Road Management & Engineering Journal
Road Management & Engineering Journal
Copyright © 1998 by TranSafety, Inc.
September 1, 1998
TranSafety, Inc.
(U.S. and Canada)
(360) 683-6276
Fax: (360) 335-6402

Canadian Researchers Test Driver Response to Horizontal Curves

Researchers have questioned the safety of horizontal curves on two-lane rural highways, where "the degree of horizontal curvature has been found to be the strongest geometric variable related to accident rates." Horizontal curve standards, based mainly on a driver's "comfort" on the curves, were established before 1940 and have changed little since then. These early standards do not reflect contemporary roadway and vehicle designs or modern drivers, and they may not be safe. Drivers often exceed the "advised speeds for horizontal curves."

A Canadian study used a testing ground and an existing highway to test speed and lateral acceleration on both wet and dry pavement on horizontal curves. Emmanuel Felipe and Francis Navin discussed the study in "Automobiles on Horizontal Curves: Experiments and Observations," a paper prepared for the Transportation Research Board's 77th Annual Meeting (January 1998). They found that "comfortable lateral acceleration" and "speed environment" limited a driver's speed, while pavement surface conditions (dry or wet) and the driver's gender did not.


Part of the study took place "on an abandoned runway used by the Pacific Traffic Education Center (PTEC) for driver training." Four male and four female "regular" drivers (ages 20-50) volunteered to drive a mid-size sedan with Michelin tires (30-40 percent tread wear). A video camera on the car's right side recorded equally spaced marks on the road's curves; "the lapse of time over the distance between two marks provided the speed of the vehicle." The drivers also took turns being passengers in the car, and each was a driver and passenger eight times--four times in one direction and four in the opposite direction. Drivers became familiar with the car and the road's curves before the test. A senior author seated in the rear seat gave instructions and operated the measuring devices. "Two expert drivers" also "drove the curves at their maximum safe speed (speed before skidding event) which provided the assumed threshold of the dynamic parameters for all experimental driving conditions."

Research shows "the best descriptor of car-driver behavior is lateral acceleration." Drivers and passengers feel the lateral acceleration, and they adjust speed according to "their level of comfort." The drivers chose their speeds based on two speed scenarios. Driving the curve at a "comfortable speed" was scenario V1 and at a "very difficult speed" (the safe maximum but uncomfortable) was scenario V2. Four, 4-meter-wide curves designated R1, R2, R3, and R4 had respective center lane radii of 16, 26, 60, and 100 meters, and curve lengths of 65, 109, 104, and 99 meters. The curves "were not superelevated" (banked). A sprinkler truck watered the pavement for the wet conditions to a water depth of about 0.5 millimeter.

"To compare the experimental data gathered at PTEC with what really happens on existing horizontal curves," the other portion of the study occurred on "four curves on a mountainous section of Highway 99." The curves were chosen "based on curve radii and the ability to observe the entire curve." Table 1 shows their geometric characteristics. Researchers measured speed and lateral placement on this two-lane highway (lane width 3.7 meters)with a hidden video camera located on a hillside or rock outcrop. Drivers drove either at a comfortable or uncomfortable speed, or they "tracked a free-moving passenger car (no 'obstruction vehicle' ahead)." These four curves "were designed with proper superelevation."

Curve Characteristics

#1 #2 #3 #4
Radius in metres (m) 120 450 180 90
Length (m) 140 180 140 100
Superelevation (m) 0.07 0.04 0.03 0.04
Grade (%) +/-1% 0.8 1.0 0.5 1.4
North B     South B Right     Left Left     Right Right     Left Left     Right
location (in km) 5.28 7.10 9.20 14.14


Results showed that "the speed distribution in horizontal curves was . . . proportional to the curvature." In both speed scenarios, on the small radii curves (R1 and R2) regular drivers "reduced their speed to a minimum" at about the center of the curves, then accelerated as they exited them. On the two larger radii curves (R3 and R4), however, drivers "usually maintained" their "selected" speed. Speeds were higher when the small curves were driven counterclockwise (left) as opposed to clockwise (right). This finding "was statistically significant at the 95 percent level of confidence for the small radius R1 at both speed scenarios, and significant for R2 only when the curve was driven for scenario V2."

Pavement surface conditions had a "statistically insignificant" effect on speed, i.e., "drivers did not significantly reduce their speed on the wet pavement." The fact that "there was no speed difference between male and female drivers" was most likely the result of the small sample size, since other research shows "significant differences of speed between genders." The two expert drivers reached "the theoretical maximum speeds" on curves R1 and R2, but "limited by the car's performance, . . . could approach the maximum safe speed on R3 and R4 on wet pavement only." To a "statistically significant" degree, the expert drivers drove more slowly on wet pavement than on dry.

Figure 1 shows that as the radii increased, the driver speed increased and "the corresponding coefficient of friction decreased." Comparing speeds between the regular and expert drivers defined "the relative level of safety." On "the tight radius of 16 metres," speeds for some regular drivers were similar to those of expert drivers, which meant the regular drivers "had no margin of safety." On the "100 metres radius curve," speeds were "within roughly 10 kilometers per hour of the experts' speed," for "some margin of safety." Passengers felt comfortable with a lateral acceleration in a small curve of 0.35g to 0.40g.

Figures 2 and 3 show the lateral acceleration and speed for V1 and V2, respectively. On the smaller radii curves, "drivers adjusted their comfortable speed according to their comfortable lateral acceleration tolerance (approximately between 0.35 and 0.40g)." On the longer radii curves, speeds were as comfortable as they would be on a straight road section. Figure 3 shows that at maximum speed "the variation of speed between drivers became larger than when they drove at a comfortable speed."


On the larger radii curves, drivers "mostly followed the center of the lane for each direction," but on the smaller radii curves, they "cut" the curves in both directions. Reducing the speed change, "drivers flattened the bends either by driving on the shoulder or, in some cases, by driving partly in the opposite lane."

Table 2 shows that "as expected, there is a direct relationship between the speed selected by drivers and the radius of the bends. The smaller the radius, the lower the speed of the car-driver system."

Speeds of Free-Moving Passenger-Cars

Curves Speed in kilometers per hour
Northbound Southbound
85th % Mean Stdev n 85th % Mean Stdev n
#1 78.0 70.0 6.4 40 79.0 73.5 7.0 34
#2 92.0 83.8 5.2 42 92.0 84.5 6.9 41
#3 86.0 5.2 8.2 88 86.0 75.2 8.4 91
#4 75.0 70.0 6.2 50 70.0 65.0 5.5 51

Figure 4 helps show that while today's vehicles may be more efficient than earlier models, "it seems that the speed selected by the car-driver system in a horizontal curve has not significantly changed over time."

Higher speeds on Highway 99 than at PTEC (on curves with the same radii) may have been related to differences in speed environment and superelevation. If the study had used "an isolated curve of a straight and level rural road" instead of a mountainous section, speeds may have been "slightly different."


In this study, neither pavement surface condition (wet or dry) nor driver gender "significantly impact[ed]" regular driver speed. The writers observed, "As expected, the influence of both the radius and driving scenario were very influential on the selected speed." They concluded, "In general, drivers limit their speed on small radius curves, based on their comfortable lateral acceleration [0.35g to 0.40g]. On large radius curves, they limit their speed by both their comfortable lateral acceleration and speed environment."

Copyright © 1998 by TranSafety, Inc.

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