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HFG CURVES (HORIZONTAL ALIGNMENT) Version 1.0 THE INFLUENCE OF PERCEPTUAL FACTORS ON CURVE DRIVING Introduction The perceptual factors in curve driving refer to the driver's use of visual information to assess the curvature of an upcoming curve. This activity is important because a driver's perception of an upcoming curve's radius forms the primary basis for making speed and path adjustments prior to curve entry. The curve radius as seen from the driver's perspective is called the apparent radius. Although drivers will use speed information from signs, in practice, driver speed selection in curves is heavily influenced by roadway features (1), and the apparent radius appears be the primary determining factor of speed at curve entry (2). The primary design challenge regarding curve perception is that the apparent radius can appear distorted--either flatter or sharper--depending on the topography and other road elements. Of particular concern are combination curves that include a vertical sag superimposed on a horizontal curve. From the driver's perspective, this combination makes the horizontal curve appear flatter than it actually is (See A in the figure below). Consequently, drivers may be inclined to adopt a curve entry speed that is faster than appropriate based on horizontal curvature alone. Design Guidelines Sag horizontal curves that have a visual appearance (apparent horizontal radius) that is substantially different from the plan radius should be given careful consideration because they may lead to curve entry speeds that are faster than expected based on horizontal curvature alone. Based Primarily on Based Equally on Expert Judgment Based Primarily on Expert Judgment and Empirical Data Empirical Data A B From Long Tangent From Preceding Curve Apparent Curvature 9000 9000 Radius of Sag Vertical Curvature (m) Radius of Sag Vertical Curvature (m) Potential encroachment 8000 8000 Recommended Range 7000 Recommended 7000 e Actual Curvature Range ng 6000 e 6000 Ra ng le Ideal trajectory Ra p ta b Trajectory along 5000 le 5000 ce pta b Ac apparent curvature 4000 ce 4000 Ac 3000 3000 2000 2000 Curve entry speed based on 1000 Unacceptable Range 1000 Unacceptable Range apparent curvature is too high to safety traverse the actual curvature 0 0 0 100 200 300 400 500 600 700 800 0 100 200 300 400 500 600 700 800 Radius of Horizontal Curve (m) Radius of Horizontal Curve (m) A. A vertical sag curve produces a visual image (shaded roadway) that a driver would perceive as having an apparent radius that is larger than the actual radius. B. Nomographs indicating vertical and horizontal curve radius combinations that result in apparent radii that may result in curve entry speeds that are unintentionally faster than expected based on horizontal curvature alone (red shaded region), and which possibly represent a safety risk (2). Note that the nomographs present vertical curvature in terms of radius (in meters) and not K, which is the typical approach for representing vertical curvature. The reason for presenting curvature as a radius is that the geometric calculations for computing visual distortion rely on circular arcs. The nomographs can be used to provide a "rule of thumb" check for potentially problematic curve combinations assuming the vertical curvature component can be generally approximated by a circle with an arc intersecting the low point of Type III curves and vertical points of curvature on both sides. 6-4
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HFG CURVES (HORIZONTAL ALIGNMENT) Version 1.0 Discussion Curve perception is an important part of curve driving because, in the absence of extensive experience with a curve, drivers must rely on their judgments about a curve to select a safe speed for curve entry. Speed signage information can assist drivers; however, evidence suggests that this information is not a primary source for speed selection in curves (1). Therefore, driver expectations (influenced by design consistency) and the visual information the driver obtains about the curve are the primary basis for speed selection. Sag horizontal curves can cause drivers to significantly underestimate the sharpness of a curve because of a visual distortion from the driver's viewing perspective; i.e., the apparent radius appears to be longer than the plan radius. Thus, these sag horizontal curves, are also associated with higher entry speeds and crash rates (2, 3). The optical aspects of this phenomenon have been derived analytically, and the results were used to make the nomographs presented on the previous page. Horizontal and vertical curve radius combinations that fall in the unacceptable range are associated with significant visual distortion, and also associated with higher than 85 th percentile speeds and higher crash rates (2). Note that this validation is based on European data, and these findings have not been investigated on US roads. However, the optical properties of this phenomenon are universal and should be equally applicable to all drivers (4). This analytical work also assumes a 75 m viewing distance, which is comparable to the start of the Curve Discovery segment of curve driving, in which drivers spend most of their time inspecting the curve. Distortion effects may be reduced somewhat at further viewing distances; however, assuming a 75 m viewing distance is consistent with driver behavior and is more conservative. Visual distortion also occurs when crest vertical curves are superimposed on horizontal curves; such curves appear sharper than the plan radius. This typically results in slower 85th percentile entry speeds (2, 3). However, a crest horizontal curve with a vertical curvature that approximates a circular radius of less than 3 times the horizontal curve radius could present a discontinuous visual image of the curve (e.g., the part of the roadway just behind the crest is occluded) (2). Such a crest horizontal curve is potentially inconsistent with driver expectations and could compromise roadway safety by causing drivers to suddenly brake hard if they are surprised by the curve appearance. However, there are currently no empirical data showing that this is an actual safety issue. Design Issues A summary of the relevant research findings regarding curve perception in general and the corresponding degree of empirical support is shown in the table below. While no specific values or recommendations can be made for these aspects, it is useful to take them into consideration during curve design, especially if other aspects of the curve design suggest that there may be a potential problem with driver perception of the curve radius. Aspect Effect Empirical Support Superimposed Vertical Sag Makes a curve appear flatter Strong Cross Slope For sag horizontal curves, the greater the cross slope and lane width, the Analytical evidence greater the apparent flattening of the horizontal curve Superimposed Vertical Crest Makes a curve appear sharper and may cause discontinuities in curve Strong Deflection Angle Holding radius constant, greater deflection angle makes the curve Moderate appear sharper, especially for smaller radii Delineators Delineators provide drivers with more information to judge the curve Moderate radius, which improves accuracy of these judgments Spiral May make curve appear flatter, or make curve perception more Indirect difficult, because the onset of the curve is less apparent Signage Drivers perceive curve as "riskier" if signs indicate that the curve is Suggestive hazardous Cross References Task Analysis of Curve Driving, 6-2 Key References 1. Fitzpatrick, K., Carlson, P., Brewer, M. A., Wooldridge, M. D., and Miaou, S.-P. (2003). NCHRP Report 504: Design Speed, Operating Speed, and Posted Speed Practices. Washington, DC: Transportation Research Board. 2. Appelt, V. (2000). New approaches to the assessment of the spatial alignment of rural roads--apparent radii and visual distortion. Proceedings of the 2nd International Symposium on Highway Geometric Design (pp. 620-631). Cologne, Germany: Verlag. 3. Hassan, Y., and Easa, S. M. (2003). Effect of vertical alignment on driver perception of horizontal curves. Journal of Transportation Engineering, 129(4), 399-407. 4. Bidulka, S., Sayed, T., and Hassan, Y. (2002). Influence of vertical alignment on horizontal curve perception: Phase I: Examining the hypothesis. Transportation Research Record, 1796, 12-23. 6-5