ra sh F re qu en cy (c ra sh es /y r) All lanes Rural & urban freeway Ramp exit length = 350 ft Lex = length of ramp exit (mi). The SPF coefficients and the inverse dispersion parameter are provided in Table 18-11. The variable n is used in this table to describe the number of through lanes in the portion of freeway adjacent to the speed- change lane plus those freeway lanes in the opposing travel direction. Table 18-11. SPF Coefficients for Ramp-Exit-Related Crashes in Speed-Change Lanes Crash Severity (z) Area Type Number of Through Lanes (n) SPF Coefficient Inverse Dispersion Parameter Ksc, nEX, at, z a b c Fatal and injury (fi) Rural 4, 6, 8 -2.679 0.903 0.0005 1.78 Urban 4, 6, 8, 10 -2.679 0.903 0.0005 1.78 Property damage only (pdo) Rural 4, 6, 8 -1.798 0.932 0.0005 1.58 Urban 4, 6, 8, 10 -1.798 0.932 0.0005 1.58 The SPFs are illustrated in Figure 18-15. The Ramp exit CMF is combined with the fatal-and-injury SPF to create the trend lines shown in the figure for fatal-and-injury crashes. This CMF is a function of the speed-change lane length. This variable (in combination with the SPF length variable) does not readily lend itself to the specification of a representative base condition. For this reason, the CMF is combined with the SPF for the graphical presentation. The Ramp exit CMF is described in Section 18.7.2 a. Fatal-and-Injury Crash Frequency b. Property-Damage-Only Crash Frequency Figure 18-15. Graphical Form of the SPFs for Ramp Exit Speed-Change Lanes The overdispersion parameter associated with the SPFs for ramp exit speed-change lanes is computed as: zatnEXsc zatnEXsc K k ,,, ,,, 1= Where: ksc, nEX, at, z = overdispersion parameter for ramp exit speed-change lane on a freeway with n lanes, all crash types at, and severity z; and Equation 18-23

428 Ksc, nEX, at, z = inverse dispersion parameter for ramp exit speed-change lane on a freeway with n lanes, all crash types at, and severity z. The inverse dispersion parameter for speed-change lanes adjacent to freeways with 4, 6, 8, or 10 through lanes is provided in Table 18-11. A procedure is described in Section B.2.7 in Appendix B to Part C for using these parameters to estimate the overdispersion parameter for speed-change lanes adjacent to freeways with 5, 7, or 9 lanes. The crash frequency obtained from Equation 18-22 can be multiplied by the proportions in Table 18-12 to estimate the predicted average ramp-exit-related crash frequency by crash type or crash type category. These proportions are based on ramp-exit speed-change lane crashes. They do not include crashes associated with a ramp exit that drops a lane from the cross section. Table 18-12. Default Distribution of Ramp-Exit-Related Crashes by Crash Type Area Type Crash Type Crash Type Category Proportion of Crashes by Severity Fatal and Injury Property Damage Only Rural Multiple vehicle Head-on 0.000 0.000 Right-angle 0.015 0.000 Rear-end 0.463 0.304 Sideswipe 0.104 0.243 Other multiple-vehicle crash 0.000 0.009 Single vehicle Crash with animal 0.000 0.061 Crash with fixed object 0.224 0.235 Crash with other object 0.030 0.061 Crash with parked vehicle 0.000 0.017 Other single-vehicle crashes 0.164 0.070 Urban Multiple vehicle Head-on 0.005 0.002 Right-angle 0.011 0.012 Rear-end 0.549 0.565 Sideswipe 0.158 0.138 Other multiple-vehicle crash 0.016 0.016 Single vehicle Crash with animal 0.000 0.007 Crash with fixed object 0.196 0.207 Crash with other object 0.016 0.030 Crash with parked vehicle 0.000 0.000 Other single-vehicle crashes 0.049 0.023

429 18.7. CRASH MODIFICATION FACTORS This section describes the CMFs applicable to the SPFs presented in Section 18.6. These CMFs were calibrated along with the SPFs. They are summarized in Table 18-13. Table 18-13. Freeway Crash Modification Factors and their Corresponding SPFs Applicable SPF(s) CMF Variable a CMF Description CMF Equations b Freeway segments or speed- change lanes CMF1, w, x, y, z Horizontal curve Equation 18-24, Equation 18-40 CMF2, w, x, y, fi Lane width Equation 18-25, Equation 18-41 CMF3, w, x, y, z Inside shoulder width Equation 18-26, Equation 18-42 CMF4, w, x, y, z Median width Equation 18-27, Equation 18-43 CMF5, w, x, y, z Median barrier Equation 18-28, Equation 18-44 CMF6, w, x, y, z High volume Equation 18-29, Equation 18-45 Multiple-vehicle crashes on freeway segments CMF7, fs, ac, mv, z Lane change Equation 18-30 Single-vehicle crashes on freeway segments CMF8, fs, ac, sv, z Outside shoulder width Equation 18-35 CMF9, fs, ac, sv, fi Shoulder rumble strip Equation 18-36 CMF10, fs, ac, sv, fi Outside clearance Equation 18-38 CMF11, fs, ac, sv, z Outside barrier Equation 18-39 Ramp entrances CMF12, sc, nEN, at, z Ramp entrance Equation 18-46 Ramp exits CMF13, sc, nEX, at, z Ramp exit Equation 18-47 Notes: a Subscripts to the CMF variables use the following notation: • Site type w (w = fs: freeway segment, sc: speed-change lane), • Cross section x (x = n: n-lane freeway, nEN: ramp entrance speed-change lane adjacent to a freeway with n lanes, nEX: ramp exit speed-change lane adjacent to a freeway with n lanes, ac: any cross section), • Crash type y (y = sv: single vehicle, mv: multiple vehicle, at: all types), and • Severity z (z = fi: fatal and injury, pdo: property damage only, as: all severities). b Where two equations are listed, the first equation is applicable to freeway segments, and the second equation is applicable to speed-change lanes. Many of the CMFs in Table 18-13 are developed for specific site types, cross sections, crash types, or crash severities. This approach was undertaken to make the predictive model sensitive to the geometric design and traffic control features of specific sites with specific cross sections, in terms of their influence on specific crash types and severities. The subscripts for each CMF variable indicate the sites, cross sections, crash types, and severities to which each CMF is applicable. The subscript definitions are provided in the table footnote. In some cases, a CMF is applicable to several site types, cross sections, crash types, or severities. In these cases, the subscript retains the generic letter w, x, y, or z, as appropriate. The discussion of these CMFs in Section 18.7.1 or 18.7.2 identifies the specific site types, cross sections, crash types, or severities to which they apply. As indicated in Table 18-13, some of the CMFs apply to both freeway segments and speed-change lanes. These CMFs are presented in Section 18.7.1 and referenced in Section 18.7.2. For some of the CMFs, supplemental calculations must be performed before the CMF value can be computed. For example, to apply the Median width CMF, the proportion of the segment length having inside barrier and the length-

430 weighted average barrier offset (as measured from the edge of the inside shoulder) must be computed. Procedures for supplemental calculations are described in Section 18.7.3. 18.7.1. Crash Modification Factors for Roadway Segments The CMFs for geometric design and traffic control features of freeway segments are presented in this section. CMF1, w, x, y, z—Horizontal Curve Four CMFs are used to describe the relationship between horizontal curve geometry and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury multiple-vehicle crashes, specified number of lanes (fs, n, mv, fi);  SPF for property-damage-only multiple-vehicle crashes, specified number of lanes (fs, n, mv, pdo);  SPF for fatal-and-injury single-vehicle crashes, specified number of lanes (fs, n, sv, fi); and  SPF for property-damage-only single-vehicle crashes, specified number of lanes (fs, n, sv, pdo). The base condition is an uncurved (i.e., tangent) segment. The CMFs are described using the following equation.         ××      ×+=  = m i icic i zyacfs fPR aCMF 1 ,, 2 *,,,,1 730,50.1 Where: CMF1, fs, ac, y, z = crash modification factor for horizontal curvature in a freeway segment with any cross section ac, crash type y, and severity z; Ri* = equivalent radius of curve i (= [0.5/Ra,i2 + 0.5/Rb,i2]-0.5 if both roadbeds are curved, Ra,i if only one roadbed is curved) (ft); Ra,i = radius of curve i in one roadbed (ft); Rb,i = radius of curve i in second roadbed (used if both roadbeds are curved) (ft); Pc, i = proportion of segment length with curve i; fc, i = roadbed adjustment factor for curve i (= 1.0 if both roadbeds are curved, 0.5 if only one roadbed is curved); and m = number of horizontal curves in the segment. The coefficient for Equation 18-24 is provided in Table 18-14. Equation 18-24 is derived to recognize that more than one curve may exist in a segment and that a curve may be located only partially in the segment (and partially on an adjacent segment). The variable Pc, i is computed as the ratio of the length of curve i in the segment to the length of the freeway segment Lfs. For example, consider a segment that is 0.5 mi long and a curve that is 0.2 mi long. If one-half of the curve is in the segment, then Pc, i = 0.20 (= Equation 18-24

431 0.1/0.5). In fact, this proportion is the same regardless of the curve’s length (provided that it is 0.1 mi or longer and 0.1 mi of this curve is located in the segment). The roadbed adjustment factor fc, i is used to modify the CMF so that it can be applied to freeway segments where only one roadbed is curved (and the other roadbed is tangent). This situation occurs on some freeway segments in rural areas (although, it can also occur in urban areas). Table 18-14. Coefficients for Horizontal Curve CMF–Freeway Segments Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Any cross section (ac) Multiple vehicle (mv) Fatal and injury (fi) CMF1, fs, ac, mv, fi 0.0172 Property damage only (pdo) CMF1, fs, ac, mv, pdo 0.0340 Single vehicle (sv) Fatal and injury (fi) CMF1, fs, ac, sv, fi 0.0719 Property damage only (pdo) CMF1, fs, ac, sv, pdo 0.0626 Details regarding the measurement of radius, curve length, and other variables associated with this CMF are provided in Section 18.4.2. The CMF is applicable to curves with a radius of 1,000 ft or larger. CMF2, w, x, y, fi—Lane Width Two CMFs are used to describe the relationship between average lane width and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury multiple-vehicle crashes, specified number of lanes (fs, n, mv, fi); and  SPF for fatal-and-injury single-vehicle crashes, specified number of lanes (fs, n, sv, fi). The base condition is a 12-ft lane width. The CMFs are described using the following equation. ( ) ftWIf ftWIf b Wa CMF l ll fiyacfs 13: 13:]12[exp ,,,,2 ≥ <    −× = Where: CMF2, fs, ac, y, fi = crash modification factor for lane width in a freeway segment with any cross section ac, crash type y, and fatal-and-injury crashes fi; and Wl = lane width (ft). The coefficients for Equation 18-25 are provided in Table 18-15. In fact, the coefficient values are the same for both crash types listed in the table, which indicates that the CMF value is the same for the corresponding SPFs. The CMF is discontinuous, breaking at a lane width of 13 ft. The CMF is applicable to lane widths in the range of 10.5 to 14 ft. Equation 18-25

432 Table 18-15. Coefficients for Lane Width CMF–Freeway Segments Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficients a b Any cross section (ac) Multiple vehicle (mv) Fatal and injury (fi) CMF2, fs, ac, mv, fi -0.0376 0.963 Single vehicle (sv) Fatal and injury (fi) CMF2, fs, ac, sv, fi -0.0376 0.963 CMF3, w, x, y, z —Inside Shoulder Width Four CMFs are used to describe the relationship between average inside shoulder width and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury multiple-vehicle crashes, specified number of lanes (fs, n, mv, fi);  SPF for property-damage-only multiple-vehicle crashes, specified number of lanes (fs, n, mv, pdo);  SPF for fatal-and-injury single-vehicle crashes, specified number of lanes (fs, n, sv, fi); and  SPF for property-damage-only single-vehicle crashes, specified number of lanes (fs, n, sv, pdo). The base condition is a 6-ft inside shoulder width. The CMFs are described using the following equation. ( )]6[exp,,,,3 −×= iszyacfs WaCMF Where: CMF3, fs, ac, y, z = crash modification factor for inside shoulder width in a freeway segment with any cross section ac, crash type y, and severity z; and Wis = paved inside shoulder width (ft). The coefficient for Equation 18-26 is provided in Table 18-16. For a given severity, the coefficient values are the same for both crash types listed in the table, which indicates that the CMF value is the same for the corresponding SPFs. The CMF is applicable to shoulder widths in the range of 2 to 12 ft. Table 18-16. Coefficients for Inside Shoulder Width CMF–Freeway Segments Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Any cross section (ac) Multiple vehicle (mv) Fatal and injury (fi) CMF3, fs, ac, mv, fi -0.0172 Property damage only (pdo) CMF3, fs, ac, mv, pdo -0.0153 Single vehicle (sv) Fatal and injury (fi) CMF3, fs, ac, sv, fi -0.0172 Property damage only (pdo) CMF3, fs, ac, sv, pdo -0.0153 Equation 18-26

433 CMF4, w, x, y, z—Median Width Four CMFs are used to describe the relationship between median width and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury multiple-vehicle crashes, specified number of lanes (fs, n, mv, fi);  SPF for property-damage-only multiple-vehicle crashes, specified number of lanes (fs, n, mv, pdo);  SPF for fatal-and-injury single-vehicle crashes, specified number of lanes (fs, n, sv, fi); and  SPF for property-damage-only single-vehicle crashes, specified number of lanes (fs, n, sv, pdo). The base condition is a 60-ft median width, a 6-ft inside shoulder width, and no barrier present in the median. The CMFs are described using the following equation. ( ) ( ) ( )]482[exp]482[exp0.1,,,,4 −×××+−×−××−= icbibismibzyacfs WaPWWaPCMF Where: CMF4, fs, ac, y, z = crash modification factor for median width in a freeway segment with any cross section ac, crash type y, and severity z; Pib = proportion of segment length with a barrier present in the median (i.e., inside); Wm = median width (measured from near edges of traveled way in both directions) (ft); and Wicb = distance from edge of inside shoulder to barrier face (ft). The coefficient for Equation 18-27 is provided in Table 18-17. These CMFs are derived to be applicable to a segment that has median barrier present along some portion of the segment. Guidance for computing the variables Pib and Wicb is provided in Section 18.7.3. Table 18-17. Coefficients for Median Width CMF–Freeway Segments Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Any cross section (ac) Multiple vehicle (mv) Fatal and injury (fi) CMF4, fs, ac, mv, fi -0.00302 Property damage only (pdo) CMF4, fs, ac, mv, pdo -0.00291 Single vehicle (sv) Fatal and injury (fi) CMF4, fs, ac, sv, fi 0.00102 Property damage only (pdo) CMF4, fs, ac, sv, pdo -0.00289 The CMF is applicable to median widths of 9 ft or more, Wicb values in the range of 0.75 to 17 ft, and shoulder widths in the range of 2 to 12 ft. If the median width exceeds 90 ft, then 90 ft should be used for Wm in Equation 18-27. Equation 18-27

434 CMF5, w, x, y, z—Median Barrier Four CMFs are used to describe the relationship between median barrier presence and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury multiple-vehicle crashes, specified number of lanes (fs, n, mv, fi);  SPF for property-damage-only multiple-vehicle crashes, specified number of lanes (fs, n, mv, pdo);  SPF for fatal-and-injury single-vehicle crashes, specified number of lanes (fs, n, sv, fi); and  SPF for property-damage-only single-vehicle crashes, specified number of lanes (fs, n, sv, pdo). The base condition is no barrier present in the median. The CMFs are described using the following equation. ( )       ×+×−= icb ibibzyacfs W aPPCMF exp0.10.1,,,,5 Where: CMF5, fs, ac, y, z = crash modification factor for median barrier in a freeway segment with any cross section ac, crash type y, and severity z. The coefficient for Equation 18-28 is provided in Table 18-18. For a given severity, the coefficient values are the same for both crash types listed in the table, which indicates that the CMF value is the same for the corresponding SPFs. Guidance for computing the variables Pib and Wicb is provided in Section 18.7.3. Table 18-18. Coefficients for Median Barrier CMF–Freeway Segments Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Any cross section (ac) Multiple vehicle (mv) Fatal and injury (fi) CMF5, fs, ac, mv, fi 0.131 Property damage only (pdo) CMF5, fs, ac, mv, pdo 0.169 Single vehicle (sv) Fatal and injury (fi) CMF5, fs, ac, sv, fi 0.131 Property damage only (pdo) CMF5, fs, ac, sv, pdo 0.169 The CMF is applicable to Wicb values in the range of 0.75 to 17 ft. This CMF is applicable to cable barrier, concrete barrier, guardrail, and bridge rail. CMF6, w, x, y, z—High Volume As volume nears capacity, average freeway speed tends to decrease and headway is reduced. Logically, these changes have some influence on crash characteristics, including crash frequency, crash type, and crash severity. This CMF was developed to provide some sensitivity to volume variation during the average day and specifically to those peak hours where traffic volume is likely to be near (or in excess of) capacity. Equation 18-28

435 A statistic was developed to describe the degree of volume concentration during peak hours of the average day. It represents the proportion of the AADT that occurs during hours where the volume exceeds 1,000 vehicles per hour per lane (veh/h/ln). It has a value of zero if the volume on the associated segment does not exceed the threshold value for any hour of the day. It has a value of one if the volume during each hour of the average day exceeds the threshold value. In general, its value is large when hourly volumes are continuously high or when there is a peak few hours with an exceptionally large volume. Typical freeway speed-volume relationships show that the average speed tends to drop as flow rates increase beyond 1,000 veh/h/ln. This trend suggests that drivers reduce their speed to improve their comfort and safety as their headway gets shorter than 3.6 s/veh (= 3,600/1,000). Four CMFs are used to describe the relationship between volume concentration and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury multiple-vehicle crashes, specified number of lanes (fs, n, mv, fi);  SPF for property-damage-only multiple-vehicle crashes, specified number of lanes (fs, n, mv, pdo);  SPF for fatal-and-injury single-vehicle crashes, specified number of lanes (fs, n, sv, fi); and  SPF for property-damage-only single-vehicle crashes, specified number of lanes (fs, n, sv, pdo). The base condition is no hours having a volume that exceeds 1,000 veh/h/ln. The CMFs are described using the following equation. ( )hvzyacfs PaCMF ×= exp,,,,6 Where: CMF6, fs, ac, y, z = crash modification factor for high volume in a freeway segment with any cross section ac, crash type y, and severity z; and Phv = proportion of AADT during hours where volume exceeds 1,000 veh/h/ln. The coefficient for Equation 18-29 is provided in Table 18-19. The CMF is applicable to Phv values in the range of 0.0 to 1.0. Table 18-19. Coefficients for High Volume CMF–Freeway Segments Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Any cross section (ac) Multiple vehicle (mv) Fatal and injury (fi) CMF6, fs, ac, mv, fi 0.350 Property damage only (pdo) CMF6, fs, ac, mv, pdo 0.283 Single vehicle (sv) Fatal and injury (fi) CMF6, fs, ac, sv, fi -0.0675 Property damage only (pdo) CMF6, fs, ac, sv, pdo -0.611 Equation 18-29

436 CMF7, fs, ac, mv, z—Lane Change Two CMFs are used to describe the relationship between lane change activity and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury multiple-vehicle crashes, specified number of lanes (fs, n, mv, fi); and  SPF for property-damage-only multiple-vehicle crashes, specified number of lanes (fs, n, mv, pdo). The base condition is no significant lane changing due to ramp entry or exit. More specifically, the base condition is no ramp entrance or ramp exit within 0.5 mi of the segment. The CMFs are described using the following equations: ( ) ( )declcdecwevinclcincwevzmvacfs ffffCMF ,,,,,,,,7 5.05.0 ××+××= with, ( )        ×+×−= incwev incwevBincwevBincwev L aPPf , ,,, exp0.10.1 ( )        ×+×−= decwev decwevBdecwevBdecwev L aPPf , ,,, exp0.10.1 [ ]( ) ( )[ ] [ ]( ) ( )[ ]       ×−−× × ××+×− +×         ×−−× × ××+×− += fs fs exteexte fs fs entbentb inclc Lb Lb AADTcdXb Lb Lb AADTcdXb f exp0.1 lnexp 0.1 exp0.1 lnexp 0.1 ,, ,, , [ ]( ) ( )[ ] [ ]( ) ( )[ ]       ×−−× × ××+×− +×         ×−−× × ××+×− += fs fs extbextb fs fs enteente declc Lb Lb AADTcdXb Lb Lb AADTcdXb f exp0.1 lnexp 0.1 exp0.1 lnexp 0.1 ,, ,, , Where: CMF7, fs, ac, mv, z = crash modification factor for lane changes in a freeway segment with any cross section ac, multiple-vehicle crashes mv, and severity z; flc, inc = lane change adjustment factor for travel in increasing milepost direction; flc, dec = lane change adjustment factor for travel in decreasing milepost direction; fwev, inc = weaving section adjustment factor for travel in increasing milepost direction; fwev, dec = weaving section adjustment factor for travel in decreasing milepost direction; Equation 18-30 Equation 18-31 Equation 18-32 Equation 18-33 Equation 18-34

437 PwevB, inc = proportion of segment length within a Type B weaving section for travel in increasing milepost direction; PwevB, dec = proportion of segment length within a Type B weaving section for travel in decreasing milepost direction; Lwev, inc = weaving section length for travel in increasing milepost direction (may extend beyond segment boundaries) (mi); Lwev, dec = weaving section length for travel in decreasing milepost direction (may extend beyond segment boundaries) (mi); Xb, ent = distance from segment begin milepost to nearest upstream entrance ramp gore point, for travel in increasing milepost direction (mi); Xb, ext = distance from segment begin milepost to nearest downstream exit ramp gore point, for travel in decreasing milepost direction (mi); Xe, ent = distance from segment end milepost to nearest upstream entrance ramp gore point, for travel in decreasing milepost direction (mi); Xe, ext = distance from segment end milepost to nearest downstream exit ramp gore point, for travel in increasing milepost direction (miles); AADTb, ent = AADT volume of entrance ramp located at distance Xb, ent (veh/day); AADTb, ext = AADT volume of exit ramp located at distance Xb, ext (veh/day); AADTe, ent = AADT volume of entrance ramp located at distance Xe, ent (veh/day); and AADTe, ext = AADT volume of exit ramp located at distance Xe, ext (veh/day). The coefficients for Equation 18-31 to Equation 18-34 are provided in Table 18-20. Table 18-20. Coefficients for Lane Change CMF–Freeway Segments Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficients a b c d Any cross section (ac) Multiple vehicle (mv) Fatal and injury (fi) CMF7, fs, ac, mv, fi 0.175 12.56 0.001 -0.272 Property damage only (pdo) CMF7, fs, ac, mv, pdo 0.123 13.46 0.001 -0.283 If the segment is in a Type B weaving section, then the length of the weaving section is an input to the CMF. The variables for weaving section length (i.e., Lwev, inc, Lwev, dec) in Equation 18-31 and Equation 18- 32 are intended to reflect the degree to which the weaving activity is concentrated along the freeway. The sign of the coefficient in these two equations indicates that the lane change CMF value will increase if the segment is in a Type B weaving section. The amount of this increase is inversely related to the length of the weaving section. Guidance for determining if a weaving section is Type B is provided in Section 18.4.

438 The variables PwevB, inc and PwevB, dec in Equation 18-31 and Equation 18-32, respectively, are computed as the ratio of the length of the weaving section in the segment to the length of the freeway segment Lfs. If the segment is wholly located in the weaving section, then this variable is equal to 1.0. The X and AADT variables describe the distance to (and volume of) the four nearest ramps to the subject segment. Two of the ramps of interest are on the side of the freeway with travel in the increasing milepost direction. One ramp on this side of the freeway is upstream of the segment, and one ramp is downstream of the segment. Similarly, one ramp on the other side of the freeway is upstream of the segment and one ramp is downstream. Only those entrance ramps that contribute volume to the subject segment are of interest. Hence, a downstream entrance ramp is not of interest. For similar reasons, an upstream exit ramp is not of interest. The Lane change CMF is applicable to any segment in the vicinity of one or more ramps. It is equally applicable to segments in a weaving section (regardless of the weaving section type) and segments in a non-weaving section (i.e., segments between an entrance ramp and an exit ramp where both ramps have a speed-change lane). If the weaving section is Type B, then an additional adjustment is made using Equation 18-31 and Equation 18-32. The CMF is applicable to weaving section lengths between 0.10 and 0.85 mi. It is applicable to any value for the distance variable X and to the range of ramp AADTs in Table 19-4 of Chapter 19. The two SPFs for predicting speed-change-related crash frequency (i.e., Equation 18-20 and Equation 18- 22) are not used when evaluating a weaving section because the ramps that form the weaving section do not have a speed-change lane. As a result, the predicted crash frequency for the set of segments that comprise a weaving section will tend to be smaller than that predicted for a similar set of segments located in a non-weaving section but having entrance and exit ramps. This generalization will always be true for weaving sections that are not Type B. It may or may not hold for the Type B weaving section, depending on the length of the weaving section. CMF8, fs, ac, sv, z—Outside Shoulder Width Two CMFs are used to describe the relationship between average outside shoulder width and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury single-vehicle crashes, specified number of lanes (fs, n, sv, fi); and  SPF for property-damage-only single-vehicle crashes, specified number of lanes (fs, n, sv, pdo). The base condition is a 10-ft outside shoulder width. The CMFs are described using the following equation. ( ) ( )]10[exp]10[exp0.1 1 , 1 ,,,,,8 −××        +−××        −=  == s m i ics m i iczsvacfs WbPWaPCMF Where: CMF8, fs, ac, sv, z = crash modification factor for outside shoulder width in a freeway segment with any cross section ac, single-vehicle crashes sv, and severity z; and Ws = paved outside shoulder width (ft). Equation 18-35

439 The coefficients for Equation 18-35 are provided in Table 18-21. The variable Pc,i is computed as the ratio of the length of curve i in the segment to the length of the freeway segment Lfs. The CMF is applicable to shoulder widths in the range of 4 to 14 ft. Table 18-21. Coefficients for Outside Shoulder Width CMF–Freeway Segments Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficients a b Any cross section (ac) Single vehicle (sv) Fatal and injury (fi) CMF8, fs, ac, sv, fi -0.0647 -0.0897 Property damage only (pdo) CMF8, fs, ac, sv, pdo 0.00 -0.0840 CMF9, fs, ac, sv, fi—Shoulder Rumble Strips One CMF is used to describe the relationship between shoulder rumble strip presence and predicted crash frequency. The SPF to which it applies is identified in the following list:  SPF for fatal-and-injury single-vehicle crashes, specified number of lanes (fs, n, sv, fi). The base condition is no shoulder rumble strips present. The CMF is described using the following equation. 0.10.1 1 , 1 ,,,,,9 ×        +×        −=  == m i ictan m i icfisvacfs PfPCMF ( ) ( )811.00.1]0.1[5.0811.00.1]0.1[5.0 ×+×−×+×+×−×= ororirirtan PPPPf Where: CMF9, fs, ac, sv, fi = crash modification factor for shoulder rumble strips in a freeway segment with any cross section ac and fatal-and-injury fi single-vehicle crashes sv; ftan = factor for rumble strip presence on tangent portions of the segment; Pir = proportion of segment length with rumble strips present on the inside shoulders; and Por = proportion of segment length with rumble strips present on the outside shoulders. The proportion Pir represents the proportion of the segment length with rumble strips present on the inside shoulders. It is computed by summing the length of roadway with rumble strips on the inside shoulder in both travel directions and dividing by twice the freeway segment length Lfs. The proportion Por represents the proportion of the segment length with rumble strips present on the outside shoulders. It is computed by summing the length of roadway with rumble strips on the outside shoulder in both travel directions and dividing by twice the freeway segment length Lfs. This CMF addresses shoulder rumble strip placement on curved and uncurved (i.e., tangent) segments. It has a value less than 1.0 on tangent segments with shoulder rumble strips suggesting that crash frequency Equation 18-36 Equation 18-37

440 is lowered by the presence of rumble strips. This trend was not found in the calibration data for curved segments. CMF10, fs, ac, sv, fi—Outside Clearance One CMF is used to describe the relationship between average outside clearance and predicted crash frequency. The SPF to which it applies is identified in the following list:  SPF for fatal-and-injury single-vehicle crashes, specified number of lanes (fs, n, sv, fi). The base condition is a 30-ft clear zone, a 10-ft outside shoulder width, and no barrier present in the clear zone. The CMF is described using the following equation. ( ) ( ) ( )]20[00451.0exp ]20[00451.0exp0.1,,,,10 −×−×+ −−×−×−= ocbob shcobfisvacfs WP WWPCMF Where: CMF10, fs, ac, sv, fi = crash modification factor for outside clearance in a freeway segment with any cross section ac, single-vehicle sv, fatal-and-injury fi crashes; Pob = proportion of segment length with a barrier present on the roadside (i.e., outside); Whc = clear zone width (ft); and Wocb = distance from edge of outside shoulder to barrier face (ft). This CMF is derived to be applicable to a segment that has roadside barrier present along some portion of the segment. Guidance for computing the variables Pob and Wocb is provided in Section 18.7.3. The CMF is applicable to clear zone widths of 30 ft or less, Wocb values in the range of 0.75 to 17 ft, and to shoulder widths in the range of 4 to 14 ft. CMF11, fs, ac, sv, z—Outside Barrier Two CMFs are used to describe the relationship between outside barrier presence and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury single-vehicle crashes, specified number of lanes (fs, n, sv, fi); and  SPF for property-damage-only single-vehicle crashes, specified number of lanes (fs, n, sv, pdo). The base condition is no barrier present in the clear zone. The CMFs are described using the following equation. ( )       ×+×−= ocb obobzsvacfs W aPPCMF exp0.10.1,,,,11 Where: CMF11, fs, ac, sv, z = crash modification factor for roadside barrier in a freeway segment with any cross section ac, single-vehicle crashes sv, and severity z. Equation 18-38 Equation 18-39

441 The coefficient for Equation 18-39 is provided in Table 18-22. Guidance for computing the variables Pob and Wocb is provided in Section 18.7.3. Table 18-22. Coefficients for Outside Barrier CMF–Freeway Segments Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Any cross section (ac) Single vehicle (sv) Fatal and injury (fi) CMF11, fs, ac, sv, fi 0.131 Property damage only (pdo) CMF11, fs, ac, sv, pdo 0.169 The variable Wocb represents the distance from the edge of outside shoulder to roadside barrier face. The value used for this variable in Equation 18-39 is an average for the segment. The CMF is applicable to Wocb values in the range of 0.75 to 17 ft. This CMF is applicable to cable barrier, concrete barrier, guardrail, and bridge rail. 18.7.2. Crash Modification Factors for Speed-Change Lanes The CMFs for geometric design and traffic control features of speed-change lanes are presented in this section. CMF1, w, x, y, z—Horizontal Curve Two CMFs are used to describe the relationship between horizontal curve geometry and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes, ramp entrance, freeway lanes n (sc, nEN, at, fi);  SPF for property-damage-only crashes, ramp entrance, freeway lanes n (sc, nEN, at, pdo);  SPF for fatal-and-injury crashes, ramp exit, freeway lanes n (sc, nEX, at, fi); and  SPF for property-damage-only crashes, ramp exit, freeway lanes n (sc, nEX, at, pdo). The base condition is an uncurved (i.e., tangent) alignment through the speed-change lane. The CMFs are described using the following equation.         ×      ×+=  = m i ic i zatacsc PR aCMF 1 , 2 ,,,,1 730,50.1 Where: CMF1, sc, ac, at, z = crash modification factor for horizontal curvature at a speed-change lane with any cross section ac, all crash types at, and severity z; Ri = radius of curve i (ft); Pc, i = proportion of speed-change lane length with curve i; and m = number of horizontal curves in the speed-change lane. Equation 18-40

442 The coefficient for Equation 18-40 is provided in Table 18-23. The variable Pc, i is computed as the ratio of the length of curve i in the speed-chanage lane to the length of the speed-change lane Len or Lex. Additional discussion of this CMF is provided in Section 18.7.1. Table 18-23. Coefficients for Horizontal Curve CMF–Speed-Change Lanes Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Any cross section (ac) All types (at) Fatal and injury (fi) CMF1, sc, ac, at, fi 0.0172 Property damage only (pdo) CMF1, sc, ac, at, pdo 0.0340 CMF2, w, x, y, fi—Lane Width One CMF is used to describe the relationship between average lane width and predicted crash frequency. The SPFs to which it applies are identified in the following list:  SPF for fatal-and-injury crashes, ramp entrance, freeway lanes n (sc, nEN, at, fi); and  SPF for fatal-and-injury crashes, ramp exit, freeway lanes n (sc, nEX, at, fi). The base condition is a 12-ft lane width. The CMF is described using the following equation. ( ) ftWIf ftWIfW CMF l ll fiatacsc 13: 13: 963.0 ]12[0376.0exp ,,,,2 ≥ <    −×− = Where: CMF2, sc, ac, at, fi = crash modification factor for lane width at a speed-change lane with any cross section ac, all crash types at, and fatal-and-injury crashes fi; and Wl = lane width (ft). The CMF is applicable to lane widths in the range of 10.5 to 14 ft. CMF3, w, x, y, z —Inside Shoulder Width Two CMFs are used to describe the relationship between average inside shoulder width and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes, ramp entrance, freeway lanes n (sc, nEN, at, fi);  SPF for property-damage-only crashes, ramp entrance, freeway lanes n (sc, nEN, at, pdo);  SPF for fatal-and-injury crashes, ramp exit, freeway lanes n (sc, nEX, at, fi); and  SPF for property-damage-only crashes, ramp exit, freeway lanes n (sc, nEX, at, pdo). The base condition is a 6-ft inside shoulder width. The CMFs are described using the following equation. Equation 18-41

443 ( )]6[exp,,,,3 −×= iszatacsc WaCMF Where: CMF3, sc, ac, at, z = crash modification factor for inside shoulder width at a speed-change lane with any cross section ac, all crash types at, and severity z; and Wis = paved inside shoulder width (ft). The coefficient for Equation 18-42 is provided in Table 18-24. The CMF is applicable to shoulder widths in the range of 2 to 12 ft. Table 18-24. Coefficients for Inside Shoulder Width CMF–Speed-Change Lanes Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Any cross section (ac) All types (at) Fatal and injury (fi) CMF3, sc, ac, at, fi -0.0172 Property damage only (pdo) CMF3, sc, ac, at, pdo -0.0153 CMF4, w, x, y, z—Median Width Two CMFs are used to describe the relationship between median width and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes, ramp entrance, freeway lanes n (sc, nEN, at, fi);  SPF for property-damage-only crashes, ramp entrance, freeway lanes n (sc, nEN, at, pdo);  SPF for fatal-and-injury crashes, ramp exit, freeway lanes n (sc, nEX, at, fi); and  SPF for property-damage-only crashes, ramp exit, freeway lanes n (sc, nEX, at, pdo). The base condition is a 60-ft median width, a 6-ft inside shoulder width, and no barrier present in the median. The CMFs are described using the following equation. ( ) ( ) ( )]482[exp]482[exp0.1,,,,4 −×××+−×−××−= icbibismibzatacsc WaPWWaPCMF Where: CMF4, sc, ac, at, z = crash modification factor for median width at a speed-change lane with any cross section ac, all crash types at, and severity z; Pib = proportion of speed-change lane length with a barrier present in the median (i.e., inside); Wm = median width (measured from near edges of traveled way in both directions) (ft); and Equation 18-42 Equation 18-43

444 Wicb = distance from edge of inside shoulder to barrier face (ft). The coefficient for Equation 18-43 is provided in Table 18-25. These CMFs are derived to be applicable to a speed-change lane that has median barrier present along some portion of its length. Guidance for computing the variables Pib and Wicb is provided in Section 18.7.3. Table 18-25. Coefficients for Median Width CMF–Speed-Change Lanes Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Any cross section (ac) All types (at) Fatal and injury (fi) CMF4, sc, ac, at, fi -0.00302 Property damage only (pdo) CMF4, sc, ac, at, pdo -0.00291 The CMF is applicable to median widths 9 ft or more, Wicb values in the range of 0.75 to 17 ft, and shoulder widths in the range of 2 to 12 ft. If the median width exceeds 90 ft, then 90 ft should be used for Wm in Equation 18-43. CMF5, w, x, y, z—Median Barrier Two CMFs are used to describe the relationship between median barrier presence and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes, ramp entrance, freeway lanes n (sc, nEN, at, fi);  SPF for property-damage-only crashes, ramp entrance, freeway lanes n (sc, nEN, at, pdo);  SPF for fatal-and-injury crashes, ramp exit, freeway lanes n (sc, nEX, at, fi); and  SPF for property-damage-only crashes, ramp exit, freeway lanes n (sc, nEX, at, pdo). The base condition is no barrier present in the median. The CMFs are described using the following equation. ( )       ×+×−= icb ibibzatacsc W aPPCMF exp0.10.1,,,,5 Where: CMF5, sc, ac, at, z = crash modification factor for median barrier at a speed-change lane with any cross section ac, all crash types at, and severity z. The coefficient for Equation 18-44 is provided in Table 18-26. Guidance for computing the variables Pib and Wicb is provided in Section 18.7.3. Table 18-26. Coefficients for Median Barrier CMF–Speed-Change Lanes Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Equation 18-44

445 Any cross section (ac) All types (at) Fatal and injury (fi) CMF5, sc, ac, at, fi 0.131 Property damage only (pdo) CMF5, sc, ac, at, pdo 0.169 The CMF is applicable to Wicb values in the range of 0.75 to 17 ft. This CMF is applicable to cable barrier, concrete barrier, guardrail, and bridge rail. CMF6, w, x, y, z—High Volume Two CMFs are used to describe the relationship between volume concentration and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes, ramp entrance, freeway lanes n (sc, nEN, at, fi);  SPF for property-damage-only crashes, ramp entrance, freeway lanes n (sc, nEN, at, pdo);  SPF for fatal-and-injury crashes, ramp exit, freeway lanes n (sc, nEX, at, fi); and  SPF for property-damage-only crashes, ramp exit, freeway lanes n (sc, nEX, at, pdo). The base condition is no hours having a volume that exceeds 1,000 veh/h/ln. The CMFs are described using the following equation. ( )hvzatacsc PaCMF ×= exp,,,,6 Where: CMF6, sc, ac, at, z = crash modification factor for high volume at a speed-change lane with any cross section ac, all crash types at, and severity z; and Phv = proportion of AADT during hours where volume exceeds 1,000 veh/h/ln. The coefficient for Equation 18-45 is provided in Table 18-27. Additional discussion of this CMF is provided in Section 18.7.1. Table 18-27. Coefficients for High Volume CMF–Speed-Change Lanes Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Any cross section (ac) All types (at) Fatal and injury (fi) CMF6, sc, ac, at, fi 0.350 Property damage only (pdo) CMF6, sc, ac, at, pdo 0.283 CMF12, sc, nEN, at, z—Ramp Entrance Two CMFs are used to describe the relationship between ramp entrance geometry and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes, ramp entrance, freeway lanes n (sc, nEN, at, fi); and Equation 18-45

446  SPF for property-damage-only crashes, ramp entrance, freeway lanes n (sc, nEN, at, pdo). The CMFs are described using the following equation.       ××++×= ]ln[exp,,,,12 r en leftzatnENsc AADTcdL bIaCMF Where: CMF12, sc, nEN, at, z = crash modification factor for ramp entrance geometry on a freeway with n lanes with all crash types at and severity z; Len = length of ramp entrance (mi); Ileft = ramp side indicator variable (= 1.0 if entrance or exit is on left side of through lanes, 0.0 if it is on right side); and AADTr = AADT volume of ramp (veh/day). The coefficients for Equation 18-46 are provided in Table 18-28. Table 18-28. Coefficients for Ramp Entrance CMF–Speed-Change Lanes Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficients a b c d Ramp entrance, n lanes (nEN) All types (at) Fatal and injury (fi) CMF12, sc, nEN, at, fi 0.594 0.0318 0.001 0.198 Property damage only (pdo) CMF12, sc, nEN, at, pdo 0.824 0.0252 0.001 0.00 This CMF is applicable to a ramp entrance speed-change lane, as shown in Figure 18-10. The ramp entrance length is measured using the reference points identified in Figure 18-3. The variable for ramp entrance length Len in Equation 18-46 is intended to reflect the degree to which the lane-changing activity is concentrated along the ramp entrance. The CMF is applicable to ramp entrance lengths in the range of 0.04 to 0.30 mi (210 to 1,600 ft). It is applicable to the range of ramp AADTs in Table 19-4 of Chapter 19. The indicator variable for ramp side Ileft is associated with a positive coefficient. This sign indicates that a ramp entrance on the left side of the through lanes is associated with an increase in crash frequency, relative to one on the right side. The data used to calibrate this CMF represent freeways where ramp entrances are typically located on the right side. CMF13, sc, nEX, at, z—Ramp Exit Two CMFs are used to describe the relationship between ramp exit geometry and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes, ramp exit, freeway lanes n (sc, nEX, at, fi); and Equation 18-46

447  SPF for property-damage-only crashes, ramp exit, freeway lanes n (sc, nEX, at, pdo). The CMFs are described using the following equation.       +×= ex leftzatnEXsc L bIaCMF exp,,,,13 Where: CMF13, sc, nEX, at, z = crash modification factor for ramp exit geometry on a freeway with n lanes with all crash types at and severity z; Lex = length of ramp exit (mi); and Ileft = ramp side indicator variable (= 1.0 if entrance or exit is on left side of through lanes, 0.0 if it is on right side). The coefficients for Equation 18-47 are provided in Table 18-29. Table 18-29. Coefficients for Ramp Exit CMF–Speed-Change Lanes Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficients a b Ramp exit, n lanes (nEX) All types (at) Fatal and injury (fi) CMF13, sc, nEX, at, fi 0.594 0.0116 Property damage only (pdo) CMF13, sc, nEX, at, pdo 0.824 0.00 This CMF is applied to a ramp exit speed-change lane, as shown in Figure 18-10. The ramp exit length is measured using the reference points identified in Figure 18-3. The variable for ramp exit length Lex in Equation 18-47 is intended to reflect the degree to which the lane- changing activity is concentrated along the ramp exit. The CMF is applicable to ramp exit lengths in the range of 0.02 to 0.30 mi (106 to 1600 ft). The indicator variable for ramp side Ileft is associated with a positive coefficient. This sign indicates that a ramp exit on the left side of the through lanes is associated with an increase in crash frequency, relative to one on the right side. The data used to calibrate this CMF represent freeways where ramp exits are typically located on the right side. 18.7.3. Supplemental Calculations to Apply Crash Modification Factors Some of the CMFs in Section 18.7.1 and Section 18.7.2 require the completion of supplemental calculations before they can be applied to the SPFs in Section 18.6. These CMFs are:  Median width.  Median barrier.  Outside clearance. Equation 18-47

448  Outside barrier. These four CMFs include variables that describe the presence of barrier in the median or on the roadside. These variables include barrier offset, length, and width. Barrier offset represents a lateral distance measured from the near edge of the shoulder to the face of the barrier (i.e., it does not include the width of the shoulder). Barrier length represents the length of lane paralleled by a barrier; it is a total for both travel directions. For example, if the outside barrier extends for the length of the roadway on both sides of the roadway, then the outside barrier length equals twice the segment length. Median barrier width represents either (a) the physical width of the barrier if only one barrier is used or (b) the lateral distance between barrier “faces” if two parallel barriers are provided in the median area. A barrier face is the side of the barrier that is exposed to traffic. Two key variables that are needed for the evaluation of barrier presence are the inside barrier offset distance Wicb and the outside barrier offset distance Wocb. As indicated in Equation 18-28 and Equation 18- 39, this distance is included as a divisor in the exponential term. This relationship implies that the correlation between barrier distance and crash frequency is an inverse one (i.e., crash frequency decreases with increasing distance to the barrier). When multiple sections of barrier exist along the segment, a length-weighted average of the reciprocal of the individual distances is needed to properly reflect this inverse relationship. The length used to weight the average is the barrier length. Additional key variables include the proportion of segment length with a barrier present in the median Pib and the proportion of segment length with a barrier present on the roadside Pob. Equations for calculating these proportions and the aforementioned distances are described in the following paragraphs. The length of segment L used in the following equations is equal to that of the freeway segment Lfs or speed-change lane Lex, Len, as appropriate for the CMF to which the calculated value will be applied. If the median width exceeds 90 ft, then 90 ft should be used for Wm in the following equations. For segments or speed-change lanes with a continuous barrier centered in the median (i.e., symmetric median barrier), the following equations are used to estimate Wicb and Pib. ( )  −×−× −× + − ×= ibism iib isiinoff iib icb WWW LL WW L LW 25.0 2 2 , ,, , 0.1=ibP Where: Wicb = distance from edge of inside shoulder to barrier face (ft); Pib = proportion of segment length with a barrier present in the median (i.e., inside); L = length of segment (mi); Lib, i = length of lane paralleled by inside barrier i (include both travel directions) (mi); Equation 18-48 Equation 18-49

449 Wib = inside barrier width (measured from barrier face to barrier face) (ft); Wis = paved inside shoulder width (ft); Wm = median width (measured from near edges of traveled way in both directions) (ft); and Woff, in, i = horizontal clearance from the edge of the traveled way to the face of inside barrier i (ft). The first summation term “∑” in Equation 18-48 applies to short lengths of barrier in the median. It indicates that the ratio of barrier length Lib, i to clearance distance (= Woff, in, i – Wis) should be computed for each individual length of barrier that is found in the median along the segment (e.g., a barrier protecting a sign support). The continuous median barrier is not considered in this summation. Any clearance distance that is less than 0.75 ft should be set to 0.75 ft. Similarly, if the distance “0.5 ×(Wm –2 ×Wis – Wib)” is less than 0.75 ft, then it should be set to 0.75 ft. For segments or speed-change lanes with a continuous barrier adjacent to one roadbed (i.e., asymmetric median barrier), the following equations should be used to estimate Wicb and Pib.   −−×− − + − + − ×= nearibism iib isiinoff iib isnear icb WWWW LL WW L WW L LW 2 2 , ,, , 0.1=ibP Where: Wnear = “near” horizontal clearance from the edge of the traveled way to the continuous median barrier (measure for both travel directions and use the smaller distance) (ft). Similar to the previous guidance, the first summation term “∑” in Equation 18-50 applies to short lengths of barrier in the median. The ratio of barrier length Lib to the clearance distance (= Woff, in, i - Wis) should be computed for each individual length of barrier that is found in the median along the segment. The continuous median barrier is not considered in this summation. Any clearance distance that is less than 0.75 ft should be set to 0.75 ft. Similarly, if the distance “Wnear –Wis” or the distance “Wm –2 ×Wis – Wib – Wnear” is less than 0.75 ft, then it should be set to 0.75 ft. For segments or speed-change lanes with a depressed median and some short sections of barrier in the median (e.g., bridge rail), the following equations should be used to estimate Wicb and Pib.   − = isiinoff iib iib icb WW L L W ,, , , L L P iibib × =  2 , Any clearance distance (= Woff, in, i – Wis) that is less than 0.75 ft should be set to 0.75 ft. For segments or speed-change lanes with depressed medians without a continuous barrier or short sections of barrier in the median, the following equation should be used to estimate Pib. Equation 18-50 Equation 18-51 Equation 18-52 Equation 18-53

450 0.0=ibP As suggested by Equation 18-28, the calculation of Wicb is not required when Pib = 0.0. For segments or speed-change lanes with barrier on the roadside, the following equations should be used to estimate Wocb and Pob.   − = siooff iob iob ocb WW L L W ,, , , L L P iobob × =  2 , Where: Lob, i = length of lane paralleled by outside barrier i (include both travel directions) (mi); Pob = proportion of segment length with a barrier present on the roadside (i.e., outside); Wocb = distance from edge of outside shoulder to barrier face (ft); Ws = paved outside shoulder width (ft); and Woff, o, i = horizontal clearance from the edge of the traveled way to the face of outside barrier i (ft). Any clearance distance (= Woff, o, i – Ws) that is less than 0.75 ft should be set to 0.75 ft. For segments or speed-change lanes without barrier on the roadside, the following equation should be used to estimate Pob. 0.0=obP As suggested by Equation 18-39, the calculation of Wocb is not required when Pob = 0.0. 18.8. SEVERITY DISTRIBUTION FUNCTIONS The severity distribution functions (SDFs) are presented in this section. They are used in the predictive model to estimate the expected average crash frequency for the following severity levels: fatal K, incapacitating injury A, non-incapacitating injury B, and possible injury C. Each SDF was developed as a regression model using observed crash data for a set of similar sites as the dependent variable. The SDF, like all regression models, estimates the value of the dependent variable as a function of a set of independent variables. The independent variables include various geometric features, traffic control features, and area type (i.e., rural or urban). The SDFs described in this section are equally applicable to freeway segments and speed-change lanes. The general model form for the severity distribution prediction is shown in the following equation. jatacwfiyxwejyxwe PNN ,,,,,,,,,,, ×= Where: Equation 18-54 Equation 18-55 Equation 18-56 Equation 18-57 Equation 18-58

451 Ne, w, x, y, j = expected average crash frequency for site type w, cross section or control type x, crash type y, and severity level j ( j = K: fatal, A: incapacitating injury, B: non-incapacitating injury, C: possible injury) (crashes/yr); Ne, w, x, y, fi = expected average crash frequency for site type w, cross section or control type x, crash type y, and fatal-and-injury crashes fi (crashes/yr); and Pw, x, at, j = probability of the occurrence of severity level j ( j = K: fatal, A: incapacitating injury, B: non-incapacitating injury, C: possible injury) for all crash types at at site type w with cross section or control type x. There is one SDF associated with each probability level j in the predictive model. An SDF predicts the probability of occurrence of severity level j for a crash based on various geometric design and traffic control features at the subject site. Each SDF also contains a calibration factor that is used to calibrate it to local conditions. The SDFs for freeway segments and speed-change lanes are described by the following equations. ( ) ( ) ( ) ( )BAK scfssdf K Katacscfs VVV C VP expexpexp0.1 exp , ,,, +++ = + + ( ) ( ) ( ) ( )BAK scfssdf A Aatacscfs VVV C VP expexpexp0.1 exp , ,,, +++ = + + ( ) ( ) ( ) ( )BAK scfssdf B Batacscfs VVV C VP expexpexp0.1 exp , ,,, +++ = + + )(0.1,,, BAKCatacscfs PPPP ++−=+ with, ( ) ( ) ( ) ( )rurallicorirhvobibj IgWfPePPdPcPPbaV ×+×+×+      +×+×+      +×+=  ,22 Where: Vj = systematic component of crash severity likelihood for severity level j; Csdf, fs+sc = calibration factor to adjust SDF for local conditions for freeway segments and speed- change lanes; Pib = proportion of segment length with a barrier present in the median (i.e., inside); Equation 18-59 Equation 18-60 Equation 18-61 Equation 18-62 Equation 18-63

452 Pob = proportion of segment length with a barrier present on the roadside (i.e., outside); Phv = proportion of AADT during hours where volume exceeds 1,000 veh/h/ln; Pir = proportion of segment length with rumble strips present on the inside shoulders; Por = proportion of segment length with rumble strips present on the outside shoulders; Pc, i = proportion of segment length with curve i; Wl = lane width (ft); Irural = area type indicator variable (= 1.0 if area is rural, 0.0 if it is urban); and a, b, c, d, e, f, g = regression coefficients. The SDF coefficients in Equation 18-63 are provided in Table 18-30. Guidance for computing the variables Pib and Pob is provided in Section 18.7.3. Table 18-30. SDF Coefficients for Freeway Segments and Speed-Change Lanes Severity Level ( j) Variabl e SDF Coefficients a b c d e f g Fatal (K) VK -0.171 -0.388 -0.924 0.387 0.208 -0.261 0.492 Incapacitating injury (A) VA -2.393 -0.325 -0.853 0.391 0.243 0.00 0.430 Non-incapacitating inj. (B) VB 0.0732 -0.250 -0.872 0.135 0.131 -0.0464 0.208 The proportion of AADT during hours where the volume exceeds 1,000 veh/h/ln is computed using the average hourly volume distribution associated with the subject segment. This distribution will typically be computed using the data obtained from the continuous traffic counting station that (1) is nearest to the subject freeway and (2) has similar traffic demand and peaking characteristics. The SDF is applicable to Phv values in the range of 0.0 to 1.0. Additional discussion of this variable is provided in Section 18.7.1 for the High Volume CMF. The proportion Pir is computed by summing the length of roadway with rumble strips on the inside shoulder in both travel directions and dividing by twice the freeway segment length Lfs. The proportion Por is computed by summing the length of roadway with rumble strips on the outside shoulder in both travel directions and dividing by twice the freeway segment length Lfs. The variable Pc, i is computed as the ratio of the length of curve i in the segment to the length of the freeway segment Lfs. For example, consider a segment that is 0.5 mi long and a curve that is 0.2 mi long. If one-half of the curve is in the segment, then Pc, i = 0.20 (= 0.1/0.5). In fact, this proportion is the same regardless of the curve’s length (provided that it is 0.1 mi or longer and 0.1 mi of this curve is located in the segment). When the SDF is applied to a speed-change lane, the variable Pc, i is computed as the ratio of the length of curve i in the speed-chanage lane to the length of the speed-change lane Len or Lex. The SDF is applicable to lane widths in the range of 10.5 to 14 ft.

453 The sign of a coefficient in Table 18-30 indicates the change in the proportion of crashes associated with a change in the corresponding variable. For example, the negative coefficient associated with barrier presence indicates that the proportion of fatal K crashes decreases with an increase in the proportion of barrier present in the segment. A similar trend is indicated for barrier presence on incapacitating injury A crashes and non-incapacitating injury B crashes. By inference, the proportion of possible injury C crashes increases with an increase in the proportion of barrier present. 18.9. CALIBRATION OF THE SPFS AND SDFS TO LOCAL CONDITIONS Crash frequencies, even for nominally similar freeway segments or speed-change lanes, can vary widely from one jurisdiction to another. Geographic regions differ markedly in climate, animal population, driver populations, crash-reporting threshold, and crash-reporting practices. These variations may result in some jurisdictions experiencing a different number of traffic crashes on freeways than others. Calibration factors are included in the methodology to allow transportation agencies to adjust the SPFs and SDFs to match actual local conditions. The SPF calibration factors will have values greater than 1.0 for segments or speed-change lanes that, on average, experience more crashes than those used in the development of the SPFs. Similarly, the calibration factors for segments or speed-change lanes that experience fewer crashes on average than those used in the development of the SPFs will have values less than 1.0. The calibration procedures for SPFs are presented in Section B.1.1 of Appendix B to Part C. The SDF calibration factors will have values greater than 1.0 for segments or speed-change lanes that, on average, experience more severe crashes than those used in the development of the SDFs. Similarly, the calibration factors for segments or speed-change lanes that experience fewer severe crashes on average than those used in the development of the SDFs will have values less than 1.0. The calibration procedures for SDFs are presented in Section B.1.4 of Appendix B to Part C. Default values are also provided for the crash type distributions used in the methodology. These values can also be replaced with locally derived values. The derivation of these values is addressed in Section B.1.3 of Appendix B to Part C. 18.10. LIMITATIONS OF PREDICTIVE METHOD The limitations of the predictive method which apply generally across all of the Part C chapters are discussed in Section C.14 of Part C. This section discusses limitations of the predictive models described in this chapter. The predictive method described in this chapter can be applied to the combinations of area type (rural or urban) and number of lanes that are listed in Section 18.6. The method can be extended to freeway segments with unequal number of lanes in opposing directions, but only if the number of lanes is within the ranges listed in Section 18.6.1 and varies by no more than one lane between the two travel directions. The predictive method does not account for the influence of the following conditions on freeway safety:  Freeways with 11 or more through lanes in urban areas.  Freeways with 9 or more through lanes in rural areas.  Freeways with continuous access high-occupancy vehicle (HOV) lanes.  Freeways with limited access managed lanes that are buffer-separated from the general purpose lanes.  Ramp metering.

454  Use of safety shoulders as travel lanes.  Toll plazas.  Reversible lanes. The predictive method does not distinguish between barrier types (i.e., cable barrier, concrete barrier, guardrail, and bridge rail) in terms of their possible different influence on crash severity. 18.11. APPLICATION OF PREDICTIVE METHOD The predictive method presented in this chapter is applied to a freeway facility by following the 18 steps presented in Section 18.4. Worksheets are provided in Appendix 13A for applying calculations in the predictive method. All computations of crash frequencies within these worksheets are conducted with values expressed to three decimal places. This level of precision is needed only for consistency in computations. In the last stage of computations, rounding the final estimates of expected average crash frequency to one decimal place is appropriate. 18.11.1. Freeways with Barrier-Separated Managed Lanes The predictive method can be used to evaluate freeways with barrier-separated managed lanes. The managed lanes are considered to be part of the median (i.e., the median width is measured between the near edges of the traveled way for the general purpose lanes) and the managed lane’s entry or exit points are treated as entrance or exit ramps, respectively, on the adjacent freeway. The average lane width is based on the general purpose lanes (i.e., the managed lanes are not considered). The shoulder width is measured from the edge of the general-purpose-lanes traveled way. The barrier between the general purpose lanes and managed lanes is treated as median barrier. The safety of the managed lanes is not addressed by this technique. The estimate of expected average crash frequency only includes crashes that occur in the general purpose lanes. 18.11.2. Freeways with Toll Facilities The predictive method can be used to evaluate a freeway section that is part of toll facility provided that the section is sufficiently distant from the toll facility that the facility does not influence vehicle operation. The predictive method is not directly applicable to any portion of the freeway that (a) is in the immediate vicinity of a toll plaza, (b) is widened to accommodate vehicle movements through the toll plaza, (c) experiences toll-related traffic queues, or (d) experiences toll-related speed changes. 18.12. SUMMARY The predictive method for freeways is applied by following the 18 steps of the predictive method presented in Section 18.4. It is used to estimate the expected average crash frequency for a series of contiguous sites, or a single individual site. If a freeway facility is being evaluated, then it is divided into a series of sites in Step 5 of the predictive method. Predictive models are applied in Steps 9, 10, and 11 of the method. Each predictive model consists of a safety performance function (SPF), crash modification factors (CMFs), a severity distribution function (SDF), and calibration factors. The SPF is selected in Step 9. It is used to estimate the predicted average crash frequency for a site with base conditions. CMFs are selected in Step 10. They are combined with the estimate from the SPF to produce the predicted average crash frequency. When observed crash data are available, the EB Method is applied in Step 13 or 15 of the predictive method to estimate the expected average crash frequency. The EB Method can be applied at the site- specific level in Step 13, or at the project level in Step 15. The choice of level will depend on (a) the

455 required reliability of the estimate and (b) the accuracy with which each observed crash can be associated with an individual site. The EB Method is described in Section B.2 of Appendix B to Part C. Optionally, SDFs are selected in Step13. They can be used to estimate the average crash frequency for one or more crash severity levels (i.e., fatal, incapacitating injury, non-incapacitating injury, or possible injury crash). Optionally, the crash type distribution can be used in Step 13 to estimate the average crash frequency for one or more crash types (e.g., head-on, fixed object). The SPF should be calibrated to the specific state or geographic region in which the project is located. Calibration accounts for differences in state or regional crash frequencies, relative to the states and regions represented in the data used to define the predictive models described in this chapter. The process for determining calibration factors for the predictive models is described in Section B.1 of Appendix B to Part C. Section 18.13 presents several sample problems that detail the application of the predictive method. A series of worksheets are used to guide the method application and document the calculations. The use of these worksheets is illustrated in the sample problems. Appendix 18A contains blank worksheets that can be copied to document future method applications. 18.13. SAMPLE PROBLEMS In this section, six sample problems are presented using the predictive method steps for freeway facilities. Sample Problems 1 and 2 illustrate how to calculate the predicted average crash frequency for freeway segments. Sample Problem 3 illustrates how to calculate the predicted average crash frequency for an entrance-ramp speed-change lane. Sample Problem 4 illustrates a similar calculation for an exit-ramp speed-change lane. Sample Problem 5 illustrates how to combine the results from Sample Problems 1 and 2 in a case where site-specific observed crash data are available (i.e., using the site-specific EB Method). Sample Problem 6 illustrates how to combine the results from Sample Problems 1 and 2 in a case where crash data are available but cannot be assigned to specific segments (i.e., using the project-level EB Method). Table 18-31. List of Sample Problems Problem No. Description 1 Predicted average crash frequency for a tangent six-lane urban freeway segment 2 Predicted average crash frequency for a six-lane urban freeway segment with a curve 3 Predicted average crash frequency for a urban freeway entrance-ramp speed-change lane 4 Predicted average crash frequency for a urban freeway exit-ramp speed-change lane 5 Expected average crash frequency for a facility when site-specific observed crash data are available 6 Expected average crash frequency for a facility when crash data are available, but cannot be assigned to specific segments 18.13.1. Sample Problem 1 The Site/Facility A tangent six-lane urban freeway segment.

456 The Question What is the predicted average crash frequency of the freeway segment for a one-year period? The Facts The study year is 2011. The conditions present during this year are provided in the following list.  0.75-mi length  120,000 veh/day  10 percent of AADT volume occurs during high-volume hours  No horizontal curvature  12-ft lane width  10-ft outside shoulder width (paved)  6-ft inside shoulder width (paved)  40-ft median width  No rumble strips on inside or outside shoulders  No median or roadside barrier  30-ft clear zone width  No Type B weaving sections  Data to describe four ramps in the vicinity of the segment

457 Variable Subscript (a,b) Distance from Segment, Xa,b (mi) Ramp Volume, AADTa,b (veh/day) b, ent 0.5 8,000 e, ext 0.85 7,150 e, ent 0.85 6,750 b, ext 0.5 7,675 Assumptions  Crash type distributions used are the default values presented in Table 18-6 and Table 18-8.  The calibration factor is 1.00. Results Using the predictive method steps as outlined below, the predicted average fatal-and-injury crash frequency for the roadway segment in Sample Problem 1 is determined to be 6.0 crashes per year, and the predicted average property-damage-only crash frequency is determined to be 14.7 crashes per year (rounded to one decimal place). Steps Step 1 through 8 To determine the predicted average crash frequency of the freeway segment in Sample Problem 1, only Steps 9 through 13 are conducted. No other steps are necessary because only one freeway segment is analyzed for one year, and the EB Method is not applied. Step 9 – For the selected site, determine and apply the appropriate SPF. For a six-lane urban freeway segment, SPF values for multiple-vehicle and single-vehicle crashes are determined.

458 Multiple-Vehicle Crashes The SPF for multiple-vehicle fatal-and-injury crashes is calculated from Equation 18-15 and Table 18-5 as follows: [ ]( ) [ ]( ) arcrashes/ye555.3 000,120001.0ln492.1587.5exp75.0 lnexp*,,6,, = ××+−×= ××+×= fsfimvfsspf AADTcbaLN Similarly, the SPF for multiple-vehicle property-damage-only crashes is calculated from Equation 18-15 and Table 18-5 to yield the following result: arcrashes/ye775.8,,6,, =pdomvfsspfN Single-Vehicle Crashes The SPF for single-vehicle fatal-and-injury crashes is calculated from Equation 18-18 and Table 18-7 as follows: [ ]( ) [ ]( ) arcrashes/ye117.2 000,120001.0ln646.0055.2exp75.0 lnexp*,,6,, = ××+−×= ××+×= fsfisvfsspf AADTcbaLN Similarly, the SPF for single-vehicle property-damage-only crashes is calculated from Equation 18-18 and Table 18-7 to yield the following result: arcrashes/ye115.5,,6,, =pdosvfsspfN Step 10 – Multiply the result obtained in Step 9 by the appropriate CMFs. Each CMF used in the calculation of the predicted average crash frequency of the freeway segment is calculated in this step. Horizontal Curve (CMF1, fs, 6, y, z ) The segment does not have horizontal curvature. Hence, CMF1, fs, 6, y, fi and CMF1, fs, 6, y, pdo are equal to 1.000. Lane Width (CMF2, fs, 6, y, z ) The segment has 12-ft lanes, which is the base condition for the lane width CMF. Hence, CMF2, fs, 6, y, fi and CMF2, fs, 6, y, pdo are equal to 1.000. Inside Shoulder Width (CMF3, fs, 6, y, z ) The segment has 6-ft inside shoulders, which is the base condition for the inside shoulder width CMF. Hence, CMF3, fs, 6, y, fi and CMF3, fs, 6, y, pdo are equal to 1.000. Median Width (CMF4, fs, 6, y, z ) CMF4, fs, 6, y, fi is calculated from Equation 18-27 as follows: ( ) [ ]( ) [ ]( )482exp482exp0.1,,6,,4 −×××+−×−××−= icbibismibfiyfs WaPWWaPCMF

459 The segment does not have inside barrier, so Pib = 0.0 and the calculation of Wicb does not apply. From Table 18-17, a = -0.00302 for multiple-vehicle fatal-and-injury crashes. CMF4, fs, 6, mv, fi is calculated as follows: ( ) [ ]( ) [ ]( ) 062.1 48200302.0exp0.048624000302.0exp0.00.1,,6,,4 = −××−×+−×−×−×−= icbfimvfs WCMF Calculations using the other coefficients from Table 18-17 yield the following results: 980.0,,6,,4 =fisvfsCMF 060.1,,6,,4 =pdomvfsCMF 060.1,,6,,4 =pdosvfsCMF Median Barrier (CMF5, fs, 6, y, z ) The segment does not have inside barrier. Hence, CMF5, fs, 6, y, fi and CMF5, fs, 6, y, pdo are equal to 1.000. High Volume (CMF6, fs, 6, y, z ) CMF6, fs, 6, mv, fi is calculated from Equation 18-29 and the coefficient a = 0.350 from Table 18-19 as follows: ( ) ( ) 036.1 1.0350.0exp exp,,6,,6 = ×= ×= hvfimvfs PaCMF Calculations using the other coefficients from Table 18-19 yield the following results: 993.0,,6,,6 =fisvfsCMF 029.1,,6,,6 =pdomvfsCMF 941.0,,6,,6 =pdosvfsCMF Lane Change (CMF7, fs, 6, mv, z ) The segment does not have a ramp entrance or a ramp exit within 0.5 mi, which is the base condition for the lane change CMF. Hence, CMF7, fs, 6, mv, fi and CMF7, fs, 6, mv, pdo are equal to 1.000. Outside Shoulder Width (CMF8, fs, 6, sv, z ) The segment has 10-ft outside shoulders, which is the base condition for the outside shoulder width CMF. Hence, CMF8, fs, 6, sv, fi and CMF8, fs, 6, sv, pdo are equal to 1.000. Shoulder Rumble Strip (CMF9, fs, 6, sv, z )

460 The segment does not have shoulder rumble strips. Hence, CMF9, fs, 6, sv, fi and CMF9, fs, 6, sv, pdo are equal to 1.000. Outside Clearance (CMF10, fs, 6, sv, z ) The segment has 30-ft clear zones and no outside barrier, which are the base conditions for the outside clearance CMF. Hence, CMF10, fs, 6, sv, fi and CMF10, fs, 6, sv, pdo are equal to 1.000. Outside Barrier (CMF11, fs, 6, sv, z ) The segment does not have outside barrier. Hence, CMF11, fs, 6, sv, fi and CMF11, fs, 6, sv, pdo are equal to 1.000. Multiple-Vehicle Crashes The CMFs are applied to the multiple-vehicle fatal-and-injury SPF as follows: ( ) ( ) arcrashes/ye911.3 100.1555.3 000.1036.1000.1062.1000.1000.1000.1555.3 ,,6,,7,,6,,1,,6,,,,6,*, = ×= ×××××××= ×××= fimvfsfimvfsfimvfsspffimvfsp CMFCMFNN  The CMFs are applied to the multiple-vehicle property-damage-only SPF as follows: ( ) ( ) arcrashes/ye569.9 091.1775.8 000.1029.1000.1060.1000.1000.1000.1775.8 ,,6,,7,,6,,1,,6,,,,6,*, = ×= ×××××××= ×××= pdomvfspdomvfspdomvfsspfpdomvfsp CMFCMFNN  Single-Vehicle Crashes The CMFs are applied to the single-vehicle fatal-and-injury SPF as follows: ( ) ( ) arcrashes/ye060.2 973.0117.2 000.1000.1000.1000.1993.0000.1980.0000.1000.1000.1117.2 ,,6,,11,,6,,8,,6,,6,,6,,1,,6,,,,6,*, = ×= ××××××××××= ××××××= fisvfsfisvfsfisvfsfisvfsfisvfsspffisvfsp CMFCMFCMFCMFNN  The CMFs are applied to the single-vehicle property-damage-only SPF as follows: ( ) ( ) arcrashes/ye099.5 997.0115.5 000.1000.1000.1000.1941.0000.1060.1000.1000.1000.1115.5 ,,6,,11,,6,,8,,6,,6,,6,,1,,6,,,,6,*, = ×= ××××××××××= ××××××= pdosvfspdosvfspdosvfspdosvfspdosvfsspfpdosvfsp CMFCMFCMFCMFNN  Step 11 – Multiply the result obtained in Step 10 by the appropriate calibration factor. It is assumed that a calibration factor of 1.00 has been determined for local conditions. As a result, Np, fs, 6, y, z = Np*, fs, 6, y, z for both crash types y (y = mv: multiple-vehicle, sv: single-vehicle) and both crash severities z (z = fi: fatal-and-injury, pdo: property-damage-only). See Section B.1 of Appendix B to Part C for further discussion on calibration of the predicted models.

461 Calculation of Predicted Average Crash Frequency The predicted average crash frequency is calculated using Equation 18-2 based on the results obtained in Steps 9 through 11 as follows. Fatal-and-injury crashes: arcrashes/ye971.5 060.2911.3 ,,6,,,,6,,,,6,, = += += fisvfspfimvfspfiatfsp NNN Property-damage-only crashes: arcrashes/ye668.14 099.5569.9 ,,6,,,,6,,,,6,, = += += pdosvfsppdomvfsppdoatfsp NNN Step 12—If there is another year to be evaluated in the evaluation period for the selected site, return to Step 8. Otherwise, proceed to Step 13. The study period is one year (2011), so steps 8 through 11 need not be repeated. Step 13—Apply site-specific EB Method (if applicable) and apply SDFs. This step consists of three optional sets of calculations—site-specific EB Method, severity distribution functions, and crash type distribution. Apply the site-specific EB Method to a future time period, if appropriate. The site-specific EB Method is not applied in this sample problem because crash data are not available. Apply the severity distribution functions (SDFs), if desired. To apply the SDFs, the systematic component of crash severity likelihood Vj is computed for each severity level j using Equation 18-63 as follows: ( ) ( ) ( ) ( )rurallicorirhvobibj IgWfPePPdPcPPbaV ×+×+×+      +×+×+      +×+=  ,22 The coefficients a, b, c, d, e, f, and g are obtained from Table 18-30 for each severity level j. The segment does not have barrier, rumble strips, or horizontal curvature, so Pib, Pob, Pir, Por, and Pc, i are equal to 0.0. Vj is computed for fatal crashes as follows: ( ) ( ) ( ) ( ) 392.3 0.0492.012261.00.0208.0 2 0.00.0387.01.0924.0 2 0.00.0388.0171.0 −= ×+×−+×+       +×+×−+      +×−+−=KV Calculations using the coefficients for incapacitating injury crashes and non-incapacitating injury crashes from Table 18-30 yield the following results: 478.2−=AV

462 571.0−=BV Using these computed VK, VA, and VB values, and assuming a calibration factor Csdf, fs+sc of 1.0, the probability of occurrence of a fatal crash is computed using Equation 18-59 as follows: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 020.0 571.0exp478.2exp392.3exp 0.1 0.1 392.3exp expexpexp0.1 exp , ,,, = −+−+−+ −= +++ = + + BAK scfssdf K Katacscfs VVV C VP Similar calculations using Equation 18-60 and Equation 18-61 yield the following results: 050.0,,, =+ AatacscfsP 336.0,,, =+ BatacscfsP The probability of occurrence of a possible-injury crash is computed using Equation 18-62 as follows: 594.0 )336.0050.0020.0(0.1 )(0.1 ,,,,,,,,,,,, = ++−= ++−= ++++ BatacscfsAatacscfsKatacscfsCatacscfs PPPP The probability of occurrence of a fatal crash is multiplied by the fatal-and-injury crash frequency obtained in Step 11 using Equation 18-58 as follows: arcrashes/ye119.0 020.0971.5 ,,,,,6,,,,6,, = ×= ×= + KatacscfsfiatfseKatfse PNN Similar calculations using Equation 18-58 and the probabilities of occurrences of the other crash severities yield the following results: arcrashes/ye298.0,,6,, =AatfseN arcrashes/ye005.2,,6,, =BatfseN arcrashes/ye549.3,,6,, =CatfseN Note that the sum of the estimates by severity equals the total fatal-and-injury crash frequency (i.e., 5.971 = 0.119 + 0.298 + 2.005 + 3.549). Apply the crash type distribution, if desired. The crash type distributions are applied by multiplying the default crash type distribution proportions in Table 18-6 and Table 18-8 by the predicted average crash frequencies obtained in Step 11.

463 Worksheets The step-by-step instructions are provided to illustrate the predictive method for calculating the predicted average crash frequency for a freeway segment. To apply the predictive method steps to multiple segments, a series of worksheets are provided for determining the predicted average crash frequency. The worksheets include:  Table 18-32. Freeway Segment Worksheet (1 of 4)—Sample Problem 1  Table 18-33. Freeway Segment Worksheet (2 of 4)—Sample Problem 1  Table 18-34. Freeway Segment Worksheet (3 of 4)—Sample Problem 1  Table 18-35. Freeway Segment Worksheet (4 of 4)—Sample Problem 1 Filled versions of these worksheets are provided below. Blank versions of worksheets used in the Sample Problems are provided in Appendix 18A. Table 18-32 is a summary of general information about the freeway segment, analysis, input data (i.e., “The Facts”), and assumptions for Sample Problem 1. The input data include area type, crash data, basic roadway data, alignment data, and cross section data. Table 18-33 is a summary of general information about the freeway segment, analysis, input data (i.e., “The Facts”), and assumptions for Sample Problem 1. The input data include roadside data, ramp access data, and traffic data. Table 18-34 is a tabulation of the CMF and SPF computations for Sample Problem 1. Table 18-35 is a tabulation of the crash severity and crash type distributions for Sample Problem 1.

464 Table 18-32. Freeway Segment Worksheet (1 of 4)—Sample Problem 1 General Information Location Information Analyst Roadway Agency or company Roadway section Date performed Study year Area type X Urban Rural Input Data Crash Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Crash data time period First year -- Last year -- Count of multiple-vehicle FI crashes N*o, fs, n, mv, fi -- Count of single-vehicle FI crashes N*o, fs, n, sv, fi -- Count of multiple-vehicle PDO crashes N*o, fs, n, mv, pdo -- Count of single-vehicle PDO crashes N*o, fs, n, sv, pdo -- Basic Roadway Data Number of through lanes n 6 Same value for crash period and study year. Segment length L (mi) -- 0.75 Alignment Data Horizontal Curve Data 1 Presence of horizontal curve 1 -- Y/N N Y/N If Yes, then enter data in the next three rows. Equivalent curve radius R1* (ft) -- -- Length of curve Lc1 (mi) -- -- Length of curve in segment Lc1, seg (mi) -- -- 2 Presence of horizontal curve 2 -- Y/N N Y/N If Yes, then enter data in the next three rows. Equivalent curve radius R2* (ft) -- -- Length of curve Lc2 (mi) -- -- Length of curve in segment Lc2, seg (mi) -- -- Cross Section Data Lane width Wl (ft) -- 12 Outside shoulder width Ws (ft) -- 10 Inside shoulder width Wis (ft) -- 6 Median width Wm (ft) -- 40 Presence of rumble strips on outside shoulder -- Y/N N Y/N If Yes, then enter data in the next two rows. Length of rumble strip in increasing milepost dir. (mi) -- -- Length of rumble strip in decreasing milepost dir. (mi) -- -- Presence of rumble strips on inside shoulder -- Y/N N Y/N If Yes, then enter data in the next two rows. Length of rumble strip in increasing milepost dir. (mi) -- -- Length of rumble strip in decreasing milepost dir. (mi) -- -- Presence of barrier in median -- Y/N N Y/N If Yes, then use the freeway barrier worksheet.

465 Table 18-33. Freeway Segment Worksheet (2 of 4)—Sample Problem 1 Input Data Roadside Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Clear zone width Whc (ft) -- 30 Presence of barrier on roadside -- Y/N N Y/N If Yes, then use the freeway barrier worksheet. Ramp Access Data Travel in Increasing Milepost Direction Ent. ramp Distance from begin milepost to upstream entrance ramp gore Xb, ent (mi) -- 0.5 If ramp entrance is in the segment, enter 0.0. Presence of speed-change lane in segment -- Y/N N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Len,seg, inc (mi) -- -- Exit ramp Distance from end milepost to upstream exit ramp gore Xe, ext (mi) -- 0.85 If ramp exit is in the segment, enter 0.0. Presence of speed-change lane in segment -- Y/N N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Lex,seg, inc (mi) -- -- Weave Presence of a Type B weave in segment -- Y/N N Y/N If Yes, then enter data in the next two rows. Length of weaving section Lwev, inc (mi) -- -- Length of weaving section in seg. Lwev, seg, inc (mi) -- -- Travel in Decreasing Milepost Direction Ent. ramp Distance from end milepost to upstream entrance ramp gore Xe, ent (mi) -- 0.85 If ramp entrance is in the segment, enter 0.0. Presence of speed-change lane in segment -- Y/N N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Len,seg, dec (mi) -- -- Exit ramp Distance from begin milepost to downstream exit ramp gore Xb, ext (mi) -- 0.5 If ramp exit is in the segment, enter 0.0. Presence of speed-change lane in segment -- Y/N N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Lex,seg, dec (mi) -- -- Weave Presence of a Type B weave in segment -- Y/N N Y/N If Yes, then enter data in the next two rows. Length of weaving section Lwev, dec (mi) -- -- Length of weaving section in seg. Lwev, seg, dec (mi) -- -- Traffic Data Proportion of AADT during high-volume hours Phv -- 0.1 Freeway segment AADT AADTfs (veh/day) -- 120,000 AADT of entrance ramp for travel in increasing milepost direction AADTb,ent (veh/day) -- 8,000 AADT of exit ramp for travel in increasing milepost direction AADTe,ext (veh/day) -- 7,150 AADT of entrance ramp for travel in decreasing milepost direction AADTe,ent (veh/day) -- 6,750 AADT of exit ramp for travel in decreasing milepost direction AADTb,ext (veh/day) -- 7,675

466 Table 18-34. Freeway Segment Worksheet (3 of 4)—Sample Problem 1 Crash Modification Factors Fatal and Injury Property Damage Only Complete the study year column. Complete the crash period column if the EB Method is used. Multiple Vehicle Single Vehicle Multiple Vehicle Single Vehicle Equation Crash Period Study Year Crash Period Study Year Crash Period Study Year Crash Period Study Year Horizontal curve CMF1, fs, ac, y, z 18-24 -- 1.000 -- 1.000 -- 1.000 -- 1.000 Lane width CMF2, fs, ac, y, fi 18-25 -- 1.000 -- 1.000 Inside shoulder width CMF3, fs, ac, y, z 18-26 -- 1.000 -- 1.000 -- 1.000 -- 1.000 Median width CMF4, fs, ac, y, z 18-27 -- 1.062 -- 0.980 -- 1.060 -- 1.060 Median barrier CMF5, fs, ac, y, z 18-28 -- 1.000 -- 1.000 -- 1.000 -- 1.000 High volume CMF6, fs, ac, y, z 18-29 -- 1.036 -- 0.993 -- 1.029 -- 0.941 Lane change CMF7, fs, ac, mv, z 18-30 -- 1.000 -- 1.000 Outside shoulder width CMF8, fs, ac, sv, z 18-35 -- 1.000 -- 1.000 Shoulder rumble strip CMF9, fs, ac, sv, fi 18-36 -- 1.000 Outside clearance CMF10, fs, ac, sv, fi 18-38 -- 1.000 Outside barrier CMF11, fs, ac, sv, z 18-39 -- 1.000 -- 1.000 Combined CMF (multiply all CMFs evaluated) -- 1.100 -- 0.973 -- 1.091 -- 0.997 Expected Average Crash Frequency a Fatal and Injury Property Damage Only Complete the study year column. Complete the crash period column if the site-specific EB Method is used. Multiple Vehicle Single Vehicle Multiple Vehicle Single Vehicle Crash Period Study Year Crash Period Study Year Crash Period Study Year Crash Period Study Year Calibration factor Cfs, ac, y, z 1.00 1.00 1.00 1.00 Overdispersion parameter kfs, n, y, z -- -- -- -- Observed crash count N*o, fs, n, y, z (cr) -- -- -- -- Reference year r -- -- -- -- Predicted average crash freq. for reference year Np, fs, n, y, z, r (cr/yr) -- -- -- -- Predicted number of crashes for crash period (sum all years) N*p, fs, n, y, z (cr) -- -- -- -- Equivalent years associated with crash count Cb, fs, n, y, z, r (yr) -- -- -- -- Adjusted average crash freq. for ref. year given N*o, Na, fs, n, y, z, r (cr/yr) -- -- -- -- Study year s 2011 2011 2011 2011 Predicted average crash freq. for study year Np, fs, n, y, z, s (cr/yr) 3.911 2.060 9.568 5.099 Expected average crash freq. for study year Ne, fs, n, y, z, s (cr/yr) 3.911 2.060 9.568 5.099 Expected average crash freq. for study year (all crash types) Ne, fs, n, at, z, s (cr/yr) 5.971 14.668 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”.

467 Table 18-35. Freeway Segment Worksheet (4 of 4)—Sample Problem 1 Expected Average Crash Frequency a Crash Severity Distribution K A B C Total FI PDO Total FI + PDO Proportion by injury level 0.020 0.050 0.336 0.594 1.000 Expected average crash freq. for study year (all crash types) Ne, fs, n, at, z, s (cr/yr) 0.119 0.298 2.005 3.548 5.971 14.668 20.638 Crash Type Distribution Fatal and Injury Property Damage Only Total Crash Type Category Proportion Expected Average Crash Frequency for Study Year Ne, fs, n, y, fi, s (cr/yr) Proportion Expected Average Crash Frequency for Study Year Ne, fs, n, y, pdo, s (cr/yr) Expected Average Crash Frequency for Study Year Ne, fs, n, y, as, s (cr/yr) Table Multiple-Vehicle Crashes 18-6 Head-on 0.008 0.031 0.002 0.019 0.050 Right-angle 0.031 0.121 0.018 0.172 0.293 Rear-end 0.750 2.933 0.690 6.602 9.535 Sideswipe 0.180 0.704 0.266 2.545 3.249 Other multiple-vehicle crashes 0.031 0.121 0.024 0.230 0.351 Total 1.000 3.911 1.000 9.568 13.479 Single-Vehicle Crashes 18-8 Crash with animal 0.004 0.008 0.022 0.112 0.120 Crash with fixed object 0.722 1.487 0.716 3.651 5.138 Crash with other object 0.051 0.105 0.139 0.709 0.814 Crash with parked vehicle 0.015 0.031 0.016 0.082 0.112 Other single-vehicle crashes 0.208 0.428 0.107 0.546 0.974 Total 1.000 2.060 1.000 5.099 7.159 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”. 18.13.2. Sample Problem 2 The Site/Facility A six-lane urban freeway segment with a horizontal curve. The Question What is the predicted average crash frequency of the freeway segment for a one-year period? The Facts The study year is 2011. The conditions present during this year are provided in the following list.  0.75-mi length

468  120,000 veh/day  10 percent of AADT volume occurs during high-volume hours  One horizontal curve  2,100-ft equivalent radius  0.25-mi length, entirely in the segment  Curve exists on both roadbeds  12-ft lane width  7-ft outside shoulder width (paved)  6-ft inside shoulder width (paved)  40-ft median width  0.25 mi of rumble strips on outside shoulders in both travel directions  0.25 mi of rumble strips on inside shoulders in both travel directions  No median or roadside barrier  30-ft clear zone width  No Type B weaving sections  Data to describe four ramps in the vicinity of the segment

469 Variable Subscript (a,b) Distance from Segment, Xa,b (mi) Ramp Volume, AADTa,b (veh/day) b, ent 1.25 8,000 e, ext 0.1 7,150 e, ent 0.1 6,750 b, ext 1.25 7,675 Assumptions  Crash type distributions used are the default values presented in Table 18-6 and Table 18-8.  The calibration factor is 1.00. Results Using the predictive method steps as outlined below, the predicted average fatal-and-injury crash frequency for the freeway segment in Sample Problem 2 is determined to be 7.8 crashes per year, and the predicted average property-damage-only crash frequency is determined to be 17.0 crashes per year (rounded to one decimal place). Steps Step 1 through 8 To determine the predicted average crash frequency of the freeway segment in Sample Problem 2, only Steps 9 through 13 are conducted. No other steps are necessary because only one freeway segment is analyzed for one year, and the EB Method is not applied. Step 9 – For the selected site, determine and apply the appropriate SPF. For a six-lane urban freeway segment, SPF values for multiple-vehicle and single-vehicle crashes are determined.

470 Multiple-Vehicle Crashes The SPF for multiple-vehicle fatal-and-injury crashes is calculated from Equation 18-15 and Table 18-5 as follows: [ ]( ) [ ]( ) arcrashes/ye555.3 000,120001.0ln492.1587.5exp75.0 lnexp*,,6,, = ××+−×= ××+×= fsfimvfsspf AADTcbaLN Similarly, the SPF for multiple-vehicle property-damage-only crashes is calculated from Equation 18-15 and Table 18-5 to yield the following result: arcrashes/ye775.8,,6,, =pdomvfsspfN Single-Vehicle Crashes The SPF for single-vehicle fatal-and-injury crashes is calculated from Equation 18-18 and Table 18-7 as follows: [ ]( ) [ ]( ) arcrashes/ye117.2 000,120001.0ln646.0055.2exp75.0 lnexp*,,6,, = ××+−×= ××+×= fsfisvfsspf AADTcbaLN Similarly, the SPF for single-vehicle property-damage-only crashes is calculated from Equation 18-18 and Table 18-7 to yield the following result: arcrashes/ye115.5,,6,, =pdosvfsspfN Step 10 – Multiply the result obtained in Step 9 by the appropriate CMFs. Each CMF used in the calculation of the predicted average crash frequency of the freeway segment is calculated in this step. Horizontal Curve (CMF1, fs, 6, y, z ) CMF1, fs, 6, y, fi is calculated from Equation 18-24 as follows:         ××      ×+=  = m i icic i fiyfs fPR aCMF 1 ,, 2 *,,6,,1 730,50.1 The segment is 0.75 mi long, the curve is 0.25 mi long, and its entire length is in the segment. Hence, Pc, i = 0.33. The curve exists on both roadbeds, so fc, i = 1.0. From Table 18-14, a = 0.0172 for multiple- vehicle fatal-and-injury crashes. CMF1, fs, 6, mv, fi is calculated as follows: 043.1 0.133.0 100,2 730,50172.00.1 1 2 ,,6,,1 =         ××     ×+=  = m i fimvfsCMF Calculations using the other coefficients from Table 18-14 yield the following results:

471 178.1,,6,,1 =fisvfsCMF 084.1,,6,,1 =pdomvfsCMF 155.1,,6,,1 =pdosvfsCMF Lane Width (CMF2, fs, 6, y, z ) The segment has 12-ft lanes, which is the base condition for the lane width CMF. Hence, CMF2, fs, 6, y, fi and CMF2, fs, 6, y, pdo are equal to 1.000. Inside Shoulder Width (CMF3, fs, 6, y, z ) The segment has 6-ft inside shoulders, which is the base condition for the inside shoulder width CMF. Hence, CMF3, fs, 6, y, fi and CMF3, fs, 6, y, pdo are equal to 1.000. Median Width (CMF4, fs, 6, y, z ) CMF4, fs, 6, y, fi is calculated from Equation 18-27 as follows: ( ) [ ]( ) [ ]( )482exp482exp0.1,,6,,4 −×××+−×−××−= icbibismibzyfs WaPWWaPCMF The segment does not have inside barrier, so Pib = 0.0 and the calculation of Wicb does not apply. From Table 18-17, a = -0.00302 for multiple-vehicle fatal-and-injury crashes. CMF4, fs, 6, mv, fi is calculated as follows: ( ) [ ]( ) [ ]( ) 062.1 48200302.0exp0.048624000302.0exp0.00.1,,6,,4 = −××−×+−×−×−×−= icbfimvfs WCMF Calculations using the other coefficients from Table 18-17 yield the following results: 980.0,,6,,4 =fisvfsCMF 060.1,,6,,4 =pdomvfsCMF 060.1,,6,,4 =pdosvfsCMF Median Barrier (CMF5, fs, 6, y, z ) The segment does not have inside barrier. Hence, CMF5, fs, 6, y, fi and CMF5, fs, 6, y, pdo are equal to 1.000. High Volume (CMF6, fs, 6, y, z ) CMF6, fs, 6, mv, fi is calculated from Equation 18-29 and the coefficient a = 0.350 from Table 18-19 as follows: ( ) ( ) 036.1 1.0350.0exp exp,,6,,6 = ×= ×= hvfimvfs PaCMF Calculations using the other coefficients from Table 18-19 yield the following results:

472 993.0,,6,,6 =fisvfsCMF 029.1,,6,,6 =pdomvfsCMF 941.0,,6,,6 =pdosvfsCMF Lane Change (CMF7, fs, 6, mv, z ) CMF7, fs, 6, mv, fi is calculated from Equation 18-30 as follows: ( ) ( )lcdecwevdeclcincwevincfimvfs ffffCMF ,,,,,,6,,7 5.05.0 ××+××= The segment does not have Type B weaving sections, so the weaving section adjustment factors finc, wev and fdec, wev are equal to 1.00. The lane change adjustment factors finc, lc and fdec, lc are calculated from Equation 18-33 and Equation 18-34 as follows: [ ]( ) ( )[ ] [ ]( ) ( )[ ]       ×−−× × ××+×− +×         ×−−× × ××+×− += fs fs exteexte fs fs entbentb lcinc Lb Lb AADTcdXb Lb Lb AADTcdXb f exp0.1 lnexp 0.1 exp0.1 lnexp 0.1 ,, ,, , [ ]( ) ( )[ ] [ ]( ) ( )[ ]       ×−−× × ××+×− +×         ×−−× × ××+×− += fs fs extbextb fs fs enteente lcdec Lb Lb AADTcdXb Lb Lb AADTcdXb f exp0.1 lnexp 0.1 exp0.1 lnexp 0.1 ,, ,, , From Table 18-20, the coefficients b, c, and d for fatal-and-injury crashes are 12.56, 0.001, and -0.272, respectively. The lane change adjustment factors are calculated as follows: [ ]( ) ( )[ ] [ ]( ) ( )[ ] 018.1 75.056.12exp0.1 75.056.12 150,7001.0ln272.01.056.12exp0.1 75.056.12exp0.1 75.056.12 000,8001.0ln272.025.156.12exp0.1, =       ×−−× × ××−×− +×       ×−−× × ××−×− +=lcincf [ ]( ) ( )[ ] [ ]( ) ( )[ ] 018.1 75.056.12exp0.1 75.056.12 675,7001.0ln272.025.156.12exp0.1 75.056.12exp0.1 75.056.12 750,6001.0ln272.01.056.12exp0.1, =       ×−−× × ××−×− +×       ×−−× × ××−×− +=lcdecf CMF7, fs, 6, mv, fi is calculated using the weaving section and lane change adjustment factors as follows:

473 ( ) ( ) 018.1 018.100.15.0018.100.15.0,,6,,7 = ××+××=fimvfsCMF Similar calculations using the property-damage-only coefficients from Table 18-20 yield the following results: 015.1,,6,,7 =pdomvfsCMF Outside Shoulder Width (CMF8, fs, 6, sv, z ) CMF8, fs, 6, sv, fi is calculated from Equation 18-35 as follows: ( ) ( ) ( ) ( )]10[exp]10[exp0.1 ,,,,,,8 −××+−××−=  sicsiczsvacfs WbPWaPCMF The segment is 0.75 mi long, the curve is 0.25 mi long, and its entire length is in the segment. Hence, Pc,i = 0.33. From Table 18-21, a = -0.0647 and b = -0.0897. CMF8, fs, 6, sv, fi is calculated as follows: ( ) ( ) ( ) ( ) 246.1 ]107[0897.0exp33.0]107[0647.0exp33.00.1,,6,,8 = −×−×+−×−×−=fisvfsCMF Similar calculations using the property-damage-only coefficients from Table 18-21 yield the following results: 096.1,,6,,8 =pdosvfsCMF Shoulder Rumble Strip (CMF9, fs, 6, sv, z ) CMF9, fs, 6, sv, fi is calculated from Equation 18-36 as follows: ( ) ( ) 0.10.1 ,,,,6,,9 ×+×−=  ictanicfisvfs PfPCMF The factor ftan is calculated from Equation 18-37 as follows: ( ) ( ) ( ) ( ) 906.0 811.033.00.1]33.00.1[5.0811.033.00.1]33.00.1[5.0 811.00.1]0.1[5.0811.00.1]0.1[5.0 = ×+×−×+×+×−×= ×+×−×+×+×−×= ororirirtan PPPPf CMF9, fs, 6, sv, fi is calculated as follows: ( ) ( ) 958.0 0.133.0906.033.00.1,,6,,9 = ×+×−=fisvfsCMF Outside Clearance (CMF10, fs, 6, sv, z ) The segment has 30-ft clear zones and no outside barrier, which are the base conditions for the outside clearance CMF. Hence, CMF10, fs, 6, sv, fi and CMF10, fs, 6, sv, pdo are equal to 1.000. Outside Barrier (CMF11, fs, 6, sv, z ) The segment does not have outside barrier. Hence, CMF11, fs, 6, sv, fi and CMF11, fs, 6, sv, pdo are equal to 1.000.

474 Multiple-Vehicle Crashes The CMFs are applied to the multiple-vehicle fatal-and-injury SPF as follows: ( ) ( ) arcrashes/ye150.4 168.1555.3 018.1036.1000.1062.1000.1000.1043.1555.3 ,,6,,7,,6,,1,,6,,,,6,*, = ×= ×××××××= ×××= fimvfsfimvfsfimvfsspffimvfsp CMFCMFNN  The CMFs are applied to the multiple-vehicle property-damage-only SPF as follows: ( ) ( ) arcrashes/ye530.10 200.1775.8 015.1029.1000.1060.1000.1000.1084.1775.8 ,,6,,7,,6,,1,,6,,,,6,*, = ×= ×××××××= ×××= pdomvfspdomvfspdomvfsspfpdomvfsp CMFCMFNN  Single-Vehicle Crashes The CMFs are applied to the single-vehicle fatal-and-injury SPF as follows: ( ) ( ) arcrashes/ye858.2 351.1117.2 000.1987.0958.0246.1993.0000.1980.0000.1000.1178.1117.2 ,,6,,11,,6,,8,,6,,6,,6,,1,,6,,,,6,*, = ×= ××××××××××= ××××××= fisvfsfisvfsfisvfsfisvfsfisvfsspffisvfsp CMFCMFCMFCMFNN  The CMFs are applied to the single-vehicle property-damage-only SPF as follows: ( ) ( ) arcrashes/ye454.6 263.1115.5 000.1000.1000.1096.1941.0000.1060.1000.1000.1155.1115.5 ,,6,,11,,6,,8,,6,,6,,6,,1,,6,,,,6,*, = ×= ××××××××××= ××××××= pdosvfspdosvfspdosvfspdosvfspdosvfsspfpdosvfsp CMFCMFCMFCMFNN  Step 11 – Multiply the result obtained in Step 10 by the appropriate calibration factor. It is assumed that a calibration factor of 1.00 has been determined for local conditions. As a result, Np, fs, 6, y, z = Np*, fs, 6, y, z for both crash types y (y = mv: multiple-vehicle, sv: single-vehicle) and both crash severities z (z = fi: fatal-and-injury, pdo: property-damage-only). See Section B.1 of Appendix B to Part C for further discussion on calibration of the predicted models. Calculation of Predicted Average Crash Frequency The predicted average crash frequency is calculated using Equation 18-2 based on the results obtained in Steps 9 through 11 as follows. Fatal-and-injury crashes:

475 arcrashes/ye008.7 858.2150.4 ,,6,,,,6,,,,6,, = += += fisvfspfimvfspfiatfsp NNN Property-damage-only crashes: arcrashes/ye984.16 454.6530.10 ,,6,,,,6,,,,6,, = += += pdosvfsppdomvfsppdoatfsp NNN Step 12—If there is another year to be evaluated in the evaluation period for the selected site, return to Step 8. Otherwise, proceed to Step 13. The study period is one year (2011), so steps 8 through 11 need not be repeated. Step 13—Apply site-specific EB Method (if applicable) and apply SDFs. This step consists of three optional sets of calculations—site-specific EB Method, severity distribution functions, and crash type distribution. Apply the site-specific EB Method to a future time period, if appropriate. The site-specific EB Method is not applied in this sample problem because crash data are not available. Apply the severity distribution functions (SDFs), if desired. To apply the SDFs, the systematic component of crash severity likelihood Vj is computed for each severity level j using Equation 18-63 as follows: ( ) ( ) ( ) ( )rurallicorirhvobibj IgWfPePPdPcPPbaV ×+×+×+      +×+×+      +×+=  ,22 The coefficients a, b, c, d, e, f, and g are obtained from Table 18-30 for each severity level j. The segment does not have barrier, so Pib and Pob are equal to 0.0. Vj is computed for fatal crashes as follows: ( ) ( ) ( ) ( ) 194.3 0.0492.012261.033.0208.0 2 33.033.0387.01.0924.0 2 0.00.0388.0171.0 −= ×+×−+×+       +×+×−+      +×−+−=KV Calculations using the coefficients for incapacitating injury crashes and non-incapacitating injury crashes from Table 18-30 yield the following results: 267.2−=AV 482.0−=BV Using these computed VK, VA, and VB values, and assuming a calibration factor Csdf, fs+sc of 1.0, the probability of occurrence of a fatal crash is computed using Equation 18-59 as follows:

476 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 023.0 482.0exp267.2exp194.3exp 0.1 0.1 194.3exp expexpexp0.1 exp , ,,, = −+−+−+ −= +++ = + + BAK scfssdf K Katacscfs VVV C VP Similar calculations using Equation 18-60 and Equation 18-61 yield the following results: 059.0,,, =+ AatacscfsP 350.0,,, =+ BatacscfsP The probability of occurrence of a possible-injury crash is computed using Equation 18-62 as follows: 567.0 )336.0050.0020.0(0.1 )(0.1 ,,,,,,,,,,,, = ++−= ++−= ++++ BatacscfsAatacscfsKatacscfsCatacscfs PPPP The probability of occurrence of a fatal crash is multiplied by the fatal-and-injury crash frequency obtained in Step 11 using Equation 18-58 as follows: arcrashes/ye163.0 023.0008.7 ,,,,,6,,,,6,, = ×= ×= + KatacscfsfiatfseKatfse PNN Similar calculations using Equation 18-58 and the probabilities of occurrences of the other crash severities yield the following results: arcrashes/ye412.0,,6,, =AatfseN arcrashes/ye456.2,,6,, =BatfseN arcrashes/ye977.3,,6,, =CatfseN Apply the crash type distribution, if desired. The crash type distributions are applied by multiplying the default crash type distribution proportions in Table 18-6 and Table 18-8 by the predicted average crash frequencies obtained in Step 11. Worksheets The step-by-step instructions are provided to illustrate the predictive method for calculating the predicted average crash frequency for a freeway segment. To apply the predictive method steps to multiple segments, a series of worksheets are provided for determining the predicted average crash frequency. The worksheets include:

477  Table 18-36. Freeway Segment Worksheet (1 of 4)—Sample Problem 2  Table 18-37. Freeway Segment Worksheet (2 of 4)—Sample Problem 2  Table 18-38. Freeway Segment Worksheet (3 of 4)—Sample Problem 2  Table 18-39. Freeway Segment Worksheet (4 of 4)—Sample Problem 2 Filled versions of these worksheets are provided below. Blank versions of worksheets used in the Sample Problems are provided in Appendix 18A. Table 18--36 is a summary of general information about the freeway segment, analysis, input data (i.e., “The Facts”), and assumptions for Sample Problem 2. The input data include area type, crash data, basic roadway data, alignment data, and cross section data. Table 18-37 is a summary of general information about the freeway segment, analysis, input data (i.e., “The Facts”), and assumptions for Sample Problem 2. The input data include roadside data, ramp access data, and traffic data. Table 18-38 is a tabulation of the CMF and SPF computations for Sample Problem 2. Table 18-39 is a tabulation of the crash severity and crash type distributions for Sample Problem 2.

478 Table 18-36. Freeway Segment Worksheet (1 of 4)—Sample Problem 2 General Information Location Information Analyst Roadway Agency or company Roadway section Date performed Study year Area type X Urban Rural Input Data Crash Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Crash data time period First year -- Last year -- Count of multiple-vehicle FI crashes N*o, fs, n, mv, fi -- Count of single-vehicle FI crashes N*o, fs, n, sv, fi -- Count of multiple-vehicle PDO crashes N*o, fs, n, mv, pdo -- Count of single-vehicle PDO crashes N*o, fs, n, sv, pdo -- Basic Roadway Data Number of through lanes n 6 Same value for crash period and study year. Segment length L (mi) -- 0.75 Alignment Data Horizontal Curve Data 1 Presence of horizontal curve 1 -- Y/N Y Y/N If Yes, then enter data in the next three rows. Equivalent curve radius R1* (ft) -- 2,100 Length of curve Lc1 (mi) -- 0.25 Length of curve in segment Lc1, seg (mi) -- 0.25 2 Presence of horizontal curve 2 -- Y/N N Y/N If Yes, then enter data in the next three rows. Equivalent curve radius R2* (ft) -- -- Length of curve Lc2 (mi) -- -- Length of curve in segment Lc2, seg (mi) -- -- Cross Section Data Lane width Wl (ft) -- 12 Outside shoulder width Ws (ft) -- 7 Inside shoulder width Wis (ft) -- 6 Median width Wm (ft) -- 40 Presence of rumble strips on outside shoulder -- Y/N Y Y/N If Yes, then enter data in the next two rows. Length of rumble strip in increasing milepost dir. (mi) -- 0.25 Length of rumble strip in decreasing milepost dir. (mi) -- 0.25 Presence of rumble strips on inside shoulder -- Y/N Y Y/N If Yes, then enter data in the next two rows. Length of rumble strip in increasing milepost dir. (mi) -- 0.25 Length of rumble strip in decreasing milepost dir. (mi) -- 0.25 Presence of barrier in median -- Y/N N Y/N If Yes, then use the freeway barrier worksheet.

479 Table 18-37. Freeway Segment Worksheet (2 of 4)—Sample Problem 2 Input Data Roadside Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Clear zone width Whc (ft) -- 30 Presence of barrier on roadside -- Y/N N Y/N If Yes, then use the freeway barrier worksheet. Ramp Access Data Travel in Increasing Milepost Direction Ent. ramp Distance from begin milepost to upstream entrance ramp gore Xb, ent (mi) -- 1.25 If ramp entrance is in the segment, enter 0.0. Presence of speed-change lane in segment -- Y/N N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Len,seg, inc (mi) -- -- Exit ramp Distance from end milepost to upstream exit ramp gore Xe, ext (mi) -- 0.1 If ramp exit is in the segment, enter 0.0. Presence of speed-change lane in segment -- Y/N N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Lex,seg, inc (mi) -- -- Weave Presence of a Type B weave in segment -- Y/N N Y/N If Yes, then enter data in the next two rows. Length of weaving section Lwev, inc (mi) -- -- Length of weaving section in seg. Lwev, seg, inc (mi) -- -- Travel in Decreasing Milepost Direction Ent. ramp Distance from end milepost to upstream entrance ramp gore Xe, ent (mi) -- 0.1 If ramp entrance is in the segment, enter 0.0. Presence of speed-change lane in segment -- Y/N N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Len,seg, dec (mi) -- -- Exit ramp Distance from begin milepost to downstream exit ramp gore Xb, ext (mi) -- 1.25 If ramp exit is in the segment, enter 0.0. Presence of speed-change lane in segment -- Y/N N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Lex,seg, dec (mi) -- -- Weave Presence of a Type B weave in segment -- Y/N N Y/N If Yes, then enter data in the next two rows. Length of weaving section Lwev, dec (mi) -- -- Length of weaving section in seg. Lwev, seg, dec (mi) -- -- Traffic Data Proportion of AADT during high-volume hours Phv -- 0.1 Freeway segment AADT AADTfs (veh/day) -- 120,000 AADT of entrance ramp for travel in increasing milepost direction AADTb,ent (veh/day) -- 8,000 AADT of exit ramp for travel in increasing milepost direction AADTe,ext (veh/day) -- 7,150 AADT of entrance ramp for travel in decreasing milepost direction AADTe,ent (veh/day) -- 6,750 AADT of exit ramp for travel in decreasing milepost direction AADTb,ext (veh/day) -- 7,675

480 Table 18-38. Freeway Segment Worksheet (3 of 4)—Sample Problem 2 Crash Modification Factors Fatal and Injury Property Damage Only Complete the study year column. Complete the crash period column if the EB Method is used. Multiple Vehicle Single Vehicle Multiple Vehicle Single Vehicle Equation Crash Period Study Year Crash Period Study Year Crash Period Study Year Crash Period Study Year Horizontal curve CMF1, fs, ac, y, z 18-24 -- 1.043 -- 1.178 -- 1.084 -- 1.155 Lane width CMF2, fs, ac, y, fi 18-25 -- 1.000 -- 1.000 Inside shoulder width CMF3, fs, ac, y, z 18-26 -- 1.000 -- 1.000 -- 1.000 -- 1.000 Median width CMF4, fs, ac, y, z 18-27 -- 1.062 -- 0.980 -- 1.060 -- 1.060 Median barrier CMF5, fs, ac, y, z 18-28 -- 1.000 -- 1.000 -- 1.000 -- 1.000 High volume CMF6, fs, ac, y, z 18-29 -- 1.036 -- 0.993 -- 1.029 -- 0.941 Lane change CMF7, fs, ac, mv, z 18-30 -- 1.018 -- 1.015 Outside shoulder width CMF8, fs, ac, sv, z 18-35 -- 1.246 -- 1.096 Shoulder rumble strip CMF9, fs, ac, sv, fi 18-36 -- 0.958 Outside clearance CMF10, fs, ac, sv, fi 18-38 -- 0.987 Outside barrier CMF11, fs, ac, sv, z 18-39 -- 1.000 -- 1.000 Combined CMF (multiply all CMFs evaluated) -- 1.168 -- 1.351 -- 1.200 -- 1.263 Expected Average Crash Frequency a Fatal and Injury Property Damage Only Complete the study year column. Complete the crash period column if the site-specific EB Method is used. Multiple Vehicle Single Vehicle Multiple Vehicle Single Vehicle Crash Period Study Year Crash Period Study Year Crash Period Study Year Crash Period Study Year Calibration factor Cfs, ac, y, z 1.00 1.00 1.00 1.00 Overdispersion parameter kfs, n, y, z -- -- -- -- Observed crash count N*o, fs, n, y, z (cr) -- -- -- -- Reference year r -- -- -- -- Predicted average crash freq. for reference year Np, fs, n, y, z, r (cr/yr) -- -- -- -- Predicted number of crashes for crash period (sum all years) N*p, fs, n, y, z (cr) -- -- -- -- Equivalent years associated with crash count Cb, fs, n, y, z, r (yr) -- -- -- -- Adjusted average crash freq. for ref. year given N*o, Na, fs, n, y, z, r (cr/yr) -- -- -- -- Study year s 2011 2011 2011 2011 Predicted average crash freq. for study year Np, fs, n, y, z, s (cr/yr) 4.150 2.858 10.530 6.454 Expected average crash freq. for study year Ne, fs, n, y, z, s (cr/yr) 4.150 2.858 10.530 6.454 Expected average crash freq. for study year (all crash types) Ne, fs, n, at, z, s (cr/yr) 7.008 16.984 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”.

481 Table 18-39. Freeway Segment Worksheet (4 of 4)—Sample Problem 2 Expected Average Crash Frequency a Crash Severity Distribution K A B C Total FI PDO Total FI + PDO Proportion by injury level 0.023 0.059 0.350 0.567 1.000 Expected average crash freq. for study year (all crash types) Ne, fs, n, at, z, s (cr/yr) 0.163 0.412 2.456 3.977 7.008 16.984 23.992 Crash Type Distribution Fatal and Injury Property Damage Only Total Crash Type Category Proportion Expected Average Crash Frequency for Study Year Ne, fs, n, y, fi, s (cr/yr) Proportion Expected Average Crash Frequency for Study Year Ne, fs, n, y, pdo, s (cr/yr) Expected Average Crash Frequency for Study Year Ne, fs, n, y, as, s (cr/yr) Table Multiple-Vehicle Crashes 18-6 Head-on 0.008 0.033 0.002 0.021 0.054 Right-angle 0.031 0.129 0.018 0.190 0.318 Rear-end 0.750 3.113 0.690 7.265 10.378 Sideswipe 0.180 0.747 0.266 2.801 3.548 Other multiple-vehicle crashes 0.031 0.129 0.024 0.253 0.381 Total 1.000 4.150 1.000 10.530 14.680 Single-Vehicle Crashes 18-8 Crash with animal 0.004 0.011 0.022 0.142 0.153 Crash with fixed object 0.722 2.063 0.716 4.621 6.685 Crash with other object 0.051 0.146 0.139 0.897 1.043 Crash with parked vehicle 0.015 0.043 0.016 0.103 0.146 Other single-vehicle crashes 0.208 0.594 0.107 0.691 1.285 Total 1.000 2.858 1.000 6.454 9.312 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”. 18.13.3. Sample Problem 3 The Site/Facility A ramp-entrance speed-change lane on a six-lane urban freeway. The Question What is the predicted average crash frequency of the speed-change lane for a one-year period? The Facts The study year is 2011. The conditions present during this year are provided in the following list.  0.1-mi length

482  Freeway mainline data  120,000 veh/day  10 percent of AADT volume occurs during high-volume hours  No horizontal curvature  12-ft lane width  6-ft inside shoulder width (paved)  40-ft median width  No median barrier  Ramp entrance data  6,750 veh/day  On right side of mainline Assumptions  Crash type distributions used are the default values presented in Table 18-10.  The calibration factor is 1.00. Results Using the predictive method steps as outlined below, the predicted average fatal-and-injury crash frequency for the speed-change lane in Sample Problem 3 is determined to be 0.5 crashes per year, and the predicted average property-damage-only crash frequency is determined to be 1.0 crashes per year (rounded to one decimal place). Steps Step 1 through 8 To determine the predicted average crash frequency of the speed-change lane in Sample Problem 3, only Steps 9 through 11 are conducted. No other steps are necessary because only one speed-change lane is analyzed for one year, and the EB Method is not applied. Step 9 – For the selected site, determine and apply the appropriate SPF. For a ramp-entrance speed-change lane on a six-lane urban freeway, an SPF value for ramp entrance crashes is determined. Ramp Entrance Crashes The SPF for fatal-and-injury ramp entrance crashes is calculated from Equation 18-20 and Table 18-9 as follows:

483 [ ]( ) [ ]( ) arcrashes/ye229.0 000,1200005.0ln173.1974.3exp10.0 lnexp,,6,, = ××+−×= ××+×= fsenfiatENscspf AADTcbaLN Similarly, the SPF for property-damage-only ramp entrance crashes is calculated from Equation 18-20 and Table 18-9 to yield the following result: arcrashes/ye722.0,,6,, =pdoatENscspfN Step 10 – Multiply the result obtained in Step 9 by the appropriate CMFs. Each CMF used in the calculation of the predicted average crash frequency of the speed-change lane is calculated below: Horizontal Curve (CMF1, sc, 6EN, at, z ) The speed-change lane does not have horizontal curvature. Hence, CMF1, sc, 6EN, at, fi and CMF1, sc, 6EN, at, pdo are equal to 1.000. Lane Width (CMF2, sc, 6EN, at, z ) The segment has 12-ft lanes, which is the base condition for the lane width CMF. Hence, CMF2, sc, 6EN, at, fi and CMF2, sc, 6EN, at, pdo are equal to 1.000. Inside Shoulder Width (CMF3, sc, 6EN, at, z ) The segment has 6-ft inside shoulders, which is the base condition for the inside shoulder width CMF. Hence, CMF3, sc, 6EN,at, fi and CMF3, sc, 6EN, at, pdo are equal to 1.000. Median Width (CMF4, sc, 6EN, at, z ) CMF4, sc, 6EN, at, fi is calculated from Equation 18-43 as follows: ( ) [ ]( ) [ ]( )482exp482exp0.1,,6,,4 −×××+−×−××−= icbibismibfiatENsc WaPWWaPCMF The segment does not have inside barrier, so Pib = 0.0 and the calculation of Wicb does not apply. From Table 18-25, a = -0.00302. CMF4, sc, 6EN, at, fi is calculated as follows: ( ) [ ]( ) [ ]( ) 062.1 48200302.0exp0.048624000302.0exp0.00.1,,6,,4 = −××−×+−×−×−×−= icbfiatENsc WCMF Similar calculations using the property-damage-only coefficient from Table 18-25 yield the following results: 060.1,,6,,4 =pdoatENscCMF Median Barrier (CMF5, sc, 6EN, at, z ) The segment does not have inside barrier. Hence, CMF5, sc, 6EN, at, fi and CMF5, sc, 6EN, at, pdo are equal to 1.000. High Volume (CMF6, sc, 6EN, at, z ) CMF6, sc, 6EN, at, fi is calculated from Equation 18-45 and the coefficient a = 0.350 from Table 18-27 as follows:

484 ( ) ( ) 036.1 1.0350.0exp exp,,6,,6 = ×= ×= hvfimvfs PaCMF Similar calculations using the property-damage-only coefficients from Table 18-27 yield the following results: 029.1,,6,,6 =pdoatENscCMF Ramp Entrance (CMF12, sc, 6EN, at, z ) CMF12, sc, 6EN, at, fi is calculated from Equation 18-46 as follows: [ ]      ××++×= r en leftfiatENsc AADTcdL bIaCMF lnexp,,6,,12 The ramp entrance connects to the right side of the freeway mainline. Hence, Ileft = 0.0. From Table 18- 28, the coefficients a, b, c, and d for fatal-and-injury crashes are 0.594, 0.0318, 0.001, and 0.198, respectively. CMF12, sc, 6EN, at, fi is calculated as follows: [ ] 006.2750,6001.0ln198.0 1.0 0318.00.0594.0exp,,6,,12 =      ××++×=fiatENscCMF Similar calculations using the property-damage-only coefficients from Table 18-28 yield the following results: 287.1,,6,,12 =pdoatENscCMF Ramp Entrance Crashes The CMFs are applied to the ramp entrance fatal-and-injury SPF as follows: ( ) ( ) arcrashes/ye505.0 207.2229.0 006.2036.1000.1062.1000.1000.1000.1229.0 ,,6,,12,,6,,6,,6,,1,,6,,,,6,*, = ×= ×××××××= ××××= fiatENscfiatENscfiatENscfiatENscspffiatENscp CMFCMFCMFNN  The CMFs are applied to the ramp entrance property-damage-only SPF as follows: ( ) ( ) arcrashes/ye013.1 403.1722.0 287.1029.1000.1060.1000.1000.1000.1722.0 ,,6,,12,,6,,6,,6,,1,,6,,,,6,*, = ×= ×××××××= ××××= pdoatENscpdoatENscpdoatENscpdoatENscspfpdoatENscp CMFCMFCMFNN  Step 11 – Multiply the result obtained in Step 10 by the appropriate calibration factor. It is assumed that a calibration factor of 1.00 has been determined for local conditions. See Section B.1 of Appendix B to Part C for further discussion on calibration of the predicted models.

485 Calculation of Predicted Average Crash Frequency The predicted average crash frequency is calculated using Equation 18-2 based on the results obtained in Steps 9 through 11 as follows. Fatal-and-injury crashes: arcrashes/ye505.0 00.1505.0 ,,6,,,,6,*,,,6,, = ×= ×= fiatENscfsfiatENscspffiatENscp CNN Property-damage-only crashes: arcrashes/ye013.1 00.1013.1 ,,6,,,,6,*,,,6,, = ×= ×= pdoatENscfspdoatENscspfpdoatENscp CNN Step 12—If there is another year to be evaluated in the evaluation period for the selected site, return to Step 8. Otherwise, proceed to Step 13. The study period is one year (2011), so steps 8 through 11 need not be repeated. Step 13—Apply site-specific EB Method (if applicable) and apply SDFs. This step consists of three optional sets of calculations—site-specific EB Method, severity distribution functions, and crash type distribution. Apply the site-specific EB Method to a future time period, if appropriate. The site-specific EB Method is not applied in this sample problem because crash data are not available. Apply the severity distribution functions (SDFs), if desired. To apply the SDFs, the systematic component of crash severity likelihood Vj is computed for each severity level j using Equation 18-63 as follows: ( ) ( ) ( ) ( )rurallicorirhvobibj IgWfPePPdPcPPbaV ×+×+×+      +×+×+      +×+=  ,22 The coefficients a, b, c, d, e, f, and g are obtained from Table 18-30 for each severity level j. The segment does not have barrier, rumble strips, or horizontal curvature, so Pib, Pob, Pir, Por, and Pc, i are equal to 0.0. Vj is computed for fatal crashes as follows: ( ) ( ) ( ) ( ) 392.3 0.0492.012261.00.0208.0 2 0.00.0387.01.0924.0 2 0.00.0388.0171.0 −= ×+×−+×+       +×+×−+      +×−+−=KV Calculations using the coefficients for incapacitating injury crashes and non-incapacitating injury crashes from Table 18-30 yield the following results: 478.2−=AV

486 571.0−=BV Using these computed VK, VA, and VB values, and assuming a calibration factor Csdf, fs+sc of 1.0, the probability of occurrence of a fatal crash is computed using Equation 18-59 as follows: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 020.0 571.0exp478.2exp392.3exp 0.1 0.1 392.3exp expexpexp0.1 exp , ,,, = −+−+−+ −= +++ = + + BAK scfssdf K Katacscfs VVV C VP Similar calculations using Equation 18-60 and Equation 18-61 yield the following results: 050.0,,, =+ AatacscfsP 336.0,,, =+ BatacscfsP The probability of occurrence of a possible-injury crash is computed using Equation 18-62 as follows: 594.0 )336.0050.0020.0(0.1 )(0.1 ,,,,,,,,,,,, = ++−= ++−= ++++ BatacscfsAatacscfsKatacscfsCatacscfs PPPP The probability of occurrence of a fatal crash is multiplied by the fatal-and-injury crash frequency obtained in Step 11 using Equation 18-58 as follows: arcrashes/ye010.0 020.0505.0 ,,,,,6,,,,6,, = ×= ×= + KatacscfsfiatENsceKatENsce PNN Similar calculations using Equation 18-58 and the probabilities of occurrences of the other crash severities yield the following results: arcrashes/ye025.0,,6,, =AatENsceN arcrashes/ye170.0,,6,, =BatENsceN arcrashes/ye300.0,,6,, =CatENsceN Apply the crash type distribution, if desired. The crash type distributions are applied by multiplying the default crash type distribution proportions in Table 18-10 by the predicted average crash frequencies obtained in Step 11.

487 Worksheets The step-by-step instructions are provided to illustrate the predictive method for calculating the predicted average crash frequency for a freeway segment. To apply the predictive method steps to multiple segments, a series of worksheets are provided for determining the predicted average crash frequency. The worksheets include:  Table 18-40. Freeway Speed-Change Lane Worksheet (1 of 3)—Sample Problem 3  Table 18-41. Freeway Speed-Change Lane Worksheet (2 of 3)—Sample Problem 3  Table 18-42. Freeway Speed-Change Lane Worksheet (3 of 3)—Sample Problem 3 Filled versions of these worksheets are provided below. Blank versions of worksheets used in the Sample Problems are provided in Appendix 18A. Table 18-40 is a summary of general information about the freeway speed-change lane, analysis, input data (i.e., “The Facts”), and assumptions for Sample Problem 3. The input data include area type, crash data, basic roadway data, alignment data, cross section data, and traffic data. Table 18-41 is a tabulation of the CMF and SPF computations for Sample Problem 3. Table 18-42 is a tabulation of the crash severity and crash type distributions for Sample Problem 3.

488 Table 18-40. Freeway Speed-Change Lane Worksheet (1 of 3)—Sample Problem 3 General Information Location Information Analyst Roadway Agency or company Roadway section Date performed Study year Area type X Urban Rural Input Data Crash Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Crash data time period First year -- Last year -- Count of speed-change-related FI crashes N*o, sc, x, at, fi -- Count of speed-change-related PDO crashes N*o,sc,x,at,pdo -- Basic Roadway Data Number of through lanes n 6 Same value for crash period and study year. Segment length L (mi) -- 0.1 Equals the length of the speed-change lane. Configuration Entrance Choices: Entrance, Exit Alignment Data Horizontal Curve Data 1 Presence of horizontal curve 1 -- Y/N N Y/N If Yes, then enter data in the next three rows. Curve radius R1 (ft) -- -- Length of curve Lc1 (mi) -- -- Length of curve in segment Lc1, seg (mi) -- -- 2 Presence of horizontal curve 2 -- Y/N N Y/N If Yes, then enter data in the next three rows. Curve radius R2 (ft) -- -- Length of curve Lc2 (mi) -- -- Length of curve in segment Lc2, seg (mi) -- -- Cross Section Data Lane width Wl (ft) -- 12 Inside shoulder width Wis (ft) -- 6 Median width Wm (ft) -- 40 Presence of barrier in median -- Y/N N Y/N If Yes, then use the freeway barrier worksheet. Entrance or exit side (left- or right-hand side) -- L/R R L/R Traffic Data Proportion of AADT during high-volume hours Phv -- 0.1 Freeway segment AADT AADTfs (veh/day) -- 120,000 AADT of ramp AADTr (veh/day) -- 6,750 Only needed for entrance ramp.

489 Table 18-41. Freeway Speed-Change Lane Worksheet (2 of 3)—Sample Problem 3 Crash Modification Factors Complete the study year column. Complete the crash period column if the EB Method is used. Fatal and Injury Property Damage Only Equation Crash Period Study Year Crash Period Study Year Horizontal curve CMF1, sc, ac, at, z 18-40 -- 1.000 -- 1.000 Lane width CMF2, sc, ac, at, fi 18-41 -- 1.000 Inside shoulder width CMF3, sc, ac, at, z 18-42 -- 1.000 -- 1.000 Median width CMF4, sc, ac, at, z 18-43 -- 1.062 -- 1.060 Median barrier CMF5, sc, ac, at, z 18-44 -- 1.000 -- 1.000 High volume CMF6, sc, ac, at, z 18-45 -- 1.036 -- 1.029 Ramp entrance CMF12, sc, nEN, at, z 18-46 -- 2.006 -- 1.287 Ramp exit CMF13, sc, nEX, at, z 18-47 -- 1.000 -- 1.000 Combined CMF (multiply all CMFs evaluated) -- 2.207 -- 1.403 Expected Average Crash Frequency a Complete the study year column. Complete the crash period column if the site-specific EB Method is used. Fatal and Injury Property Damage Only Crash Period Study Year Crash Period Study Year Calibration factor Csc, x, at, z 1.00 1.00 Overdispersion parameter ksc, x, at, z -- -- Observed crash count N*o, sc, x, at, z (cr) -- -- Reference year r -- -- Predicted average crash freq. for reference year Np, sc, x, at, z, r (cr/yr) -- -- Predicted number of crashes for crash period (sum all years) N*p, sc, x, at, z (cr) -- -- Equivalent years associated with crash count Cb, sc, x, at, z, r (yr) -- -- Adjusted average crash freq. for ref. year given N*o, Na, sc, x, at, z, r (cr/yr) -- -- Study year s 2011 2011 Predicted average crash freq. for study year Np, sc, x, at, z, s (cr/yr) 0.505 1.013 Expected average crash freq. for study year Ne, sc, x, at, z, s (cr/yr) 0.505 1.013 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”.

490 Table 18-42. Freeway Speed-Change Lane Worksheet (3 of 3)—Sample Problem 3 Expected Average Crash Frequency a Crash Severity Distribution K A B C Total FI PDO Total FI + PDO Proportion by injury level 0.020 0.050 0.336 0.594 1.000 Expected average crash freq. for study year Ne, sc, x, at, z, s (cr/yr) 0.010 0.025 0.170 0.300 0.505 1.013 1.518 Crash Type Distribution Fatal and Injury Property Damage Only Total Crash Type Category Table 18-10 or 18-12 Proportion Expected Average Crash Frequency for Study Year Ne, sc, x, at, fi, s (cr/yr) Proportion Expected Average Crash Frequency for Study Year Ne, sc, x, at, pdo, s (cr/yr) Expected Average Crash Frequency for Study Year Ne, sc, x, at, as, s (cr/yr) Multiple-Vehicle Crashes Head-on 0.004 0.002 0.001 0.001 0.003 Right-angle 0.019 0.010 0.016 0.016 0.026 Rear-end 0.543 0.274 0.530 0.537 0.811 Sideswipe 0.133 0.067 0.252 0.255 0.322 Other multiple-vehicle crashes 0.017 0.009 0.015 0.015 0.024 Single-Vehicle Crashes Crash with animal 0.000 0.000 0.002 0.002 0.002 Crash with fixed object 0.194 0.098 0.129 0.131 0.229 Crash with other object 0.019 0.010 0.036 0.036 0.046 Crash with parked vehicle 0.004 0.002 0.003 0.003 0.005 Other single-vehicle crashes 0.067 0.034 0.016 0.016 0.050 Total 1.000 0.505 1.000 1.013 1.518 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”. 18.13.4. Sample Problem 4 The Site/Facility A ramp-exit speed-change lane on a six-lane urban freeway. The Question What is the predicted average crash frequency of the speed-change lane for a one-year period? The Facts The study year is 2011. The conditions present during this year are provided in the following list.  0.1-mi length  Freeway mainline data  120,000 veh/day

491  10 percent of AADT volume occurs during high-volume hours  No horizontal curvature  12-ft lane width  6-ft inside shoulder width (paved)  40-ft median width  No median barrier  Ramp exit data  On right side of mainline Assumptions  Crash type distributions used are the default values presented in Table 18-12.  The calibration factor is 1.00. Results Using the predictive method steps as outlined below, the predicted average fatal-and-injury crash frequency for the speed-change lane in Sample Problem 4 is determined to be 0.3 crashes per year, and the predicted average property-damage-only crash frequency is determined to be 0.8 crashes per year (rounded to one decimal place). Steps Step 1 through 8 To determine the predicted average crash frequency of the speed-change lane in Sample Problem 4, only Steps 9 through 11 are conducted. No other steps are necessary because only one speed-change lane is analyzed for one year, and the EB Method is not applied. Step 9 – For the selected site, determine and apply the appropriate SPF. For a ramp-exit speed-change lane on a six-lane urban freeway, SPF values for ramp exit crashes are determined. Ramp Exit Crashes The SPF for fatal-and-injury ramp exit crashes is calculated from Equation 18-22 and Table 18-11 as follows: [ ]( ) [ ]( ) arcrashes/ye277.0 000,1200005.0ln903.0679.2exp10.0 lnexp,,6,, = ××+−×= ××+×= fsexfiatEXscspf AADTcbaLN Similarly, the SPF for property-damage-only ramp exit crashes is calculated from Equation 18-22 and Table 18-11 to yield the following result:

492 arcrashes/ye752.0,,6,, =pdoatEXscspfN Step 10 – Multiply the result obtained in Step 9 by the appropriate CMFs. Each CMF used in the calculation of the predicted average crash frequency of the speed-change lane is calculated in this step. Horizontal Curve (CMF1, sc, 6EX, at, z ) The segment does not have horizontal curvature. Hence, CMF1, sc, 6EX, at, fi and CMF1, sc, 6EX, at, pdo are equal to 1.000. Lane Width (CMF2, sc, 6EX, at, fi ) The segment has 12-ft lanes, which is the base condition for the lane width CMF. Hence, CMF2, sc, 6EX, at, fi is equal to 1.000. Inside Shoulder Width (CMF3, sc, 6EX, at, z ) The segment has 6-ft inside shoulders, which is the base condition for the inside shoulder width CMF. Hence, CMF3, sc, 6EX, at, fi and CMF3, sc, 6EX, at, pdo are equal to 1.000. Median Width (CMF4, sc, 6EX, at, z ) CMF4, sc, 6EX, at, fi is calculated from Equation 18-43 as follows: ( ) [ ]( ) [ ]( )482exp482exp0.1,,6,,4 −×××+−×−××−= icbibismibfiatEXsc WaPWWaPCMF The segment does not have inside barrier, so Pib = 0.0 and the calculation of Wicb does not apply. From Table 18-25, a = -0.00302 for fatal-and-injury crashes. CMF4, sc, 6EX, at, fi is calculated as follows: ( ) [ ]( ) [ ]( ) 062.1 48200302.0exp0.048624000302.0exp0.00.1,,6,,4 = −××−×+−×−×−×−= icbfiatEXsc WCMF Similar calculations using the property-damage-only coefficients from Table 18-25 yield the following results: 060.1,,6,,4 =pdoatEXscCMF Median Barrier (CMF5, sc, 6EX, at, z ) The segment does not have inside barrier. Hence, CMF5, sc, 6EX, at, fi and CMF5, sc, 6EX, at, pdo are equal to 1.000. High Volume (CMF6, sc, 6EX, at, z ) CMF6, sc, 6EX, at, fi is calculated from Equation 18-45 and the coefficient a = 0.350 from Table 18-27 as follows: ( ) ( ) 036.1 1.0350.0exp exp,,6,,6 = ×= ×= hvfimvfs PaCMF Similar calculations using the property-damage-only coefficients from Table 18-27 yield the following results:

493 029.1,,6,,6 =pdoatEXscCMF Ramp Exit (CMF13, sc, 6EX, at, z ) CMF13, sc, 6EX, at, fi is calculated from Equation 18-47 as follows:       +×= ex leftfiatEXsc L bIaCMF exp,,6,,13 The ramp entrance connects to the right side of the freeway mainline. Hence, Ileft = 0.0. From Table 18- 29, the coefficients a and b for fatal-and-injury crashes are 0.594 and 0.0116, respectively. CMF13, sc, 6EX, at, fi is calculated as follows: 123.1 1.0 0116.00.0594.0exp,,6,,13 =      +×=fiatEXscCMF Similar calculations using the property-damage-only coefficients from Table 18-29 yield the following results: 000.1,,6,,13 =pdoatEXscCMF Ramp Exit Crashes The CMFs are applied to the ramp exit fatal-and-injury SPF as follows: ( ) ( ) arcrashes/ye342.0 235.1277.0 123.1036.1000.1062.1000.1000.1000.1277.0 ,,6,,13,,6,,6,,6,,1,,6,,,,6,*, = ×= ×××××××= ××××= fiatEXscfiatEXscfiatEXscfiatEXscspffiatEXscp CMFCMFCMFNN  The CMFs are applied to the ramp exit property-damage-only SPF as follows: ( ) ( ) arcrashes/ye820.0 090.1752.0 000.1029.1000.1060.1000.1000.1000.1752.0 ,,6,,13,,6,,6,,6,,1,,6,,,,6,*, = ×= ×××××××= ××××= pdoatEXscpdoatEXscpdoatEXscpdoatEXscspfpdoatEXscp CMFCMFCMFNN  Step 11 – Multiply the result obtained in Step 10 by the appropriate calibration factor. It is assumed that a calibration factor of 1.00 has been determined for local conditions. See Section B.1 of Appendix B to Part C for further discussion on calibration of the predicted models. Calculation of Predicted Average Crash Frequency The predicted average crash frequency is calculated using Equation 18-2 based on the results obtained in Steps 9 through 11 as follows. Fatal-and-injury crashes:

494 arcrashes/ye342.0 00.1342.0 ,,6,,,,6,*,,,6,, = ×= ×= fiatEXscfsfiatEXscspffiatEXscp CNN Property-damage-only crashes: arcrashes/ye820.0 00.1820.0 ,,6,,,,6,*,,,6,, = ×= ×= pdoatEXscfspdoatEXscspfpdoatEXscp CNN Step 12—If there is another year to be evaluated in the evaluation period for the selected site, return to Step 8. Otherwise, proceed to Step 13. The study period is one year (2011), so steps 8 through 11 need not be repeated. Step 13—Apply site-specific EB Method (if applicable) and apply SDFs. This step consists of three optional sets of calculations—site-specific EB Method, severity distribution functions, and crash type distribution. Apply the site-specific EB Method to a future time period, if appropriate. The site-specific EB Method is not applied in this sample problem because crash data are not available. Apply the severity distribution functions (SDFs), if desired. To apply the SDFs, the systematic component of crash severity likelihood Vj is computed for each severity level j using Equation 18-63 as follows: ( ) ( ) ( ) ( )rurallicorirhvobibj IgWfPePPdPcPPbaV ×+×+×+      +×+×+      +×+=  ,22 The coefficients a, b, c, d, e, f, and g are obtained from Table 18-30 for each severity level j. The segment does not have barrier, rumble strips, or horizontal curvature, so Pib, Pob, Pir, Por, and Pc, i are equal to 0.0. Vj is computed for fatal crashes as follows: ( ) ( ) ( ) ( ) 392.3 0.0492.012261.00.0208.0 2 0.00.0387.01.0924.0 2 0.00.0388.0171.0 −= ×+×−+×+       +×+×−+      +×−+−=KV Calculations using the coefficients for incapacitating injury crashes and non-incapacitating injury crashes from Table 18-30 yield the following results: 478.2−=AV 571.0−=BV Using these computed VK, VA, and VB values, and assuming a calibration factor Csdf, fs+sc of 1.0, the probability of occurrence of a fatal crash is computed using Equation 18-59 as follows:

495 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 020.0 571.0exp478.2exp392.3exp 0.1 0.1 392.3exp expexpexp0.1 exp , ,,, = −+−+−+ −= +++ = + + BAK scfssdf K Katacscfs VVV C VP Similar calculations using Equation 18-60 and Equation 18-61 yield the following results: 050.0,,, =+ AatacscfsP 336.0,,, =+ BatacscfsP The probability of occurrence of a possible-injury crash is computed using Equation 18-62 as follows: 594.0 )336.0050.0020.0(0.1 )(0.1 ,,,,,,,,,,,, = ++−= ++−= ++++ BatacscfsAatacscfsKatacscfsCatacscfs PPPP The probability of occurrence of a fatal crash is multiplied by the fatal-and-injury crash frequency obtained in Step 11 using Equation 18-58 as follows: arcrashes/ye007.0 020.0342.0 ,,,,,6,,,,6,, = ×= ×= + KatacscfsfiatEXsceKatEXsce PNN Similar calculations using Equation 18-58 and the probabilities of occurrences of the other crash severities yield the following results: arcrashes/ye017.0,,6,, =AatEXsceN arcrashes/ye115.0,,6,, =BatEXsceN arcrashes/ye203.0,,6,, =CatEXsceN Apply the crash type distribution, if desired. The crash type distributions are applied by multiplying the default crash type distribution proportions in Table 18-12 by the predicted average crash frequencies obtained in Step 11. Worksheets The step-by-step instructions are provided to illustrate the predictive method for calculating the predicted average crash frequency for a freeway segment. To apply the predictive method steps to multiple segments, a series of worksheets are provided for determining the predicted average crash frequency. The worksheets include:  Table 18-43. Freeway Speed-Change Lane Worksheet (1 of 3)—Sample Problem 4

496  Table 18-44. Freeway Speed-Change Lane Worksheet (2 of 3)—Sample Problem 4  Table 18-45. Freeway Speed-Change Lane Worksheet (3 of 3)—Sample Problem 4 Filled versions of these worksheets are provided below. Blank versions of worksheets used in the Sample Problems are provided in Appendix 18A. Table 18-43 is a summary of general information about the freeway speed-change lane, analysis, input data (i.e., “The Facts”), and assumptions for Sample Problem 4. The input data include area type, crash data, basic roadway data, alignment data, cross section data, and traffic data. Table 18-44 is a tabulation of the CMF and SPF computations for Sample Problem 4. Table 18-45 is a tabulation of the crash severity and crash type distributions for Sample Problem 4.

497 Table 18-43. Freeway Speed-Change Lane Worksheet (1 of 3)—Sample Problem 4 General Information Location Information Analyst Roadway Agency or company Roadway section Date performed Study year Area type X Urban Rural Input Data Crash Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Crash data time period First year -- Last year -- Count of speed-change-related FI crashes N*o, sc, x, at, fi -- Count of speed-change-related PDO crashes N*o,sc,x,at,pdo -- Basic Roadway Data Number of through lanes n 6 Same value for crash period and study year. Segment length L (mi) -- 0.1 Equals the length of the speed-change lane. Configuration Exit Choices: Entrance, Exit Alignment Data Horizontal Curve Data 1 Presence of horizontal curve 1 -- Y/N N Y/N If Yes, then enter data in the next three rows. Curve radius R1 (ft) -- -- Length of curve Lc1 (mi) -- -- Length of curve in segment Lc1, seg (mi) -- -- 2 Presence of horizontal curve 2 -- Y/N N Y/N If Yes, then enter data in the next three rows. Curve radius R2 (ft) -- -- Length of curve Lc2 (mi) -- -- Length of curve in segment Lc2, seg (mi) -- -- Cross Section Data Lane width Wl (ft) -- 12 Inside shoulder width Wis (ft) -- 6 Median width Wm (ft) -- 40 Presence of barrier in median -- Y/N N Y/N If Yes, then use the freeway barrier worksheet. Entrance or exit side (left- or right-hand side) -- L/R R L/R Traffic Data Proportion of AADT during high-volume hours Phv -- 0.1 Freeway segment AADT AADTfs (veh/day) -- 120,000 AADT of ramp AADTr (veh/day) -- -- Only needed for entrance ramp.

498 Table 18-44. Freeway Speed-Change Lane Worksheet (2 of 3)—Sample Problem 4 Crash Modification Factors Complete the study year column. Complete the crash period column if the EB Method is used. Fatal and Injury Property Damage Only Equation Crash Period Study Year Crash Period Study Year Horizontal curve CMF1, sc, ac, at, z 18-40 -- 1.000 -- 1.000 Lane width CMF2, sc, ac, at, fi 18-41 -- 1.000 Inside shoulder width CMF3, sc, ac, at, z 18-42 -- 1.000 -- 1.000 Median width CMF4, sc, ac, at, z 18-43 -- 1.062 -- 1.060 Median barrier CMF5, sc, ac, at, z 18-44 -- 1.000 -- 1.000 High volume CMF6, sc, ac, at, z 18-45 -- 1.036 -- 1.029 Ramp entrance CMF12, sc, nEN, at, z 18-46 -- 1.000 -- 1.000 Ramp exit CMF13, sc, nEX, at, z 18-47 -- 1.123 -- 1.000 Combined CMF (multiply all CMFs evaluated) -- 1.235 -- 1.090 Expected Average Crash Frequency a Complete the study year column. Complete the crash period column if the site-specific EB Method is used. Fatal and Injury Property Damage Only Crash Period Study Year Crash Period Study Year Calibration factor Csc, x, at, z 1.00 1.00 Overdispersion parameter ksc, x, at, z -- -- Observed crash count N*o, sc, x, at, z (cr) -- -- Reference year r -- -- Predicted average crash freq. for reference year Np, sc, x, at, z, r (cr/yr) -- -- Predicted number of crashes for crash period (sum all years) N*p, sc, x, at, z (cr) -- -- Equivalent years associated with crash count Cb, sc, x, at, z, r (yr) -- -- Adjusted average crash freq. for ref. year given N*o, Na, sc, x, at, z, r (cr/yr) -- -- Study year s 2011 2011 Predicted average crash freq. for study year Np, sc, x, at, z, s (cr/yr) 0.342 0.820 Expected average crash freq. for study year Ne, sc, x, at, z, s (cr/yr) 0.342 0.820 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”.

499 Table 18-45. Freeway Speed-Change Lane Worksheet (3 of 3)—Sample Problem 4 Expected Average Crash Frequency a Crash Severity Distribution K A B C Total FI PDO Total FI + PDO Proportion by injury level 0.020 0.050 0.336 0.594 1.000 Expected average crash freq. for study year Ne, sc, x, at, z, s (cr/yr) 0.007 0.017 0.115 0.203 0.342 0.820 1.162 Crash Type Distribution Fatal and Injury Property Damage Only Total Crash Type Category Table 18-10 or 18-12 Proportion Expected Average Crash Frequency for Study Year Ne, sc, x, at, fi, s (cr/yr) Proportion Expected Average Crash Frequency for Study Year Ne, sc, x, at, pdo, s (cr/yr) Expected Average Crash Frequency for Study Year Ne, sc, x, at, as, s (cr/yr) Multiple-Vehicle Crashes Head-on 0.004 0.001 0.001 0.001 0.002 Right-angle 0.019 0.006 0.016 0.013 0.020 Rear-end 0.543 0.186 0.530 0.435 0.620 Sideswipe 0.133 0.045 0.252 0.207 0.252 Other multiple-vehicle crashes 0.017 0.006 0.015 0.012 0.018 Single-Vehicle Crashes Crash with animal 0.000 0.000 0.002 0.002 0.002 Crash with fixed object 0.194 0.066 0.129 0.106 0.172 Crash with other object 0.019 0.006 0.036 0.030 0.036 Crash with parked vehicle 0.004 0.001 0.003 0.002 0.004 Other single-vehicle crashes 0.067 0.023 0.016 0.013 0.036 Total 1.000 0.342 1.000 0.820 1.162 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”. 18.13.5. Sample Problem 5 The Project A project of interest consists of two sites located on a six-lane urban freeway: a tangent segment and a segment with a horizontal curve. (This project is a compilation of the freeway segments from Sample Problems 1 and 2.) The Question What is the expected crash frequency of the project for a particular year incorporating both the predicted crash frequencies from Sample Problems 1 and 2 and the observed crash frequencies using the site- specific EB Method? The Facts The study year is 2011. The conditions present during this year are provided in the following list.

500  2 freeway segments—segment 1 (tangent), segment 2 (curved)  Crash period is 2009 and 2010  Use the same AADT volumes for 2009 to 2011  30 observed fatal-and-injury crashes  Segment 1: 10 multiple-vehicle, 4 single-vehicle  Segment 2: 8 multiple-vehicle, 8 single-vehicle  50 observed property-damage-only crashes  Segment 1: 14 multiple-vehicle, 12 single-vehicle  Segment 2: 10 multiple-vehicle, 14 single-vehicle Outline of Solution To calculate the expected crash frequency, observed crash frequencies are combined with predicted crash frequencies on a site-by-site basis for the project. Observed crashes are assigned to specific speed-change lanes or freeway segments. The site-specific EB Method presented in Section B.2.4 of Appendix B to Part C is used for this purpose. Results The expected average crash frequency for the project is 13.5 fatal-and-injury crashes per year and 27.5 property-damage-only crashes per year (rounded to one decimal place). Steps The expected average crash frequency for reference year r at a site i with type w(i) and cross section or control type x(i) for a specified crash type y and severity z is computed using Equation B-5 through Equation B-7 as follows: ( ) rzyixiwb rzyixiwo zyixiwrzyixiwpzyixiwrzyixiwe C NwNwN ,,),(),(, ,,),(),(, * ,),(),(,,),(),(,,),(),(,,),(),(, 0.1 ×−+×=         ×+ =  = cn j rzyixiwpzyixiw zyixiw Nk w 1 ,,),(),(,,),(),( ,),(),( 0.1 0.1  = ×= cn j jzyixiwp rzyixiwp rzyixiwb NN C 1 ,,),(),(, ,,),(),(, ,,),(),(, 0.1 Cb, w(i), x(i), y, z, r = 2.0 because the same AADT volumes are used for all years in the analysis period. The overdispersion parameter for segment 1 for fatal-and-injury multiple-vehicle crashes kfs, 6, mv, fi is computed using Equation 18-17 with the segment length and the inverse dispersion parameter from Table 18-5.

501 076.0 75.06.17 0.1 ,,6, =× =fimvfsk The predicted average fatal-and-injury multiple-vehicle crash frequency Np, fs, 6, mv, fi was computed as 3.911 crashes/year in Sample Problem 1. The weighted adjustment factor wfs, 6, mv, fi is computed as follows: [ ]( ) 627.0911.3911.3076.00.1 0.1 ,,6, =+×+ =fimvfsw Then, the expected average crash frequency Ne, fs, 6, mv, fi is computed as follows: ( ) arcrashes/ye316.4 2 10627.00.1911.3627.0,,,6,, =×−+×=rfimvfseN This process is repeated for fatal-and-injury single-vehicle crashes, property-damage-only multiple- vehicle crashes, and property-damage-only single-vehicle crashes for segment 1, and for all crashes for segment 2, to obtain the following results:  Segment 1  Ne, fs, 6, mv, fi, r = 4.316 crashes/year  Ne, fs, 6, sv, fi, r = 2.050 crashes/year  Ne, fs, 6, mv, pdo, r = 8.090 crashes/year  Ne, fs, 6, sv, pdo, r = 5.456 crashes/year  Segment 2  Ne, fs, 6, mv, fi, r = 4.092 crashes/year  Ne, fs, 6, sv, fi, r = 3.089 crashes/year  Ne, fs, 6, mv, pdo, r = 7.218 crashes/year  Ne, fs, 6, sv, pdo, r = 6.702 crashes/year Worksheets The step-by-step instructions are provided to illustrate the predictive method for calculating the predicted average crash frequency for a freeway segment. To apply the predictive method steps to multiple segments, a series of worksheets are provided for determining the predicted average crash frequency. The worksheets include:  Table 18-46. Freeway Segment Worksheet (1 of 4)—Sample Problem 5  Table 18-47. Freeway Segment Worksheet (2 of 4)—Sample Problem 5  Table 18-48. Freeway Segment Worksheet (3 of 4)—Sample Problem 5

502  Table 18-49. Freeway Segment Worksheet (4 of 4)—Sample Problem 5 Filled versions of these worksheets are provided below for segment 1. The same worksheets would be used for segment 2, but are not shown. Blank versions of worksheets used in the Sample Problems are provided in Appendix 18A. Table 18-46 is a summary of general information about the freeway segment, analysis, input data (i.e., “The Facts”), and assumptions for segment 1. The input data include area type, crash data, basic roadway data, alignment data, and cross section data. Table 18-47 is a summary of general information about the freeway segment, analysis, input data (i.e., “The Facts”), and assumptions for segment 1. The input data include roadside data, ramp access data, and traffic data. Table 18-48 is a tabulation of the CMF and SPF computations for segment 1. Table 18-49 is a tabulation of the crash severity and crash type distributions for segment 1.

503 Table 18-46. Freeway Segment Worksheet (1 of 4)—Sample Problem 5 General Information Location Information Analyst Roadway Agency or company Roadway section Date performed Study year Area type X Urban Rural Input Data Crash Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Crash data time period First year 2009 Last year 2010 Count of multiple-vehicle FI crashes N*o, fs, n, mv, fi 5 Count of single-vehicle FI crashes N*o, fs, n, sv, fi 2 Count of multiple-vehicle PDO crashes N*o, fs, n, mv, pdo 7 Count of single-vehicle PDO crashes N*o, fs, n, sv, pdo 6 Basic Roadway Data Number of through lanes n 6 Same value for crash period and study year. Segment length L (mi) 0.75 0.75 Alignment Data Horizontal Curve Data 1 Presence of horizontal curve 1 N Y/N N Y/N If Yes, then enter data in the next three rows. Equivalent curve radius R1* (ft) -- -- Length of curve Lc1 (mi) -- -- Length of curve in segment Lc1, seg (mi) -- -- 2 Presence of horizontal curve 2 N Y/N N Y/N If Yes, then enter data in the next three rows. Equivalent curve radius R2* (ft) -- -- Length of curve Lc2 (mi) -- -- Length of curve in segment Lc2, seg (mi) -- -- Cross Section Data Lane width Wl (ft) 12 12 Outside shoulder width Ws (ft) 10 10 Inside shoulder width Wis (ft) 6 6 Median width Wm (ft) 40 40 Presence of rumble strips on outside shoulder N Y/N N Y/N If Yes, then enter data in the next two rows. Length of rumble strip in increasing milepost dir. (mi) -- -- Length of rumble strip in decreasing milepost dir. (mi) -- -- Presence of rumble strips on inside shoulder N Y/N N Y/N If Yes, then enter data in the next two rows. Length of rumble strip in increasing milepost dir. (mi) -- -- Length of rumble strip in decreasing milepost dir. (mi) -- -- Presence of barrier in median N Y/N N Y/N If Yes, then use the freeway barrier worksheet.

504 Table 18-47. Freeway Segment Worksheet (2 of 4)—Sample Problem 5 Input Data Roadside Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Clear zone width Whc (ft) 30 30 Presence of barrier on roadside N Y/N N Y/N If Yes, then use the freeway barrier worksheet. Ramp Access Data Travel in Increasing Milepost Direction Ent. ramp Distance from begin milepost to upstream entrance ramp gore Xb, ent (mi) 0.5 0.5 If ramp entrance is in the segment, enter 0.0. Presence of speed-change lane in segment N Y/N N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Len,seg, inc (mi) -- -- Exit ramp Distance from end milepost to upstream exit ramp gore Xe, ext (mi) 0.85 0.85 If ramp exit is in the segment, enter 0.0. Presence of speed-change lane in segment N Y/N N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Lex,seg, inc (mi) -- -- Weave Presence of a Type B weave in segment N Y/N N Y/N If Yes, then enter data in the next two rows. Length of weaving section Lwev, inc (mi) -- -- Length of weaving section in seg. Lwev, seg, inc (mi) -- -- Travel in Decreasing Milepost Direction Ent. ramp Distance from end milepost to upstream entrance ramp gore Xe, ent (mi) 0.85 0.85 If ramp entrance is in the segment, enter 0.0. Presence of speed-change lane in segment N Y/N N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Len,seg, dec (mi) -- -- Exit ramp Distance from begin milepost to downstream exit ramp gore Xb, ext (mi) 0.5 0.5 If ramp exit is in the segment, enter 0.0. Presence of speed-change lane in segment N Y/N N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Lex,seg, dec (mi) -- -- Weave Presence of a Type B weave in segment N Y/N N Y/N If Yes, then enter data in the next two rows. Length of weaving section Lwev, dec (mi) -- -- Length of weaving section in seg. Lwev, seg, dec (mi) -- -- Traffic Data Proportion of AADT during high-volume hours Phv 0.1 0.1 Freeway segment AADT AADTfs (veh/day) 120,000 120,000 AADT of entrance ramp for travel in increasing milepost direction AADTb,ent (veh/day) 8,000 8,000 AADT of exit ramp for travel in increasing milepost direction AADTe,ext (veh/day) 7,150 7,150 AADT of entrance ramp for travel in decreasing milepost direction AADTe,ent (veh/day) 6,750 6,750 AADT of exit ramp for travel in decreasing milepost direction AADTb,ext (veh/day) 7,675 7,675

505 Table 18-48. Freeway Segment Worksheet (3 of 4)—Sample Problem 5 Crash Modification Factors Fatal and Injury Property Damage Only Complete the study year column. Complete the crash period column if the EB Method is used. Multiple Vehicle Single Vehicle Multiple Vehicle Single Vehicle Equation Crash Period Study Year Crash Period Study Year Crash Period Study Year Crash Period Study Year Horizontal curve CMF1, fs, ac, y, z 18-24 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Lane width CMF2, fs, ac, y, fi 18-25 1.000 1.000 1.000 1.000 Inside shoulder width CMF3, fs, ac, y, z 18-26 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Median width CMF4, fs, ac, y, z 18-27 1.062 1.062 0.980 0.980 1.060 1.060 1.060 1.060 Median barrier CMF5, fs, ac, y, z 18-28 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 High volume CMF6, fs, ac, y, z 18-29 1.036 1.036 0.993 0.993 1.029 1.029 0.941 0.941 Lane change CMF7, fs, ac, mv, z 18-30 1.000 1.000 1.000 1.000 Outside shoulder width CMF8, fs, ac, sv, z 18-35 1.000 1.000 1.000 1.000 Shoulder rumble strip CMF9, fs, ac, sv, fi 18-36 1.000 1.000 Outside clearance CMF10, fs, ac, sv, fi 18-38 1.000 1.000 Outside barrier CMF11, fs, ac, sv, z 18-39 1.000 1.000 1.000 1.000 Combined CMF (multiply all CMFs evaluated) 1.100 1.100 0.973 0.973 1.091 1.091 0.997 0.997 Expected Average Crash Frequency a Fatal and Injury Property Damage Only Complete the study year column. Complete the crash period column if the site-specific EB Method is used. Multiple Vehicle Single Vehicle Multiple Vehicle Single Vehicle Crash Period Study Year Crash Period Study Year Crash Period Study Year Crash Period Study Year Calibration factor Cfs, ac, y, z 1.00 1.00 1.00 1.00 Overdispersion parameter kfs, n, y, z 0.076 0.044 0.071 0.064 Observed crash count N*o, fs, n, y, z (cr) 10 4 14 12 Reference year r 2009 2009 2009 2009 Predicted average crash freq. for reference year Np, fs, n, y, z, r (cr/yr) 3.911 2.060 9.568 5.099 Predicted number of crashes for crash period (sum all years) N*p, fs, n, y, z (cr) 3.911 2.060 9.568 5.099 Equivalent years associated with crash count Cb, fs, n, y, z, r (yr) 2 2 2 2 Adjusted average crash freq. for ref. year given N*o, Na, fs, n, y, z, r (cr/yr) 4.316 2.050 8.090 5.456 Study year s 2011 2011 2011 2011 Predicted average crash freq. for study year Np, fs, n, y, z, s (cr/yr) 3.911 2.060 9.568 5.099 Expected average crash freq. for study year Ne, fs, n, y, z, s (cr/yr) 4.316 2.050 8.090 5.456 Expected average crash freq. for study year (all crash types) Ne, fs, n, at, z, s (cr/yr) 6.367 13.546 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”.

506 Table 18-49. Freeway Segment Worksheet (4 of 4)—Sample Problem 5 Expected Average Crash Frequency a Crash Severity Distribution K A B C Total FI PDO Total FI + PDO Proportion by injury level 0.020 0.050 0.336 0.594 1.000 Expected average crash freq. for study year (all crash types) Ne, fs, n, at, z, s (cr/yr) 0.127 0.317 2.138 3.784 6.367 13.546 19.912 Crash Type Distribution Fatal and Injury Property Damage Only Total Crash Type Category Proportion Expected Average Crash Frequency for Study Year Ne, fs, n, y, fi, s (cr/yr) Proportion Expected Average Crash Frequency for Study Year Ne, fs, n, y, pdo, s (cr/yr) Expected Average Crash Frequency for Study Year Ne, fs, n, y, as, s (cr/yr) Table Multiple-Vehicle Crashes 18-6 Head-on 0.008 0.035 0.002 0.016 0.051 Right-angle 0.031 0.134 0.018 0.146 0.279 Rear-end 0.750 3.237 0.690 5.582 8.819 Sideswipe 0.180 0.777 0.266 2.152 2.929 Other multiple-vehicle crashes 0.031 0.134 0.024 0.194 0.328 Total 1.000 4.316 1.000 8.090 12.406 Single-Vehicle Crashes 18-8 Crash with animal 0.004 0.008 0.022 0.120 0.128 Crash with fixed object 0.722 1.480 0.716 3.907 5.387 Crash with other object 0.051 0.105 0.139 0.758 0.863 Crash with parked vehicle 0.015 0.031 0.016 0.087 0.118 Other single-vehicle crashes 0.208 0.427 0.107 0.584 1.010 Total 1.000 2.050 1.000 5.456 7.507 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”. 18.13.6. Sample Problem 6 The Project A project of interest consists of two sites located on a six-lane urban freeway: a tangent segment and a segment with a horizontal curve. (This project is a compilation of freeway segments from Sample Problems 1 and 2.) The Question What is the expected crash frequency of the project for a particular year incorporating both the predicted crash frequencies from Sample Problems 1 and 2 and the observed crash frequencies using the project- level EB Method?

507 The Facts The study year is 2011. The conditions present during this year are provided in the following list.  2 freeway segments—segment 1 (tangent), segment 2 (curved)  Crash period is 2009 and 2010  Use the same AADT volumes for 2009 to 2011  30 observed fatal-and-injury crashes and 50 observed property-damage-only crashes (but no information is available to attribute specific crashes to specific sites) Outline of Solution To calculate the expected crash frequency, the observed crash frequency for the project as a whole is combined with predicted crash frequency for the project. The predicted crash frequency for the project is based on the sum of the predicted crash frequency for each site within the project. The project-level EB Method presented in Section B.2.5 of Appendix B to Part C is used for this purpose. Results The expected average crash frequency for the project is 13.9 fatal-and-injury crashes per year and 27.1 property-damage-only crashes per year (rounded to one decimal place). Steps Step 1—Sum the predicted average crash frequency and observed crash counts. The predicted average crash frequencies for segments 1 and 2 were computed in Sample Problems 1 and 2, respectively. For freeway segments, separate values are obtained for multiple-vehicle and single- vehicle crashes, and for fatal-and-injury and property-damage-only crashes. The following values were obtained:  Segment 1  Np, fs, 6, mv, fi, r = 3.911 crashes/year  Np, fs, 6, sv, fi, r = 2.060 crashes/year  Np, fs, 6, mv, pdo, r = 9.568 crashes/year  Np, fs, 6, sv, pdo, r = 5.099 crashes/year  Segment 2  Np, fs, 6, mv, fi, r = 4.150 crashes/year  Np, fs, 6, sv, fi, r = 2.858 crashes/year  Np, fs, 6, mv, pdo, r = 10.530 crashes/year  Np, fs, 6, sv, pdo, r = 6.454 crashes/year  All fatal-and-injury crashes: Np, aS, ac, at, fi, r = 12.979 crashes/year

508  All property-damage-only crashes: Np, aS, ac, at, pdo, r = 31.651 crashes/year The crash period is two years, and the same AADT volumes were used for the two years. Hence, the predicted numbers of crashes in the crash period are simply double the predicted average crash frequency. That is:  All fatal-and-injury crashes: N*p, aS, ac, at, fi = 25.958 crashes/year  All property-damage-only crashes: N*p, aS, ac, at, pdo = 63.302 crashes/year The observed crash counts were given as 30 fatal-and-injury crashes and 50 property-damage-only crashes in the years 2009 and 2010. That is:  N*o, aS, ac, at, fi = 30 crashes/year  N*o, aS, ac, at, pdo = 50 crashes/year Step 2—Compute the variance of the predicted average crash frequency. Two variance estimates are computed in this step. One estimate is based on the assumption that the sites are independent and the other estimate is based on the assumption that the sites are perfectly correlated. Equation B-11 and Equation B-12 are used for these computations. The overdispersion parameters kfs, 6, mv, fi and kfs, 6, sv, fi were computed in Sample Problem 5 as 0.076 and 0.044, respectively. The two variance estimates for fatal-and-injury crashes are computed as follows. Assuming independence: ( ) ( ) ( ) ( ) 053.12 858.22044.0150.42076.0060.22044.0911.32076.0 2222 2 ,,6,,,,6,,,,,0 = ××+××+××+××=         ×=   sites all i types crash all k n j fiatfspfiatfsfiatacfs c NkV Assuming perfect correlation: ( ) ( ) ( ) ( ) 346.42 858.22044.0150.42076.0 060.22044.0911.32076.0 2 22 22 2 2 ,,6,,,,6,,,,,1 =         ××+××+ ××+×× =                     ×=    sites all i types crash all k n j fiatfspfiatfsfiatacfs c NkV Similar calculations using the property-damage-only crash frequencies and counts yield the following results.

509 Assuming independence: 858.74,,,,0 =pdoatacfsV Assuming perfect correlation: 531.274,,,,1 =pdoatacfsV Step 3—Compute the weighted adjustment factor. Two weighted adjustment factors are computed in this step. One estimate is based on the assumption that the sites are independent and the other estimate is based on the assumption that the sites are perfectly correlated. Equation B-13 and Equation B-14 are used for these computations. The two weighted adjustment factor estimates for fatal-and-injury crashes are computed as follows. Assuming independence: 683.0 958.25 053.120.1 0.1 0.1 0.1 ,,,, * ,,,,0 ,,,,0 = + = + = fiatacfsp fiatacfs fiatacfs N V w Assuming perfect correlation: 380.0 958.25 346.420.1 0.1 0.1 0.1 ,,,, * ,,,,1 ,,,,1 = + = + = fiatacfsp fiatacfs fiatacfs N V w Similar calculations using the property-damage-only variances yield the following results. Assuming independence: 458.0,,,,0 =pdoatacfsw Assuming perfect correlation: 187.0,,,,1 =pdoatacfsw Step 4—Compute the equivalent years in the crash period. The crash period is two years, and the same AADT volumes were used for the two years. Hence, the number of equivalent years in the crash period is 2.000.

510 Step 5—Compute the expected average crash frequency. The expected average fatal-and-injury crash frequency for the reference year (2009) is computed as follows. Assuming independence: ( ) ( ) arcrashes/ye619.13 2 30683.00.1979.12683.0 0.1 ,,,,, ,,,,, * ,,,,0,,,,,,,,,0,,,,,0 = ×−+×= ×−+×= rfiatacfsb rfiatacfso fiatacfsrfiatacfspfiatacfsrfiatacfs C NwNwN Assuming perfect correlation: ( ) ( ) arcrashes/ye232.14 2 30380.00.1979.12380.0 0.1 ,,,,, ,,,,, * ,,,,1,,,,,,,,,1,,,,,1 = ×−+×= ×−+×= rfiatacfsb rfiatacfso fiatacfsrfiatacfspfiatacfsrfiatacfs C NwNwN Expected average fatal-and-injury crash frequency: arcrashes/ye926.13 2 232.14619.13 2 ,,,,,1,,,,,0 ,,,,, = += + = rfiatacfsrfiatacfsrfiatacfse NN N Similar calculations yield the expected average property-damage-only crash frequency: arcrashes/ye147.27,,,,, =rpdoatacfseN Worksheets To apply the project-level EB Method to multiple freeway segments and speed-change lanes on a freeway combined, two worksheets are provided for determining the expected average crash frequency. The two worksheets include:  Table 18-50. Project-Level EB Method Worksheet (1 of 2)—Sample Problem 6  Table 18-51. Project-Level EB Method Worksheet (2 of 2)—Sample Problem 6 Filled versions of these worksheets are provided below for fatal-and-injury crashes. The same worksheets would be used for property-damage-only crashes, but are not shown. Blank versions of worksheets used in the Sample Problems are provided in Appendix 18A.

511 Table 18-50 is a summary of the predicted average crash frequencies for segments 1 and 2 that were obtained in Sample Problems 1 and 2. It also contains calculations of the variances of the predicted average crash frequencies. Table 18-51 is a summary of the expected average crash frequency calculations. These calculations involve applying weights to the predicted average crash frequencies (based on their variances) and their observed crash counts to obtain a refined estimate of expected average crash frequency. Table 18-50. Project-Level EB Method Worksheet (1 of 2)—Sample Problem 6 Calculations by Site Crash severity category addressed z X FI PDO Site Summary b Total Site type and number a F1 F2 Overdispersion Parameter c (1) Multiple-vehicle crashes kw, x, mv, z 0.076 0.076 (2) Single-vehicle crashes kw, x, sv, z 0.044 0.044 (3) All crash types kw, x, at, z Predicted Number of Crashes during the Crash Period c (4) Multiple-vehicle crashes N*p, w, x, mv, z (cr) 7.8 8.3 16.1 (5) Single-vehicle crashes N*p, w, x, sv, z (cr) 4.1 5.7 9.8 (6) All crash types N*p, w, x, at, z (cr) Predicted number of crashes N*p, aS, ac, at, z (cr) = (4) + (5) + (6) 26.0 Predicted Average Crash Frequency for Reference Year c (7) Multiple-vehicle crashes Np, w, x, mv, z, r (cr/yr) 3.9 4.2 8.1 (8) Single-vehicle crashes Np, w, x, sv, z, r (cr/yr) 2.1 2.9 4.9 (9) All crash types Np, w, x, at, z, r (cr/yr) Predicted freq. for reference year Np, aS, ac, at, z, r (cr/yr) = (7) + (8) + (9) 13.0 Predicted Average Crash Frequency for Study Year c (10) Multiple-vehicle crashes Np, w, x, mv, z, s (cr/yr) 3.9 4.2 8.1 (11) Single-vehicle crashes Np, w, x, sv, z, s (cr/yr) 2.1 2.9 4.9 (12) All crash types Np, w, x, at, z, s (cr/yr) Predicted freq. for study year Np, aS, ac, at, z, s (cr/yr) = (10) + (11) + (12) 13.0 Variance of Predicted Average Crash Frequency c (13) Multiple-vehicle product [= (1) × (4)2] 4.7 5.2 (14) Single-vehicle product [= (2) × (5)2] 0.7 1.4 (15) All crash types [= (3) × (6)2] Variance if independent V0, aS, ac, at, z = (13) + (14) + (15) 12.1 (16) Multiple-vehicle product [= (1) 0.5 × (4)] 2.15 2.29 (17) Single-vehicle product [= (2) 0.5 × (5)] 0.86 1.20 (18) All crash types [= (3) 0.5 × (6)] Variance if correlated V1, aS, ac, at, z = [(16) + (17) + (18)]2 42.3 Notes: a Site numbering convention: X,y. X: site type; F = freeway segment, R = ramp segment, C = C-D road segment, T = crossroad ramp terminal. y: site number; 1, 2, 3, ... b Use additional sheets if there are more than nine sites in the project limits. c Use the “multiple-vehicle” and “single-vehicle” rows for segments. Use the “all crash types” rows for speed-change lanes and crossroad ramp terminals.

512 Table 18-51. Project-Level EB Method Worksheet (2 of 2)—Sample Problem 6 Calculations for Project Crash Period Study Year Observed crash count during the crash period N*o, aS, ac, at, z (cr) 30 Include crashes of all types at all sites during the crash period. Reference year r 2009 Choose the first year of the crash period. Predicted average crash freq. for reference year Np, aS, ac, at, z, r (cr/yr) 12.979 Predicted number of crashes for crash period (sum all years) N*p, aS, ac, at, z (cr) 25.958 Equivalent years associated with crash count Cb, aS, ac, at, z, r (yr) 2.000 = N *p, aS, ac, at, z /Np, aS, ac, at, z, r Independent Sites Crash Analysis Variance if independent V0, aS, ac, at, z 12.053 Weight associated with Np,..., r w0, aS, ac, at, z 0.683 = 1.0 /(1.0 + V0, aS, ac, at, z /N*p, aS, ac, at, z) Adjusted average crash freq. for reference year given N*o, N0, aS, ac, at, z, r 13.619 = w0, aS, ac, at, z × Np, aS, ac, at, z, r + (1.0 − w0, aS, ac, at, z) × N*o, aS, ac, at, z /Cb, aS, ac, at, z, r Correlated Sites Crash Analysis Variance if correlated V1, aS, ac, at, z 42.346 Weight associated with Np,..., r w1, aS, ac, at, z 0.380 = 1.0 /(1.0 + V1, aS, ac, at, z /N*p, aS, ac, at, z) Adjusted average crash freq. for reference year given N*o, N1, aS, ac, at, z, r 14.232 = w1, aS, ac, at, z × Np, aS, ac, at, z, r + (1.0 − w1, aS, ac, at, z) × N*o, aS, ac, at, z /Cb, aS, ac, at, z, r Expected Average Crash Frequency Adjusted average crash freq. for reference year given N*o, Na, aS, ac, at, z, r (cr/yr) 13.926 = (N0, aS, ac, at, z, r + N1, aS, ac, at, z, r)/2.0 Study year s 2011 Predicted average crash freq. for study year Np, aS, ac, at, z, s (cr/yr) 12.979 Expected average crash freq. for study year Ne, aS, ac, at, z, s (cr/yr) 13.926 = Na, aS, ac, at, z, r × Np, aS, ac, at, z, s /Np, aS, ac, at, z, r 18.14. REFERENCES (1) Bonneson, J., S. Geedipally, M. Pratt, and D. Lord. Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges. Final Report. NCHRP Project 17-45. Texas Transportation Institute, College Station, Texas, 2012. http://apps.trb.org/cmsfeed/TRBNetProjectDisplay.asp?ProjectID=2512 (2) AASHTO. Roadside Design Guide. American Association of State Highway and Transportation Officials, Washington, D.C. 2011.

513 APPENDIX 18A—WORKSHEETS FOR PREDICTIVE METHOD FOR FREEWAYS Freeway Segment Worksheet (1 of 4) General Information Location Information Analyst Roadway Agency or company Roadway section Date performed Study year Area type Urban Rural Input Data Crash Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Crash data time period First year Last year Count of multiple-vehicle FI crashes N*o, fs, n, mv, fi Count of single-vehicle FI crashes N*o, fs, n, sv, fi Count of multiple-vehicle PDO crashes N*o, fs, n, mv, pdo Count of single-vehicle PDO crashes N*o, fs, n, sv, pdo Basic Roadway Data Number of through lanes n Same value for crash period and study year. Segment length L (mi) Alignment Data Horizontal Curve Data 1 Presence of horizontal curve 1 Y/N Y/N If Yes, then enter data in the next three rows. Equivalent curve radius R1* (ft) Length of curve Lc1 (mi) Length of curve in segment Lc1, seg (mi) 2 Presence of horizontal curve 2 Y/N Y/N If Yes, then enter data in the next three rows. Equivalent curve radius R2* (ft) Length of curve Lc2 (mi) Length of curve in segment Lc2, seg (mi) Cross Section Data Lane width Wl (ft) Outside shoulder width Ws (ft) Inside shoulder width Wis (ft) Median width Wm (ft) Presence of rumble strips on outside shoulder Y/N Y/N If Yes, then enter data in the next two rows. Length of rumble strip in increasing milepost dir. (mi) Length of rumble strip in decreasing milepost dir. (mi) Presence of rumble strips on inside shoulder Y/N Y/N If Yes, then enter data in the next two rows. Length of rumble strip in increasing milepost dir. (mi) Length of rumble strip in decreasing milepost dir. (mi) Presence of barrier in median Y/N Y/N If Yes, then use the freeway barrier worksheet.

514 Freeway Segment Worksheet (2 of 4) Input Data Roadside Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Clear zone width Whc (ft) Presence of barrier on roadside Y/N Y/N If Yes, then use the freeway barrier worksheet. Ramp Access Data Travel in Increasing Milepost Direction Ent. ramp Distance from begin milepost to upstream entrance ramp gore Xb, ent (mi) If ramp entrance is in the segment, enter 0.0. Presence of speed-change lane in segment Y/N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Len,seg, inc (mi) Exit ramp Distance from end milepost to upstream exit ramp gore Xe, ext (mi) If ramp exit is in the segment, enter 0.0. Presence of speed-change lane in segment Y/N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Lex,seg, inc (mi) Weave Presence of a Type B weave in segment Y/N Y/N If Yes, then enter data in the next two rows. Length of weaving section Lwev, inc (mi) Length of weaving section in seg. Lwev, seg, inc (mi) Travel in Decreasing Milepost Direction Ent. ramp Distance from end milepost to upstream entrance ramp gore Xe, ent (mi) If ramp entrance is in the segment, enter 0.0. Presence of speed-change lane in segment Y/N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Len,seg, dec (mi) Exit ramp Distance from begin milepost to downstream exit ramp gore Xb, ext (mi) If ramp exit is in the segment, enter 0.0. Presence of speed-change lane in segment Y/N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Lex,seg, dec (mi) Weave Presence of a Type B weave in segment Y/N Y/N If Yes, then enter data in the next two rows. Length of weaving section Lwev, dec (mi) Length of weaving section in seg. Lwev, seg, dec (mi) Traffic Data Proportion of AADT during high-volume hours Phv Freeway segment AADT AADTfs (veh/day) AADT of entrance ramp for travel in increasing milepost direction AADTb,ent (veh/day) AADT of exit ramp for travel in increasing milepost direction AADTe,ext (veh/day) AADT of entrance ramp for travel in decreasing milepost direction AADTe,ent (veh/day) AADT of exit ramp for travel in decreasing milepost direction AADTb,ext (veh/day)

515 Freeway Segment Worksheet (3 of 4) Crash Modification Factors Fatal and Injury Property Damage Only Complete the study year column. Complete the crash period column if the EB Method is used. Multiple Vehicle Single Vehicle Multiple Vehicle Single Vehicle Equation Crash Period Study Year Crash Period Study Year Crash Period Study Year Crash Period Study Year Horizontal curve CMF1, fs, ac, y, z 13-24 Lane width CMF2, fs, ac, y, fi 13-25 Inside shoulder width CMF3, fs, ac, y, z 13-26 Median width CMF4, fs, ac, y, z 13-27 Median barrier CMF5, fs, ac, y, z 13-28 High volume CMF6, fs, ac, y, z 13-29 Lane change CMF7, fs, ac, mv, z 13-30 Outside shoulder width CMF8, fs, ac, sv, z 13-35 Shoulder rumble strip CMF9, fs, ac, sv, fi 13-36 Outside clearance CMF10, fs, ac, sv, fi 13-38 Outside barrier CMF11, fs, ac, sv, z 13-39 Combined CMF (multiply all CMFs evaluated) Expected Average Crash Frequency a Fatal and Injury Property Damage Only Complete the study year column. Complete the crash period column if the site-specific EB Method is used. Multiple Vehicle Single Vehicle Multiple Vehicle Single Vehicle Crash Period Study Year Crash Period Study Year Crash Period Study Year Crash Period Study Year Calibration factor Cfs, ac, y, z Overdispersion parameter kfs, n, y, z Observed crash count N*o, fs, n, y, z (cr) Reference year r Predicted average crash freq. for reference year Np, fs, n, y, z, r (cr/yr) Predicted number of crashes for crash period (sum all years) N*p, fs, n, y, z (cr) Equivalent years associated with crash count Cb, fs, n, y, z, r (yr) Adjusted average crash freq. for ref. year given N*o, Na, fs, n, y, z, r (cr/yr) Study year s Predicted average crash freq. for study year Np, fs, n, y, z, s (cr/yr) Expected average crash freq. for study year Ne, fs, n, y, z, s (cr/yr) Expected average crash freq. for study year (all crash types) Ne, fs, n, at, z, s (cr/yr) Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”.

516 Freeway Segment Worksheet (4 of 4) Expected Average Crash Frequency a Crash Severity Distribution K A B C Total FI PDO Total FI + PDO Proportion by injury level 1.000 Expected average crash freq. for study year (all crash types) Ne, fs, n, at, z, s (cr/yr) Crash Type Distribution Fatal and Injury Property Damage Only Total Crash Type Category Proportion Expected Average Crash Frequency for Study Year Ne, fs, n, y, fi, s (cr/yr) Proportion Expected Average Crash Frequency for Study Year Ne, fs, n, y, pdo, s (cr/yr) Expected Average Crash Frequency for Study Year Ne, fs, n, y, as, s (cr/yr) Table Multiple-Vehicle Crashes 13-6 Head-on Right-angle Rear-end Sideswipe Other multiple-vehicle crashes Total 1.000 1.000 Single-Vehicle Crashes 13-8 Crash with animal Crash with fixed object Crash with other object Crash with parked vehicle Other single-vehicle crashes Total 1.000 1.000 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”.

517 Freeway Speed-Change Lane Worksheet (1 of 3) General Information Location Information Analyst Roadway Agency or company Roadway section Date performed Study year Area type Urban Rural Input Data Crash Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Crash data time period First year Last year Count of speed-change-related FI crashes N*o, sc, x, at, fi Count of speed-change-related PDO crashes N*o,sc,x,at,pdo Basic Roadway Data Number of through lanes n Same value for crash period and study year. Segment length L (mi) Equals the length of the speed-change lane. Configuration Choices: Entrance, Exit Alignment Data Horizontal Curve Data 1 Presence of horizontal curve 1 Y/N Y/N If Yes, then enter data in the next three rows. Curve radius R1 (ft) Length of curve Lc1 (mi) Length of curve in segment Lc1, seg (mi) 2 Presence of horizontal curve 2 Y/N Y/N If Yes, then enter data in the next three rows. Curve radius R2 (ft) Length of curve Lc2 (mi) Length of curve in segment Lc2, seg (mi) Cross Section Data Lane width Wl (ft) Inside shoulder width Wis (ft) Median width Wm (ft) Presence of barrier in median Y/N Y/N If Yes, then use the freeway barrier worksheet. Entrance or exit side (left- or right-hand side) L/R L/R Traffic Data Proportion of AADT during high-volume hours Phv Freeway segment AADT AADTfs (veh/day) AADT of ramp AADTr (veh/day) Only needed for entrance ramp.

518 Freeway Speed-Change Lane Worksheet (2 of 3) Crash Modification Factors Complete the study year column. Complete the crash period column if the EB Method is used. Fatal and Injury Property Damage Only Equation Crash Period Study Year Crash Period Study Year Horizontal curve CMF1, sc, ac, at, z 13-40 Lane width CMF2, sc, ac, at, fi 13-41 Inside shoulder width CMF3, sc, ac, at, z 13-42 Median width CMF4, sc, ac, at, z 13-43 Median barrier CMF5, sc, ac, at, z 13-44 High volume CMF6, sc, ac, at, z 13-45 Ramp entrance CMF12, sc, nEN, at, z 13-46 Ramp exit CMF13, sc, nEX, at, z 13-47 Combined CMF (multiply all CMFs evaluated) Expected Average Crash Frequency a Complete the study year column. Complete the crash period column if the site-specific EB Method is used. Fatal and Injury Property Damage Only Crash Period Study Year Crash Period Study Year Calibration factor Csc, x, at, z Overdispersion parameter ksc, x, at, z Observed crash count N*o, sc, x, at, z (cr) Reference year r Predicted average crash freq. for reference year Np, sc, x, at, z, r (cr/yr) Predicted number of crashes for crash period (sum all years) N*p, sc, x, at, z (cr) Equivalent years associated with crash count Cb, sc, x, at, z, r (yr) Adjusted average crash freq. for ref. year given N*o, Na, sc, x, at, z, r (cr/yr) Study year s Predicted average crash freq. for study year Np, sc, x, at, z, s (cr/yr) Expected average crash freq. for study year Ne, sc, x, at, z, s (cr/yr) Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”.

519 Freeway Speed-Change Lane Worksheet (3 of 3) Expected Average Crash Frequency a Crash Severity Distribution K A B C Total FI PDO Total FI + PDO Proportion by injury level 1.000 Expected average crash freq. for study year Ne, sc, x, at, z, s (cr/yr) Crash Type Distribution Fatal and Injury Property Damage Only Total Crash Type Category Table 13-10 or 13-12 Proportion Expected Average Crash Frequency for Study Year Ne, sc, x, at, fi, s (cr/yr) Proportion Expected Average Crash Frequency for Study Year Ne, sc, x, at, pdo, s (cr/yr) Expected Average Crash Frequency for Study Year Ne, sc, x, at, as, s (cr/yr) Multiple-Vehicle Crashes Head-on Right-angle Rear-end Sideswipe Other multiple-vehicle crashes Single-Vehicle Crashes Crash with animal Crash with fixed object Crash with other object Crash with parked vehicle Other single-vehicle crashes Total 1.000 1.000 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”.

520 Freeway Barrier Worksheet Input Data Segment length L (mi) Crash period Study year Inside shoulder width Wis (ft) Outside shoulder width Ws (ft) Nearest distance from edge of traveled way to median barrier face (only needed when continuous barrier present and adjacent to one roadbed) Wnear (ft) Inside barrier width Wib (ft) Median width Wm (ft) Distance from edge of traveled way to outside barrier face, increasing milepost direction (only needed when continuous barrier is present) Woff, inc (ft) Distance from edge of traveled way to outside barrier face, decreasing milepost (only needed when continuous barrier is present) Woff, dec (ft) Individual Median Barrier Element Data Barrier Location Length Lib, i (mi) Width from Edge of Traveled Way to Face of Barrier Woff , in, i (ft) Ratio Lib,i/(Woff,in,i– Wis) 1. 2. 3. 4. 5. 6. 7. Sum1 Sum2 Individual Outside Barrier Element Data Barrier Location Length Lob, i (mi) Width from Edge of Traveled Way to Face of Barrier Woff , o, i (ft) Ratio Lob,i/(Woff,o,i–Ws) 1. 2. 3. 4. 5. 6. 7. Sum3 Sum4 Median Barrier Calculations Inside Clearance - Some Barrier Present Proportion of segment length with barrier in median Pib = Sum1 / [2×L] Width from edge of shoulder to barrier face Wicb = Sum1 / Sum2 (ft) Inside Clearance – Full Barrier Present Width from edge of shoulder to barrier face Wicb (ft) For barrier in center of median Wocb = [2×L] / [Sum2 + 2×(2×L – Sum1) / (Wm – 2×Wis – Wib)] For barrier adjacent to one roadbed Wocb = [2×L] / [L/(Wnear–Wis) + Sum2 + (L–Sum1) / (Wm–2×Wis–Wib– Wnear)] Outside Barrier Calculations Outside Clearance - Some Barrier Present Proportion of segment length with barrier in median Pob = Sum3 / [2×L] Width from edge of shoulder to barrier face Wocb = Sum3 / Sum4 (ft) Outside Clearance – Full Barrier Present Width from edge of shoulder to barrier face Wocb = [2×L] / [1.0/(Woff, inc – Ws) + 1.0/(Woff, dec – Ws)] (ft)

521 Project-Level EB Method Worksheet (1 of 2) Calculations by Site Crash severity category addressed z FI PDO Site Summary b Total Site type and number a Overdispersion Parameter c (1) Multiple-vehicle crashes kw, x, mv, z (2) Single-vehicle crashes kw, x, sv, z (3) All crash types kw, x, at, z Predicted Number of Crashes during the Crash Period c (4) Multiple-vehicle crashes N*p, w, x, mv, z (cr) (5) Single-vehicle crashes N*p, w, x, sv, z (cr) (6) All crash types N*p, w, x, at, z (cr) Predicted number of crashes N*p, aS, ac, at, z (cr) = (4) + (5) + (6) Predicted Average Crash Frequency for Reference Year c (7) Multiple-vehicle crashes Np, w, x, mv, z, r (cr/yr) (8) Single-vehicle crashes Np, w, x, sv, z, r (cr/yr) (9) All crash types Np, w, x, at, z, r (cr/yr) Predicted freq. for reference year Np, aS, ac, at, z, r (cr/yr) = (7) + (8) + (9) Predicted Average Crash Frequency for Study Year c (10) Multiple-vehicle crashes Np, w, x, mv, z, s (cr/yr) (11) Single-vehicle crashes Np, w, x, sv, z, s (cr/yr) (12) All crash types Np, w, x, at, z, s (cr/yr) Predicted freq. for study year Np, aS, ac, at, z, s (cr/yr) = (10) + (11) + (12) Variance of Predicted Average Crash Frequency c (13) Multiple-vehicle product [= (1) × (4)2] (14) Single-vehicle product [= (2) × (5)2] (15) All crash types [= (3) × (6)2] Variance if independent V0, aS, ac, at, z = (13) + (14) + (15) (16) Multiple-vehicle product [= (1) 0.5 × (4)] (17) Single-vehicle product [= (2) 0.5 × (5)] (18) All crash types [= (3) 0.5 × (6)] Variance if correlated V1, aS, ac, at, z = [(16) + (17) + (18)]2 Notes: a Site numbering convention: X,y. X: site type; F = freeway segment, R = ramp segment, C = C-D road segment, T = crossroad ramp terminal. y: site number; 1, 2, 3, ... b Use additional sheets if there are more than nine sites in the project limits. c Use the “multiple-vehicle” and “single-vehicle” rows for segments. Use the “all crash types” rows for speed-change lanes and crossroad ramp terminals.

522 Project-Level EB Method Worksheet (2 of 2) Calculations for Project Crash Period Study Year Observed crash count during the crash period N*o, aS, ac, at, z (cr) Include crashes of all types at all sites during the crash period. Reference year r Choose the first year of the crash period. Predicted average crash freq. for reference year Np, aS, ac, at, z, r (cr/yr) Predicted number of crashes for crash period (sum all years) N*p, aS, ac, at, z (cr) Equivalent years associated with crash count Cb, aS, ac, at, z, r (yr) = N *p, aS, ac, at, z /Np, aS, ac, at, z, r Independent Sites Crash Analysis Variance if independent V0, aS, ac, at, z Weight associated with Np,..., r w0, aS, ac, at, z = 1.0 /(1.0 + V0, aS, ac, at, z /N*p, aS, ac, at, z) Adjusted average crash freq. for reference year given N*o, N0, aS, ac, at, z, r = w0, aS, ac, at, z × Np, aS, ac, at, z, r + (1.0 − w0, aS, ac, at, z) × N*o, aS, ac, at, z /Cb, aS, ac, at, z, r Correlated Sites Crash Analysis Variance if correlated V1, aS, ac, at, z Weight associated with Np,..., r w1, aS, ac, at, z = 1.0 /(1.0 + V1, aS, ac, at, z /N*p, aS, ac, at, z) Adjusted average crash freq. for reference year given N*o, N1, aS, ac, at, z, r = w1, aS, ac, at, z × Np, aS, ac, at, z, r + (1.0 − w1, aS, ac, at, z) × N*o, aS, ac, at, z /Cb, aS, ac, at, z, r Expected Average Crash Frequency Adjusted average crash freq. for reference year given N*o, Na, aS, ac, at, z, r (cr/yr) = (N0, aS, ac, at, z, r + N1, aS, ac, at, z, r)/2.0 Study year s Predicted average crash freq. for study year Np, aS, ac, at, z, s (cr/yr) Expected average crash freq. for study year Ne, aS, ac, at, z, s (cr/yr) = Na, aS, ac, at, z, r × Np, aS, ac, at, z, s /Np, aS, ac, at, z, r