Superelevation Criteria for Sharp Horizontal Curves on Steep Grades (2014)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

162 S E C T I O N 6 The objective of this research was to develop superelevation criteria for sharp horizontal curves on steep grades. For this research, a sharp horizontal curve is defined as a minimum- radius curve as determined based upon the design speed, maximum rate of superelevation, and maximum side friction factor. Through a combination of field studies, crash analyses, and vehicle dynamics simulations, many horizontal curve– grade combinations were evaluated. This section of the report describes the general conclusions reached based on analyses performed in the study. Then, potential changes proposed for consideration in future editions of the Green Book and MUTCD are described, followed by recommendations for future research needs. Appendix C presents suggested modifications to text in the Green Book and MUTCD based upon the findings and con- clusions of this research. The vehicle types considered in this research are as follows: • Passenger vehicles – E-class sedan – E-class SUV – Full-size SUV • Trucks – Single-unit truck – Tractor semi-trailer truck – Tractor semi-trailer/full-trailer truck (double) The vehicle-maneuver scenarios studied in this research are as follows: • Vehicle maintains constant speed equal to the design speed of the curve (no deceleration, i.e., 0 ft/s2). • Vehicle brakes at a deceleration rate that drivers typically use when entering a curve (-3 ft/s2). • Vehicle brakes on the curve at a deceleration rate equiva- lent to that assumed for stopping sight distance design cri- teria (-11.2 ft/s2). • Vehicle brakes on the curve at a deceleration rate greater than that assumed for stopping sight distance design cri- teria, equivalent to the deceleration used in an emergency braking maneuver (-15 ft/s2). Each of these vehicle-maneuver scenarios was considered for a vehicle maintaining its lane position and also for a vehi- cle changing lanes while traversing the curve and decelerat- ing, as described above. The vehicle-maneuver scenarios were assessed, and it was concluded that the following scenarios occur so rarely that they do not represent a reasonable basis for design: • Deceleration at rates greater than -11.2 ft/s2 while tra- versing a curve (i.e., an emergency stop with decelera- tion greater than that assumed for stopping sight distance design criteria) • Deceleration at rates of -11.2 ft/s2 or greater (i.e., a con- trolled stop with deceleration greater than or equal to that assumed for stopping sight distance design criteria) while traversing a curve and simultaneously changing lanes on the curve Thus, modifications to current AASHTO Green Book hori- zontal curve–superelevation design policy should be based on the assumption that a vehicle should be able to maintain its desired trajectory within the same lane while undergoing deceleration equivalent to that considered for stopping sight distance design criteria (-11.2 ft/s2). 6.1 General Conclusions • The AASHTO Green Book maximum side friction factors (fmax) used in horizontal curve design are below friction sup- ply curves for lateral (cornering) and longitudinal (braking) directions, for both passenger vehicles and trucks, as mea- sured in the field for design speeds greater than 20 mph. Thus, current horizontal curve design policy appears to provide reasonable lateral friction margins against skidding Conclusions, Geometric Design Guidance, and Future Research

163 in most situations. However, the more complex vehicle dyna mics models (i.e., the transient bicycle and multibody models) indicate that the point-mass model generally over- estimates the margins of safety against skidding and roll- over across all vehicle types. • There is no concern of a passenger vehicle rolling over while traveling at the design speed on a sharp horizontal curve with a steep downgrade, when designed according to current AASHTO Green Book policy. • Based upon a review of the literature, the lowest rollover thresholds for tanker trucks (i.e., liquid-cargo tank trucks) are in the range of 0.28 to 0.30. Because carriers are discour- aged from hauling half-filled tanks and because completely filled and empty tanks produce rigid-load behaviors that are generally more predictable and the rollover thresholds are closer to 0.56 than 0.30 and because crash data show that few crashes involve vehicles with rollover thresholds less than 0.35, horizontal curve design and superelevation criteria should not be based upon tanker trucks with roll- over thresholds of 0.28 to 0.30. Rather horizontal curve design and superelevation criteria should be based upon more typical loading and truck configurations. For vehi- cles considered in the simulation modeling in this study, the minimum rollover threshold was 0.56. • On downgrades, the lowest margins of safety against skid- ding and rollover generally occur at design speeds of 40 mph and lower for all vehicle types. This appears to be the result of higher side friction factors used in design for horizontal curves with lower design speeds. • Steep vertical downgrade–sharp horizontal curve combina- tions that necessitate braking to maintain a constant speed (and maintain lane position) from the approach tangent through a horizontal curve for a passenger car sedan have large margins of safety against skidding (>0.33) for design speeds ranging from 25 to 85 mph (see Figure 87). Similarly, positive margins of safety against skidding (≥0.23) for pas- senger cars that decelerate at a rate of -3 ft/s2 (similar to rates measured in the field for the present study and reported by Bonneson [2000b]) or at a rate of -11.2 ft/s2 (stopping sight distance deceleration) exist for all design speed–downgrade combinations considered in the present study. Deceleration rates of -15 ft/s2 (emergency braking) produce negative mar- gins of safety for many design speeds for vertical downgrade– sharp horizontal curve combinations when the passenger car sedan enters the horizontal curve. However, the latter sce- nario does not seem likely to occur with sufficient frequency to constitute a reasonable basis for design. • Steep vertical downgrade–sharp horizontal curve com- binations that necessitate braking to maintain a constant speed (and maintain lane position) from the approach tangent through a horizontal curve for a E-class SUV have large margins of safety against skidding (>0.34) for design speeds ranging from 25 to 85 mph (see Figure 88). Simi- larly, margins of safety against skidding for a mid-size SUV that decelerates at a rate of -3 ft/s2 exceed 0.3 for all design speeds for vertical downgrade–sharp horizontal curve combinations considered in the present study. When mid- size SUVs must decelerate at a rate of -11.2 ft/s2 (stop- ping sight distance braking), positive margins of safety (>0.15) were produced for all design speeds for vertical downgrade–sharp horizontal curve combinations consid- ered in the present study. Deceleration rates of -15 ft/s2 (emergency braking) produce negative margins of safety for most designs considered in the present study. However, the latter scenario does not seem likely to occur with suffi- cient frequency to constitute a reasonable basis for design. • The margins of safety against skidding for a full-size SUV were similar to those reported for the mid-size SUV (see Figures 88 and 89). • Steep vertical downgrade–sharp horizontal curve combi- nations that necessitate braking for a single-unit truck to maintain a constant speed (and maintain lane position) from the approach tangent through a horizontal curve have large margins of safety against skidding (>0.25) for design speeds ranging from 25 to 85 mph (see Figure 90). Simi- larly, margins of safety against skidding for the single-unit truck that decelerates at a rate of -3 ft/s2 exceed 0.10 for all design speeds for vertical downgrade–sharp horizontal curve combinations considered in the present study. Based upon the steady-state and transient bicycle models for a vehicle, when single-unit trucks must decelerate at a rate of -11.2 ft/s2 (stopping sight distance braking) or a rate equivalent to emergency braking (-15 ft/s2), significant negative margins of safety against skidding result across all design speed–downgrade combinations considered in the present study. However, based on multibody model analy- ses for deceleration rates of -11.2 ft/s2 (and -15 ft/s2) by a single-unit truck on a curve, the single-unit truck is able to maintain control on the curve when equipped with ABS. • Steep vertical downgrade–sharp horizontal curve combi- nations that necessitate braking for a tractor semi-trailer to maintain a constant speed (and maintain lane position) from the approach tangent through a horizontal curve have large margins of safety against skidding (>0.28) for design speeds ranging from 25 to 85 mph (see Figure 91). Similarly, margins of safety against skidding for a tractor semi-trailer that decelerates at a rate of -3 ft/s2 exceed 0.26 for all design speeds for vertical downgrade–sharp horizontal curve com- binations considered in the present study, and when a tractor semi-trailer must decelerate at a rate of -11.2 ft/s2, the mar- gins of safety exceed 0.11. For emergency braking (-15 ft/s2), a tractor semi-trailer will experience negative lateral friction margins at low design speeds (e.g., 35 mph or less). The mar- gins of safety against skidding were slightly higher for the

164 tractor semi-trailer/full-trailer truck when compared to the tractor semi-trailer. However, the emergency braking sce- nario does not seem likely to occur frequently enough to constitute a reasonable basis for design. • When maintaining a vehicle operating speed at or near the design speed on a horizontal curve, grade and maximum superelevation rate (emax) appear to have little effect on the margins of safety against skidding and rollover for all vehicle types. • Eck and French (2002) suggest that high superelevation rates (e.g., between 8% and 16%) make horizontal curves on steep downgrades more forgiving. The vehicle dynam- ics simulations in the present study suggest that maximum rates of superelevation (emax) should not exceed 12% on downgrades because the superelevation transition occur- ring on the approach tangent can begin to reduce the mar- gins of safety against skidding prior to curve entry. On curves designed with emax greater than 12%, the margin of safety against skidding by a vehicle may be smaller in the superelevation transition area than on the curve proper. Thus, the results of this research do not support the recom- mendation by Eck and French that emax values up to 16% should be considered in some cases. On upgrades of 4% and greater, emax should be limited to 9% for minimum- radius curves with design speeds of 55 mph and higher, to avoid the possibility of wheel-lift events. Alternatively, emax values up to 12% could be used for minimum-radius curves if it can be verified that the available sight distance is such that deceleration at -11.2 ft/s2 is unlikely to be required. • When vehicles change lanes in a horizontal curve, the mar- gins of safety against skidding decrease considerably for all vehicle types considered in the present study. When lane changing occurs during a stopping sight distance or emer- gency braking maneuver, all vehicles exhibited negative margins of safety against skidding, as shown in Figures 132 through 143. For those situations (i.e., combinations of horizontal curvature, grade, and vehicle maneuvers) in which the transient bicycle model predicted skidding (i.e., negative lateral friction margins), the multibody model showed that if a vehicle has ABS, and the driver properly responds to minor lateral skidding, then the vehicle can maintain its intended path. In cases where the driver does not correct the steering input in response to a lateral shift, and the vehicle is not equipped with ABS, the transient bicycle model showed the lateral skidding of passenger sedan vehicles with negative margins of safety is small (i.e., less than 1.5 ft in lateral direction) across all combinations of vertical downgrade, design speed, deceleration rate, and lane-change maneuvers. A mid-size SUV, full-size SUV, and single-unit truck without ABS all exhibit large lateral shifts when the margin of safety against skidding is negative in certain conditions, most notably situations when more aggressive braking is needed such as deceleration rates similar to those used to develop stopping sight distance or emergency braking design criteria (-11.2 or -15 ft/s2). The case of a tractor semi-trailer without ABS need not be considered because all tractor semi-trailers are mandated to have ABS. [Note: Federal Motor Vehicle Safety Standard No. 121 mandates ABS on all new air-braked vehicles with gross vehicle weight ratings of 10,000 lb or greater. ABS is required on tractors manufactured on or after March 1, 1997, and air-braked semi-trailers and single-unit trucks manufactured on or after March 1, 1998 (Allen, 2010).] • Based on current AASHTO Green Book horizontal curve– superelevation design policy, a vehicle that performs an emergency braking maneuver (-15 ft/s2 deceleration) on a steep downgrade–horizontal curve combination will likely skid off the roadway in many cases if the vehicle is not equipped with ABS. • The method used in the current AASHTO Green Book policy to distribute superelevation and side friction on tangent–curve transitions is adequate and produces posi- tive margins of safety against skidding and rollover for all vehicle types on horizontal curves designed using maximum superelevation and minimum curve radii. However, the superelevation attained at the point of curve entry should be checked and compared to a lateral friction margin con- dition to ensure that the lateral friction margin on the curve entry is not less than the margin within the curve. • AASHTO policy uses superelevation to balance the effects of sharper curvature. This balance may be imperfect when axle-to-axle differences are considered. The balancing effect is slightly more conservative with higher superel evation rates, often resulting in lower lateral friction margins occur- ring for lower superelevations (e.g., 0% superelevation). However, differences in lateral friction margins between different superelevations are very small. • The crash analysis performed in the present study showed that the predicted number of single-vehicle run-off-road and single-vehicle rollover crashes decreases as the mar- gins of safety against skidding and rollover increase for both passenger vehicles and trucks. 6.2 Geometric Design Guidance • Figures 30 and 32 of this report show passenger vehicle and truck tire measurements of skidding wet-tire friction in the lateral (cornering) and longitudinal (braking) direc- tions. It is recommended that the lateral friction curves (two standard deviations below the mean) be integrated into AASHTO Green Book Figures 3-4 and 3-5, which show the maximum side friction factors (fmax) used in horizon- tal curve design for high-speed and low-speed streets and highways, respectively. Incorporating these curves into

165 Figures 3-4 and 3-5 of the Green Book would be infor- mative to designers. The modified figures would, for the first time, illustrate friction measurements that take into consideration the effects of cornering. For a conservative design policy, horizontal curve–superelevation design policy recommendations should be based upon the 2nd percentile (i.e., mean friction minus two standard devia- tions) of the friction supply provided at the tire–pavement interface. • For a simple horizontal curve, the maximum rate of super- elevation (emax) should not exceed 12% on a downgrade. If considering a maximum superelevation rate greater than 12%, a spiral curve transition is recommended to increase the margins of safety against skidding between the approach tangent and horizontal curve. On upgrades of 4% and greater, the maximum superelevation rate should be lim- ited to 9% for minimum-radius curves with design speeds of 55 mph and higher, to avoid the possibility of wheel-lift events. Alternatively, if it can be verified that the available sight distance is such that deceleration at -11.2 ft/s2 is unlikely to be required on upgrades of 4% or more (i.e., the available sight distance is greater than minimum stopping sight dis- tance design values), emax values up to 12% may be used for minimum-radius curves. • For sharp horizontal curves (or near minimum-radius curves) on downgrades of 4% or more, the “Stay in Lane” sign (R4-9) should be installed in advance of the curve on multilane highways. Consideration may also be given to using solid white lane line markings to supplement the R4-9 sign. • Sharp horizontal curves (or near minimum-radius curves) on downgrades of 4% or more should not be designed for low design speeds (i.e., 30 mph or less). In the event that such situations cannot be avoided, warning signs to reduce speeds well in advance of the start of the horizontal curve should be used. • The following condition should be used to check that the superelevation achieved at the point of curvature (PC) of a simple horizontal curve (i.e., with no spiral transition curves) is less than the threshold value computed based on the given design speed–curve radius combination: 100 1 1 tangent 2e p V gR < + × where: e = superelevation at PC of horizontal curve; ptangent = proportion of the maximum superelevation that is attained at the PC of horizontal curve; V = design speed (ft/s); g = gravitational constant (32.2 ft/s2); R = radius of horizontal curve (ft). If the condition presented above is met, the superelevation transition may be placed as indicated in Green Book Table 3-18. If the condition presented above is not met, designers should reduce the proportion of the maximum superelevation attained at the PC of the horizontal curve, or introduce a spi- ral transition curve between the approach tangent and sim- ple horizontal curve. Based on an analysis completed for the present study, the condition above is satisfied for maximum superelevation–minimum-radius curves for all design speeds. However, the condition above may be violated when using greater than minimum horizontal curve radii. In such cases, it is important to check the superelevation condition above, and if the condition is not met, it is recommended that a lower pro- portion of the superelevation runoff (e.g., 70%) be introduced prior to horizontal curve entry. 6.3 Future Research • Although not the primary focus of the present study, the vehicle dynamics simulations performed in the present study found that, for design speeds of 10 and 15 mph, the maximum side friction factors (fmax) used for horizon- tal curve design (0.38 and 0.32 for 10 mph and 15 mph, respectively) exceed truck rollover thresholds. Maximum side friction factors used for low-speed design also exceed or are very near rollover thresholds of 0.28 to 0.30 for partially filled tanker trucks. Additional research is rec- ommended using a combination of simulation, field, and crash data to further investigate the relationship between truck rollover thresholds and maximum side friction fac- tors used for horizontal curve design, particularly at low design speeds. Since low design speeds and a normal crown roadway cross section are often used in urban areas, the effects of adverse superelevation should also be investi- gated as part of this research. • It would be of interest to include a tractor-trailer truck with a tanker trailer in the simulation analyses. However, existing models do not have the capability to simulate the dynamic effects of liquid sloshing in a tank trailer. When multibody models become sophisticated enough to simu- late the dynamic effects of liquid sloshing in a tank trailer, the scope of this research should be revisited to incorpo- rate tanker trucks in the analytical and simulation model- ing analyses. • Future research should be directed at collecting infor- mation concerning the relative propensity of emergency braking maneuvers under normal travel conditions to determine if these should be considered in horizontal curve –vertical grade geometric design policy. Naturalis- tic driving studies may provide the opportunity to collect these data from equipment installed on vehicles partici- pating in such studies, provided that steering, braking,

166 and throttle conditions can be geo-located on the roadway network. • The margins of safety against skidding and rollover are generally lowest for horizontal curves with low design speeds (40 mph or lower). This suggests that the differ- ence between friction demanded by vehicles in relation to design side friction factors (fmax) is lower at low design speeds relative to higher design speeds. Because design side friction factors are based on driver comfort levels, future research should be directed at determining comfort thresholds acceptable to drivers on horizontal curves that are designed using low-speed criteria while taking into consideration vehicle dynamic capabilities. • With a few exceptions, this research focused on simulating scenarios for maximum superelevation–minimum-radius curves for a range of design speeds. This research could be expanded to more thoroughly investigate conditions for above-minimum-radii curves. In particular, additional guid- ance could be sought for the design of above-minimum-radii curves for low design speeds and the need and use of “Stay in Lane” signs (R4-9) for above-minimum-radii curves on multilane highways and/or ramps.