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86 CHAPTER 7 DISCUSSION ON AASHTO GUIDELINES The potential changes to the AASHTO policy on the design of sag vertical curves discussed in Chapter 5 â a result of the literature review and survey â must be reconsidered with the additional data from the visibility experiments. A review of each solution follows. Solution 1: Extend Sag Curve Length The initial argument for extending the length of the curve came from the assumption that the headlight SD is shortened by the terrain. The results of the visibility experiments suggest that this may not be the case, however. In the Public Road study, the majority of curves provided detection distances that were not significantly different from the flat roadway. Decreased SD with respect to a flat roadway only occurred in the two residential curves, with design speeds of 25 mph. While lengthening these curves may provide a benefit, the mean detection distance for a target on flat roadway was found to be 110 ft in the Public Road study, and 230 ft in the Smart Road study (excluding high beam headlamps). Even using the longer of the two distances, the detection distance is still 20 ft shorter than the SSD for a 35 mph design speed. This suggests that even if the curves were completely flattened, the detection distance of an object may still only satisfy the SSD of a 30 mph design speed or less. In the Public Road study, participants only identified small targets which were approximately 7 inches (178 mm) square, while the Green Book (AASHTO, 2004) assumes an object height of 2 ft (600 mm). It was believed this difference may have accounted for at least some of the discrepancy between detection distance and SSD. However, in the Smart Road study, the mean detection distance for a pedestrian â a considerably larger object â was 224 ft on flat roadway (using low beam headlamps), which was shorter than the mean detection distance for a target under the same conditions (230 ft). A study conducted by Fambro, Fitzpatrick, and Koppa (1997) found a similar result, with participants able to detect a pedestrian using low beam headlamps at approximately 250 ft. Another study by Wood, Tyrrell, and Carberry (2002) found a mean detection distance of 251 ft for pedestrians using low beam headlamps. However, this mean distance included pedestrians wearing reflective vests and biomotion reflectors. Figure 43 shows the response distance by clothing and age for the low beam headlamps. As shown, the response distance for pedestrians not wearing reflective materials was much shorter.
87 Figure 43. Mean detection distance for pedestrians by clothing and age (Source: Wood, Tyrrell, & Carberry, 2002). This data suggests that extending the length of a sag vertical curve may provide a benefit for curves with design speeds less than 30 mph. For curves with design speeds greater than 30 mph, extending the length will provide no benefit as the visibility distance provided by the headlamps will be the limiting factor. Solution 2: Increase Deceleration Rate The second suggested solution was to increase the deceleration rate to a value which more closely matches the braking patterns of a typical driver. AASHTO defines the SSD as: (9) Where t is brake reaction time in seconds, V is the design speed in mph, and a is the deceleration rate in ft/s2. 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 (AASHTO, 2004). If we consider the detection of a target on flat roadway from the Smart Road study (which had the highest mean distance found in the visibility experiments), we can plug in the detection distance for d, and determine what deceleration rate would be needed to stop in this distance, which was 230 ft. Transforming the equation to solve for a, we find that: (10)
88 Using AASHTOâs values for brake reaction time, and a visibility distance of 230 ft, we find the deceleration rates required to stop in that distance by design speed. Table 38 shows these results. The standard deceleration rate of 11.2 ft/s2 would need to be increased beginning at a design speed of 35 mph, and increasing exponentially from there to unrealistic values. At a design speed of 65 mph, the distance traveled during the braking reaction time has already exceeded the 230 ft distance, which was the highest mean detection distance found. Table 38. Needed Deceleration for a Visibility Distance of 230 ft Design Speed (mph) Deceleration Rate (ft/s2) 15 1.38 20 2.75 25 4.86 30 8.08 35 12.99 40 20.72 45 > g 50 > g 55 > g 60 > g 65 > g 70 > g 75 > g 80 > g * g = 32ft/s2 Based on the detection distances found in the visibility experiments, increasing the deceleration rate would not be a practical way to bring SSD closer to headlight SD. Using the best case scenario of viewing a target on flat roadway, increasing the deceleration rate would only be feasible at one design speed (35 mph). Any speeds greater than that would require excessive or impossible rates of deceleration. Solution 3: Decrease Design Speed As already demonstrated, the best case scenario for object detection was for a target on flat roadway, with a detection distance of 230 ft. If we assume that this is the maximum distance for object detection using low beam headlamps, a design speed of less than 35 mph would be required in order for SSD to fall within this range. It would be impractical to decrease the design speed for a sag vertical curve from 55 mph to 30 mph, for example. Even if such a method were used, this would not address the fact that the headlight SD would still fall short of SSD for every other part of the roadway for any design speed greater than 30 mph.
89 Discussion of the Appropriateness of SSD The AASHTO design requirements for sag vertical curves are based on four factors: headlight SD, passenger comfort, drainage control, and general appearance. The headlight SD is typically the primary factor, however, because: 1) it requires a minimum rate of curvature which is higher than the minimum required for passenger comfort, 2) drainage control is a maximum rate of curvature which is not often approached, and 3) the general appearance criteria is of lower priority, and is often satisfied by meeting the headlight SD requirements. The original intent of this project was to determine how modern headlamps impact headlight SD, since the calculations for SSD are based on older sealed-beam headlamps. It was discovered that standard-beam headlamps do provide significantly longer detection distances than that of VOR headlamps in most conditions, but the same is not true for VOL headlamps. VOL headlamps performed similarly or sometimes better than the standard beams in each of the conditions tested (refer to Figure 33 and Figure 35). More importantly, however, it was discovered that all headlamps - including the standard-beam headlamps - were not able to provide mean detection distances that met requirements for SSD in most conditions. So while there were some differences among the different beam patterns, the larger issue became that the assumed SD used in the determination of SSD overestimates the actual visibility provided by ALL headlamps â not just modern beam patterns. At the same time, however, the majority of states which responded to the survey indicated that sag vertical curves are only occasionally or almost never problematic locations. This suggests that even though the SD falls short of SSD in many cases, it still allows enough visibility for generally safe driving. If this is the case, does that mean sag vertical curves are being over-designed for SSD requirements which are not met and not needed? If we assume that headlight SD is adequate for safety, then a combination of these criteria could be used for the design of sag curves where the design speed determines whether the SSD, SD, or comfort criteria will be used. Figure 44 shows a simplification of the K values for different design speeds based on the SSD and comfort criteria as stated by AASHTO, as well as the calculated K for an SD of 230 ft (which was the longest mean detection distance for flat roadway in the visibility experiments). For speeds less than 35 mph, the SSD is less than the headlight SD. For this range of design speeds, the SSD would be the criterion used, as increasing the curve length to reach headlight SD would provide no benefit. For speeds above 45 mph, the comfort criterion would be used because the headlight SD would also be satisfied within that criterion. For speeds between 35 and 45 mph, the headlight SD would be used because there would be no benefit in designing up to the SSD criterion.
90 Figure 44. K values for sag vertical curves. **Please notice that this plot is not valid for very low algebraic differences and very short curves where the stopping sight distance is less than the length of the curve as explained in Chapter 3. The model illustrated in Figure 44 used the mean detection distance; however, the concept works for other values as well. Roadway designers may wish to design for a longer detection distance, such as the 95th percentile, so as not to handicap drivers who have above average vision. Figure 45 shows how different levels of SD would affect the shape of the combined curve. Figure 45. K values for different headlight sight distances. The benefit of such a design approach would be potential cost savings due to decreased curve lengths. However, this approach is based on the assumption that current visibility distances provided by headlamps are sufficient for safety. Further research is required to test this assertion before any true design alternative could be proposed. 0 50 100 150 200 250 0 20 40 60 80 100 K va lu e Speed (mph) K, SSD K, Comfort K, SD (230 f t) Combined 0 50 100 150 200 250 0 50 100 K va lu e Speed (mph) K, SD (150 f t) K, SD (200 f t) K, SD (250 f t) K, SD (300 f t) K, SD (350 f t) K, SD (400 f t) K, SD (450 f t) K, SSD K, Comfort
