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HFG CURVES (HORIZONTAL ALIGNMENT) Version 1.0 COUNTERMEASURES FOR IMPROVING STEERING AND VEHICLE CONTROL THROUGH CURVES Introduction Successful navigation of curves depends on accurate steering and speed control in order to minimize lateral acceleration within the lane. Design of alignments that conform to driver expectations and typical behaviors will enhance the driver's ability to control the vehicle. This guideline provides strategies for im plementing curve geometries that help drivers maintain proper lane position, speed, and lateral control through curves. Delineation treatments that improve vehicle control are presented in the "Countermeasures to Improve Pavement Delineation" guideline. Design Guidelines The following guidelines present strategies for designing geometric features that will enhance steering control. Curvature Minimize the use of controlling curvature (i.e., maximum allowable curvature for a given design speed). Spirals Spiral transition curves should be used whenever possible, particularly for curves on roads with high design speeds (e.g., 60 mi/h or greater). Spiral curve lengths should equal the distance traveled during steering time (i.e., 2 to 5 s, which equates to roughly 60140 m for two-lane highways and 80140 m for freeways). The recommended curve radius for two-lane highways with a speed limit of 50 mi/h is 120 to 230 m, with clothoid parameters between 0.33 and 0.5 R. Circular arc lengths should equate to at least a 5 s pass-through time. Reverse Curves Do not use tangent sections in reverse curves when the distance between the exit of the first curve and the entrance of the second curve is short enough to encourage a curved path through the tangent (e.g., 80 m or less for two-lane highways and 135 m for freeways). Superelevation Superelevation should be designed to result in zero lateral acceleration through the curve at design speed. Design Avoid sharp, isolated curves and maintain consistency in the design of superelevation, Consistency road width, and other curve features to improve conformance with drivers' expectations. Based Primarily on Based Equally on Expert Judgment Based Primarily on Expert Judgment and Empirical Data Empirical Data The figure below illustrates the various concepts that describe how drivers navigate a curve: visual components related to guidance and lane-keeping, the path choice model, and the combination of processes that govern curve traversal. Heading Direction of gaze · Driver enters curve to the left of the Ideal Trajectory lane center Far region: dmin Actual Trajectory curvature · Far region provides cues for predicting information curvature and steering angle in closed- (anticipatory loop anticipatory control process. process) T = Tangent point ractual = Vehicle radius of travel · Near region (7 degrees down from T rideal = Ideal radius of travel dmin = Minimum acceptable horizon) provides cues for correcting distance from lane edge deviations from path in open-loop ractual compensatory control process. rideal · Driver follows trajectory with radius of curvature (ractual) greater than radius at Near region: position-in-lane center of lane (rideal) and that brings the information vehicle to a minimum distance (dmin) (compensatory from the roadway edge line at its apex. process) · Driver fixates on curve tangent point through the curve. Adapted from Donges (1); Levison, Bittner, Robbins, and Campbell (2); and Spacek (3). Figure not to scale. 6-8
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HFG CURVES (HORIZONTAL ALIGNMENT) Version 1.0 Discussion The steering control task has been modeled as a two-level process composed of an open-loop anticipatory component (far view) for predicting curvature and steering angle, and a closed-loop compensatory component (near view) for correcting deviations from the desired path (1). However, this two-level model does not adequately describe some path-decision behaviors such as curve-cutting. Also, drivers often make anticipatory steering actions based on an internal estimate of the vehicle characteristics and on previously perceived curvature, rather than on direct visual feedback, while paying attention to other aspects of the driving task (4). Geometric alignment and delineation features affect the driver's perception of curvature and therefore influence curve entry speed. Curve geometries that do not meet the driver's perceptual expectations may result in inappropriate entry speeds that require speed and steering corrections within the curve in order to avoid excessive lateral acceleration and a potential loss of control. Inaccuracies in anticipatory assessment prior to curve entry generally increase with curvature, and compensatory control actions to correct these errors are greatest in sharp curves (4, 5). In general, drivers tend to cut curves. In one study (3), almost one-third of drivers cut left-hand curves and 22% cut right-hand curves. Drivers compensate for inadequate steering adjustment at curve entry by following a trajectory with a radius that is larger than the ideal radius (i.e., radius at the center of the lane), with the vehicle traveling within some minimum distance of the edge line at its apex (2, 7). Vehicle path radius at the point of highest lateral acceleration correlates with higher crash rates. Design Issues Curvature: Road curvature significantly affects average lateral position error. As curves become sharper, there is a corresponding increase in workload, which can result in an increase in edge line encroachments on the inside lane (6, 7). Restrictive geometric characteristics (e.g., sharper curves, narrower shoulders, and steeper grades) are more likely to lead to centerline encroachments than those that are less constraining; however, high curvature has the greatest adverse effect on crash rates and driving performance in horizontal curves. Spiral curves: Spirals that are designed to match drivers' natural steering behavior offer a gradual increase in centrifugal force and facilitate superelevation transitions, which can improve the vehicle's lateral stability (6, 7, 8). However, overly long spiral transitions can lead to misleading perception of the sharpness of curvature, inappropriate entry speed, and unexpected steering and speed corrections within the curve. The most desirable spiral length is equal to the distance traveled during the steering time (nominally 2 to 5 s depending on radius). Reverse curves: Tangent sections of appropriate length can provide effective transitions between curves in a reverse curve alignment. However, if the tangent section is too short, drivers may follow a curved rather than straight trajectory through the tangent section (7). To match the alignment to drivers' typical steering behavior, the transitional tangent should be long enough to allow straightening of the vehicle through the transition (if possible); otherwise, the transitional tangent should not be used. Design consistency: Drivers are more likely to make appropriate speed and steering decisions when the roadway design meets their perceptual expectations. Consistency in curve features, such as superelevation, lane width, curvature, etc., help reduce workload and therefore improve stability in steering control (6). Cross References The Influence of Perceptual Factors on Curve Driving, 6-4 Speed Selection on Horizontal Curves, 6-6 Countermeasures to Improve Pavement Delineation, 6-10 Key References 1. Donges, E. (1978). Two-level model of driver steering behavior. Human Factors, 20(6), 691-707. 2. Levison, W. H., Bittner, A. C., Robbins, T., and Campbell, J. L. (2001). Development of Prototype Driver Models for Highway Design. Task C: Develop and Test Prototype Driver Performance Module (DPM). Washington, DC: FHWA. 3. Spacek, P. (2005). Track behavior in curve areas: Attempt at typology. Journal of Transportation Engineering, 131(9), 669-676. 4. Godthelp, H. (1986). Vehicle control during curve driving. Human Factors, 28(2), 211-221. 5. Simsek, O., Bittner, A. C., Levison, W. H., and Garness, S. (2000). Development of Prototype Driver Models for Highway Design. Task B: Curve-Entry Speed-Decision Vehicle Experiment. Washington, DC: FHWA. 6. Reinfurt, D. W., Zegeer, C. V., Shelton, B. J., and Neuman, T. R. (1991). Analysis of vehicle operations on horizontal curves. Transportation Research Record, 1318, 43-50. 7. Said, D. G., Hassan, Y., and Abd El Halim, O. (2007). Quantification and utilization of driver path in improving design of highway horizontal curves. Transportation Research Board 86th Annual Meeting Compendium of Papers [CD-ROM]. 8. Perco, P. (2006). Desirable length of spiral curves for two-lane rural roads. Transportation Research Record, 1961, 1-8. 6-9