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

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51 CHAPTER 5 POTENTIAL CHANGES TO THE AASHTO POLICY Based on the results of the literature review and the practitioner survey, modifications to the AASHTO methodologies can be considered. As there were very few exceptions to the AASHTO methodologies, the confines of the existing methods must be considered. Three alternatives are proposed below in dealing with the headlight issue: extend sag curve length, increase deceleration rate, or decrease design speed at locations where the minimum requirement for SD is not met. The applicability of these potential changes will be considered at the completion of the experimental process. SOLUTION 1: EXTEND SAG CURVE LENGTH Due to the angle change, the road segment illuminated by the headlight is shorter than before. To ensure a timely stop within the visible distance, an extension of sag curve is needed to lengthen the headlight SD to the minimum SSD. The SDs illuminated by the headlight (assuming S < L ) are calculated using the equation below: (4) The results are listed in Table 20. As can be seen, the SD at the speed of 80 mph decreases nearly 20% when the angle is 0.75. Table 20. Sight Distance Affected by Headlight Up Angle Design Speed Angle 1 Angle 0.95 Angle 0.90 Angle 0.85 Angle 0.80 Angle 0.75 Angle 0.70 Angle 0.65 Angle 0.60 15 mph 80 78.97 77.95 76.94 75.94 74.95 73.97 73.00 72.04 20 mph 115 113.09 111.20 109.33 107.49 105.67 103.87 102.09 100.34 25 mph 155 151.89 148.82 145.79 142.80 139.85 136.95 134.08 131.26 30 mph 200 195.37 190.80 186.29 181.84 177.46 173.15 168.90 164.73 35 mph 250 243.52 237.12 230.81 224.60 218.47 212.45 206.53 200.71 40 mph 305 296.34 287.80 279.38 271.08 262.90 254.86 246.97 239.21 45 mph 360 349.07 338.27 327.62 317.13 306.79 296.63 286.65 276.86 50 mph 425 411.27 397.71 384.33 371.14 358.15 345.37 332.82 320.51 55 mph 495 478.17 461.54 445.12 428.93 412.98 397.28 381.87 366.74 60 mph 570 549.78 529.78 510.02 490.52 471.31 452.40 433.82 415.59 65 mph 645 621.32 597.89 574.73 551.86 529.32 507.12 485.30 463.88 70 mph 730 702.35 674.97 647.89 621.14 594.76 568.76 543.20 518.10 75 mph 820 788.09 756.48 725.20 694.29 663.77 633.69 604.09 575.02 80 mph 910 873.80 837.92 802.39 767.26 732.56 698.34 664.65 631.54 𝑺𝑺 = 𝟐𝟐𝟐𝟐𝟐𝟐 ∗ 𝐭𝐭𝐭𝐭𝐭𝐭(𝜶𝜶) ∗ 𝑳𝑳 + �(𝟐𝟐𝟐𝟐𝟐𝟐 ∗ 𝐭𝐭𝐭𝐭𝐭𝐭(𝜶𝜶) ∗ 𝑳𝑳)𝟐𝟐 + 𝒕𝒕𝟏𝟏𝟐𝟐𝟐𝟐 ∗ 𝑨𝑨 ∗ 𝑳𝑳 𝟐𝟐𝑨𝑨

52 To ensure a long enough SD, the headlight SDs at an angle of 1º, which are equal to the stopping SDs, were used in equation (2) to re-calculate the curve lengths needed under different uplight angles. The updated curve lengths are shown in Figure 19. As can be seen, when the design speed is low and the A is small, minimum lengths of sag curve at different headlamp angles are more similar. The curve lengths spread to the right dramatically with the increasing of speeds and grades. Figure 19. Curve lengths by headlamp uplight angle. Extending sag curve lengths, however, is not feasible at certain locations due to terrain, drainage, or financial limitations. Therefore, two other approaches were proposed. The following two solutions were proposed as alternatives in the case that it was found that the actual length was not sufficient and needed to be modified. The first was in based on evidence that the parameters used to compute the length of the vertical curve do not reflect some new research (less reaction time that 2.5 sec, maximum acceleration greater than 11.2ft/s2, and different friction values for different types of roads). The second solution was a practical solution, that under the same expectation that the length curve is not sufficient, the more direct approach to solve a specific problem was to reduce the speed as a countermeasure. However, it must be recognized that a change in the accepted deceleration rate, perception-reaction time or pavement friction will have implications in the guide that go beyond the design of sag vertical curves. 6 7 8 9 10 11 12 13 14 15 16 0 500 1000 1500 2000 2500 Al ge br ai c Di ffe re nc e in G ra de (% ) Length of Curve (ft) Sag Curve Length by Headlamp Uplight Angle angle 1.00 angle 0.95 angle 0.90 angle 0.85 Design Speed (mph) 25 30 35 40 45 50 55 60

53 SOLUTION A.1: INCREASE DECELERATION RATE According to AASHTO, the current SSD assumes that: 1) the reaction time is 2.5 s, and 2), the deceleration rate is 11.2 ft/s2. These assumptions are made because “…a 2.5 second brake reaction time for stopping sight situations encompasses the capabilities of most drivers including those of older drivers…” and “…most vehicle braking systems and the tire-pavement friction of most roadways are capable of providing of at least 11.2 ft/s2.” (AASHTO, 2004) Due to changes of the visible distance ahead of vehicles incurred by headlight angle changes, the vehicles are required to stop within a shorter distance. Because of this, a larger deceleration rate is desired. Using the equation below, the deceleration rate needed to make a timely stop is calculated: (5) Where is the decreased headlight SD, V is the design speed, and t is the reaction time. The results are plotted in Figure 20. As can be seen, the deceleration rates at 1° are all under the assumed criterion, 11.2 ft/s2. With decreased uplight angles, the required deceleration level increases rapidly. At a speed of 65 mph, the deceleration rate needed at the angle of 0.75° increases to 15.638 ft/s2, which is almost 40% higher. Figure 20. Desired deceleration rate by design speed. 𝒕𝒕 = 𝒕𝒕.𝟐𝟐𝟎𝟎𝟎𝟎 ∗ 𝑽𝑽𝟐𝟐(𝑺𝑺 − 𝒕𝒕.𝟒𝟒𝟎𝟎 ∗ 𝑽𝑽 ∗ 𝒕𝒕) 8 9 10 11 12 13 14 15 16 17 18 19 20 21 0.600.650.700.750.800.850.900.951.00 De ce le ra tio n (ft /s 2 ) Headlamp Uplight Angle (degrees) Deceleration Rate Needed to Stop within Sight Distance 15 mph 20 mph 25 mph 30 mph 35 mph 40 mph 45 mph 50 mph 55 mph 60 mph 65 MPH 70 mph 75 mph 80 mph

54 Although increasing deceleration rate can be obtained in some cases, given a satisfactory road surface, tire quality, and weather condition, it is not always an efficient solution. A third solution is therefore proposed. SOLUTION A.2: DECREASE DESIGN SPEED When extending curve or increasing deceleration rate are both infeasible, another alternative is to decrease design speed on partial segments on a highway. Equation (6) below is used to calculate the design speed: (6) Where a is the deceleration rate and d is the headlight SD under different headlight angles. The results are exhibited in Table 21. As can be seen, at the angle of 0.75 and the original design speed of 65 mph, to achieve a timely stop within a shorter distance (529.32 ft in Table 21), the design speed needs to be decreased to 58 mph (a decrease of 10.8 percent) to guarantee a timely stop. Table 21. Speeds Changes for Decreased Headlight Sight Distance Design Speed at the Angle of 1 Angle 0.95 Angle 0.90 Angle 0.85 Angle 0.80 Angle 0.75 Angle 0.70 Angle 0.65 Angle 0.60 15 MPH 15 15 15 14 14 14 14 14 20 MPH 20 20 19 19 19 19 18 18 25 MPH 25 24 24 24 23 23 23 22 30 MPH 30 29 29 28 28 27 27 26 35 MPH 34 34 33 33 32 31 31 30 40 MPH 39 38 38 37 36 35 35 34 45 MPH 44 43 42 41 41 40 39 38 50 MPH 49 48 47 46 45 44 43 42 55 MPH 54 53 51 50 49 48 47 45 60 MPH 59 57 56 55 53 52 51 49 65 MPH 64 62 61 59 58 56 54 53 70 MPH 68 67 65 63 62 60 58 57 75 MPH 73 71 70 68 66 64 62 60 80 MPH 78 76 74 72 70 68 66 64 𝑽𝑽 = −𝟑𝟑.𝟏𝟏𝟎𝟎𝟎𝟎 ∗ 𝒕𝒕 + �(𝟑𝟑.𝟏𝟏𝟎𝟎𝟎𝟎 ∗ 𝒕𝒕)𝟐𝟐 + 𝟒𝟒.𝟑𝟑 ∗ 𝒅𝒅 ∗ 𝒕𝒕 𝟐𝟐.𝒕𝒕𝟎𝟎

55 ISSUES FOR THE POTENTIAL GUIDELINE RECOMMENDATIONS 1. The changes in headlight angles do affect the design of sag vertical curves due to a decreasing of SD. The guideline in AASHTO needs to incorporate these changes and provide more details under situations in which the requirement for SD is not satisfied. 2. The discussions and recommendations in this section assume that even with the angle changes, the headlight SD is always longer than SSD on flat ground. According to the research by the team members, for some types of headlights, this assumption may not be valid when design speeds are in the higher end. In those cases, the S used in the equations above needs to be replaced by “minimum (headlight sight distance, stopping sight distance).” 3. In addition to SSDs on a regular sag vertical curve, AASHTO defines SDs through undercrossings as: When S (in feet) is less than L (in feet) (7) When S (in feet) is greater than L (in feet) (8) Where C is the bridge clearance. As can be seen, the major concern here is the blockage of sight by the overpass. Therefore, the change of uplight angle of headlights will not affect the design of sag curve through undercrossings as long as the curve meets the minimum length requirement discussed above. 𝑳𝑳 = 𝑨𝑨𝑺𝑺𝟐𝟐 𝟖𝟖𝟐𝟐𝟐𝟐(𝑪𝑪 − 𝟎𝟎) 𝑳𝑳 = 𝟐𝟐𝑺𝑺 − (𝟖𝟖𝟐𝟐𝟐𝟐(𝑪𝑪 − 𝟎𝟎) 𝑨𝑨 )