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

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2 CHAPTER 2 REVIEW OF CURRENT AASHTO METHODOLOGIES The sag vertical curve requirements have not changed since 1965. The definition for the limits of sag vertical curves in the AASHTO guidelines in terms of length, speed, or grades is based on the assumption of a 1° uplight condition for headlamps (AASHTO, 2004). For safety, vehicles traveling on a vertical curve should be provided with sufficient SD for a timely stop before hitting another car or object. When establishing lengths of sag vertical curves, four different criteria are recognized: passenger comfort, drainage control, general appearance, and headlight SD. According to AASHTO (2004), the general expression for passenger comfort on a sag vertical curve is: (1) Where L is the length of the sag vertical curve in feet; A is the algebraic difference in grades in percent; and V is the design speed in miles per hour (mph). AASHTO states that the length of vertical curve needed to satisfy this comfort factor is only about 50% of that needed to satisfy the headlight SD criterion; thus, this criterion will not be the emphasis of this report. For drainage requirements, sag curve length will become an issue in Type III curves (shown in Figure 1) where the Vertical Point of Intersection (VPI) is the lowest part on the curve and curbed sections are used. AASHTO defines a maximum of 167 for K (ratio of curve length, L, to the algebraic difference in grade, A) in such situations. This criterion differs from other criteria in that it determines the maximum length of the curve. Figure 1. Type III sag vertical curve. For general appearance of sag vertical curves, the rule-of-thumb for minimum curve length is 100 * A. Also defined in AASHTO is a minimum length of vertical curves for flat gradients, which is 3 * V. These two criteria are used to avoid curves that are too sharp or too short and are not directly related to the design modifications incurred by the evolution of headlamps. The headlight SD, which is the portion of lighted highway ahead when a vehicle traverses a sag vertical curve at night, is the primary design control for sag curves. On a sag vertical curve, the SD during daytime is not an issue. However, when vehicles travel at night, the

3 distance that drivers can detect is decided by headlight SD, which is shown as “Sight Distance S” in Figure 2. Figure 2. Sight distance and curve length on a sag curve. Headlight SD is affected by the position of the headlights and the direction of the light beam. As stated in the current version of the AASHTO (2004) guidelines, a height of 600 mm (2 ft) and a 1-degree upward divergence of the light beam from the longitudinal axis of the vehicle are assumed when calculating SD. The equations used by AASHTO to calculate sag curve length: When S (in feet) is less than L (in feet) (2) When S (in feet) is greater than L (in feet) (3) Where S is the headlight SD (in feet), L is the length of a sag vertical curve (in feet), and A is the algebraic difference in grade (%). The headlight SD should be at least as long as the stopping SD for the driver to make a prompt stop when needed. In the equations above, Stopping Sight Distance (SSD) values are used in place of S with the assumption that a sag vertical curve should be long enough that the light beam distance is nearly the same as the SSD. SSD refers to the distance a vehicle travels from the instant the driver sees an obstacle that requires a stop, to the instant that the vehicle reaches a complete stop. The basic model for determining SSD was developed by AASHTO in 1940. This basic model consists of four parameters: design or initial speed, driver perception-reaction time, friction between the tires and the pavement, and percent grade. While these parameters have been revised several times since 1940, the basic model has remained the same (Fambro, Fitzpatrick, & Koppa, 1997). As mentioned, the change in uplight angle in recent years caused a decrease in headlight SD. As shown in Figure 3, with a smaller upward divergence of the light from the axis of the vehicle, the point where the beam strikes the road surface is closer to the vehicle than before. To ensure the safety criterion is still met, modifications to the guideline need to be considered. 𝑳𝑳 = 𝑨𝑨𝑺𝑺𝟐𝟐 𝟐𝟐𝟐𝟐𝟐𝟐[𝟐𝟐.𝟐𝟐 + 𝑺𝑺(𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕°)] 𝑳𝑳 = 𝟐𝟐𝑺𝑺 − 𝟐𝟐𝟐𝟐𝟐𝟐[𝟐𝟐.𝟐𝟐 + 𝑺𝑺(𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕°)] 𝑨𝑨

4 Figure 3. Sight distance and curve length on a sag curve.