A Performance-Based Highway Geometric Design Process (2016)

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C-1 Demonstration of Cost-effectiveness Approach to Horizontal Curve Design Policy Horizontal curvature has a proven effect on substantive safety performance and operational performance. This Appendix demonstrates how the knowledge base can be applied to develop a more performance-based approach to geometric design processes and criteria for horizontal cur- vature. For illustrative purposes the focus is on two-lane rural highways, but a similar approach may be applied to other road types and contexts. Safety Performance The AASHTO HSM describes the safety effect of curvature for two-lane rural highways. Crash frequency is a function of the radius of curve, length of curve, and traffic volume. The research team assembled a spreadsheet to describe the predicted, uncalibrated crash frequency using the Chapter 10 model for curvature, with the following assumptions: • 12-foot lane width • 6-foot shoulder width • Paved shoulder • Roadside Hazard Rating of 3 • 5 driveways per mile • Flat vertical alignment • No centerline rumble strips, passing lanes, lighting, or automated speed enforcement • Superelevation within AASHTO policy values • No spiral transitions • Average Daily Traffic ranging from 400 to 17500 vpd Comparison of differing curve designs requires a common section definition. An analysis seg- ment was set consistent with that produced by alignment defined by a 3,000 foot radius curve for a range of central angles, with the greatest being a 90 degree central angle, which produces a curve length of 0.8925 miles. For curves with radii less than 3,000 feet, the same starting and ending points apply (for a given central angle). In other words, when comparing curves using different radii, a comparable section is one defined by the central angle of the curve. An alignment with common starting and ending points and lesser radius would be composed of a combination of tangents and curve, with the tangents increas- ing in length as the radius decreases. Given the geometry of horizontal curves, one can compute the long tangent of the curve, which thus produces the tangent alignment based on the set PC and PT. As the starting and ending points are based on the PC and PT of the 3,000-foot radius, the length of alignment that is tangent within the section is 0, and the length of alignment that is curved is given by the computed curve length for a 3,000-foot radius and given central angle. A p p e n d i x C Horizontal Curve Analysis

C-2 A performance-Based Highway Geometric design process Table C-1 shows the alignment design values for an array of central angles from 15 degrees to 90 degrees. As the curve radius changes, the amount of alignment that is tangent versus curved changes. The implications of this are as follows: • The smaller the radius, the less of the alignment is subject to the effect of curvature on crashes. • The smaller the radius, the longer the total travel distance is (the shortest distance for any central angle is that produced by the greatest radius, in the case here, 3,000 feet). For any given deflection angle, a comparative alignment design thus involves differing tangent and curve lengths based on the radii being compared. For example, comparing a 45 degree cen- tral angle with radii of 500 feet and 1,500 feet yields the following (Figure C-1): • 3,000 foot radius  0.4462 mi. length of curve (PC to PT); 0.0 tangent length; and travel distance of 0.4462 miles. 400 1,000 2,500 4,000 5,500 7,000 8,500 10,000 15 1.136 0.132 0.331 0.828 1.325 1.822 2.319 2.815 3.312 30 1.135 0.132 0.331 0.827 1.324 1.820 2.317 2.813 3.309 45 1.132 0.132 0.330 0.825 1.321 1.816 2.311 2.806 3.302 60 1.126 0.131 0.329 0.821 1.314 1.807 2.300 2.793 3.285 75 1.115 0.130 0.326 0.814 1.302 1.790 2.279 2.767 3.255 90 1.096 0.128 0.320 0.801 1.282 1.762 2.243 2.723 3.204 15 1.136 0.127 0.317 0.793 1.269 1.745 2.221 2.698 3.174 30 1.134 0.127 0.317 0.792 1.267 1.742 2.218 2.693 3.168 45 1.128 0.126 0.315 0.788 1.261 1.734 2.207 2.680 3.153 60 1.116 0.125 0.312 0.780 1.248 1.716 2.184 2.652 3.120 75 1.094 0.122 0.306 0.765 1.224 1.683 2.142 2.601 3.060 90 1.055 0.118 0.296 0.739 1.183 1.626 2.070 2.514 2.957 15 1.136 0.125 0.313 0.782 1.251 1.720 2.189 2.658 3.127 30 1.133 0.125 0.312 0.780 1.248 1.715 2.183 2.651 3.119 45 1.124 0.124 0.310 0.774 1.238 1.703 2.167 2.631 3.096 60 1.106 0.122 0.305 0.762 1.219 1.676 2.133 2.590 3.047 75 1.072 0.118 0.296 0.739 1.183 1.626 2.070 2.513 2.957 90 1.014 0.112 0.280 0.701 1.121 1.541 1.962 2.382 2.802 15 1.136 0.124 0.310 0.776 1.241 1.707 2.173 2.638 3.104 30 1.132 0.124 0.309 0.773 1.237 1.701 2.165 2.629 3.093 45 1.120 0.122 0.306 0.765 1.225 1.684 2.143 2.602 3.062 60 1.096 0.120 0.300 0.749 1.199 1.648 2.097 2.547 2.996 75 1.051 0.115 0.288 0.719 1.151 1.582 2.014 2.445 2.877 90 0.974 0.107 0.267 0.668 1.068 1.469 1.870 2.270 2.671 15 1.136 0.124 0.309 0.772 1.236 1.699 2.163 2.626 3.089 30 1.131 0.123 0.308 0.769 1.230 1.692 2.153 2.614 3.076 45 1.116 0.121 0.304 0.759 1.215 1.670 2.126 2.581 3.037 60 1.085 0.118 0.296 0.739 1.182 1.625 2.069 2.512 2.955 75 1.030 0.112 0.281 0.701 1.122 1.543 1.964 2.385 2.806 90 0.933 0.102 0.255 0.637 1.019 1.402 1.784 2.166 2.548 15 1.136 0.123 0.308 0.770 1.232 1.694 2.156 2.618 3.080 30 1.129 0.123 0.306 0.766 1.225 1.685 2.144 2.604 3.063 45 1.112 0.121 0.302 0.754 1.207 1.659 2.112 2.564 3.017 60 1.075 0.117 0.292 0.730 1.168 1.605 2.043 2.481 2.919 75 1.008 0.110 0.274 0.685 1.096 1.507 1.918 2.329 2.740 90 0.892 0.097 0.243 0.608 0.972 1.337 1.701 2.066 2.431 500 Radius Central Angle Travel Distance Total Predicted Crashes by Volume 2,500 3,000 1,000 1,500 2,000 Table C-1. HSM predicted annual crashes for varying combinations of radius, central angle, and volume.

Horizontal Curve Analysis C-3 • 1,500 foot radius  0.2231 miles length of curve (PC’ to PT’); 0.901 miles total tangent length (PC to PC’ + PT’ to PT); and travel distance of 1.124 miles. One can compute the crash frequency for each combination of tangent/curve alignment pro- duced by the radii and central angles, using the HSM models for curvature and tangent, applying each to the appropriate length for the given design condition. These are shown in Table C-1, which shows predicted annual crashes. Figures C-2 through C-7 display the results graphically. For ease of understanding, consider Tables C-2 and C-3 which demonstrate a small subsection of Table C-1. For the purposes of considering safety performance as a basis for curve design policy, the following is evident: • For lower-volume curves, the predicted crashes vary only slightly if at all both for differing radii and a common central angle, or differing central angles and the same radius. Figure C-1. Comparison of travel distance with same central angle. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 Pr ed ic te d Cr as he s ( to ta l c ra sh es p er y ea r) AADT (vehicles per day) 500 1,000 1,500 2,000 2,500 3,000 Radius () Figure C-2. Annual predicted crash frequency by radius for a 15° deflection angle.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 Pr ed ic te d Cr as he s ( to ta l c ra sh es p er y ea r) AADT (vehicles per day) 500 1,000 1,500 2,000 2,500 3,000 Radius () Figure C-3. Annual predicted crash frequency by radius for a 30° deflection angle. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 Pr ed ic te d Cr as he s ( to ta l c ra sh es p er y ea r) AADT (vehicles per day) 500 1,000 1,500 2,000 2,500 3,000 Radius () Figure C-4. Annual predicted crash frequency by radius for a 45° deflection angle.

Horizontal Curve Analysis C-5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 Pr ed ic te d Cr as he s ( to ta l c ra sh es p er y ea r) AADT (vehicles per day) 500 1,000 1,500 2,000 2,500 3,000 Radius () Figure C-5. Annual predicted crash frequency by radius for a 60° deflection angle. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 Pr ed ic te d Cr as he s ( to ta l c ra sh es p er y ea r) AADT (vehicles per day) 500 1,000 1,500 2,000 2,500 3,000 Radius () Figure C-6. Annual predicted crash frequency by radius for a 75° deflection angle.

C-6 A performance-Based Highway Geometric design process 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 Pr ed ic te d Cr as he s ( to ta l c ra sh es p er y ea r) AADT (vehicles per day) 500 1,000 1,500 2,000 2,500 3,000 Radius () Figure C-7. Annual predicted crash frequency by radius for a 90° deflection angle. Radius of Curve 4,000 vpd 7,000 vpd 10,000 vpd 500 1.321 2.311 3.302 1,000 1.261 2.207 3.153 1,500 1.238 2.167 3.096 2,000 1.225 2.143 3.062 2,500 1.215 2.126 3.037 3,000 1.207 2.112 3.017 Predicted Annual Crashes for Central Angle of 45 degrees Table C-2. Predicted annual crashes for ranges of traffic volume and varying combinations of radius and central angle. • As volumes increase (say, to 4000 vpd or greater) the differences become meaningful. • As the relationships among radius, central angle and length of curve are non-linear, the changes in crash prediction, and differences between radii for the same central angle, are non-linear. From the perspective of design policy, any predicted crash reduction greater than 0.02 is meaningful for the purposes of cost-effectiveness analysis. Even for traffic volumes as low as

Horizontal Curve Analysis C-7 4,000 vpd 7,000 vpd 10,000 vpd 500 to 1,000 0.06 0.104 0.149 500 to 1,500 0.083 0.144 0.206 500 to 2,000 0.096 0.168 0.24 1,000 to 2,000 0.036 0.064 0.091 1,000 to 3,000 0.054 0.095 0.136 Change in Radius of Curve Predicted Reduction in Crashes for Central Angle of 45 degrees Table C-3. Predicted changes in annual crashes for changes in radius (from Table C-2). 4,000 vpd, a change from 500 to 1,000 foot radius (0.06) translates to one crash every 16 years. Depending on the severity profile, this may translate to a meaningful valuation. Finally, in the context of a longer service life, which is proposed in the Interim Report, dif- ferences in safety performance become even more meaningful. Table C-4 shows the differences based on the annual crash reductions from Table C-3, multiplied by 50 based on an assumed 50-year service life (and assuming no change in traffic volume). The implications and value of applying predictive models to formulation of design policy for both new roads and existing roads are clear. A useful approach could further expand the analysis to illustrate safety effects assuming differing base conditions that would be consistent with dif- fering contexts (e.g., narrower lanes and/or shoulders that would be designed in mountainous terrain, including effects of grade, illustrating effects of spiral usage, etc.). Also, individual state models or calibration factors may produce important, different crash reduction values. In any event, this analysis demonstrates the importance of including traffic volume in some manner in horizontal curvature design policy. Even at a very general level, one can conclude that vari- ance in allowable curvature is much less critical for lower-volume roads and, in fact, may not be critical at all for volumes less than, say, 1,000 vpd (as the ongoing effort on very low-volume road criteria is demonstrating). Crash reductions can be translated to user benefits in dollar terms, applying an agency’s crash costs and adjusting for crash severity. (For existing roads being reconstructed, an Empirical Bayes’ approach that combines predicted with actual crash history would be used, thus incorpo- rating the specific context of the site.) To illustrate the order of magnitude of crash reductions, one could apply an approximate value of $100,000 per curve crash, in which case the dollar 4,000 vpd 7,000 vpd 10,000 vpd 500 to 1,000 3 5.2 7.45 500 to 1,500 4.15 7.2 10.3 500 to 2,000 4.8 8.4 12 1,000 to 2,000 1.8 3.2 4.55 1,000 to 3,000 2.7 4.75 6.8 Predicted Reduction in Crashes for Central Angle of 45 degrees Change in Radius of Curve Table C-4. Total predicted crash reductions from Table C-3 for a 50-year service life.

C-8 A performance-Based Highway Geometric design process benefits over a 50 year life would range from $200,000 for lower-volume, moderate curvature to $1,200,000 for higher-volume, sharper curvature (per values in Table C-4). And, as previously noted, crash reductions could be greater for other contexts. Operational Implications The geometry of alignment also produces small but potentially meaningful operational effects that are worthy of further investigation. As described above, for any given central angle the com- bination of curvature and tangent length produces varying total alignment lengths. Table C-5 illustrates the magnitude of the differences in length associated with the range of radii for 45 degree and 75 degree central angles. Flattening a 45 degree central angle curve from 500 foot radius to 3000 foot shortens the alignment length by 0.02 miles. For the 75 degree central angle, the difference is even greater - 0.107 miles. Although these length reductions appear small, when translated to traffic over a year, the reductions in total travel as measured by vehicle miles traveled (VMT) can become significant, particularly for volumes above 7,000 vpd (Table C-6). Finally, even small reductions in travel distance can produce meaningful aggregate operating cost savings, particularly for higher-volume roads, and when computed over a longer service life. Table C-7 illustrates the savings taken from multiplying the VMT values in Table C-6 by the Radius of Curve Length of Curve Lengths of Tangents Total Travel Distance Length of Curve Lengths of Tangents Total Travel Distance 500 0.0744 1.058 1.132 0.124 0.991 1.115 1,000 0.1487 0.979 1.128 0.2479 0.846 1.094 1,500 0.2231 0.901 1.124 0.3719 0.7 1.072 2,000 0.2975 0.823 1.12 0.4958 0.555 1.051 2,500 0.3719 0.744 1.116 0.6198 0.41 1.03 3,000 0.4462 0.666 1.112 0.7437 0.264 1.008 75 degree Central Angle Travel Distance for Range of Alignments 45 degree Central Angle Table C-5. Effect of horizontal curve geometry on travel distance. Change in Alignment Length (miles) 0.01 0.02 0.03 0.04 0.05 4,000 14,600 29,200 43,800 58,400 73,000 7,000 25,550 51,100 76,650 102,200 127,750 10,000 36,500 73,000 109,500 146,000 182,500 17,000 62,050 124,100 186,150 248,200 310,250 Annual Reduction in Vehicle Miles of Travel for Range of Average Daily Traffic Volumes Table C-6. Annual reduction in vehicle miles of travel for each 0.01 mile reduction in travel distance.

Horizontal Curve Analysis C-9 $0.61 per mile operating cost cited in the Interim Report (from AASHTO) and computed over a 50 year service life. (Note that in most cases, alignment length changes will be on the order of 0.03 miles or less.) Based on this analysis, one should expect that the life-cycle operational ben- efits of curve flattening will be on the order of $1.0 to $3.0 million for typical design decisions and moderate to higher volumes. The values in Table C-7 would be inputs to a cost-effectiveness design policy and/or a design process for existing curves. Other influencing factors include the effect of the curve on speeds, and traffic distribution including specifically trucks. From the perspective of developing a more cost-effective design policy for curvature, both the crash and operating cost implications of curve geometry are compelling. The complex relationships of curve geometry, other design fac- tors cited previously, and cost effects attributable to context variance all bear further study. As a minimum, the findings reinforce the recommendation that traffic volume be a direct input or factor in the formulation of curve design policy. Table C-7. Total vehicle operating cost savings for 50 year project life for reductions in travel distance.