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HFG CURVES (HORIZONTAL ALIGNMENT) Version 1.0 SPEED SELECTION ON HORIZONTAL CURVES Introduction Various sources attempt to examine speed data for roadway geometry and to determine desirable speeds for horizontal curves. AASHTO policy defines design speed as "a selected speed used to determine the various geometric design features of the roadway" (1). The design speeds on horizontal curves should be set at a value determined by AASHTO policy and factors determined from a survey of state DOTs. AASHTO policy (1) considers factors such as functional classification, rural vs. urban environment, and terrain type; state DOTs typically consider factors such as functional classification, legal speed limit (as well as legal speed limit plus an adjustment value of 5 or 10 mi/h), anticipated volume, terrain type, development, costs, and design consistency. Design Guidelines A number of vehicle, driver, and roadway variables should be considered when determining speed limits for horizontal curves. A procedure to calculate appropriate speeds has been adapted from Charlton and de Pont (2) and is outlined below. If these factors are common at an intersection location, then consideration should be given to modifying the gap acceptance design assumptions. Step Procedures for Determining Curve Advisory Speed Limits 1 Determine curve radius (R), superelevation, and offset distance from center of lane to any visual obstruction (O). 2 Determine the vehicle's maximum possible lateral acceleration and braking coefficient. The maximum lateral acceleration is limited by rollover stability for most heavy vehicles and by tire adhesion for passenger cars. Typical values to use for dry conditions are 0.35 g for laden heavy vehicles, 0.7 g for buses and SUVs, and 0.8 g for passenger cars. The braking coefficient reflects the maximum braking efficiency that can be achieved and should be 0.91.0 for passenger cars and 0.5 0.6 for heavy vehicles. Assume a reaction time (Tr) of 2 s. 3 Calculate the maximum possible speed (in km/h) limited by lateral acceleration using the formula: V 127 R (lateral_acc superelevation ) 4 4.1 From this speed, calculate the safety factor (SF) using the equation: SF 1 0.03476 V 0.00004762 V 2 4.2 Divide the maximum lateral acceleration value by the safety factor (SF), and recalculate the speed using the equation in step 3. This is the desirable maximum speed limited by lateral acceleration, Vacc. lateral_acc Vacc 127 R superelevation SF 5 5.1 Calculate the sight distance using the equation: 1 R O SDacc 2 R cos R 5.2 Based on a safety factor of 2, set the braking coefficient (d) to half the maximum braking efficiency value. Then, set the stopping sight distance equal to the sight distance calculated above and solve for speed (Vsight) in the following stopping distance equation: 2 2 Tr Vsight Vsight Tr Tr 4 SDacc SDstop SDacc Vsight 127 d 3.6 254d 3.6 3.6 254 d 6 The maximum desirable speed for the particular vehicle in the curve is the lesser of the two maximum speed values, Vacc and Vsight. Variables V = Vehicle Speed (km/h) R = Curve Radius (m) SDstop = Stopping Sight Distance O = Offset Distance from center of the lane to the obstruction (m) SDacc = Sight Distance Tr = Driver Reaction time (seconds) Vacc= Desirable maximum speed limited by lateral acceleration (km/h) d = Breaking Coefficient Vsight = Desirable maximum speed limited by sight distance (km/h) Based Primarily on Based Equally on Expert Judgment Based Primarily on Expert Judgment and Empirical Data Empirical Data 6-6
HFG CURVES (HORIZONTAL ALIGNMENT) Version 1.0 Discussion Drivers' failure to accurately judge the appropriate driving speed on horizontal curves can have safety consequences. The Fatality Analysis Reporting System (FARS) indicates that 42,815 people were killed in 38,309 fatal crashes on the US highway system in 2002. Approximately 25% of these crashes occurred along horizontal curves. These crashes occurred predominantly on two-lane rural highways that are often not part of the state DOT system. Approximately 76% of curve-related fatal crashes were single-vehicle crashes in which the vehicle left the roadway and struck a fixed object or overturned; conversely only 11% of curve-related crashes were head-on crashes. Speed selection by drivers on horizontal curves reflects a variety of vehicle, driver, and roadway factors. For example, drivers of vehicles with larger engines, and greater acceleration capacity, approach curves differently than other drivers (3). Experienced and middle-aged drivers report less accurate estimates of perceived speed than do younger and less- experienced drivers along roadway curves (4). Visual misperceptions may occur when the horizontal curve is combined with a vertical curve. For example, on-road records of vehicle speed were demonstrated to be consistent with a misperception hypothesis on crest combinations (5); i.e., the horizontal radius is perceived to be shorter than it actually is. In a safety research study (6), relationships of safety to geometric design consistency measures were found to predict speed reduction by motorists on a horizontal curve relative to preceding curve or tangent, average radius, and rate of vertical curvature on a roadway section and ratio of an individual curve radius to the average radius for the roadway sections as a whole. A review of vehicle speed distributions and the variation of vehicle speed around single road curves found that the pattern of variation in vehicle speeds along a road curve was highly dependant on the level of curvature; this effect was more pronounced for curves of radius less than 250 m (7). While radius of curvature is not the only factor that influences selected speed on horizontal curves (8), it may be the most important factor (9). Determining speeds for horizontal alignment is a complex mix of personal judgment, empirical analysis, and AASHTO/state DOT guidelines. A number of sources provide equations and procedures that reflect the complexity of speed selection on curves by drivers. A series of speed prediction equations for passenger vehicles on two-lane highways as a function of various characteristics of the horizontal curve is provided in Anderson, Bauer, Harwood, and Fitzpatrick (6). A series of steps that can be used to determine maximum desirable speed is provided in Charlton and de Pont (2). Design Issues Transportation Research Circular 414 (10) stated factors contributing to higher crash frequency on horizontal curves include higher traffic volumes, sharper curvature, greater central angle, lack of a transition curve, a narrower roadway, more hazardous roadway conditions, less stopping distance, steep grade on curve, long distance since last curve, lower pavement friction, and lack of proper signs and delineation. Cross References The Influence of Perceptual Factors on Curve Driving, 6-4 Key References 1. American Association of State Highway and Transportation Officials (AASHTO) (2004). A Policy on Geometric Design of Highways and Streets. Washington, DC. 2. Charlton, S.G., and de Pont, J.J. (2007). Curve Speed Management (Research Report 323). Waterloo Quay, Wellington: Land Transport New Zealand. 3. Bald, S. (1987). Investigation of Determinants of Choice of Speed: Evaluation of Speed Profiles on Country Roads [Abstract]. Darmstadt, Germany: Technical University of Darmstadt. 4. Milosevic, S., and Milic, J. (1990). Speed perception in road curves. Journal of Safety Research, 21(1), 19-23. 5. Bella, F. (2006). Effect of driver perception of combined curves on speed and lateral placement. Transportation Research Board 85th Annual Meeting Compendium of Papers [CD-ROM]. 6. Anderson, I., Bauer, L., Harwood, D., and Fitzpatrick, K. (1999). Relationship to safety of geometric design consistency measures for rural two-lane highways. Transportation Research Record, 1658, 43-51. 7. Mintsis, G. (1998). Speed distribution on road curves. Traffic Engineering and Control, 29(1), 21-27. 8. Andjus, V., and Maletin, M. (1998). Speeds of cars on horizontal curves. Transportation Research Record, 1612, 42-47. 9. Bird, R. N., and Hashim, I. H. (2005). Operating speed and geometry relationships for rural single carriageways in the UK. Proceedings of the 3rd Symposium on Highway Geometric Design [CD-ROM]. Washington, DC: Transportation Research Board. 10. Transportation Research Board, National Research Council (1993).Transportation Research Circular 414: Human Factors Research in Highway Safety. Washington, DC. 6-7
