Design Guidelines for Horizontal Sightline Offsets (2019)

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10 2.1 Current SSD Design Criteria This section presents an overview of the current AASHTO SSD design criteria and their application to vertical and horizontal sight restrictions. The review of SSD design criteria pre- sented here is based on the 2011 edition of the Green Book. The forthcoming 2018 edition of the AASHTO Green Book is not expected to include any substantive revisions to the policies on SSD and HSO presented here. 2.1.1 AASHTO SSD Model Sight distance is the length of the roadway ahead that is visible to a driver at any point on the roadway. Geometric design policies include design criteria for SSD, defined as the minimum length of roadway ahead that a driver needs to be able to see in order to stop before reaching a stationary object in the driver’s path. The AASHTO Green Book establishes SSD design criteria based on the following model: = +1.47 1.075 (2) 2 S Vt V a where S = SSD (ft); V = design speed (mph); t = brake reaction time (perception-reaction time prior to braking) (sec); and a = deceleration rate (ft/s2). Table 1 presents the current SSD design criteria derived from Equation (2). The rightmost column in Table 1 presents values of DSSD used in designing U.S. roads. Designers seek to pro- vide ASSD at least equal to the DSSD value for the applicable design speed. These Green Book SSD criteria are used by most highway agencies in the United States. The SSD model in Equation (2) consists of two terms. The first term (1.47 Vt) represents the distance traveled by a vehicle traveling at constant speed equal to the roadway design speed during the driver’s perception-reaction time (i.e., the elapsed time from the moment an object in the road ahead comes into the driver’s view until the moment the driver begins to apply the vehicle brakes). Perception-reaction time consists of the time needed for the driver to perceive that there is an object ahead (assumed to be 1.5 sec) plus the time needed for the driver to react and begin to apply the brakes (assumed to be 1.0 sec). Thus, the total assumed perception- reaction time is 2.5 sec. C H A P T E R 2 Design Criteria for HSOs

Design Criteria for HSOs 11 The second term in the SSD model (1.075 V2/a) is the distance needed for the vehicle to come to a stop once the driver begins to apply the brakes. The braking distances are based on braking at a constant deceleration equal to 11.2 ft/s2, independent of the initial speed at the beginning of the braking maneuver. This deceleration is comfortable to most drivers. Most vehicle braking systems and the tire-pavement friction levels of most roadways are capable of providing this deceleration. Vehicles need slightly longer braking distances on downgrades and slightly shorter braking distances on upgrades. Thus, on roadways that are not level, the SSD model in Equation (2) changes to: = +     ±    1.47 30 32.2 (3) 2 S Vt V a G where G is grade expressed as rise/run (ft/ft). In implementing the Green Book SSD design criteria, highway designers must consider both vertical and horizontal sight distance limitations. Design for each of these types of sight distance limitations is discussed in the following sections. 2.1.2 Design for Vertical Sight Distance Limitations Vertical sight distance limitations arise mostly from the geometry of the road itself. Crest vertical curves limit the driver’s view of the roadway beyond the crest. Sag vertical curves may limit the driver’s view of the roadway ahead at night by redirecting the vehicle’s headlights away from the roadway ahead. In addition, overpass structures on sag vertical curves may also limit the driver’s sight distance. Figure 6 shows four types of vertical curves found on roadway systems. At crest vertical curves (Types a and b in Figure 2), the roadway profile itself limits SSD. The Green Book (AASHTO 2011) specifies that crest vertical curves should be designed so that a driver whose eyes are 3.5 ft above the roadway surface should be able to see a 2-ft high object in the road ahead (equivalent to the typical taillight height of passenger vehicles) over Design speed (mph) Brake reaction distance (ft) Braking distance on level (ft) SSD (ft) Calculated (S) Design (DSSD) 15 55.1 21.6 76.7 80 20 73.5 38.4 111.9 115 25 91.9 60.0 151.9 155 30 110.3 86.4 196.7 200 35 128.6 117.6 246.2 250 40 147.0 153.6 300.6 305 45 165.4 194.4 359.8 360 50 183.8 240.0 423.8 425 55 202.1 290.3 492.4 495 60 220.5 345.5 566.0 570 65 238.9 405.5 644.4 645 70 257.3 470.3 727.6 730 75 275.6 539.9 815.5 820 80 294.0 614.3 908.3 910 Table 1. Current AASHTO SSD design criteria for level roadways (AASHTO 2011).

12 Design Guidelines for Horizontal Sightline Offsets the full distance given by the DSSD criteria presented in Table 1. This requires minimum crest vertical curve length given by: when DSSD is less than L, ( ) ( ) = +100 2 2 (4) 2 1 2 2L A DSSD h h VC when DSSD is greater than L, 2 200 (5) 1 2 L DSSD h h A VC ( ) = − + where LVC = length of vertical curve (ft); DSSD = design value of stopping sight distance (ft); A = algebraic difference in grade between entering percent grade (G1) and departing percent grade (G2), percent; h1 = height of driver’s eye above roadway surface (ft); and h2 = height of object above roadway surface (ft). Figure 6. Types of vertical curves [adapted from AASHTO (2011)].

Design Criteria for HSOs 13 Figure 7 shows the parameters considered in determining the length of a crest vertical curve to provide SSD. Figure 8 shows the minimum lengths of crest vertical curves for specific values of algebraic difference in grade (A) to provide the minimum SSD for each design speed. Figure 8 enables users to determine the value of K, the length of vertical curve per unit of algebraic difference in grade, needed to provide the minimum SSD. In other words, = (6)K L A VC where K is length of vertical curve per unit of algebraic difference in grade (ft). The values of K for crest vertical curves to provide SSD range from 3 ft per percent difference in grade at 15 mph to 384 ft per percent difference in grade at 80 mph. Design criteria for length of sag vertical curves (Types 1 and 2 in Figure 6) consider four sepa- rate criteria based on headlight sight distance, passenger comfort, drainage control, and general appearance. Of these four criteria, only headlight sight distance is a function of SSD. SSD is not limited on sag vertical curves under daylight conditions (unless an overpass or some other object over the roadway is present), but the shape of a sag vertical curve may limit the distance that headlights illuminate the roadway ahead at night. Headlight sight distance may be less of a concern than commonly supposed because most motorists travel at night at speeds such that their stopping distance is greater than their headlight sight distance, even on level roads where headlight sight distance is not limited by roadway geometry. At design speeds of 55 mph and more, sag vertical curves are generally shorter than comparable crest vertical curves. The values of K for sag vertical curves range from 10 ft per percent difference in grade at 15 mph to 231 ft per percent difference in grade at 80 mph. 2.1.3 Horizontal Sight Distance Obstructions Horizontal sight distance obstructions are opaque objects that limit the driver’s view of the roadway ahead and are located on the inside of horizontal curves. If the inside of a horizontal curve is clear of sight obstructions, the driver of a vehicle will be able to see objects or other vehicles on the roadway ahead by looking along a sight line that traverses a portion of the shoulder and/or the roadside area. However, where sight obstructions such as buildings, rock cuts, retaining walls, roadside barriers, bridge piers and abutments, fences, Figure 7. Parameters considered in determining the length of a crest vertical curve to provide SSD (AASHTO 2011).

14 Design Guidelines for Horizontal Sightline Offsets trees, bushes, crops, or other vegetation are present on the inside of a horizontal curve, a driver’s ability to see a sufficient distance ahead may be limited. The smaller the radius of a horizontal curve, the larger the distance from the roadway, or HSO, that should be clear of obstructions for the driver to have available at least the applicable DSSD specified in the Green Book (AASHTO 2011). Because horizontal sight distance limitations are the primary focus of this research, the computation of HSOs is discussed separately in Section 2.3, and more fully in Appendix A. 2.2 Components of AASHTO SSD Criteria Each component of the AASHTO SSD model is discussed in the following sections. 2.2.1 Design Speed Design speed is defined as a selected speed used to determine the various geometric design features of the roadway (AASHTO 2011). The design speed selected for a roadway should be logical with respect to the anticipated operating speed, topography, adjacent land use, and functional classification of the roadway. The selection of an appropriate design speed is a decision made by the designer for each individual project. As shown in Table 1, the selected design speed of the roadway directly influences the DSSD that should be provided on horizontal curves. Figure 8. Chart to determine the length of a crest vertical curve needed to provide DSSD (AASHTO 2011).

Design Criteria for HSOs 15 2.2.2 Initial Speed at Beginning of Braking Maneuver In deriving SSD values, the first term of Equations (2) and (3) shows that the initial speed of the vehicle at the beginning of a braking maneuver is assumed to be equal to the roadway design speed. 2.2.3 Perception-Reaction Time Perception-reaction time is the sum of perception time and brake reaction time. Brake reaction time was assumed as 1 sec in the 1940 AASHO sight distance policy (AASHO 1940), and remains at that value today. The assumption concerning perception time was set at 1.5 sec in the 1954 AASHO Blue Book (AASHO 1954), for a total perception-reaction time of 2.5 sec, and remains at that value today. The AASHTO Green Book (AASHTO 2011) cites the 2.5 sec value of perception-reaction time as consistent with the findings of a 1971 study by Johanson and Rumar (1971). 2.2.4 Vehicle Deceleration and Braking Maneuver The pavement condition and vehicle deceleration/braking maneuver assumed as the basis for SSD design has evolved over the years. AASHTO policy formerly assumed that the braking maneuver was an emergency locked-wheel stop on wet pavement. Research by Fambro et al. (1997) concluded that a locked-wheel stop was not appropriate for SSD design because most drivers who encounter an object in the roadway use controlled braking rather than a locked- wheel braking. Beginning with the 2001 Green Book, the SSD design criteria have been based on controlled braking on a wet pavement surface (AASHTO 2001). The change to controlled braking is especially appropriate today, given that most vehicles are now equipped with anti- lock brakes. The 2001 Green Book, and more recent editions, assume a comfortable, controlled deceleration of 11.2 ft/s2, or just under 0.35 g. 2.2.5 Driver Eye Height Driver eye height is based on a combination of vehicle and human characteristics—the vertical position of the driver’s seat in the vehicle, which varies between vehicles, and the distance from the driver’s seat to the driver’s eye, which varies between people. The driver eye heights assumed in SSD design have decreased over the years, from 4.5 ft in 1940 to 3.5 ft today, primarily because of changes in vehicle design. 2.2.6 Object Height SSD design policy has always recognized that, while maintaining sight distance from the driver’s eye to the pavement surface might be desirable, such an approach would not be cost-effective. Research by Fambro et al. (1997) found that most objects struck by vehicles on the roadway were at least 2 ft in height. The object most often struck by a vehicle is another vehicle, and vehicle taillights are typically 2 ft above the roadway surface. Based on the Fambro et al. research, the 2001 Green Book adopted a 2-ft object height for SSD design. 2.3 HSO Design Criteria HSOs are provided in design so that objects on the inside of horizontal curves do not limit a driver’s view of the roadway ahead for at least the established SSD design criteria. As discussed in Section 2.2, the vertical component of SSD is fully defined by the vertical profile

16 Design Guidelines for Horizontal Sightline Offsets of the roadway (except on sag vertical curves where an overhead structure may be present). However, the horizontal component of SSD depends on both the vertical and horizontal geo- metrics of the roadway as well as the varied nature and height of roadside sight obstructions on the inside of horizontal curves. Sight obstructions can occur on either the right or left side of the roadway, or in a divided highway median. A variety of roadside objects can constitute a horizontal sight obstruction—rock cuts, retaining walls, embankments, median barriers, guardrails, bridge piers and abutments, structures, trees, bushes, and utility poles. Figure 1 illustrates the design situation for HSO to roadside sight obstructions on the inside of the curve, as presented in the Green Book (AASHTO 2011). The figure illustrates a driver’s line of sight to the roadway ahead which, on a horizontal curve, is a chord of that curve. The dimension labeled HSO in Figure 1, which in terms of analytic geometry is known as the middle ordinate of the curve, is now called the horizontal sightline offset in the Green Book. The HSO, or middle ordinate of the curve, for the situation shown in Figure 1 is determined as shown in Equation (1). The Green Book (AASHTO 2011) states that horizontal sightlines are assessed along the centerline of the lane closest to the inside of the horizontal curve. Figure 9 presents the design controls from the Green Book for providing SSD on horizontal curves, based on Equation (1). To use Figure 9, plot a horizontal line equivalent to the radius of the horizontal curve (R). Then, identify the point where that horizontal line intersects the curve corresponding to the design speed of the curve. Finally, plot a vertical line through that point of intersection, and the value of HSO where the vertical line intersects the horizontal axis is the horizontal sightline offset shown in Figure 1. Equation (1) and Figure 9 might be read simplistically to indicate that a horizontal sightline offset equal to HSO is needed throughout each horizontal curve. Thus, casual readers of the Green Book might be under the impression that HSO needs on a horizontal curve are like those shown in Figure 10. However, Figure 10 is purely hypothetical, because Figure 1 illustrates only the simplest case for HSOs since, in Figure 1, both the driver’s eye and the object to be seen at a distance of S from the driver’s eye are on the horizontal curve. The Green Book notes that the full HSO determined from Equation (1) or Figure 9 is needed only in the middle portion of a horizontal curve, but that the value of HSO shown in Equation (1) or Figure 9 is “approximate” for other locations. However, the Green Book fails to note explicitly that Equation (1) and Figure 9 only apply directly to horizontal curves that are longer than the DSSD, S. If the horizontal curve is shorter than the DSSD, S, the horizontal sightline offset needed is always less than HSO determined with Equation (1) or Figure 9. Figure 11 shows with shading the extent of the areas that actually need to be clear of road- side sight obstructions. In particular: • If L > S, the area that needs to be clear of sight obstructions is shown in Figure 11(a). The area for which the horizontal sightline offset is equal to HSO in Equation (1) and Figure 9 extends from Station PC + 0.5S to PT – 0.5S. • If L = S, the area that needs to be clear of roadside sight obstructions is shown in Figure 11(b). A horizontal sightline offset equal to HSO is needed only at a single point located at the center of the curve, Station PC + 0.5L. • If L < S, the area that needs to be clear of roadside sight obstructions is shown in Figure 11(c). At no point does the horizontal sightline offset need to be as great as HSO in Equation (1) and Figure 9. The vertical dimensions of the cross section of the roadway, including superelevation, do not factor into the dimensions of the shaded areas in Figure 11. Figure 11 is based purely on the plan view of the roadway.

Design Criteria for HSOs 17 Figure 9. SSD on horizontal curves (AASHTO 2011).

18 Design Guidelines for Horizontal Sightline Offsets (a) L > S (b) L = S (c) L < S Figure 11. Actual areas that need to be clear of sight obstructions on the inside of a horizontal curve. Figure 10. Simplistic view of area that needs to be clear of sight obstructions on the inside of a horizontal curve. Figure 11 shows that the shaded area that should be clear of sight obstructions extends beyond the ends of the horizontal curve, represented in the figure by the point of curvature (PC) and the point of tangency (PT). The shaded area actually begins at Station PC – S and ends at Station PT + S. It should also be noted that a portion of the shaded area shown in Figure 11 should already be free of sight obstructions. The driver’s path from the PC to PT shown in Figure 11 is along the centerline of the lane closest to the inside of the curve. Since HSOs are measured from the centerline of the inside lane and the travel lanes and shoulder are, by definition, clear of sight obstructions (with the possible exception of vehicles

Design Criteria for HSOs 19 stopped temporarily on the shoulder), the value of HSO, m, is only of practical importance to design where: > + 2 (7)m LW SW where m = HSO on the inside of the curve (ft); LW = lane width for the inside lane on the curve (ft); and SW = shoulder width (ft). The width of the roadside area (outside of the shoulder) that should be clear of sight obstructions at any location along the curve is: = − − 2 (8)m m LW SWroadside where mroadside is portion of HSO that is on the roadside area outside of the shoulder (ft). If mroadside is less than or equal to zero, then no portion of the roadside (i.e., outside of the roadway shoulder) needs to be clear of sight obstructions. There will undoubtedly be design situations in which the variations among the three cases for measurement of HSO shown in Figure 11 have important consequences for design. At some locations (e.g., where a rock cut or retaining wall is present on the roadside), it could be substantially more expensive to assume a roadside clear area like that shown in Figure 10, when one of the cases shown in Figure 11 actually applies. Thus, it appears that the Green Book oversimplifies in stating that HSO is an “approximation” of horizontal sightline offset for those cases shown in Figure 11 in which m is less than HSO. This Green Book discussion of HSOs can be improved to encourage better understanding of the issue of HSOs. In Figure 11, the variable m is used to represent the value of horizontal sightline offsite that should be provided at any point along a horizontal curve. The value of HSO computed with Equation (1) or Figure 9 represents the maximum value that m can take on any specific hori- zontal curve; m will reach the value of HSO only if the length of the curve equals or exceeds the DSSD (L ≥ S). Thus, HSO can also be referred to as mmax. The current Green Book does not address the computation of determining specific dimensions of the shaded areas in Figure 11 that are less than HSO in width. Papers by Mauga (2014, 2015b) present a computational method for determining HSO at any point in the vicinity of a horizontal curve from Station PC − S to Station PC + S. The Mauga method can be applied in new construc- tion to identify roadside areas that should be clear of roadside sight obstructions; the method can also be applied in the assessment of existing roadways. The Mauga method is summarized in Appendix A. The Mauga method may be too complex for manual application, but can readily be incorporated in CADD systems to show the designer the area that needs to be clear of horizontal sight obstructions. Raymond (1972) presents graphs for determining HSO, and the roadside area that should be clear of sight obstructions is influenced by the presence of spiral curve transitions with increasing HSOs needed as the length of spiral increases (see Figure 1). An analysis by Easa (1991, 1993) developed a sight distance model and concluded that HSOs needed on compound curves analyzed together may exceed those for the individual curves analyzed separately. Mauga (2015a) also examined HSOs for compound curves.

20 Design Guidelines for Horizontal Sightline Offsets Liu and Wang (2012) and Liu (2013) provide a 3D analysis methodology, based on vector algebra, for determining sight distance on combined horizontal curves and crest vertical curves. The design criteria in the Green Book and its predecessors were developed prior to the computer era, at a time when the conservative “approximation” discussed earlier may have been necessary. Today, given that virtually all design is done with CADD systems, more exact methods of analysis can be implemented. It is likely that the complete computational method is too complex to be incorporated in the Green Book, but its value for CADD systems is evident. 2.4 Alternative Assumptions for Measuring Horizontal Sight Distance This section presents assumptions that may be considered for measuring horizontal sight distance in design analyses as alternatives to the traditional AASHTO (Green Book) assump- tions. Three issues are addressed: lateral position of the driver’s eye, the height of the driver’s eye, and the height of the object to be seen. 2.4.1 Lateral Position of Driver’s Eye The AASHTO Green Book assumes that horizontal sight distance should be measured along the centerline of the inside travel lane on the horizontal curve. Since the driver sits on the left side of the vehicle, it may be more realistic to consider an off-center position for the driver’s eye. The reliability analysis model presented in Chapter 5 and Appendix B allows the designer to consider the effect on ASSD of the lateral placement of the driver’s eye anywhere within the travel lane. A suggested value for the distance from the left edge of the travel lane to the driver’s eye is one-quarter of the lane width. This positioning assumption provides an advantage in sight distance for curves to the right, but a disadvantage in sight distance for curves to the left. 2.4.2 Height of Driver’s Eye The AASHTO Green Book assumes that the driver’s eye is positioned 3.5 ft above the road- way. This is an appropriate assumption for a typical driver in a typical passenger car. The reli- ability analysis model presented in Chapter 5 and Appendix B allows the designer to consider the effect on ASSD of positioning the driver’s eye lower or higher than the AASHTO value. For example, a driver eye height of 3.0 ft might be used as representation of a low-profile vehicle such as a sports car, while a driver eye height of 8.0 ft might be used as representative of a truck. 2.4.3 Height of Object to Be Seen The AASHTO Green Book assumes that the object to be seen is 2.0 ft above the roadway, equivalent to the taillight height of a typical passenger car. As a result there are horizontal curve locations appearing not to provide sufficient SSD when assessed with AASHTO criteria, but at which the driver can see stopped vehicles ahead in the travel lane over the sight obstruction. For example, the upper portion of passenger vehicles is often visible ahead over roadside or median barriers. The reliability analysis model presented in Chapter 5 and Appendix B allows the designer to consider the effect on ASSD of modifying the height of the object to be seen. For example, if the object height is set at 3.5 or 4.0 ft, it may still be possible for approaching drivers to see the upper portion of a 4.5-ft passenger car ahead on the roadway.