Study guide
9.1 Highway Safety Manual (HSM) Predictive Methodology & Part C Models
Professional Traffic Operations Engineer PTOE
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1 Introduction & PTOE Exam Overview
1.1 The PTOE Credential: Certification Overview & Industry Value 1.2 Core Industry Reference Standards in Traffic Operations 1.3 Study Guide Architecture, Blueprint Alignment & Exam-Day Strategy
2 Domain 1: Traffic Flow Theory & Fundamental Concepts
2.1 Macroscopic Traffic Stream Models & Fundamental Diagram (q = k × u) 2.2 Microscopic Traffic Characteristics & Car-Following Models 2.3 Hydrodynamic Shockwave Analysis & Traffic Queuing Models
3 Domain 1: Highway & Interrupted Flow Capacity Analysis (HCM)
3.1 Basic Freeway Segments & Multilane Highways (HCM 7th Edition) 3.2 Freeway Weaving, Merging, and Diverging Segments 3.3 Signalized Intersection Capacity & Delay Modeling (HCM)
4 Domain 1: Managed Lanes, Transit Priority, TSMO & Travel Demand Management
4.1 Unsignalized Intersections (TWSC, AWSC) & Modern Roundabouts Capacity 4.2 Managed Lanes, HOV/HOT Operations, & Ramp Metering 4.3 Transit Priority & Multimodal Signal Operations (TSP) 4.4 Transportation Systems Management and Operations (TSMO) & Regional ITS 4.5 Travel Demand Management (TDM) & Trip Reduction Strategies
5 Domain 2: Geometric Design Controls, Criteria, & Sight Distance
5.1 Functional Classification, Design Controls, & Context-Sensitive Design 5.2 Sight Distance Principles: Stopping, Decision, & Passing (AASHTO) 5.3 Horizontal Alignment, Curve Radius, & Superelevation Design
6 Domain 2: Roadway Cross-Sections & Access Management
6.1 Vertical Alignment: Tangent Grades, Crest & Sag Vertical Curves 6.2 Roadway Cross-Section Elements & AASHTO Clear Zone Concepts 6.3 Access Management Principles & Driveway Spacing Criteria
7 Domain 2: Intersection & Interchange Geometric Design
7.1 Intersection Channelization, Turn Lane Design, & Storage Length 7.2 Interchange Configurations & Operational Comparisons (Diamond, Cloverleaf, SPUI) 7.3 Diverging Diamond Interchanges (DDI / DCMI) Operational Principles 7.4 Modern Roundabout Geometric Design Elements & Fastest Paths 7.5 Multimodal Geometric Design: Pedestrian Facilities, Bikeways, & ADA
8 Domain 3: Traffic Safety Concepts, Human Factors, & Safe System
8.1 The Safe System Approach & Vision Zero Principles 8.2 Human Factors, Driver Expectancy, & Perception-Reaction Time (PRT) 8.3 Crash Collision Typologies & Statistical Rate Formulations (MEV, MVMT)
9 Domain 3: Highway Safety Manual (HSM) Predictive Methods & EB
9.1 Highway Safety Manual (HSM) Predictive Methodology & Part C Models 9.2 Safety Performance Functions (SPFs) & Crash Modification Factors (CMFs) 9.3 Empirical Bayes (EB) Method & Regression-to-the-Mean (RTM) Correction 9.4 Economic Appraisal of Safety Projects (Benefit-Cost Analysis, NPV)
10 Domain 3: Safety Countermeasures & Road Safety Audits (RSA)
10.1 Roadway Departure Countermeasures (Rumble Strips, Safety Edge, Barriers) 10.2 Intersection Safety Countermeasures (Sight Triangles, Left-Turn Calming, Roundabouts) 10.3 Vulnerable Road User (VRU) Safety Countermeasures (PHB/HAWK, RRFB, Curb Extensions) 10.4 Road Safety Audits (RSAs) & Systemic Safety Analysis
11 Domain 4: Traffic Signal Warrants & Isolated Timing (MUTCD/ITE)
11.1 MUTCD Traffic Signal Warrants (Warrants 1 through 9) 11.2 Signal Phasing Principles & NEMA Dual-Ring Operations 11.3 Clearance Intervals (ITE Kinematic Equations) & Pedestrian Timing Parameters
12 Domain 4: Signal Coordination, Networks, & ATSPMs
12.1 Actuated Signal Controller Parameters (Passage Time, Gap Reduction, Max Recall) 12.2 Traffic Signal Coordination: Bandwidth, Offsets, & Progression Models 12.3 Traffic Responsive & Adaptive Traffic Signal Control Systems (ASCS) 12.4 Automated Traffic Signal Performance Measures (ATSPMs) & High-Resolution Data
13 Domain 4: Signing, Markings, Work Zones, Grade Crossings & School Zones (MUTCD)
13.1 MUTCD Regulatory, Warning, & Guide Signs Principles and Placement 13.2 Sign Retroreflectivity Standards & Nighttime Visual Maintenance 13.3 Longitudinal Pavement Markings, Delineators, & Object Markers 13.4 Temporary Traffic Control (TTC) & Work Zone Safety (MUTCD Part 6) 13.5 Highway-Rail Grade Crossings: Warning Devices, Preemption & Storage 13.6 School Zone Traffic Control & Student Walk Route Planning
14 Domain 5: Traffic Studies & Applied Statistical Methods
14.1 Applied Statistical Distributions & Sample Size Determination 14.2 Spot Speed Studies, 85th Percentile Speed, & 10-mph Pace 14.3 Volume Count Methodologies & Expansion Factoring (ADT, AADT, PHF)
15 Domain 5: Traffic Impact Studies & Trip Generation (ITE)
15.1 Travel Time, Delay, & Intersection Queue Studies 15.2 Parking Supply, Duration, & Turnover Analysis 15.3 Traffic Impact Study (TIS) Scoping, Horizon Years, & Mitigation 15.4 ITE Trip Generation Handbook: Average Rates vs. Regression Equations
16 Domain 6: Environmental, Institutional, Ethics & Equity Issues
16.1 Vehicle Emissions, Air Quality Conformity, & Decarbonization 16.2 Traffic Noise Modeling (TNM) & Noise Abatement Criteria (NAC) 16.3 Long-Range Transportation Planning & the NEPA Environmental Review 16.4 Professional Engineering Ethics, Tort Liability, & Risk Management 16.5 Transportation Equity, Access & Multimodal Community Considerations
9.1 Highway Safety Manual (HSM) Predictive Methodology & Part C Models
Key Takeaways Explain This Topic AI
The HSM Part C predictive methodology calculates predicted average crash frequency N_predicted = N_spf_x × (CMF_1x × CMF_2x × ... × CMF_yx) × C_x, combining baseline Safety Performance Functions with Crash Modification Factors and local jurisdictional calibration.
Part C establishes specialized statistical crash prediction models across four primary facility types: Rural Two-Lane Two-Way Roads (Chapter 10), Rural Multilane Highways (Chapter 11), Urban and Suburban Arterials (Chapter 12), and Freeways and Interchanges (Chapters 18 and 19).
The HSM 18-step predictive workflow provides a standardized protocol from project scoping and homogeneous geometric segmentation through SPF calculation, CMF application, calibration factoring, and Empirical Bayes refinement.
Local calibration factors C_x = Σ N_observed / Σ N_predicted(uncalibrated) adjust national base models for regional climate, animal populations, driver demographics, and state crash reporting thresholds; AASHTO recommends a minimum sample of 30 to 50 sites with at least 100 crashes per year.
Corridor safety analysis evaluates homogeneous roadway segments and intersections independently and aggregates them to determine total facility predicted crash frequency: N_predicted,total = Σ N_predicted,segments + Σ N_predicted,intersections.
Last updated: August 2026
9.1 Highway Safety Manual (HSM) Predictive Methodology & Part C Models
PTOE Exam Focus: The Highway Safety Manual (HSM), published by AASHTO, transitions traffic safety from historical, reactive crash counting to a science-based predictive discipline. Expect quantitative exam problems testing the general Part C predictive formulation N predicted = N spf × ∏ C M F i × C x N_{\text{predicted}} = N_{\text{spf}} \times \prod CMF_i \times C_x N predicted = N spf × ∏ CM F i × C x , facility segmentation criteria, base condition adjustments, and the derivation and application of local calibration factors ( C x C_x C x ).
1. Architecture of the Highway Safety Manual
The Highway Safety Manual is organized into four foundational parts that guide the quantitative safety management lifecycle:
Part A — Fundamentals: Human factors, vehicle dynamics, roadway design interactions, fundamentals of safety analytics, and the role of safety in the project development process.
Part B — Roadway Safety Management Process: Systemic and network-level safety management tools, including Network Screening (identifying sites with potential for improvement), Diagnosis, Countermeasure Selection, Economic Appraisal, Project Prioritization, and Safety Effectiveness Evaluation.
Part C — Predictive Method: Mathematical models (Safety Performance Functions, Crash Modification Factors, and Calibration Procedures) for estimating expected average crash frequency and severity distributions across defined facility types.
Part D — Crash Modification Factors (CMFs): Catalog of documented treatments, geometric modifications, and operational countermeasures with their associated CMFs and standard errors. +-----------------------------------------------------------------------------------------+
- | AASHTO HIGHWAY SAFETY MANUAL ARCHITECTURE |
- +-----------------------------------------------------------------------------------------+
- | Part A: Fundamentals | Human factors, collision fundamentals, safety physics |
- | Part B: Safety Management | Network screening, diagnosis, economic appraisal, B/C |
- | Part C: Predictive Method | Part C models: SPFs + CMFs + Calibration (Ch 10-12, 18)|
- | Part D: CMF Catalog | Quantitative countermeasure library and standard error |
- +-----------------------------------------------------------------------------------------+
- 2. The General Part C Predictive Formulation
The core mathematical engine of HSM Part C estimates the predicted average crash frequency ( N predicted N_{\text{predicted}} N predicted ) for a specific site (roadway segment or intersection) over a defined multi-year study period: N predicted = N spf , x × ( ∏ y = 1 m C M F y x ) × C x N_{\text{predicted}} = N_{\text{spf}, x} \times \left( \prod_{y=1}^{m} CMF_{yx} \right) \times C_x N predicted = N spf , x × ( y = 1 ∏ m CM F y x ) × C x
Where:
N predicted N_{\text{predicted}} N predicted = Predicted average crash frequency for a specific year on site x x x (crashes/year).
N spf , x N_{\text{spf}, x} N spf , x = Predicted average crash frequency for nominal baseline geometric and operational conditions determined from a statistical Safety Performance Function.
C M F y x CMF_{yx} CM F y x = Crash Modification Factor y y y for site x x x , adjusting for specific geometric or operational features that deviate from the nominal baseline condition (e.g., lane width, shoulder width, horizontal curvature, median type, driveway density).
m m m = Total number of applicable Crash Modification Factors for site x x x .
C x C_x C x = Local jurisdictional calibration factor developed by a state DOT or municipal agency to adjust national base models to local environmental, driver behavior, and statutory crash reporting practices.
For a contiguous corridor containing multiple roadway segments and intersections, the total facility predicted crash frequency is the linear sum of all individual components: N predicted, total = ∑ all segments N predicted, segment + ∑ all intersections N predicted, intersection N_{\text{predicted, total}} = \sum_{\text{all segments}} N_{\text{predicted, segment}} + \sum_{\text{all intersections}} N_{\text{predicted, intersection}} N predicted, total = all segments ∑ N predicted, segment + all intersections ∑ N predicted, intersection
3. The 18-Step HSM Predictive Workflow
The HSM establishes a rigorous 18-step protocol for conducting predictive safety analyses: +---------------------------------------------------------------------------------------+
- | THE 18-STEP HSM PREDICTIVE WORKFLOW |
- +----+------------------------------------+----+----------------------------------------+
- | 01 | Define facility and study limits | 10 | Apply local calibration factor (C_x) |
- | 02 | Divide facility into segments/nodes| 11 | Calculate N_predicted for each site |
- | 03 | Determine study period (years) | 12 | Apply crash severity distributions |
- | 04 | Select applicable facility model | 13 | Apply collision type distributions |
- | 05 | Obtain AADT for all elements | 14 | Sum segments and intersections |
- | 06 | Gather geometric and control data | 15 | Determine if observed data exist |
- | 07 | Apply base SPF (N_spf) | 16 | Apply Empirical Bayes (EB) method |
- | 08 | Calculate applicable CMFs | 17 | Assess patterns and design alternatives|
- | 09 | Calculate uncalibrated prediction | 18 | Perform economic appraisal & B/C |
- +----+------------------------------------+----+----------------------------------------+
Detailed Step Progression:
Step 1 — Define Facility & Study Limits: Identify spatial limits, project purpose (e.g., corridor reconstruction, alternative evaluation), and target design years.
Step 2 — Roadway Segmentation: Divide the physical facility into individual homogeneous roadway segments and distinct intersection nodes.
Step 3 — Determine Study Period: Establish the historical or forecast analysis timeframe (individual years or multi-year aggregate).
Step 4 — Select HSM Chapter Model: Match facility type to the appropriate HSM chapter (Chapter 10 for Rural Two-Lane Two-Way, Chapter 11 for Rural Multilane, Chapter 12 for Urban/Suburban Arterials, Chapter 18 for Freeways, Chapter 19 for Ramps).
Step 5 — Traffic Volume Input: Obtain Annual Average Daily Traffic ( A A D T AADT AA D T ) for every segment and all intersection approaches (major and minor street A A D T AADT AA D T ).
Step 6 — Geometric & Operational Data Collection: Compile lane widths, shoulder widths, shoulder types, median configurations, driveway densities, roadside hazard ratings ( R H R RHR R H R ), horizontal curve parameters, grade, lighting, and automated speed enforcement.
Step 7 — Calculate Base SPF Crash Frequency ( N spf N_{\text{spf}} N spf ): Execute the statistical regression equation corresponding to the facility type under base conditions.
Step 8 — Calculate Crash Modification Factors ( C M F 1 , C M F 2 , … , C M F m CMF_1, CMF_2, \dots, CMF_m CM F 1 , CM F 2 , … , CM F m ): Compute each CMF based on how actual site parameters deviate from baseline standards.
Step 9 — Calculate Uncalibrated Site Prediction: Multiply N spf N_{\text{spf}} N spf by the product of all computed CMFs: N uncalibrated = N spf × ∏ C M F i N_{\text{uncalibrated}} = N_{\text{spf}} \times \prod CMF_i N uncalibrated = N spf × ∏ CM F i .
Step 10 — Identify Local Calibration Factor ( C x C_x C x ): Obtain the state DOT calibrated factor C x C_x C x for that specific facility type and year.
Step 11 — Compute Final Predicted Crashes ( N predicted N_{\text{predicted}} N predicted ): Calculate N predicted = N uncalibrated × C x N_{\text{predicted}} = N_{\text{uncalibrated}} \times C_x N predicted = N uncalibrated × C x .
Step 12 — Crash Severity Disaggregation: Apply local or HSM default severity proportions (Fatal K K K , Incapacitating Injury A A A , Non-Incapacitating B B B , Possible Injury C C C , Property Damage Only O O O , or Fatal-and-Injury F I FI F I vs P D O PDO P D O ).
Step 13 — Collision Type Disaggregation: Apportion predicted crashes into collision types (rear-end, angle, sideswipe, run-off-road, head-on, pedestrian/bicycle).
Step 14 — Sum Facility Totals: Aggregate predicted crashes across all segments and intersections.
Step 15 — Check Observed Crash History: Determine whether historical observed crash data ( N observed N_{\text{observed}} N observed ) are available for the study sites.
Step 16 — Apply Empirical Bayes (EB) Method: If historical crash data are available, apply the EB weighting procedure to correct for Regression-to-the-Mean (RTM) bias and estimate expected average crash frequency ( N expected N_{\text{expected}} N expected ).
Step 17 — Evaluate Design Alternatives: Compare baseline versus alternative geometric designs (e.g., widening shoulders vs installing a roundabout).
Step 18 — Conduct Economic Appraisal: Perform Benefit-Cost analysis ( B / C B/C B / C ), Net Present Value ( N P V NPV NP V ), and incremental economic prioritization.
4. Roadway Segmentation Rules
A central practical skill on the PTOE examination is segmenting a roadway corridor into homogeneous analysis units. A new roadway segment must begin whenever any of the following characteristics change along the alignment:
Average Annual Daily Traffic ( A A D T AADT AA D T ): Change in traffic volume (e.g., crossing a major commercial generator or municipal boundary).
Number of Through Lanes: Lane addition, drop, or transition (e.g., 2 lanes to 4 lanes).
Lane Width or Shoulder Width/Type: Physical cross-sectional alteration (e.g., 12-ft lanes narrowing to 11-ft lanes, or 8-ft paved shoulders transitioning to 4-ft gravel).
Median Configuration: Transition between undivided, two-way left-turn lane (TWLTL), or raised divided median.
Horizontal Curvature: Tangent transitioning into a horizontal curve (classified by radius, length, and presence of spiral transitions).
Grade / Vertical Alignment: Change in vertical grade exceeding standard thresholds (e.g., flat ≤ 3 % \le 3\% ≤ 3% , moderate 3 – 6 % 3\text{--}6\% 3 – 6% , steep > 6 % > 6\% > 6% ).
Driveway Density: Significant change in access point density (driveways per mile).
Roadside Hazard Rating ( R H R RHR R H R ): Shift in roadside clear zone, side slope, or obstacle density (rated on a 1–7 visual scale in Chapter 10).
Intersection Influence Area: Roadway segments terminate at the boundary of an intersection influence area, defined by the HSM as extending 250 ft (75 m) along each approach leg from the intersection center (or the physical curb return/queue storage length, whichever is greater).
5. HSM Part C Facility Types & Base Conditions
Each HSM chapter establishes specific baseline geometric conditions for which C M F = 1.00 CMF = 1.00 CMF = 1.00 . Any deviation from baseline requires an explicit CMF calculation.
HSM Chapter Facility Type Nominal Base Conditions ( C M F = 1.00 CMF = 1.00 CMF = 1.00 )
Chapter 10 Rural Two-Lane, Two-Way Roads (2U) 12-ft lane width, 6-ft paved shoulder, R H R = 3 RHR = 3 R H R = 3 , 0 % 0\% 0% grade, tangent alignment (no horizontal curves), 5 driveways/mile, no centerline rumble strips, no passing lanes, no automated speed enforcement
Chapter 11 Rural Multilane Highways (4U, 4D) 12-ft lane width, 8-ft paved shoulder, 30-ft median width (for 4D), 0 % 0\% 0% grade, tangent alignment, R H R = 3 RHR = 3 R H R = 3 , no lighting
Chapter 12 Urban & Suburban Arterials (2U, 3T, 4U, 4D, 5T) 12-ft lane width, 0 driveways/mile, no on-street parking, no roadside fixed objects ( 0 objects/mi 0\text{ objects/mi} 0 objects/mi ), 0-ft clear shoulder, no median (for undivided) or 15-ft raised median (for divided)
Chapter 18/19 Freeways & Ramps 12-ft lanes, 10-ft right shoulder, 4-ft left shoulder, 60-ft median, 0 % 0\% 0% grade, 0.75-mile barrier offset, no weave/ramp influence
6. Local Calibration Factor Formulation ( C x C_x C x )
Because base SPFs were calibrated using multi-state statistical datasets (such as California, Washington, and Texas data from specific historical years), they cannot be applied directly in other jurisdictions without calibration. Differences in crash reporting thresholds, reporting completeness, driver demographics, wildlife populations, winter maintenance, and pavement friction require local calibration.
Calibration Equation: C x = ∑ all sample sites N observed ∑ all sample sites N predicted(uncalibrated) C_x = \frac{\sum_{\text{all sample sites}} N_{\text{observed}}}{\sum_{\text{all sample sites}} N_{\text{predicted(uncalibrated)}}} C x = ∑ all sample sites N predicted(uncalibrated) ∑ all sample sites N observed
Where:
∑ N observed \sum N_{\text{observed}} ∑ N observed = Total number of recorded crashes observed across all sample sites during the calibration period.
∑ N predicted(uncalibrated) \sum N_{\text{predicted(uncalibrated)}} ∑ N predicted(uncalibrated) = Total number of crashes predicted across the same sample sites using the uncalibrated HSM model ( N spf × ∏ C M F i N_{\text{spf}} \times \prod CMF_i N spf × ∏ CM F i ).
AASHTO Sampling Guidelines for Calibration:
Minimum Sample Size: 30 to 50 randomly selected sites for each facility type.
Minimum Total Crashes: The sample must represent at least 100 crashes per year (or 300 crashes over a 3-year study window) to ensure statistical stability.
Unbiased Selection: Sites must be selected randomly across the jurisdiction, not cherry-picked from high-crash locations.
Interpretation:
C x > 1.00 C_x > 1.00 C x > 1.00 : The local jurisdiction experiences more crashes than the national base model predicts (e.g., C x = 1.25 C_x = 1.25 C x = 1.25 indicates local crashes are 25% higher than baseline).
C x < 1.00 C_x < 1.00 C x < 1.00 : The local jurisdiction experiences fewer crashes than the national base model predicts (e.g., C x = 0.85 C_x = 0.85 C x = 0.85 indicates local crashes are 15% lower).
7. Worked PTOE Calculation Example
Problem Statement:
A 2.5-mile rural two-lane highway segment carries an A A D T = 4 , 000 veh/day AADT = 4,000\text{ veh/day} AA D T = 4 , 000 veh/day . The base SPF equation for rural two-lane segments is: N spf = A A D T × L × 365 × 10 − 6 × exp ( − 0.312 ) N_{\text{spf}} = AADT \times L \times 365 \times 10^{-6} \times \exp(-0.312) N spf = AA D T × L × 365 × 1 0 − 6 × exp ( − 0.312 )
Field inspection identifies the following non-base geometric characteristics:
- Lane width: 11 ft ( C M F lw = 1.05 CMF_{\text{lw}} = 1.05 CM F lw = 1.05 )
- Shoulder width: 4 ft gravel ( C M F sw = 1.10 CMF_{\text{sw}} = 1.10 CM F sw = 1.10 )
- Horizontal alignment: Tangent ( C M F c = 1.00 CMF_{\text{c}} = 1.00 CM F c = 1.00 )
- Driveway density: 5 driveways/mi ( C M F d = 1.00 CMF_{\text{d}} = 1.00 CM F d = 1.00 )
Roadside Hazard Rating: R H R = 3 RHR = 3 R H R = 3 ( C M F rhr = 1.00 CMF_{\text{rhr}} = 1.00 CM F rhr = 1.00 )
The state DOT has published a regional calibration factor for rural two-lane highways of C x = 1.20 C_x = 1.20 C x = 1.20 .
Calculate the predicted average annual crash frequency ( N predicted N_{\text{predicted}} N predicted ) for this segment.
Solution:
Base SPF Output ( N spf N_{\text{spf}} N spf ): exp ( − 0.312 ) = 0.7320 \exp(-0.312) = 0.7320 exp ( − 0.312 ) = 0.7320 N spf = 4 , 000 × 2.5 × 365 × 10 − 6 × 0.7320 = 10 , 000 × 0.000365 × 0.7320 = 2.6717 crashes/year N_{\text{spf}} = 4,000 \times 2.5 \times 365 \times 10^{-6} \times 0.7320 = 10,000 \times 0.000365 \times 0.7320 = 2.6717\text{ crashes/year} N spf = 4 , 000 × 2.5 × 365 × 1 0 − 6 × 0.7320 = 10 , 000 × 0.000365 × 0.7320 = 2.6717 crashes/year
Combined Crash Modification Factor ( ∏ C M F i \prod CMF_i ∏ CM F i ): ∏ C M F i = 1.05 × 1.10 × 1.00 × 1.00 × 1.00 = 1.1550 \prod CMF_i = 1.05 \times 1.10 \times 1.00 \times 1.00 \times 1.00 = 1.1550 ∏ CM F i = 1.05 × 1.10 × 1.00 × 1.00 × 1.00 = 1.1550
Uncalibrated Crash Prediction: N uncalibrated = N spf × ∏ C M F i = 2.6717 × 1.1550 = 3.0858 crashes/year N_{\text{uncalibrated}} = N_{\text{spf}} \times \prod CMF_i = 2.6717 \times 1.1550 = 3.0858\text{ crashes/year} N uncalibrated = N spf × ∏ CM F i = 2.6717 × 1.1550 = 3.0858 crashes/year
Final Calibrated Crash Prediction ( N predicted N_{\text{predicted}} N predicted ): N predicted = N uncalibrated × C x = 3.0858 × 1.20 = 3.703 crashes/year N_{\text{predicted}} = N_{\text{uncalibrated}} \times C_x = 3.0858 \times 1.20 = 3.703\text{ crashes/year} N predicted = N uncalibrated × C x = 3.0858 × 1.20 = 3.703 crashes/year
The segment is predicted to experience 3.70 crashes per year .