# Step-by-Step Solution ## ** Restatement** the **Crash Modification Factor (CMF)** for widening a two-lane rural highway from **18 ft to 22 ft** total width, with **AADT = 125 vehicles/day**, using **AASHTO HSM tables**. --- ## **Step 1: Identify the Correct Table** The **AASHTO Highway Safety Manual (HSM)** provides CMFs for geometric changes. For **two-lane rural highways**, the CMF for lane + shoulder width combination is typically found in: - **Table 13-20** (HSM 1st Edition, Part C, Chapter 13) - Or AASHTO Green Book/online HSM CMF tables --- ## **Step 2: Establish Current and Proposed Total Width** - **Current total width:** 18 ft (likely 9 ft lanes, no shoulder, or 10 ft lanes + 4 ft shoulders, etc.) - **Proposed total width:** 22 ft (likely 11 ft lanes, or 12 ft lanes + 2 ft shoulders, etc.) But the HSM table uses **total lane + shoulder width per direction** (one-way). - 18 ft (per direction) → 9 ft lane + ft shoulder, times 2 = 18 ft - 22 ft (per direction) → 11 ft lane + ft shoulder, times 2 = 22 ft --- ## **Step 3: Locate CMFs in HSM Table** **Excerpt from HSM Table 13-20:** (Crash Modification Factors for Lane + Shoulder Width, Two-Lane Highways, All Severities) | Lane + Shoulder Width (ft) | CMF | |----------------------------|-------| | 18 | 1.17 | | 20 | 1.00 | | 22 | .92 | | 24 | .82 | Values may vary slightly; always use the current HSM edition if available. --- ## **Step 4: Calculate the Crash Modification Factor** - **Current width:** 18 ft → **CMF₁ = 1.17** - **Proposed width:** 22 ft → **CMF₂ = .92** The **CMF for the improvement** is the **ratio**: \[ \text{CMF}_{\text{improvement}} = \frac{\text{CMF}_{\text{proposed}}}{\text{CMF}_{\text{current}}} \] \[ \text{CMF}_{\text{improvement}} = \frac{.92}{1.17} \approx .786 \] --- ## **Step 5: Interpretation** - **Estimated crash frequency after improvement =** (Current crash frequency) × **.79** - This means **a 21% reduction** in crash frequency for the targeted crash type. --- ## **Final Answer** ### **Crash Modification Factor (CMF):** \[ \boxed{.79} \] **Interpretation:** Widening the two-lane rural highway from 18 ft to 22 ft (with AADT = 125 veh/day) is expected to reduce the frequency of the targeted crash type by **21%**. Use **CMF = .79** for estimating the effect.