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Evaluation of the 13 Controlling Criteria for Geometric Design (2014)

Chapter: Section 4 - Expanded Traffic Operational and Safety Knowledge Concerning the 13 Controlling Criteria

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Suggested Citation:"Section 4 - Expanded Traffic Operational and Safety Knowledge Concerning the 13 Controlling Criteria." National Academies of Sciences, Engineering, and Medicine. 2014. Evaluation of the 13 Controlling Criteria for Geometric Design. Washington, DC: The National Academies Press. doi: 10.17226/22291.
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Suggested Citation:"Section 4 - Expanded Traffic Operational and Safety Knowledge Concerning the 13 Controlling Criteria." National Academies of Sciences, Engineering, and Medicine. 2014. Evaluation of the 13 Controlling Criteria for Geometric Design. Washington, DC: The National Academies Press. doi: 10.17226/22291.
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Suggested Citation:"Section 4 - Expanded Traffic Operational and Safety Knowledge Concerning the 13 Controlling Criteria." National Academies of Sciences, Engineering, and Medicine. 2014. Evaluation of the 13 Controlling Criteria for Geometric Design. Washington, DC: The National Academies Press. doi: 10.17226/22291.
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Suggested Citation:"Section 4 - Expanded Traffic Operational and Safety Knowledge Concerning the 13 Controlling Criteria." National Academies of Sciences, Engineering, and Medicine. 2014. Evaluation of the 13 Controlling Criteria for Geometric Design. Washington, DC: The National Academies Press. doi: 10.17226/22291.
×
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Suggested Citation:"Section 4 - Expanded Traffic Operational and Safety Knowledge Concerning the 13 Controlling Criteria." National Academies of Sciences, Engineering, and Medicine. 2014. Evaluation of the 13 Controlling Criteria for Geometric Design. Washington, DC: The National Academies Press. doi: 10.17226/22291.
×
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Suggested Citation:"Section 4 - Expanded Traffic Operational and Safety Knowledge Concerning the 13 Controlling Criteria." National Academies of Sciences, Engineering, and Medicine. 2014. Evaluation of the 13 Controlling Criteria for Geometric Design. Washington, DC: The National Academies Press. doi: 10.17226/22291.
×
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Suggested Citation:"Section 4 - Expanded Traffic Operational and Safety Knowledge Concerning the 13 Controlling Criteria." National Academies of Sciences, Engineering, and Medicine. 2014. Evaluation of the 13 Controlling Criteria for Geometric Design. Washington, DC: The National Academies Press. doi: 10.17226/22291.
×
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Suggested Citation:"Section 4 - Expanded Traffic Operational and Safety Knowledge Concerning the 13 Controlling Criteria." National Academies of Sciences, Engineering, and Medicine. 2014. Evaluation of the 13 Controlling Criteria for Geometric Design. Washington, DC: The National Academies Press. doi: 10.17226/22291.
×
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Suggested Citation:"Section 4 - Expanded Traffic Operational and Safety Knowledge Concerning the 13 Controlling Criteria." National Academies of Sciences, Engineering, and Medicine. 2014. Evaluation of the 13 Controlling Criteria for Geometric Design. Washington, DC: The National Academies Press. doi: 10.17226/22291.
×
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Suggested Citation:"Section 4 - Expanded Traffic Operational and Safety Knowledge Concerning the 13 Controlling Criteria." National Academies of Sciences, Engineering, and Medicine. 2014. Evaluation of the 13 Controlling Criteria for Geometric Design. Washington, DC: The National Academies Press. doi: 10.17226/22291.
×
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Suggested Citation:"Section 4 - Expanded Traffic Operational and Safety Knowledge Concerning the 13 Controlling Criteria." National Academies of Sciences, Engineering, and Medicine. 2014. Evaluation of the 13 Controlling Criteria for Geometric Design. Washington, DC: The National Academies Press. doi: 10.17226/22291.
×
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Suggested Citation:"Section 4 - Expanded Traffic Operational and Safety Knowledge Concerning the 13 Controlling Criteria." National Academies of Sciences, Engineering, and Medicine. 2014. Evaluation of the 13 Controlling Criteria for Geometric Design. Washington, DC: The National Academies Press. doi: 10.17226/22291.
×
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Suggested Citation:"Section 4 - Expanded Traffic Operational and Safety Knowledge Concerning the 13 Controlling Criteria." National Academies of Sciences, Engineering, and Medicine. 2014. Evaluation of the 13 Controlling Criteria for Geometric Design. Washington, DC: The National Academies Press. doi: 10.17226/22291.
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49 S E C T I O N 4 This section of the report presents the results of research per- formed as part of NCHRP Project 17-53 to expand knowledge of the traffic operational and safety effects of the 13 controlling criteria. These research results have also been incorporated in the summary of traffic operational and safety effects presented in Section 2 of this report. 4.1 Operational Effects of Lane Width on Urban and Suburban Arterials Field studies were conducted to determine the effect of lane width on traffic speeds on urban and suburban arterials using a field study procedure similar to that used by Potts et al. (23, 24). The research team identified lane-width transitions on urban and suburban arterials in three geographic regions of the United States, as shown in Table 50, and collected speed data upstream and downstream of these lane-width transitions for comparison. The wider and narrower road sections were on the same roadway, with essentially the same traffic volume, and were generally located within 2 mi of one another. The driver populations were essentially identical between the measure- ment locations on wider and narrower roadways. In some cases, a signalized intersection was located between the two measure- ment locations, but both measurement locations were located far enough from the signal that the presence of the signal would not influence traffic speeds. During field data collection, speeds of approximately 120 unimpeded vehicles were measured at each upstream and downstream location. Vehicle speeds were measured with lidar-based Kustom ProLaser speed guns. The measurement sites were sufficiently far removed from the lane-width tran- sition that no substantial accelerations or decelerations due to the change in lane width were taking place. Following data collection, four sites in the East region of the United States were excluded from the analysis because field measurements of lane width indicated that the “wide” section of roadway Expanded Traffic Operational and Safety Knowledge Concerning the 13 Controlling Criteria had lane widths less than 11 ft. The research team deter- mined that these should be classified as narrow lanes and that the change in lane width on these sections was actually from narrow to narrower, rather than from wide to narrow. The posted speed limit at the sites used in the analysis ranged from 35 to 45 mph. Lane width and speed statistics based on the 19 pairs of sites on adjacent wide and narrow roadway segments are presented in Table 51, according to geographic region. Average lane width for both narrow and wide sites and the average of their paired differences were calculated across all sites within a geographic region. The statistics for each region were then averaged to obtain overall lane width statistics. Speed statistics were calcu- lated in a similar way and are shown in the right-hand half of Table 51. The pairwise speed differences in mean speeds between nar- row and wide roadway segments were analyzed by means of an analysis of variance (ANOVA) mixed model considering the following factors: lane width (narrow or wide), change sequence (narrow to wide or wide to narrow), and region. The 19 sites were treated as a random blocking factor. All two-way interactions and the three-way interactions were considered as well. The ANOVA results showed that of all the factors and interactions included in the model, only region had a statisti- cally significant effect (p = 0.0001) on the speed change due to lane-width change (this is also evident in the last column of Table 51). A final model to estimate the effect of lane width on speed was evaluated after taking into account the regional effect. Lane width was not statistically significant (p = 0.97). The esti- mated difference in mean speed between wide and narrow lanes across all sites in the three regions is 0.2 mph with a 95-percent confidence interval of -0.96 to 0.99 mph. Thus, the analysis of the speed data collected in this research on pairs of sites on wide and narrow roadway segments shows no statistically significant effect of urban and suburban arte- rial lane width on traffic speed. In fact, the average speed dif- ference between wide and narrow lanes across all three regions

50 is nearly zero. By contrast, previous research conducted by Potts et al. (23, 24) under NCHRP Project 03-72 (which included only five site pairs) found a statistically significant average speed difference of 4 mph between arterials with narrow and wide lanes. No explanation for the difference in results between the research conducted under NCHRP Project 17-53 and previ- ous research has been found, but the reported results of the NCHRP Project 17-53 research are more credible because they are based on a larger sample size and a broad geographical distribution of sites. 4.2 Safety Effects of Lane Width on Urban and Suburban Arterials A further review of available information on the safety effect of lane width was conducted. The HSM does not include any CMF for lane width on urban and suburban arterials. Research conducted by Potts et al. (23, 24) in NCHRP Project 03-72 found that under a broad range of conditions, lane width on urban and suburban arterials has little or no effect on safety. Analysis of geometric design, traffic volume, and accident data collected by Potts et al. found that, with limited exceptions, there is no consistent, statistically significant relationship between lane width and safety for midblock sections of urban and suburban arterials. In general, there is no indication that the use of 10- or 11-ft lanes, rather than 12-ft lanes, for arterial midblock seg- ments leads to increases in crash frequency. There are situations in which use of narrower lanes may provide benefits in traffic operations, pedestrian safety, and/or reduced interference with surrounding development and may provide space for geomet- ric features that enhance safety such as medians or turn lanes. The analysis results indicate that narrow lanes can generally be used to obtain these benefits without compromising safety. Several caveats in the preceding results should be noted. First, the data from one of the two states included in the anal- ysis showed an increase in crash rates for four-lane undivided arterials with lane widths of 10 ft or less, while the data from another state showed an increase in crash rates for four- lane divided arterials with lane widths of 9 ft or less. While the results from each state were not confirmed in data from the other state, the findings indicate that lane widths of 10 ft or less on four-lane undivided arterials and lane widths of 9 ft or less on four-lane divided arterials should be used cau- tiously unless local experience indicates otherwise. Second, lane widths less than 12 ft should be used cautiously where substantial volumes of bicyclists share the road with motor vehicles, unless an alternative facility for bicycles such as a wider curb lane or paved shoulder is provided. Third, lane widths less than 12 ft should be used cautiously on streets with substantial truck and bus volumes; in particular, mirror over- hang from heavy vehicles is an issue where roadside objects are close to the road. Based on the available information, a CMF of 1.0 for a lane width of 10 ft or more on urban and suburban arterials seems Region Site locations Number of sitesa Midwest Kansas City, Missouri Columbia, Missouri St. Louis, Missouri 5 East Raleigh, North Carolina Greensboro, North Carolina Wilson, North Carolina 9b West Phoenix, Arizona 9 a A site is defined as a specific lane-width transition location in one direction of travel. Therefore, if the location was suitable for data collection in both directions of travel, that location provided two study sites. b Four sites determined to be unsuitable for analysis were excluded. Table 50. Number of sites by geographic region for the evaluation of the operational effect of lane width on urban and suburban arterials. Region Number of sites Average lane width (ft) Average lane-width difference (ft) (wide - narrow) Number of speed measurements Average speed (mph) Average difference in mean speed (mph) (wide - narrow) Narrow Wide Narrow Wide Narrow Wide East 5 9.5 12.0 2.5 599 600 41.5 40.6 −0.9 Midwest 5 9.0 11.5 2.5 600 600 38.9 38.6 −0.3 West 9 10.0 12.0 2.0 1,080 1,080 45.1 45.8 0.7 All 19 9.5 11.8 2.3 2,279 2,280 41.8 41.7 −0.1 Table 51. Mean speed difference for pairs of wide and narrow roadway segments on urban and suburban arterials.

51 reasonable, accompanied with design guidance emphasizing the importance of bicycle and heavy vehicle considerations. 4.3 Safety Effects of Bridge Width on Rural Two-Lane Highways Existing guidance suggests that the known safety effects for lane and shoulder width (i.e., the safety effects of lane and shoulder width specified in the HSM) should be applied to bridge width. However, it seems likely that the safety effects of bridge width would be different from the effects of lane and shoulder width on an open roadway section given that, on a bridge, there is always a roadside obstacle (the bridge rail) at the outside edge of the shoulder or just beyond any sidewalk present. Given the high expense associated with widening or replacing a bridge, designers need better information about the safety effects of bridge width. The most appropriate measures to represent the “nar- rowness” of a bridge are the total lane-plus-shoulder width on the bridge (i.e., curb-to-curb or rail-to-rail width) and the difference between the total lane-plus-shoulder width on the bridge and the total lane-plus-shoulder width on the bridge approach. This latter measure is referred to as the bridge-width difference. Using available data from state highway agencies, the National Bridge Inventory (NBI), and the FHWA Highway Safety Information System (HSIS), the research team assem- bled databases for bridges on two-lane highways in California and Washington. The analysis included all bridges on two-lane rural highways except the following: • Bridges longer than 200 ft • One-lane bridges • Bridges with at least one approach that included an inter- section within 500 ft of the bridge • Bridges with approach widths that are not equal to each other (i.e., the approach on one side of the bridge has a differ- ent width than the approach on the other side of the bridge) Summary statistics for the California bridge data included in the analysis, categorized by bridge-width difference, are shown in Table 52. The table also provides the average AADT for the bridges in each bridge-width difference category, the number of crashes that occurred during a 5-year period (2004 to 2008), and the average crash rate for the bridges in each category, presented in terms of crashes per million veh-mi of travel (MVMT). The data in Table 52 indicate that bridges that are only slightly narrower than their approaches experience about the same crash frequency as bridges for which the approach and bridge width are the same. Bridges with bridge-width dif- ference in the range from 2 to 10 ft experience more crashes than bridges with the same approach and bridge widths, while bridges with bridge-width differences greater than 10 ft experi- ence fewer crashes than bridges with the same approach and bridge widths. Total and fatal-and-injury crash frequencies per mile per year were each analyzed using a negative binomial regression model that included AADT and bridge-width differ- ence. The analyses showed that while AADT is highly significant (p < 0.0001), the safety effect of bridge-width difference is not statistically significant either for total crashes (p = 0.14) or for fatal-and-injury crashes (p = 0.20). Summary statistics for the Washington bridge data included in the analysis, categorized by bridge-width difference, are shown in Table 53. The table also provides the average AADT for the bridges in each bridge-width difference category, the number of crashes that occurred during a 5-year period (2004 to 2008), and the average crash rate for the bridges in each category, presented in terms of crashes per MVMT. The differences in crash rates between the bridge-width difference categories for Washington bridges have a pattern that is different from that found for California bridges. How- ever, as in the case of the California bridges, the safety effect of bridge-width difference for Washington bridges is not sta- tistically significant either for total crashes (p = 0.79) or for fatal-and-injury crashes (p = 0.84). In summary, there is no evidence of a statistically signifi- cant effect of bridge-width difference on crash frequency for either total crashes or for fatal-and-injury crashes in either the California or the Washington data, after accounting for the effect of AADT. In fact, for several of the bridge-width difference categories, bridges with widths narrower than the approach width appear to have fewer crashes than bridges with widths equal to the approach widths, although such Bridge-width difference (ft) Number of bridges Number of crashes (2004–2008) Average AADT MVMT (2004–2008) Crash rate (per MVMT) Total Fatal and injury Total Fatal and injury 0 458 546 227 5,394 494 1.11 0.46 > 0 to ≤ 2 50 37 17 4,172 41 0.90 0.41 > 2 to ≤ 5 42 65 24 5,431 45 1.44 0.53 > 5 to ≤ 10 48 63 26 5,130 50 1.26 0.52 > 10 26 19 5 5,945 31 0.61 0.16 Table 52. Summary statistics for selected California bridges on rural two-lane highways.

52 observed differences are not statistically significant. Thus, there is no evidence that there would, in general, be any documentable safety benefit from widening a rural two-lane highway bridge with a roadway narrower than its approach. Additional analyses were conducted to examine possible effects of bridge width and bridge length on the safety effect of bridge-width difference, but no statistically significant effects were found. 4.4 Operational Effects of Horizontal Alignment on Rural Multilane Divided Highways and Urban and Suburban Arterials Field data were collected to investigate the operational effect of horizontal curve radius for rural multilane highways and urban and suburban multilane highways. The number of rural and suburban sites where speed data were collected in each of three regions of the country (the Midwest, the Eastern United States, and the Western United States) is shown in Table 54. Data are available for a total of 28 rural sites and 31 suburban sites. Data collection efforts were similar to those described in Section 4.1 of this report. Speeds of approximately 120 unim- peded vehicles were measured at a position upstream of the curve and a position close to the middle of the curve for each direction of travel. Vehicle speeds were measured with lidar- based Kustom ProLaser speed guns. The upstream measure- ment sites were sufficiently far from the curve entrance that vehicles would not yet have begun to slow for the curve. Descriptive statistics are presented in Table 55 for rural multi- lane highways and in Table 56 for urban and suburban arterials. Models were developed to predict mean vehicle speed on a horizontal curve as a function of the mean vehicle speed on the tangent approach to the curve and the curve radius separately for rural multilane highways and for urban and suburban arte- rials. The pairwise speed differences in mean speeds between tangent approach and curve were analyzed using an ANOVA mixed model without intercept, considering the following fac- tors: inverse of radius, region (East, Midwest, or West), and pres- ence of median (divided or undivided). The sites were treated as a random blocking factor. The interaction between region and presence of median was not included due to missing com- binations. The ANOVA results showed that neither region nor presence of median was statistically significant for either road- way type (p-values ranged from 0.24 to 0.80). The final models included only one statistically significant variable, the inverse of radius (p < 0.0001). The final mean speed model for curves on rural multilane highways is shown in Equation 39; and the model for curves on suburban arterials is shown in Equation 40: • For rural multilane highways, Speed Speed 3,136 R (39)curve approach= − • For urban and suburban arterials, Speed Speed 2,303 R (40)curve approach= − Region Site locations Number of rural curve sitesa Number of suburban curve sitesa Midwest Kansas City metropolitan area, Missouri/Kansas 9 10 East North Carolina and Virginia 9 11 West California and Nevada 10 10 a A site is defined as one direction of travel along a curve. Therefore, if the curve was suitable for data collection in both directions of travel, that location provided two study sites. Table 54. Number of rural and suburban data collection sites for vehicle speeds on horizontal curves by region. Bridge-width difference (ft) Number of bridges Number of crashes (2004–2008) Average AADT MVMT (2004–2008) Crash rate (per MVMT) Total Fatal and injury Total Fatal and injury 0 122 164 66 2,992 76 2.16 0.87 > 0 to ≤ 2 74 84 32 2,906 43 1.95 0.74 > 2 to ≤ 5 48 63 19 2,912 29 2.17 0.66 > 5 to ≤ 10 70 92 37 3,572 53 1.74 0.70 > 10 23 42 15 3,748 19 2.21 0.79 Table 53. Summary statistics for selected Washington bridges on rural two-lane highways.

53 where Speedcurve = Speed of vehicle on horizontal curve (mph) Speedapproach = Speed of vehicle on tangent approaching curve (mph) R = Curve radius (ft) For the rural multilane highway model in Equation 39, the coefficient 3,136 has a standard error of 602.7; for the urban and suburban arterial model in Equation 40, the coefficient 2,303 has a standard error of 268.7. Figure 8 compares the two models. For both models, as the curve radius decreases, the difference between the tangent Site group Mean curve radius (ft) Speed limit range (mph) Mean total lane width (ft) Number of curves Mean tangent speed (mph) Mean curve speed (mph) Mean speed difference (mph) Divided routes East 1,448 35 to 55 23.9 7 50.6 49.3 1.3 West 935 30 to 50 21.2 5 43.5 41.7 1.8 Undivided routes East 841 35 to 45 20.1 3 46.1 42.6 3.5 Midwest 674 35 to 40 23.4 10 40.0 36.8 3.2 West 1,032 35 to 50 23.5 5 44.2 41.0 3.2 Table 56. Mean speeds on tangents and curves for urban and suburban arterials. Site group Mean curve radius (ft) Speed limit range (mph) Mean total lane width (ft) Number of curves Mean tangent speed (mph) Mean curve speed (mph) Mean speed difference (mph) Divided routes East 2,179 55 to 70 23.2 9 62.2 61.0 1.2 Midwest 2,368 65 to 70 23.3 9 66.4 65.6 0.8 West 2,060 60 to 65 22.9 8 65.6 63.4 2.2 Undivided routes West 1,435 55 22.7 2 54.0 50.5 3.5 Table 55. Mean speeds on tangents and curves for rural multilane highways. Figure 8. Comparison of models for speed reduction on horizontal curves on rural multilane highways and urban and suburban arterials.

54 speed and curve speed increases. In other words, drivers have to reduce their speed to navigate the curve more for sharper curves than for flatter curves. This result is consistent with expecta- tions and with previous modeling for rural two-lane highways. In addition, these models tell us that curves on suburban arte- rials must be sharper than curves on rural multilane highways to cause a reduction in speed of a given magnitude. This makes engineering sense given that tangent speeds are lower on subur- ban arterials than on rural multilane highways. 4.5 Safety Effects of Horizontal Alignment on Rural Freeways and Rural Multilane Highways An analysis of horizontal alignment data for rural multilane highways and rural freeways in Washington was conducted to develop relationships between horizontal curve radius and length and crash frequency and severity. This analysis used an approach similar to recent analyses conducted for FHWA by Bauer and Harwood (31). Of the 6,944 mi of roadway in the Washington HSIS data- base, 212.1 mi (3.1 percent) are on rural multilane highways and 466.3 mi (6.7 percent) on rural freeways. Of these, 182.5 mi of rural multilane highways and 432.7 mi of rural freeways were used for analysis. Rural multilane highways and rural freeways with passing or climbing lanes and segments with missing or obviously incorrect alignment data (e.g., overlap- ping curves) were excluded from the study. Of the 182.5 mi of rural multilane highways, rural four-lane undivided high- ways represented only 6.1 mi and were therefore excluded from analysis. Thus safety effects of horizontal alignment were studied for rural four-lane divided highways and rural freeways only. 4.5.1 Descriptive Statistics for Roadway, Exposure, and Crash Data Descriptive statistics for the rural roadway sections avail- able for analysis including roadway length (miles), exposure (MVMT in the 6-year period from 2003 to 2008), crash fre- quencies, and crash rates per MVMT for each horizontal align- ment are shown separately for rural four-lane divided highways and rural freeways in Table 57. Prior to statistical modeling, the parameters of interest were assessed for extreme values (both high and low); this was done using a combination of plots of crash rates per MVMT versus selected parameters and distributions of the individual parameters. The following rules were implemented: • Roadway segments less than 0.01 mi in length were excluded from analysis (such short segments are unlikely to be useful analysis sections.) • Horizontal curves with a curve radius exceeding 11,460 ft were included in the analysis but their radius was set at 11,460 ft. • Horizontal curves with a radius less than 100 ft were included in the analysis but their radius was set at 100 ft, based on guidance in HSM Chapter 10. 4.5.2 Models Developed for Horizontal Curves on Rural Four-Lane Divided Highways and Rural Freeways Separate models were developed for fatal-and-injury and property-damage-only crashes. Tangents served as the base condition in all models. The parameters considered in each model included the following: • AADT (averaged across all 6 years) • Segment length (offset—used to estimate crashes per mile) • Horizontal curve length • Horizontal curve radius The final crash prediction models for fatal-and-injury and property-damage-only crashes for horizontal curves on Horizontal alignment Rural four-lane divided highways Rural freeways ROADWAY LENGTH (MI) Tangent 122.4 306.5 Curve 54.0 126.2 Total 176.4 432.7 EXPOSURE (MVMT) Tangent 3,648 17,534 Curve 1,588 6,825 Total 5,236 24,359 FATAL-AND-INJURY CRASH FREQUENCIES IN 6 YEARS Tangent 865 2,717 Curve 353 1,321 Total 1,218 4,038 PROPERTY-DAMAGE-ONLY CRASH FREQUENCIES IN 6 YEARS Tangent 1,403 5,419 Curve 621 2,405 Total 2,024 7,824 TOTAL CRASH FREQUENCIES IN 6 YEARS Tangent 2,268 8,136 Curve 974 3,726 Total 3,242 11,862 FATAL-AND-INJURY CRASH RATE PER MVMT Tangent 0.237 0.155 Curve 0.222 0.194 PROPERTY-DAMAGE-ONLY CRASH RATE PER MVMT Tangent 0.385 0.309 Curve 0.391 0.352 TOTAL CRASH RATE PER MVMT Tangent 0.622 0.464 Curve 0.614 0.546 Table 57. Descriptive statistics by horizontal alignment type in available data from the Washington HSIS database (2003 to 2008).

55 rural four-lane divided roadways and rural freeways are the following: N exp b b ln AADT b L I b ln 2 5730 R I (41)FI 0 1 2 C HC 3 HC( ) ( ) = + + × + × ×       N exp b b ln AADT b L I b ln 2 5730 R I (42)PDO 0 1 2 C HC 3 HC( ) ( ) = + + × + × ×       where NFI = fatal-and-injury crashes/mi/yr NPDO = property-damage-only crashes/mi/yr AADT = veh/day R = curve radius (ft); missing for tangents IHC = horizontal curve indicator: 1 for horizontal curves; 0 otherwise LC = horizontal curve length (mi); not applicable for tangents ln = natural logarithm function b0, . . . , b3 = regression coefficients The regression results, including the coefficient estimate, dis- persion parameter, standard error, confidence limit, chi-square statistic, and significance level for all statistically significant parameters, are shown as follows: • Fatal-and-injury crashes on rural four-lane divided high- ways in Table 58 • Property-damage-only crashes on rural four-lane divided highways in Table 59 • Fatal-and-injury crashes on rural freeways in Table 60 • Property-damage-only crashes on rural freeways in Table 61 Parameter Estimate Standard error 95% Lower confidence limit 95% Upper confidence limit Chi-square Significance level Intercept –4.19 0.93 –6.02 –2.37 n/a n/a ln(AADT) 0.47 0.10 0.28 0.66 22.48 < .001 Horizontal curve length (mi) –0.87 0.27 –1.39 –0.35 10.20 0.001 ln(2x5730/R) 0.22 0.08 0.07 0.37 7.82 0.005 Dispersion 0.52 0.07 0.40 0.67 n/a n/a Table 58. Fatal-and-injury crash modeling results for horizontal curves on rural four-lane divided highways. Parameter Estimate Standard error 95% Lower confidence limit 95% Upper confidence limit Chi-square Significance level Intercept –5.75 0.81 –7.33 –4.16 n/a n/a ln(AADT) 0.69 0.08 0.52 0.85 61.23 < .001 Horizontal curve length (mi) –0.95 0.23 –1.41 –0.50 15.90 < .001 ln(2x5730/R) 0.26 0.07 0.13 0.39 15.47 < .001 Dispersion 0.44 0.05 0.35 0.56 n/a n/a Table 59. Property-damage-only crash modeling results for horizontal curves on rural four-lane divided highways. Parameter Estimate Standard error 95% Lower confidence limit 95% Upper confidence limit Chi-Square Significance level Intercept –7.56 0.42 –8.39 –6.74 n/a n/a ln(AADT) 0.79 0.04 0.71 0.87 295.13 < .001 Horizontal curve length (mi) –0.40 0.14 –0.68 –0.11 7.55 0.006 ln(2x5730/R) 0.35 0.04 0.27 0.44 62.31 < .001 Dispersion 0.16 0.02 0.13 0.21 n/a n/a Table 60. Fatal-and-injury crash modeling results for horizontal curves on rural freeways.

56 These results imply the following CMFs for horizontal curvature: • For fatal-and-injury crashes on rural four-lane divided highways, CMF exp 0.87L 0.22 ln 2 5730 R (43)C ( )= − + ×  • For property-damage-only crashes on rural four-lane divided highways, CMF exp 0.95L 0.26 ln 2 5730 R (44)C ( )= − + ×  • For fatal-and-injury crashes on rural freeways, CMF exp 0.40L 0.35 ln 2 5730 R (45)C ( )= − + ×  • For property-damage-only crashes on freeways, CMF exp 0.43L 0.28 ln 2 5730 R (46)C ( )= − + ×  Equations 45 and 46 generally provide lower CMF values than Equations 22 through 25. However, because Equations 22 through 25 were developed in a more comprehensive analy- sis and are in the process of being approved for use in the AASHTO Highway Safety Manual (12), Equations 22 through 25 are recommended for use in preference to Equations 45 and 46. 4.6 Safety Effect of Vertical Alignment on Rural Multilane Divided Highways An analysis of vertical alignment data for rural multilane highways in Washington was conducted to develop relation- ships between vertical alignment design parameters and crash frequency and severity for straight grades and vertical curves. The analysis used an approach similar to recent analyses con- ducted for FHWA by Bauer and Harwood (31). The same database that was used in estimating the safety effect of hori- zontal alignment on rural multilane highways in Section 4.5 was also used for this analysis. Crash data were analyzed sepa- rately for straight grades and each of the four types of vertical alignment shown in Figure 5 (see Section 2.7). 4.6.1 Descriptive Statistics for Roadway, Exposure, and Crash Data As discussed previously, only rural four-lane divided high- ways were considered. Descriptive statistics for the rural roadway sections available for analysis including roadway length (miles), exposure (MVMT in the 6-year period from 2003 to 2008), crash frequencies, and crash rates per MVMT for each vertical alignment are shown in Table 62. Parameter Estimate Standard error 95% Lower confidence limit 95% Upper confidence limit Chi-square Significance level Intercept –8.32 0.41 –9.13 –7.52 n/a n/a ln(AADT) 0.93 0.04 0.85 1.01 425.91 < .001 Horizontal curve length (mi) –0.43 0.13 –0.69 –0.16 10.01 0.002 ln(2x5730/R) 0.28 0.04 0.20 0.35 47.78 < .001 Dispersion 0.22 0.02 0.19 0.27 n/a n/a Table 61. Property-damage-only crash modeling results for horizontal curves on rural freeways. Vertical alignment Roadway length (mi) Exposure (MVMT) 6-year crash frequencies Crash rate (per MVMT) Fatal and injury Property damage only Total Fatal and injury Property damage only Total Straight grade 107.6 3,217 740 1,273 2,013 0.230 0.396 0.626 Type 1 Crest 19.9 637 125 229 354 0.196 0.360 0.556 Type 2 Crest 20.1 521 97 162 259 0.186 0.311 0.497 Type 1 Sag 12.8 393 108 177 285 0.275 0.451 0.726 Type 2 Sag 16.0 469 148 183 331 0.316 0.390 0.706 Total 176.4 5,237 1,218 2,024 3,242 n/a n/a n/a Table 62. Descriptive statistics by vertical alignment type in available data from the Washington HSIS database for rural four-lane divided highways (2003 to 2008).

57 Prior to statistical modeling, the parameters of interest were assessed for extreme values (both high and low); this was done using a combination of plots of crash rates per MVMT versus selected parameters and distributions of the individual parameters. The following rules were implemented: • Roadway segments less than 0.01 mi in length were excluded from analysis (such short segments are unlikely to be useful analysis sections) • For Type 1 crest and Type 1 sag vertical curves, segments where both initial (G1) and final (G2) grades were, in abso- lute value, less than 1 percent were excluded (such minor vertical curves are very close to being level) • For Type 2 crest and Type 2 sag vertical curves, segments where A, the algebraic difference between G1 and G2 (equiv- alent to abs [G1 – G2]),was less than 1 percent were excluded (such minor vertical curves are very close to being straight grades) • All records with K exceeding 2,500 were excluded (these are typically long vertical curves with small grade changes and could be classified as straight grades). Key design parameters for vertical curves include the following: • Algebraic difference in grade • Length of curve • Ratio of algebraic difference in grade and length of curve (K), which represents the sharpness of the vertical curve 4.6.2 Models Developed for Vertical Curves on Rural Four-Lane Divided Highways The parameters considered in each model may include the following: • AADT (averaged across all 6 years) • Segment length (offset—used to estimate crashes per mile) • Absolute value of percent grade (straight-grade models only) • Vertical curve length • A, the algebraic difference between the initial and final grades • K, a measure of the sharpness of vertical curvature; K Vertical curve length A = Separate models were developed for straight, crest, and sag vertical curves and for fatal-and-injury and property-damage- only crashes. Level roadway segments (i.e., abs(grade) < 1 per- cent) served as the base condition in all models. Straight-Grade Models on Rural Four-Lane Divided Highways The final crash prediction models for fatal-and-injury and property-damage-only crashes for straight grades on rural four-lane divided roadways are the following: N exp b b ln AADT b L (47)FI 0 1 2 VC[ ]( )= + + N exp b b ln AADT b L b Grade (48)PDO 0 1 2 VC 3[ ]( )= + + + where NFI = fatal-and-injury crashes/mi/yr NPDO = property-damage-only crashes/mi/yr AADT = veh/day LVC = vertical curve length (mi) Grade = absolute value of percent grade for non-level grades; 0 for level grades ln = natural logarithm function b0, . . . , b3 = regression coefficients Note that grade was not significant in the fatal-and-injury crash model (p = 0.22) and was therefore excluded from the model in Equation 47. The regression results, including the coefficient estimate, dispersion parameter, standard error, confidence limit, chi- square-statistic, and significance level for all statistically sig- nificant parameters are shown as follows: • Fatal-and-injury crashes in Table 63 • Property-damage-only crashes in Table 64 Parameter Estimate Standard error 95% Lower confidence limit 95% Upper confidence limit Chi-square Significance level Intercept –7.47 1.10 –9.63 –5.31 n/a n/a ln(AADT) 0.81 0.12 0.59 1.04 46.81 < .001 Vertical curve length (mi) –0.34 0.17 –0.68 –0.01 3.67 0.056 Dispersion 0.60 0.10 0.44 0.83 n/a n/a Table 63. Fatal-and-injury crash modeling results for straight grades on rural four-lane divided highways.

58 It is disappointing that the percent-grade variable was statistically significant in the model for property-damage- only crashes, but not for fatal-and-injury crashes. With this inconsistency, it does not appear that the models presented in Tables 61 and 63 can be used to represent the effect of percent grade on crashes for rural multilane divided highways. Vertical Curve Models for Rural Four-Lane Divided Highways Models including either algebraic difference in grade (A) and vertical curve length (LVC), or simply their ratio, K, in addition to ln(AADT) showed that neither A nor K were sta- tistically significant at the 10-percent significance level, across all vertical curve and crash types. As a result, the final models included ln(AADT) and vertical curve length only. The final crash prediction models for fatal-and-injury and property-damage-only crashes at Type 1 crest, Type 1 sag, Type 2 crest, and Type 2 sag vertical curves on rural four-lane divided highways are the following: N exp b b ln AADT b L (49)FI 0 1 2 VC[ ]( )= + + N exp b b ln AADT b L (50)PDO 0 1 2 VC[ ]( )= + + where NFI = fatal-and-injury crashes/mi/yr NPDO = Property-damage-only crashes/mi/yr AADT = veh/day LVC = vertical curve length (mi) ln = natural logarithm function b0, . . . , b2 = regression coefficients The regression results, including the coefficient estimate, dispersion parameter, standard error, confidence limit, chi- square statistic, and significance level for all statistically significant parameters, are shown in Table 65. The table is organized by crash type within vertical grade type. As neither A nor K was statistically significant in these models, it does not appear that they can be used to predict the effects of verti- cal curve design on crash frequency. 4.7 Safety Effects of Stopping Sight Distance at Crest Vertical Curves on Rural Two-Lane Highways The effect of stopping sight distance on crash frequency and severity for rural two-lane highways was evaluated by comparing the safety performance of vertical curves with stopping sight distance less than AASHTO design criteria to vertical curves with stopping sight distance greater than AASHTO design criteria. The research team reviewed vertical profile data for Type 1 crest vertical curves on rural two-lane highways in Washington using data available from HSIS. Type 1 crest vertical curves are hillcrests with an upgrade on the approach to the crest and a downgrade on the departure road- way (see Figure 5 in Section 2.7). For each Type 1 crest verti- cal curve, the AASHTO stopping sight distance was calculated and compared to the actual stopping sight distance available at each curve to categorize each curve as either greater or less than AASHTO SSD criteria. Each vertical curve was reviewed in videolog data (and a sample was reviewed in the field) to verify the accuracy of the curve length and algebraic difference in grade data used to compute stopping sight distance. The research team also reviewed videolog data for each curve to identify whether there were horizontal curves, intersections, or driveways within or near the vertical curve. In addition to the presence of these features, it was noted whether the feature was hidden from the view of an approaching driver by the presence of the crest vertical curve. Crash data were obtained for each crest vertical curve and for an additional 0.1 mi of roadway at each end of the vertical curve. Observed crash rates per MVMT are shown in Table 66 for Type 1 crest vertical curves with and without horizon- tal curves, intersections, or driveways present. Table 66 also includes basic site descriptives (number of sites and site length), 5-year crash frequencies, average AADT, and expo- sure. Table 67 has a similar format but addresses crash rates for vertical curves with hidden horizontal curves, intersec- tions, or driveways (i.e., curves, intersections, or driveways that are not visible to an approaching driver because of the presence of the crest vertical curve). Crash rates in the top Parameter Estimate Standard error 95% Lower confidence limit 95% Upper confidence limit Chi-square Significance level Intercept –7.77 0.92 –9.57 –5.97 n/a n/a ln(AADT) 0.90 0.10 0.71 1.08 80.42 <.001 Vertical curve length (mi) –0.38 0.15 –0.67 –0.08 5.53 0.019 Abs(Percent grade) 0.11 0.03 0.04 0.18 9.87 0.002 Dispersion 0.47 0.07 0.36 0.62 n/a n/a Table 64. Property-damage-only crash modeling results for straight grades on rural four-lane divided highways.

59 Parameter Estimate Standard error 95% Lower confidence limit 95% Upper confidence limit Chi-square Significance level Fatal-and-Injury Crashes per Mile per Year—Type 1 Crest Vertical Curves and Level Roadways Intercept –6.96 1.40 –9.70 –4.21 n/a n/a ln(AADT) 0.76 0.15 0.48 1.05 25.35 <.001 Vertical curve length (mi) –0.47 0.18 –0.82 –0.12 6.22 0.013 Dispersion 0.68 0.12 0.48 0.97 n/a n/a Property-Damage-Only Crashes per Mile per Year—Type 1 Crest Vertical Curves and Level Roadways Intercept –9.68 1.16 –12.0 –7.41 n/a n/a ln(AADT) 1.11 0.12 0.87 1.34 74.36 <.001 Vertical curve length (mi) –0.46 0.16 –0.77 –0.15 7.29 0.007 Dispersion 0.47 0.08 0.34 0.64 n/a n/a Fatal-and-Injury Crashes per Mile per Year—Type 1 Sag Vertical Curves and Level Roadways Intercept –9.02 1.42 –11.8 –6.23 n/a n/a ln(AADT) 0.99 0.15 0.70 1.28 40.74 <.001 Vertical curve length (mi) –0.54 0.18 –0.88 –0.19 7.91 0.005 Dispersion 0.66 0.12 0.46 0.94 n/a n/a Property-Damage-Only Crashes per Mile per Year—Type 1 Sag Vertical Curves and Level Roadways Intercept –10.8 1.19 –13.1 –8.49 n/a n/a ln(AADT) 1.23 0.12 0.98 1.47 86.15 <.001 Vertical curve length (mi) –0.47 0.16 –0.79 –0.16 7.56 0.006 Dispersion 0.48 0.08 0.34 0.66 n/a n/a Fatal-and-Injury Crashes per Mile per Year—Type 2 Crest Vertical Curves and Level Roadways Intercept –7.18 1.41 –9.94 –4.42 n/a n/a ln(AADT) 0.78 0.15 0.49 1.07 26.12 <.001 Vertical curve length (mi) –0.38 0.18 –0.74 –0.02 3.79 0.052 Dispersion 0.67 0.12 0.46 0.96 n/a n/a Property-Damage-Only Crashes per Mile per Year—Type 2 Crest Vertical Curves and Level Roadways Intercept –8.96 1.13 –11.2 –6.75 n/a n/a ln(AADT) 1.03 0.12 0.80 1.26 66.04 <.001 Vertical curve length (mi) –0.47 0.16 –0.77 –0.16 8.04 0.005 Dispersion 0.44 0.08 0.31 0.63 n/a n/a Fatal-and-Injury Crashes per Mile per Year—Type 2 Sag Vertical Curves and Level Roadways Intercept –8.26 1.49 –11.2 –5.34 n/a n/a ln(AADT) 0.91 0.16 0.60 1.22 31.28 < .001 Vertical curve length (mi) –0.53 0.19 –0.89 –0.16 6.80 0.009 Dispersion 0.77 0.14 0.55 1.09 n/a n/a Property-Damage-Only Crashes per Mile per Year—Type 2 Sag Vertical Curves and Level Roadways Intercept –10.8 1.23 –13.2 –8.37 n/a n/a ln(AADT) 1.22 0.13 0.97 1.47 80.19 < .001 Vertical curve length (mi) –0.43 0.16 –0.76 –0.11 6.18 0.013 Dispersion 0.49 0.08 0.35 0.67 n/a n/a Table 65. Fatal-and-injury and property-damage-only crash modeling results for vertical curves on rural four-lane divided highways.

Feature present Number of sites Combined length (mi) Number of crashes Average AADT Exposure (MVMT) Crash rate (per MVMT) FIa PDOb Total FI PDO Total Stopping sight distance above AASHTO criteria None 52 18.8 30 64 94 3,376 113 0.27 0.57 0.83 Intersection only 17 7.0 12 10 22 1,894 26 0.46 0.38 0.84 Curve only 61 23.3 48 80 128 2,338 105 0.46 0.76 1.22 Driveway only 24 8.2 20 33 53 3,868 62 0.32 0.53 0.85 Either curve or intersection or driveway 162 60.9 178 244 422 3,147 360 0.49 0.68 1.17 All cases combined 214 79.7 208 308 516 3,203 473 0.44 0.65 1.09 Stopping sight distance below AASHTO criteria None 58 16.1 33 29 62 1,651 52 0.64 0.56 1.20 Intersection only 13 3.5 4 16 20 1,956 12 0.33 1.31 1.64 Curve only 83 23.6 49 67 116 1,810 80 0.61 0.83 1.44 Driveway only 18 5.1 12 17 29 2,747 25 0.47 0.67 1.14 Either curve or intersection or driveway 180 51.5 124 186 310 2,285 218 0.57 0.85 1.42 All cases combined 238 67.6 157 215 372 2,131 270 0.58 0.80 1.38 a FI = fatal and injury. b PDO = property damage only. Table 66. Crash summary for Type 1 crest vertical curves by stopping sight distance category and presence of a horizontal curve, intersection, or driveway within or near the vertical curve. Feature present Number of sites Combined length (mi) Number of crashes Average AADT Exposure (MVMT) Crash rate (per MVMT) FIa PDOb Total FI PDO Total Stopping sight distance above AASHTO criteria No features 52 18.8 30 64 94 3,376 113 0.27 0.57 0.83 No hidden features 194 72.5 189 282 471 3,338 449 0.42 0.63 1.05 Hidden intersection only 3 1.1 6 5 11 2,870 6 1.04 0.86 1.83 Hidden curve only 16 5.8 11 21 32 1,766 18 0.62 1.18 1.78 Hidden driveway only 0 -- -- -- -- -- -- -- -- -- Either hidden curve or hidden intersection or hidden driveway 20 7.1 19 26 45 1,887 24 0.79 1.08 1.88 All cases combined 214 79.7 208 308 516 3,203 473 0.44 0.65 1.09 Stopping sight distance below AASHTO criteria No features 58 16.1 33 29 62 1,651 52 0.64 0.56 1.20 No hidden features 185 52.7 114 162 276 2,117 208 0.55 0.78 1.33 Hidden intersection only 1 0.3 3 8 11 14,111 9 0.34 0.91 1.22 Hidden curve only 37 10.2 26 27 53 1,570 30 0.86 0.89 1.75 Hidden driveway only 10 2.9 9 15 24 3,358 18 0.50 0.84 1.34 Either hidden curve or hidden intersection or hidden driveway 53 14.8 43 53 96 2,181 62 0.69 0.86 1.55 All cases combined 238 67.6 157 215 372 2,131 270 0.58 0.80 1.38 a FI = fatal and injury. b PDO = property damage only. Table 67. Crash summary for Type 1 crest vertical curves by stopping sight distance category and presence of a hidden horizontal curve, intersection, or driveway within or near the vertical curve.

61 half of each table are for Type 1 crest vertical curves with stopping sight distance greater than the AASHTO stopping sight distance design criteria, and crash rates in the lower half of each table are for Type 1 crest vertical curves that have stopping sight distance less than the AASHTO design criteria. The data shown in Table 66 indicate that crash rates for all crest vertical curves with stopping sight distance less than AASHTO stopping sight distance criteria are, on average, 27 percent higher than those for all curves with stopping sight distance greater than AASHTO stopping sight distance criteria for vertical curves (1.38 versus 1.09 crashes per million vehicle- miles of travel). Table 67 indicates that for crest vertical curves with stopping sight distance at or above AASHTO criteria but with a horizontal curve, intersection, or driveway present, the crash risk is 41 percent higher than for the base condition with no horizontal curve, intersection, or driveway present (1.17 versus 0.83 crashes per million vehicle-miles of travel). Table 67 shows that, if an intersection, horizontal curve, or driveway is present and the stopping sight distance is less than AASHTO stopping sight distance criteria, the crash rate for a crest vertical curve is 71 percent higher than the base condition (1.42 versus 0.83 crashes per million vehicle-miles of travel). Table 67 also shows that, if the intersection, horizontal curve, or driveway is not visible to opposing drivers until they reach the crest and the stopping sight distance is less than the AASHTO stopping sight distance criteria, the crash rate for a crest vertical curve is 87 percent higher than the base condition with stopping sight distance above AASHTO criteria with no horizontal curves, intersections, or driveways present (1.55 versus 0.83 crashes per million vehicle-miles of travel). These results suggest an influence of stopping sight distance and the presence of fea- tures such as horizontal curves, intersections, and driveways on crash risk. To evaluate the effect of stopping sight distance and other features of crest vertical curves further, the crash frequencies per mile per year for crest vertical curves were analyzed with a negative binomial (NB) regression model that included AADT and the factor indicating whether the stopping sight distance is at, above, or below AASHTO criteria. It should be noted that the length of each study site was calculated as the length of the crest vertical curve plus an additional 0.1 mi at each end of the vertical curve. Prior to analysis, crash fre- quencies were adjusted for the effect of lane width, shoulder width, and shoulder type based on the CMFs used in HSM Chapter 10 (12). Two additional NB regression models were considered: one including a factor that indicates whether a horizontal curve, intersection, or driveway is present, and one indicating whether a horizontal curve, intersection, or drive- way hidden from the view of approaching drivers is present. All regression models were developed separately for fatal- and-injury and property-damage-only crashes. The results of these analyses are discussed next. The first analysis, including only AADT and the AASHTO criteria, showed statistically significant differences in crash frequency between crest vertical curves with stopping sight distance less than the AASHTO stopping sight distance cri- teria and crest vertical curves with stopping sight distance above the AASHTO stopping sight distance criteria. The observed differences were statistically significant for total crashes (p = 0.07) and for fatal-and-injury crashes (p = 0.07). The estimated differences were in the expected direction with 22 percent more total crashes per mi per year and 45 per- cent more fatal-and-injury crashes per mi per year on the crest vertical curves with less stopping sight distance than AASHTO criteria in comparison to the crest vertical curves with stop- ping sight distance at or above AASHTO criteria. The second analysis, however, yielded different results when the presence of horizontal curves, intersections, or driveways hidden by the crest vertical curve was taken into account. In this analysis, the difference between crest vertical curves with limited stopping sight distance and crest vertical curves with stopping sight distance above AASHTO criteria was no lon- ger statistically significant (p = 0.17 for both total crashes and fatal-and-injury crashes), while the variable indicat- ing the presence of hidden horizontal curves, intersections, or driveways was highly statistically significant (p = 0.01 for total crashes and p = 0.02 for fatal-and-injury crashes). The observed effect on crash frequency of the presence of a hid- den horizontal curve, intersection, or driveway was a 43 per- cent increase in crashes per mi per year for total crashes and a 62 percent increase in crashes per mi per year for fatal-and- injury crashes. Further investigation established that the effect on crashes of the difference between crest vertical curves with limited stopping sight distance and crest vertical curves with stopping sight distance at or above AASHTO criteria remained statistically significant at the 10-percent significance level (p = 0.09 for total crashes and p = 0.07 for fatal-and-injury crashes) when the presence of a horizontal curve, intersection, or driveway was considered, but became not statistically sig- nificant only when the presence of a hidden horizontal curve, intersection, or driveway was considered. This finding implies that the presence of a crest vertical curve with stopping sight distance below AASHTO stopping sight distance criteria does not of itself increase crash fre- quency, but does so only when combined with the presence of a horizontal curve, intersection, or driveway hidden by the crest vertical curve. Therefore, there would appear to be little or no benefit from improving a crest vertical curve with limited stopping sight distance on a rural two-lane highway unless there is a horizontal curve, intersection, or driveway present that cannot be seen by an approaching driver because of the presence of the crest vertical curve.

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TRB’s National Cooperative Highway Research Program (NCHRP) Report 783: Evaluation of the 13 Controlling Criteria for Geometric Design describes the impact of the controlling roadway design criteria on safety and operations for urban and rural roads.

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