Sag Vertical Curve Design Criteria for Headlight Sight Distance (2013)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

16 CHAPTER 4 PRACTITIONER SURVEY RESULTS As part of assessment of practice in the design of sag curves, a survey was administered to the highway agencies in every state and a review of practices by domestic and international agencies was conducted. DOMESTIC STANDARDS The survey was administered to the departments of transportation in all 50 states and Puerto Rico. The roster of the AASHTO (Highway) Subcommittee on Design as of December 2009 was used as the primary source for contacts. Forty-two state DOT representatives responded to the survey (as indicated in Table 4). For the states that did not respond to the survey, the research team was able to gather information from the manuals for five of the states and no information was found for three of the states. Table 4 summarizes the findings. The objective of the survey was threefold: first, to identify how many states have documented guidelines for sag vertical curve design; second, to identify which criteria were used (headlight SD, passenger comfort, drainage control, general appearance, SD at undercrossing, decision passing, SD considerations, and others); and third, to identify differences between these criteria and the ones in the AASHTO policy on Geometric Design of Highways and Streets (AASHTO, 2004). In addition, the survey helped to identify: • design criteria on continuously lighted sections, • any issues identified by the States that need to be addressed, • any unpublished studies conducted by the States, • the perception of safety on sag vertical curves, and • if the state accident records identify accidents occurring on sag vertical curves. The survey is shown in Appendix A. Most of the states responded to the questions by attaching a copy of the URL of their road design manual. The research team carefully examined all the state manuals to identify any deviations to the standard from the AASHTO policy and exemptions used in each jurisdiction. While this task was very time-consuming, it provided the research team with a great understanding of the states’ policies and procedures. Any modification of the standard methodology was documented during the survey and a sample of these modifications is shown in this report.

17 Table 4. State Survey Responses St at e D oc um en te d D es ig n C ri te ri a C ri te ri a sa m e as A A SH TO Si tu at io ns w he re D iff er en t R ec om m en da tio ns ar e us ed C ri te ri a us ed w he n D es ig ni ng V er tic al C ur ve s Ex em pt io ns K ee p A cc id en t R ec or ds Y es N o Y es N o Y es N o H ea dl ig ht Pa ss en ge r C om fo rt D ra in ag e A pp ea ra nc e U nd er cr os si ng D ec is io n or Pa ss in g SD O th er Y es N o N o Y es N ot S ur e 1 X X X X X X 2 X X 3 X X X X X X X X X X 4 X X X X X X 5 X X X X X X X X 6 X X X X 7 X X X X X X X X 8 X X X X X X X X X 9 X X X X X X X X X X 10 X X X X X X X X X 11 X X X 12 X X X X X X X 13 X X X X X X 14 X X X X X X X X X X X 15 X X X X X X X X X X 16 X X X X X X X X X X 17 X X X X X X X 18 X X X X X X X X X X X 19 20 X X X X X X X X 21 X X X X X 22 X X X X X X 23 X X X X X X 24 X X X X X X 25 X X X X X X X 26 X X X X X X 27 X X X X X X X X X

18 St at e D oc um en te d D es ig n C ri te ri a C ri te ri a sa m e as A A SH TO Si tu at io ns w he re D iff er en t R ec om m en da tio ns ar e us ed C ri te ri a us ed w he n D es ig ni ng V er tic al C ur ve s Ex em pt io ns K ee p A cc id en t R ec or ds Y es N o Y es N o Y es N o H ea dl ig ht Pa ss en ge r C om fo rt D ra in ag e A pp ea ra nc e U nd er cr os si ng D ec is io n or Pa ss in g SD O th er Y es N o N o Y es N ot S ur e 28 X X X X X X 29 X X X X X X X X X 30 X X X X X X 31 X X X X X X X X 32 X X X X X X X X X X 33 X X X X X X 34 X X X X X X X 35 X X X X X X X 36 X X X X X X X X 37 X X X X X X 38 X X X X X X 39 X X X X X X X X X X X 40 41 X X X X X X X X X 42 X X X X X X X X X X 43 X X X X X X 44 X X X X X X X 45 X X X X X X X X X X X X 46 47 X X X X X X X 48 X X X X X X X 49 X X X X X X 50 X X X X X X X X X X X 51 Note: The States are not shown in any particular order and for some cases information was completed by VTTI with available public information from online state information

19 Question 1 Does your Agency have documented design criteria for vertical sag curves (Road Design Manual, Design Specifications, etc.)? Forty-three of the states which responded to this question have documented design criteria for vertical sag curves. Some of the states that do not have documented design criteria for vertical sag curves mentioned that they followed the AASHTO guide. All of the states use parabolic curves for the design of sag vertical curves. Question 2 Are these criteria the same as the AASHTO “AASHTO Policy on Geometric Design of Highways and Streets”? Most of the respondents (41) that do have documented design criteria indicated that their criteria are based on the AASHTO policy. The states that do not a have documented design criteria refer to the AASHTO policy as the design criteria used. Only two states (California and Louisiana) answered that they do not follow the AASHTO guidelines. However, a close examination of their road design manuals shows only small differences or additional criteria. Similarly, while some states indicated that they followed the AASHTO policy, a detailed examination of their manuals found small differences. In the case of the State of California, three differences are introduced: 1. Different computation of SSD, 2. Increase of SSD based on sustained downgrades, and 3. Minimum length of 10 V. One of the major differences in design criteria in the California Design Manual is that the “Stopping sight distance is measured from the driver's eyes, which are assumed to be 3 ½-feet above the pavement surface, to an object ½-foot high on the road.” In addition, “the SSDs in Table 5 should be increased by 20% on sustained downgrades steeper than 3% and longer than one mile.” (Highway Design Manual, Chapter 200, Geometric Design and Structure Standards, Topic 201, pages 200-1 200-2, 2007).

20 Table 5. Stopping Sight Distance for California Department of Transportation (DOT) as compared with AASHTO Design Speed Stopping Sight Distance AASHTO Stopping Sight Distance California 20 115 125 25 155 150 30 200 200 35 250 250 40 305 300 45 360 360 50 425 430 55 495 500 60 570 580 65 645 660 70 730 750 75 820 840 80 910 930 The formulas to calculate the length of the curve are the same as the ones in the AASHTO policy and the differences in SSDs resulted in small differences on the recommended k values ( k = L/A ratio of curve length L to the algebraic difference in grade A ) (Figure 9). Figure 9. K values for California DOT. (Source: Highway Design Manual, Index 201/204, Geometric Design and Structure Design. California Department of Transportation, Jan. 2007)

21 The third difference is that: “For algebraic grade differences of 2 percent and greater, and design speeds equal to or greater than 40 miles per hour, the minimum length of vertical curve in feet should be equal to 10V, where V = design speed. As an example, 65 miles per hour design speed would require a 650-foot minimum vertical curve length. For algebraic grade differences of less than 2 percent, or design speeds less than 40 miles per hour, the vertical curve length should be a minimum of 200 feet.” (Highway Design Manual, Chapter 200, Geometric Design and Structure Standards Topic 204, page 200-18-19, 2007) Louisiana DOT Design Standards recommend the minimum length of the vertical curve will be the longer of either 300 ft or that required by the formula LVC = KA, where K is the rate of vertical curvature and A is the algebraic difference in grades (in percent)(Roadway Design Procedures and Details, Chapter 4, Elements of Design, Cross Section Elements, page 4-7, Louisiana Department of Transportation and Development, January 2009) North Dakota DOT is the only state DOT that uses passenger comfort as the primary criterion for sag vertical curves as shown in Table 6. Table 6. Design Guidelines for New/Reconstruction Projects Traffic Data Use 20 year projected Roadway Width Use AASHTO Standards. Superelevations Use AASHTO Standards. (6% max superelevation, exhibit 3-22) Design Speed Use posted speed limit. Cross Slope Driving lanes 1.5 – 2.5%, Shoulder 6% max. Horizontal Curvature Use AASHTO Standards. Vertical Curvature Interregional System: Use stopping sight distance for crest curve design and comfort curve design for sag curves. Decision sight distance should be considered in areas where complex driver decisions are required such as intersections with major collectors or higher, interchanges, lane drops or additions, etc. Passing areas should be provided at reasonable intervals based on terrain and traffic volumes. A rule-of-thumb would be a passing area every 3 to 5 miles when the ADT <2000 and every 3 miles when the ADT >2000. State Corridors, District Corridors & Collectors: Use stopping sight distance for crest curve design and comfort curve design for sag curves. Passing areas should be provided at reasonable intervals based on terrain and traffic volumes. A rule-of-thumb would be a passing area every 3 to 5 miles when the ADT <2000 and every 3 miles when the ADT >2000. Clear Zone Use AASHTO roadside design clear zone. Inslope Use 4:1 except Interregional system > 2000 ADT and Interstate use 6:1. Pavement Slough Use AASHTO Standards. Safety Safety hardware to meet NCHRP 350 standards. Source: Design Manual, Section I-06, Design Philosophy, North Dakota Department of Transportation, 2010, Page 11

22 Florida also modified the SSD, but only for Interstates, as is shown in the corresponding question 4. Question 3 Are there any situations where your agency recommends the designer use different specifications than the ones specified in your answer for question 1? Fifteen states pointed out that there are special situations where different specifications are recommended, and 26 states answered that they do not use a different specification. For the majority of the states the different specifications correspond to reconstruction and rehabilitation projects, the use of local City or County specifications, or – when appropriate – the use of AASHTO’s Guidelines for Geometric Design of Very Low-Volume Local Roads. In Arkansas, “[R]econstruction of vertical curves should be considered when the existing curve design, based on the stopping sight distance provided, correspond to a speed that is more than 20 mph below the average running speed established for the project, the traffic volume is more than 1,500 vehicles per day, and the curve hides a major hazard from view. If curve reconstruction is not justified, appropriate safety and other mitigation measures should be applied (Geometric Design Criteria for Non Freeway Resurfacing, Restoration and Rehabilitation Projects, page 10, Arkansas State Highway and Transportation Department Approved by FHWA 8/21/89.” In Florida, “[O]nly existing sag vertical curves where crash history (related to the curve) indicates a problem must be evaluated against new construction criteria. An evaluated sag vertical curve that does not meet the minimum K value requires a Design Exception to remain. Sag vertical curves that are to be reconstructed must meet new construction criteria. Sag vertical curves without crash problems that fall below new construction criteria do not require Design Exceptions or Design Variations to remain.” (Plans Preparation Manual, Chapter 25, Florida’s Design Criteria for Resurfacing, Restoration, Rehabilitation (RRR) of Streets and Highways, page 25-23, January 1, 2010) In New York, sag vertical curve SD is not typically considered on Resurfacing Restoration and Rehabilitation (2R and 3R) projects: “Sag vertical curves need not be considered unless there are underpasses, overhead trees or there is an associated operational or safety problem.” In North Carolina, in the case of 3R on two-lane roadways, “[A]n existing vertical curve may be retained if design speed is within 20 mph of the posted or statutory speed limit and the design volumes are less than 1,500 ADT. An existing vertical curve may be retained if the curve’s design speed is within 10 mph of the posted or statutory speed limit and the crash rate is below the statewide average. A design exception is required for horizontal and vertical curves that do not meet the above RRR criteria.” For four-lane roadways, “[A]n existing vertical or horizontal curve may be retained if the curve’s design speed meets the posted or statutory speed limit. A design exception is required if the horizontal or vertical design speed is less than the posted or statutory speed.” In Utah, “Based on the stopping sight distance provided, an existing vertical curve may be retained as is without further evaluation if the existing curve design speed corresponds to a speed that is within 20 mph of the overall project design speed and the AADT [i.e., annual

23 average daily traffic] is less than 1,500 VPD [Vehicles per day]. The reconstruction of a sag vertical curve is evaluated when: 1. The AADT exceeds 1,500 VPD. 2. The design speed based on SSD is more than 20 mph below the overall project design speed. 3. The vertical curve hides a major hazard such as intersections, sharp, horizontal curves or a narrow bridge. 4. The vertical curve is identified as a high accident location, above the statewide average.” The Roadway Design Manual of Mississippi DOT shows that different K values for 3R projects (as shown in Table 7) would be used. Table 7. Minimum K Values for 3R and New Construction Projects for Sag Vertical Curves V (mph) SSD (f3et) 3R sag K value New Construction sag K values 30 200 20 37 35 250 27 49 40 305 35 64 45 360 44 79 50 425 54 96 55 495 65 115 60 570 78 136 65 645 91 157 70 730 106 181 Source: Memorandum, Vertical Curve K-Values, Mississippi Department of Transportation, October 2008 Question 4 Which criteria do you use when designing Vertical Sag Curves? When asked which criteria the state used when designing Vertical Sag Curves, the responses shown in Table 8 were obtained. Almost all states use headlight SD as the primary criteria. North Dakota is the only state that uses passenger comfort as the first criteria, and decision SD as the second criteria. The following section describes the criteria and the small differences with respect to the AASHTO guide.

24 Table 8. Criteria used by the States for Vertical Sag Curve Design Criteria Number of Responses Headlight SD 45 Passenger comfort 21 Drainage control 19 General Appearance 19 SD at Undercrossing 16 Decision or Passing SD considerations 13 Other 10 Headlight Sight Distance All the states that used Headlight SD as a criterion specified that they used the AASHTO criteria of 2 ft for headlight height and a 1-degree upward divergence of the light beam from the longitudinal axis. Furthermore, following AASHTO guidelines that “…for overall safety on highways a sag vertical curve should be long enough that the light beam distance is nearly the same as the stopping sight distance” and because it is appropriate to use stopping SD for different design speeds as the light beam distance, most of the states specify the criteria directly as SSD and occasionally reference the headlight distance. On the same note, not all the states provided specifications when the SSD is more than the length of the curve. Some states incorporate additional modifications to the headlight SD; for example, Connecticut and California make a correction for grades and Florida changes the selected design speed for some specific types of highways. In addition, some states specify (as do some international standards) a lower and upper range of K based on assumed speed conditions. Some states provide graphical representations that can slightly differ from AASHTO in the form of the curve, as is the case of Arizona (Figure 10).

25 Figure 10. Relation of minimum length of sag vertical curves to stopping sight distance (Source: Roadway Design Guidelines. Arizona Department of Transportation, 2007). In other cases (e.g., Tennessee) the criteria for sag vertical curves are listed as a range as part of the series of drawings for each roadway typical section, as shown in Table 9.

26 Table 9. Design Standards – Freeway with Median Barrier Design Standards (For given Design Speed) Design Speeds (mph) 50 60 70 Minimum, I, Stopping Sight Distance (Feet) 400-475 525-650 625-850 Minimum K Values Crest Vertical Curve 110-160 190-310 290-540 Sag Vertical Curve 90-110 120-160 150-220 Maximum Grade Level 4 3 3 Rolling 5 4 4 Mountainous 6 6 5 Source: Roadway Design Standards Section RD-TS, Tennessee Department of Transportation, March 2003 In Connecticut, whole headlight SD is the primary design control for sag vertical curves but the criteria also include minimum length grade adjustments. “When determining S for sag vertical curves, the designer should consider the effects of grade on stopping sight distance (SSD). The following thresholds may be used for determining the thresholds for ‘Level’ K values: V > 50 mph: -1% < G < +1% V < 50 mph: -2% < G < +2% The selection of “G” at a crest vertical curve will depend on which grade is steeper and whether the roadway is one-way or two-way. On a one-way roadway, “G” should always be the grade on the far side of the crest when considering the direction of travel. On a two-way roadway, “G” should always be the steeper of the two grades on either side of the sag. Only the Level SSDs are applicable for design exemption purposes. For designs where because of rounding of the charts, the “level” SSD is met but not the k values, an exception will not be required.” (Connecticut Highway Design Manual Chapter Nine, Vertical Alignment, page 9(3)-6, December 2003, Survey) (Table 10).

27 Table 10. K Values for Sag Vertical Curves Design Speed (mph) Downgrades Level Upgrades -9 % -6 % -3% 0% +3 % +6% +9% 20 20 18 18 17 16 26 15 25 31 28 27 26 25 24 22 30 44 41 38 37 37 33 32 35 60 56 52 49 47 44 43 40 77 72 66 64 60 57 55 45 97 89 84 79 74 72 68 50 119 110 103 96 91 87 83 55 143 132 122 115 108 103 99 60 170 156 144 136 128 121 115 65 198 181 168 157 149 140 135 70 227 207 193 181 170 161 154 Source: Connecticut Highway Design Manual, Chapter 9, Vertical Curves, Connecticut Department of Transportation, December 2003 In Colorado “Vertical curves are not required where algebraic grade difference is less than 0.20 percent. In rural applications, the minimum length of vertical curves on main roadways, both crest and sag, should be 300 feet. For other applications, the minimum length should be about three times the design speed”. (CDOT Roadway Design Guide, Chapter 3, Elements of Design, page 3-35). For Florida, the stopping sight distance and the corresponding k values for the Interstate Highways are computed based on design speeds of 5 mph higher than the design speed of the Interstate. Florida has specific minimum sag vertical curve lengths for Interstates and high-speed arterials and collectors (>45 mph) that exceed the AASHTO minimum length.” Plans Preparation Manual, Chapter 2, Design Geometrics and Criteria, Florida Department of Transportation, January 2010. The Kansas Design Manual states that “…the minimum length of sag vertical curves is based on SSD, except for appearance considerations, where practicable use a minimum length of sag vertical curve of 300 feet.” (Kansas Design Manual, Volume I Part A&B, Section 7.7.33, pages 7-67, November 2008 Edition.) New Hampshire specified lower and upper ranges for sag vertical curves based on the assumed speed for condition, as shown in Table 11.

28 Table 11. Design Control for Sag Vertical Curves’ Upper and Lower Ranges DESIGN CONTROL FOR VERTICAL SAG CURVES BASED ON STOPPING SIGHT DISTANCE Design Speed Assumed Speed for Condition Coefficient of Friction Stopping Sight Distance For Design Rate of Vertical Curve K (km/h) (km/h) F (m) Computed Rounded by Design 30 30-30 0.40 29.6-29.6 3.88-3.88 4-4 40 40-40 0.38 44.4-44.4 7.11-7.11 8-8 50 47-50 0.35 57.4-62.8 10.20-11.54 11-12 60 55-60 0.33 74.3-84.6 14.45-17.12 15-18 70 63-70 0.32 94.1-110.8 19.62-24-08 20-25 80 70-80 0.30 112.8-139.4 24.62-31.86 25-32 90 77-90 0.30 131.2-168.7 29.62-39.95 30-40 100 85-100 0.29 157.0-205.0 36.71-50.06 37-51 110 91-110 0.28 179-5-246.4 42.95-61.8 43-62 120 98-120 0.28 202.9-285.6 49.47-72.72 50-73 Source: New Hampshire Design Manual, 4-35 Nebraska uses the same values from AASHTO for the Minimum SSD but specified that “…these values do not meet intersection SD requirements and all intersections and driveways, except for field entrances, shall be evaluated for intersection SD” (Nebraska Department of Roads, Roadway Design Manual, Chapter 3: Roadway Alignment, page 3-34, July 2006), as shown in Figure 11.

29 Figure 11. Design control for sag vertical curves (Source: Nebraska Department of Roads Roadway Design Manual page 3-34). The Illinois DOT considers grade adjustment when the sag curve is between two downgrades and the downgrades are -3 percent or greater However, grade adjustment K values do not require a design exception when not met, as shown in Figure 12. Figure 12. K values for sag vertical curves stopping sight distances for passenger cars, adjusted for downgrades (Source: Bureau of Design & Environment Manual, Ch. 33, Vertical Alignment, Illinois Department of Transportation, December 2002, Page 33-4f).

30 Passenger Comfort Passenger comfort was specified as a criterion by 21 states. For most of the states, SSD or headlight SD is the primary control, with the exception of the North Dakota DOT that uses passenger comfort as the primary criterion for sag vertical curves and passing SD in special situations, In general, the states check for the AASHTO comfort criteria based on the assumption that riding on a sag vertical curve is comfortable when centripetal acceleration does not exceed 0.3 m/s2. The standards are shown as a graph or table, such as Minnesota’s standards are shown in Figure 13. Figure 13. Design controls for comfort sag vertical curves. (Source: Road Design Manual, Chapter 3-4, Vertical Alignment, Minnesota Department of Transportation, 2004, Page 3-4(12)).

31 Texas standards acknowledge that passenger comfort is one of the criteria recognized to some extent to define sag vertical curves, but the standards specify that: “Because cost and energy conservation considerations are factors in operating continuous lighting systems, headlight sight distance should be generally used in the design of sag vertical curves. Comfort control criteria are about 50 percent of the sag vertical curve lengths required by headlight distance and should be reserved for special use. Instances where the comfort control criteria may be appropriately used include ramp profiles where safety lighting is provided and for economical reasons in cases where an existing element, such as a structure not ready for replacement, controls the vertical profile. Comfort control criteria should be used sparingly on continuously lighted facilities since local, outside agencies often maintain and operate these systems and operations could be curtailed in the event of energy shortages.” (Roadway Design Manual, Section 5 Vertical Alignment, page 7, Texas DOT 05/01/10) Drainage Control Drainage is used as a control criterion after checking for SSD by 19 states. Most of the states use the same AASHTO criteria whereas drainage problems should not be experienced if the vertical curvature with a minimum longitudinal grade of at least 0.3 percent is reached at a point about 50 ft of the level point. This criterion corresponds to K of 51 m or 167 ft. However, some states have slightly modified criteria, as described below. For Arizona, the desirable minimum grade for a highway with a curb and gutter section is 0.4%. Special care should be taken in checking storm water drainage requirements to keep the spread of water on the travel way within tolerable limits. Above a 4,000-ft elevation, the minimum grade for roadways with curb and gutter shall be 0.5 percent (Roadway Design Guidelines, section 204.3 page 200-26, ADOT). According to Indiana DOT, drainage problems are minimize, if a minimum longitudinal gradient of at least 0.3 percent is reached at a point about 50 ft from either side of the low point (that corresponds to a K value of 167 or less) and there is at least at least 0.25 feet elevation differential between the low point in the sag and the two points 50 ft to either side of the low point. If this K value is exceeded, it may be necessary to install flanking inlets on either side of the low point (Indiana Design Manual Section 44-3.02 (03), 2010). General Appearance General Appearance was selected as a criterion by 19 states. When appearance was included as one of the criteria, most of the time it is in the form of a required minimum length and occasionally as a specific issue (such as broken back curves). Appearance concerns were an issue for broken back curves for Arizona (Roadway Design Guidelines, section 204.4, page 200-27, ADOT): “[B]roken back vertical curves consist of two vertical curves in the same direction separated by a short tangent grade section. Profile grade lines with broken back curves should be avoided, particularly in sag vertical curves where the unpleasing alignment is in full view.”

32 The Indiana Design Manual states that the minimum length of a sag vertical curve in feet should be 3.2 V (which is slightly longer than the AASHTO criteria). This condition can be avoided if the existing conditions make it impractical to use the minimum length criteria. One exception may be applied in a curved section and is as follows: “if the sag is in a “sump,” the use of the minimum length criteria may produce longitudinal slopes too flat to drain the storm water without exceeding the criteria for the limits of ponding on the travel lane.’ (Indiana Design Manual Section 44-3.02, Item 3, 2010.) The Oklahoma DOT differs from the AASHTO specification that the minimum length of a sag vertical curve should be 3V when the sag “is in a “sump.” The use of the minimum length criteria may produce longitudinal slopes too flat to drain the storrmwater without exceeding the criteria for the limits of ponding on the travel lane (Design Manual Section 7, Vertical Alignment, Oklahoma Department of Transportation July 1992, page 7.2 (11)). For Montana, the minimum length of a curve is Lmin = 3V and for aesthetics, the suggested minimum length of a sag vertical curve on a rural highway is 1,000 ft (300 m). Also, “sharp horizontal curves should not be introduced at or near the low point of pronounced sag vertical curves or at the bottom of steep vertical grades. Because visibility to the road ahead is foreshortened, only flat horizontal curvature will avoid an undesirable, distorted appearance”. (Road Design Manual, Ch 10, Vertical Alignment, Montana Department of Transportation, 10.2 (2) April 2006) New Hampshire DOT established minimum lengths of vertical curves based on design speeds, as shown in Table 12. Table 12. Minimum Vertical Curve Lengths Design Speed (km/h) Length (m) 50 30 60 50 80 70 100 80 110 100 Source: Highway Design Manual Chapter 4, Alignment and Typical Section, New Hampshire Department of Transportation, March 1999 Decision Sight Distance Decision SD was selected as a criterion by 13 states. However, for some states that mentioned this as a criterion, a detailed revision of the manual did not show any specification of decision SD for sag vertical curves. The decision SD is usually checked as a secondary criterion where there are complex decisions involved, as in the cases specified by North Dakota and Indiana and Illinois North Dakota has different rules of thumbs for passing SD depending on the type of project. The following applies to New/Reconstruction projects:

33 “Interregional System: Decision sight distance should be considered in areas where complex driver decisions are required, such as intersections with major collectors or higher, interchanges, lane drops or additions, etc. Passing areas should be provided at reasonable intervals based on terrain and traffic volumes. A rule-of-thumb would be a passing area every 3 to 5 miles when the ADT <2000 and every 3 miles when the ADT >2000. State Corridors, District Corridors & Collectors: Passing areas should be provided at reasonable intervals based on terrain and traffic volumes. A rule-of-thumb would be a passing area every 3 to 5 miles when the ADT <2000 and every 3 miles when the ADT >2000.” (North Dakota Design Manual, Section I-06.03, revised 2/4/10.) According to the Illinois DOT, sight distance may be warranted at some locations. Figure 14 shows the K values for the decision SD for specific candidates’ situations. Figure 14. Decision sight distance for sag vertical curves — passenger cars (Source: Bureau of Design & Environment Manual, Ch. 33, Vertical Alignment, Illinois Department of Transportation, December 2002, 33-4 G). Other Other was selected as a criterion by 10 states. Most of the criteria qualified under Other involved a minimum curve length (such as in Alabama, Arizona, and Connecticut), or special erosion considerations (in Florida). Alabama requires a minimum curve length of 800 ft for arterials and 1000 ft for freeways.

34 In Arizona, sag vertical curve not only shall be long enough that the light beam distance is nearly the same as the SSD, but the SD requirements for vertical curves also needs to satisfy minimum length requirements, as shown in Table 13. Table 13. Relation of Highway Types to Vertical Curves’ Minimum Length Highway Types Min Length (ft) Controlled Access Highways Rural Areas 1000 Urban Areas 800 Rural Highways 800 Urban Highways Three times design speed Source: Roadway Design Guidelines, Arizona Department of Transportation. Jan 02, 2007 On certain occasions, due to critical clearance or other controls, the use of asymmetrical curves may be required. In the case of the South Dakota Road Design Manual, (pages 6-15), “The K value for unsymmetrical curves can be computed by using the reciprocal of the following formulas: Therefore K = 1/r1 and K = 1/r2.” Florida requires paving of 4 ft of the median shoulder for 100 ft to either side of a sag vertical curve low point on divided arterials and collectors. In addition, the state has specifications for shoulder and slope treatment in sag vertical curves for protection from concentrated roadway runoff erosion and shoulder raveling. Question 8 Does your Agency have any specifications for the case of sag vertical curves underpassing a structure? Sixteen of the states mentioned that they had specifications for the case of vertical sag curves underpassing a structure. However, some states (such as Virginia) mentioned that they followed the AASHTO standard. In any case, the criterion is to check the sag vertical curves to ensure that the underpass structure does not obstruct the driver’s visibility. Illinois DOT modified the AASHTO formula

35 Question 9 What are the design criteria for vertical sag curves in the case of Continuously Lighted Sections of highway? Most of the states do not have specific design criteria for continuously lighted sections, but lighting can be considered as a mitigation factor in several states, as shown in Table 14. Table 14. Standards or Current Practices for Continuously Lighted Sections (Based on Survey Responses) Standard Same as unlighted Departmental policy on illumination does not make reference to vertical curvature. Primary design guide is AASHTO's Roadway Lighting Design Guide. Stopping Sight distance No, but is considered for cases where headlight sight distance is not met There are no special standards. An exception to standards is required when sight distance is only obtained through illumination Not available Same criteria as in unlighted sections Lighting is a mitigation strategy for substandard vertical alignment. GDOT refers to the FHWA publication, "Mitigation Strategies for Design Exceptions." Same criteria as in unlighted sections Comfort Except in the design of underpass grades, sag vertical curves may meet comfort criteria where necessary Prefer the use of headlight criteria, but comfort criteria may be acceptable upon review. No special considerations are provided in our design manual KYTC does not consider continuously lighted sections when designing vertical sag curves. The same as those from AASHTO We use the same design criteria for the sag curve regardless of lighting. No difference For S < L, lighted sag curve is a mitigation factor when stopping sight distance (K) is not met. On lighted urban streets, comfort criteria may be used. No We always meet the AASHTO design criteria if we can. If we can't and we have overhead lighting, we will get a design exception Not available None The same design controls are used for lighted sections of highways. Maintenance for lighting can be funding issue. Passenger comfort and decision sight distance in areas where complex driver decisions are required Same as the unlighted. However, the lighting can be used for mitigation of sag curves requiring design exception Same criteria as in unlighted sections

36 A "comfort" sag may be used with a design exception approved by the State Roadway Engineer None In cases of fully lighted sections of highway, the sag vertical curve may be designed to meet the comfort criteria. Design criteria for vertical sag curves in lighted sections of highway are the same as for sections of highway that are not lighted 50% of the sag vertical curve lengths When K values at or near the lower end of the design range are used, they consider providing fixed street lighting with the UDOT Traffic and Safety Division. NO change in criteria for lighted sections. However if the K value is not met, then a Design Exception is required. Mitigation for not meeting the appropriate K value is the fact that lighting is provided through the sag and they do allow the curve to be designed based on comfort No change in criteria for lighted sections. Question 10 Does your agency allow short vertical sag curves in special situations (economic reasons, ramps, etc.)? Some states allow short vertical curves in special situations. The following are examples of such cases. The Alaska Highway Preconstruction Manual states that “an analytical method is not available to analyze accidents at sag vertical curves. Generally, sag vertical curves that do not meet AASHTO requirements may remain. If a grouping of accidents at a sag vertical curve appears to be an anomaly when compared to similar curves, an improvement may be needed if cost-effective.” Alaska Preconstruction Manual, Section 1160, Page 1160-14, Roadside Geometry. Alaska Dept. of Transportation. Jan. 01, 2005 In Arizona, the ADOT’s desirable minimum length for vertical curves (800 ft or 1000 ft) can be waived if necessary to meet existing constraints, and the state makes exception for driveways and ramp vertical curves: Urban driveways: The driveway grade, up or down, should be not be greater than six percent beginning at the outer edge of sidewalk. Desirably, the driveway grade adjacent to the sidewalk should be between plus or minus two percent for a distance of 10 ft minimum for residential driveways and at least 20 ft but preferably greater than 40 ft for commercial and industrial driveways. Grade breaks greater than six percent require vertical curves at least 10 ft long. In setting the driveway grade, consideration should be given to the impact of roadway drainage on the adjacent property. (Arizona Roadway Design Guidelines, Section 404.3, pages 400-12.) Ramp vertical curves: Interchange ramp vertical curves should be a minimum of 200 ft in length at the terminus with a crossroad. Elsewhere, the ramp vertical curve lengths should be in accordance with the ramp design speed with a minimum length of 400 ft. (Arizona, Roadway Design Guidelines, Section 540.1, pages 500-100.)

37 The New Hampshire DOT “…endorses minimum desirable lengths of vertical curves, although shorter ones will comply with the “Green Book” criteria.” (Highway Design Manual Chapter 4, alignment and typical section, pages 4-38 New Hampshire DOT, March 1999.) The Utah Roadway Design Manual of Instruction states that sag vertical curves may have a length less than that required for SSD when all three of the following are provided: 1. An evaluation upgrade to justify the length reduction. 2. Continuous illumination. 3. Design for the comfort of the vehicle occupants. The sag vertical curve lengths designed for comfort are about 50 percent of those required for SD. Occasionally, the sag vertical curve can be avoided when certain conditions are met. For example, the Texas DOT states, “…designing a sag or crest vertical point of intersection without a vertical curve is generally acceptable where the grade difference (A) is: 1.0 percent or less for design speeds equal to or less than 45 mph [70 km/h] 0.5 percent or less for design speeds greater than 45 mph [70 km/h]. When a grade change without vertical curve is specified, the construction process typically results in a short vertical curve being built (i.e., the actual point of intersection is “smoothed” in the field). Conditions where grade changes without vertical curves are not recommended include: bridges (including bridge ends), direct-traffic culverts, and other locations requiring carefully detailed grades.” (Roadway Design Manual, Section 5 Vertical Alignment, page 8, Texas DOT 05/01/10) In addition the following answers were received in response to this question “…long vertical curves on urban streets are generally impractical. The designer will typically need to lay out the profile grade line to meet existing conditions. Therefore, no minimum vertical curve lengths are provided for urban streets. Where practical, VPI's should be located at or near the centerlines of cross streets. Vertical curves will not be required when the algebraic difference in grades is less than 1.0 percent. However, the use of vertical curves should be evaluated when the algebraic difference in grades is greater than 0.5 percent. In addition, at signalized and stopped controlled intersections, some flattening of the approaches may be required.” “We allow shorter vertical sag curves at some sites where bridges are being replaced and on detours” “Exceptions are granted for low speed/low-volume roadways, in the name of practical solutions.” “when the required K value does not meet design speed, then a shorter length of VC is allowed as long as the graphically plotted curve provides measured SSD through the curve in feet meets the design speed.”

38 “If the cost of bringing the vertical curve up to the standard exceeds the benefit, the department has a process to provide justification of nonstandard and nonconforming features. This justification includes the computation of advisory speed, accident analysis, cost estimates, and mitigation factors.” Question 11 Has your agency identified any issues with the current design criteria for vertical sag curve that need to be addressed? The following answers were received in response to this question: “We question the real need for this to be one of the 13 AASHTO Controlling Criteria or at least question its relative importance. If the criteria is really only based on nighttime lighting, how important is it? Lots of things are hard to see at night and other criteria are based on daylight driving. We believe the criteria should be relaxed, eliminated, or considered differently.” “We think that the criteria may need to be updated as your email suggests. We think that with the technological improvements to modern vehicles that headlight sight distance may not be as critical to safety as the current values suggest.” “No, although it is felt that meeting design speeds for sag vertical curves is less critical than for crest vertical curve.” “In some cases, the K value is not met for the sag curve, however the required stopping sight distance is actually available for the curve (determined by plotting the curve information and measuring the SSD with a ruler). This has been the case for extremely short sag vertical curves with small algebraic differences between the two grades.” “Green book criteria are applied; however we recognize that headlight considerations will not be a control.” Other All the states responded that they have not conducted any study regarding design or safety of vertical design curves. Twenty-five states did not identify using their accident records if accidents occurred in a sag vertical curve. Seven states (Alabama, Arizona, Michigan, Utah, Virginia, West Virginia, and Washington) identified accident records occurring in sag vertical curves. INTERNATIONAL STANDARDS In addition to the domestic survey, an international literature search was undertaken to consider alternatives to the U.S. methodologies. Criteria and K values for several countries were obtained with different degrees of detail, depending on information availability; the countries include Canada, England, New Zealand, Spain, and Sweden. There are some major differences between U.S. standards and those of some European countries; one being the use of circular

39 curves in some of the European countries instead of parabolic vertical curves which are used in the United States. For this case the K values represent the radius of the vertical curve. In reality, for a given K value, the differences between the alignment of the parabolic and circular curves represent only a few centimeters. In addition, for some countries, headlight SD is the dominant criteria while, for others, comfort or appearance is more prevalent. In some cases (for example, New Zealand), headlight SD is also limited. Maximum rates of vertical acceleration vary from 0.3m/s2 to 0.05g to 0.1 g. Exceptions from the absolute minimum are permitted and are computed as using Design Speed Steps (Ireland) or minimum and desirable K values (Spain). Australia’s approach was to modify the graphics for minimum size sag vertical curves and aesthetics governed for highways and high-speed freeways. In England, adequate riding comfort is the major criterion for speeds higher than 70 mph. Australia just modified the new guide and, depending on the category of road, the governing criteria as well. The following section describes the minimum K values and criteria for different countries. New Zealand The Transit New Zealand State Highway Geometric Design Manual (Section 5 Vertical Alignment; Transit New Zealand, 2002) states that vertical curves are defined by two parameters: • A comfort factor which provides for a smooth passage from one grade to another, and • A safety factor which ensures that drivers have a safe SD over the full length of the vertical curve. The profile must ensure that all relevant design speed SD requirements are met at every point on the road alignment. It is also good design practice to make the vertical alignment design speed 10 to 15 km/h greater than the horizontal alignment design speed, to provide an additional safety margin. Visibility and comfort are the most important factors in vertical curve design. Sag vertical curves must ensure vehicle occupant comfort (i.e., the rate of vertical acceleration), and headlight performance criteria must be met. Other factors which must also be considered in sag vertical curve design are drainage requirements and sight line restrictions caused by overhead structures. Appearance Requirements “For very small changes of grade, vertical curves have little effect on the appearance of the road’s profile and may usually be omitted. Short vertical curves can, however, have a significant effect on the appearance of a road’s profile; therefore, vertical curves for small changes of grade should have K values significantly greater than those needed for minimum sight distance reasons. This is particularly important on high standard roads, especially for sag curves.” (Transit New Zealand, 2002, pages 5-6.) Table 15 shows the minimum length of vertical curve for satisfactory appearance. Longer curves are preferred when they can be achieved without conflict with other design requirements (such as drainage).

40 Table 15. Vertical Curve Appearance Criteria Design Speed (km/h) Maximum Change of Grade without a Vertical Curve (9%) Minimum Length of Vertical Curve for Satisfactory Appearance (m) 40 1.0 20-30 60 0.8 40-50 80 0.5 60-80 100 0.4 80-100 120 0.2 100-150 Source: Transit New Zealand, 2002 According to the Manual, during nighttime the vehicle headlight performance limits the effective SD to between 120 and 150 m on unlit roads that is suitable only for speeds up to 90 km/h, so on dual-carriageway state highways a headlight SD of 150 m must be provided for sag vertical curves (Figure 15). Figure 15. Sight line distance. When sag vertical curves cannot be flattened to provide headlight stopping distance, they must provide an adequate level of ride comfort. Comfort Requirements Regarding Comfort Requirements the Geometric Design Manual states “For normal road design purposes, the vertical acceleration generated when passing from one the grade to another is limited to a maximum of 0.05g, where g is the acceleration due to gravity (9.8 m/sec2). On low standard roads and at intersections, a vertical acceleration of 0.10g may also be used where necessary. The vertical component of acceleration normal to the curve when traversing the path of a parabolic vertical curve at uniform speed is given by”: Where: a = vertical component of radial acceleration (m/sec2) V = speed (km/h) K = a measure of vertical curvature (m / 1% change of grade)

41 Sight Distance Requirements The length of a sag vertical curve should normally be determined by headlight SD requirements. When these cannot be met, sag vertical curve length must be determined by vehicle occupant ride comfort criteria. The length of a vertical curve for a given SD is given by the following expressions (similar to the AASHTO but defining a parameter C): (i): Where length of curve is less than the SD: (ii): Where length of curve is greater than the SD: Where: L = vertical curve length (m) Ds = sight distance (m) A = algebraic difference of vertical grading (%) C = sight line constant. Substituting the vertical curve parameter K for K is therefore a constant for a given SD and method of defining the sight line. The sag vertical curve sight line constant C: C = ' 200 ( h + Ds Tan q ) Where: h = headlight mounting height (m) Ds = stopping sight distance (max. 150 m) q = elevation angle of headlight beam A mounting height of 0.75 m and zero elevation gives: C ' 150 Table 16 shows the K values for sag vertical curve design in New Zealand.

42 Table 16. K Values for Sag Vertical Curve Design Speed (km/h) Headlight Sight Distance Control Vehicle Occupant Ride Comfort Controls Sight Distance (m) C=150 K Normal Design Situations a=0.05 g k Special Design Situations a=0.10 g k 40 40 11 3 1.5 50 55 20 4 2 60 75 38 6 3 70 95 60 8 4 80 115 88 10 5 90 140 131 13 6 >90 150 150 >15 >8 United Kingdom The Design Manual for Roads and Bridges states that the standard for vertical curves shall be provided at all changes in gradient Highways Agency et all, 2002). “The curvature shall be large enough to provide for comfort and, where appropriate, for SSDs for safe stopping at design speeds. For sag curves , comfort criteria apply (0.3 m/sec2 maximum rate of vertical acceleration). However, for design speeds of 70 km/h and below in unlit areas, shallower curves are necessary to ensure that headlamps illuminate the road surface for an SSD which is not more than one Design Speed below Desirable Minimum Stopping Sight.” (Highways Agency, Volume 6, section 4, page 4/1). Sag curves are usually designed to the Absolute Minimum k values shown in Figure 16. According to the manual, the use of the values will normally meet the requirements of visibility; however, they always recommend to check for SSD because of the horizontal alignment, superelevation, and other treatments.

43 Figure 16. Vertical curves K values. (Source: Highways Agency, 2002) Relaxation below an absolute minimum for different kinds of roads is permitted using Design Speed Steps, depending on the category of the roads. No relaxations are allowed for motorways. For design speeds of 70 km/h and less where the sag vertical curve is illuminated, the relaxation criteria can be extended by one step, and relaxations are not permitted on the immediate approach of junctions For countries receiving technical assistance from the British Government, the Transportation Research Laboratory (Overseas Road Note 6, 1998) mentioned that the use of the equations for a headlight height of 0.6 meters and 1 degree of angle of upward divergence of headlight beam can result in unrealistically long vertical curves and SD, perhaps in excess of the effective range of the headlamp beam, so they recommended to use the comfort criteria as shown in Figure 17.

44 Figure 17. Length of sag vertical curves L (m) for adequate comfort (Source: Overseas Road Note 6, 1998). Australia The recently publish Guide to Road Design Part 3 Geometric Design states that sag curves are usually designed on the basis of providing reasonable SD for a headlight beam (Austroads, 2010). According to the guide “headlight SD is limited to about 120 – 150 m, which corresponds to an SSD from 80 km/h to 90 km/h, and a maneuver time of about 5 seconds at 100 km/h….. “This shortfall in-vehicle lighting, however, cannot be provided for in road design and is not a design consideration…. and the only method of achieving fully compatibility between theoretical sight distances by day and night is by roadway lighting”(Austroads 2010, page 118) The vertical curves are in parabolic shape similar to AASHTO and the guide site three controlling factors for curves in general • Sight distance: is a requirement in all situations for driver safety. • Appearance: is generally required in low embankment and flat topography situations. • Riding comfort: is a general requirement with specific need on approaches to a floodway where the length of depression needs to be minimized. On high-speed roads consideration should be given to providing headlight sight distance When sag curves cannot be flattened to provide desirable headlight SD, they should be designed to provide adequate riding comfort based on the criterion of 0.05 g vertical acceleration, although 0.10 g may be adopted for low standard roads. On two-lane roads, extremely long sag curves over 750 m should be avoided for drainage reasons. The Guide to Road Design presents a new Algebraic Difference in Gradient A (%)

45 set of graphics for minimum size sag vertical curves, as shown in Figure 18. The graph was developed using the following criteria to determine the lower bounds: 1. Low Standard Roads – comfort criteria with a = 0.1g 2. Other Urban and Rural Roads with street lighting – comfort criteria with a = 0.05g 3. Other Urban and Rural Roads without street lighting – headlight SD with reaction time = 2.0s and coefficient of deceleration = 0.61 4. Highways and freeways: Minimum – headlight SD with reaction time = 2.5s and coefficient of deceleration = 0.36 Desirable – crest curve SSD with reaction time = 2.0s and coefficient of deceleration = 0.36. Figure 18. Minimum K values for sag curves (Source: Austroads, 2010, Figure 8.7).

46 Spain In Spain, the Design Normative for sag vertical curves states that the sag vertical curves will be designed using a parabolic curve with the following equation (Ministerio de Fomento, Gobierno de Espana, 2011) Kv=Parabolic parameter Ѳ= algebraic differences in grade percent Sight Distance requirement And And where • h1= height over the pavement (m). • h2 = height of the object over the pavement (m). • h = headlight height (m), • α = Degree of upward divergence of the light beam from the longitudinal axis • D = light beam distance (m). To compute the SSD, h1 = 1,10 m h2 = 0,20 m; h = 0,75 m; α =1°. Table 17 shows the minimum and desirable K values based on SD. Table 17. Minimum and Desirable K Values for Spain Design Speed (Km/h) Minimum Desirable 40 568 1374 60 1374 2636 80 2636 4348 100 4348 6685 120 6685 9801 Source: Ministerio de Fomento, Gobierno de Espana, 2011 Appearance Requirement To check for appearance, the following length of the curve in meters must be bigger than the design speed in km/h. L>V Where: L = Length of the curve (m) V= Design speed (km/h)

47 Canada The length of the sag vertical curve must be, at a minimum, the SSD (Transportation Association of Canada Geometric Design Guide for Canadian Roads, 1999; NCHRP 15-41 survey). The Transportation Association of Canada is currently working on a project comparing the guide to other geometric design guides published by similar agencies (e.g., AASHTO, Austroads, etc.) to determine if the Transportation Association of Canada Guide requires significant rewriting or needs only to be refreshed to incorporate state-of-the-art research findings. While headlight SD is the primary criterion, additional criteria include passenger comfort, drainage control, and general appearance. The current guidelines do not have specifications for sag vertical curves underpassing a structure. The same standards apply for both lighted and unlighted sections, but they allow reduction for comfort control where conditions warrant. Others The Road Safety Manual from the World Road Association PIARC (PIARC, 2003), designed to give highway engineers a better understanding of the impacts that infrastructure has on road safety at all phases of design and operations, lists the minimum K values for sag vertical curves for several countries, as shown in Table 18. Table 18. Minimum K Values for Sag Vertical Curves Country Design Speed (km/h) 40 50 60 70 80 90 100 110 120 Canada 7 11 20 25 30 40 50 55 60 France 15 22 30 42 Germany 15 20 25 35 50 100 Greece 14 19 25 33 42 52 63 75 Italy 6 12 22 39 58 Japan 7 10 20 30 40 South Africa 8 12 16 20 25 31 36 43 52 Switzerland 8 12 16 25 35 45 60 80 USA 9 13 18 23 30 38 45 55 63 Source: PIARC, 2003 According to Krammes and Granham (1997), German guidelines are provided for maximum and minimum grade. The guidelines for sag curves are based upon general appearance. The Italian standards are set by the Consiglio Nazionale Delle Ricerche. The criteria for sag vertical curves are the same as the ones for crest vertical curves, but in exceptional cases a lower minimum radius which guarantees nighttime visibility using headlamps is permissible. The South African standards are provided by the Committee of State Road Authorities and are based upon headlight illumination distance. In Sweden, vertical curves are parabolic and sag curves and are defined as nighttime headlight systems’ requirements. Sweden also defined a

48 range of High Standards and Low Standards for selecting the minimum K value. Switzerland defines sag vertical curves based upon SD requirements. In addition to the minimum K for sag vertical curves, the PIARC manual also lists the SSD for the different countries, as is shown in Table 19. Table 19. Stopping Sight Distances Country Time Speed (Km/h) 30 40 50 60 70 80 90 100 110 120 130 140 Stopping Sight Distance Austria 2.0 35 50 70 90 120 185 275 380 Canada 2.5 45 65 85 110 140 170 210 250 290 220 France 2.0 35 50 65 85 105 130 160 Germany 2.0 25 65 85 110 140 170 210 255 Great Britain 2.0 70 90 120 215 295 Greece 2.0 65 85 110 140 170 205 245 South Africa 2.5 50 65 80 95 115 135 155 180 210 Sweden 2.0 35 70 165 195 Switzerland 2.0 35 50 70 95 120 150 195 230 280 USA 2.5 35 50 65 85 105 130 160 185 220 250 285 - SUMMARY As part of the assessment of practice in the design of sag vertical curves, a survey was administered to the 50 states plus Puerto Rico, and responses were received from 42 states. For the states that did not respond to the survey, the research team was able to gather information from five of the states’ manuals; however, no information was found for three states. Forty-two of the respondent states have documented design criteria for sag vertical curves. The states that do not have documented design criteria for sag vertical curves mentioned that they followed the AASHTO guide. All the states use parabolic curves for the design of sag vertical curves and only two states (California and Louisiana) answered that they do not follow the AASHTO guidelines. In the case of the State of California, three major differences are introduced: a different computation of SSD, an increase of SSD based on sustained downgrades, and a minimum length of 10 V. The SSD was modified by Florida but only for Interstates. North Dakota is the only state that uses passenger comfort as the primary criterion for sag vertical curves and passing SD in special situations. Twenty-seven states pointed out that there are special situations where different specifications are recommended and 15 states answered that they do not use a different specification. The majority of the states using different specifications correspond to reconstruction and rehabilitation projects, the use of local City or County specifications or, when appropriate, they use AASHTO’s Guidelines for Geometric Design of Very Low-Volume Local Roads. When asked which criteria the state used when designing sag vertical curves, the responses indicated that 45 states use headlight SD, 21 use passenger comfort, 19 use drainage control, 19 use general appearance, and 13 use decision or passing SDs. All the states that used headlight SD as a criterion specified that they used the AASHTO criterion of 2 ft for headlight

49 height and 1-degree upward divergence of the light beam from the longitudinal axis. Some states incorporate additional modifications to the headlight SD (e.g., Connecticut and California) to make a correction for grades, or change the selected design speed for some specific type of highways (e.g., Florida) or specified (as do some international standards) a lower and upper range of K based on assumed speed conditions (e.g., South Dakota). For North Dakota, passenger comfort is the primary criterion and passing SD is used as a secondary criterion in special situations. In general, the states check for the AASHTO comfort criterion based on the assumption that riding on a sag vertical curve is comfortable when centripetal acceleration does not exceed 0.3 m/s2. Other states that use comfort control criteria (e.g., Texas) specify that control criteria should be used sparingly, because of the possibility of energy shortages. Of the 19 states that used the drainage criteria, most of them used the same criterion as AASHTO or a more exigent one. When appearance was included as one of the criteria it was most often in the form of a required minimum length and occasionally as a specific issue (such as broken back curves in Arizona). The decision SD is usually checked as a secondary criterion where there are complex decisions involved, as in the cases specified by North Dakota, Indiana and Illinois. Other criteria were also identified by 10 states which involved, in most of the cases, minimum length or special erosion considerations. Sixteen of the states mentioned that they had specifications for the case of sag vertical curves underpassing a structure. The states that have incorporated this criterion follow AASHTO or a similar formula with slightly modified parameters. Most of the states do not have specific design criteria for continuously lighted sections, but lighting can be considered as a mitigation factor in several states. Also note that several states allow shorter curves, or occasionally the sag vertical curve can be avoided, but all of these cases fall under exemptions. All the states responded that they have not conducted any studies regarding design or safety of vertical design curves. Twenty-five states do not specifically have a field on their accident records indicating if the accident occurred in a sag vertical curve. In only seven states (Alabama, Arizona, Michigan, Virginia, Utah, West Virginia and Washington) can accident records occurring in sag vertical curves be identified; most of the time this can only be determined indirectly. Criteria and K values for several countries were obtained with different degrees of detail depending on information availability; the countries included Canada, England, New Zealand, Spain, and Sweden and Australia. There are some differences between U.S. standards and those of some European countries, one being the use of circular curves in some of the European countries instead of parabolic vertical curves. In addition, for some countries, headlight SD is the dominant criterion while, for others, comfort or appearance is a more prevalent criterion. Also, in some cases (e.g., New Zealand), headlight SD is also limited and maximum rates of vertical acceleration vary from 0.3m/s2 to 0.05g to 0.1 g.

50 Exceptions from the absolute minimum length are permitted and are computed as using Design Speed Steps (e.g., as in Ireland) or minimum and desirable K values (e.g., as in Spain). Australia recently modified the new guide and, depending on the category of road, the governing criteria as well.