Effects of reverse linear perspective of transverse line markings on car-following headway: A naturalistic driving study

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Effects of reverse linear perspective of transverse line markings on carfollowing headway: A naturalistic driving study ⁎

Naikan Dinga, , Shunying Zhub, Hong Wangb, Nisha Jiaoc a

206 Guanggu 1st Road, School of Civil Engineering and Architecture, Wuhan Institute of Technology, Wuhan 430205, China 1178 Heping Avenue, School of Transportation, Wuhan University of Technology, Wuhan 430063, China c 428 Jianshe Avenue, Planning Research Studio, Department of Transportation of Hubei Province, Wuhan 430030, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Car-following Headway Reverse linear perspective Transverse line markings Distance perception

Car-following is a vital important driving status in traffic operations, and it relates greatly to the rear-end crash issues. Insufficient headway could be a major reason for this issue because the drivers have not enough time to react to a sudden brake from the leading vehicle. However, the most common countermeasures for this issue are based on speed control or management. Given that, the present study attempted to increase the car-following headway by promoting drivers’ risk perception from the perspective of driver’s speed perception as well as distance perception. In the experiment, a kind of transverse line markings that producing reverse linear perspective information were installed on the slow lane of a freeway in China, to visually intervene the drivers’ perception of speed and distance, and with naturalistic driving data collected. The results showed that the carfollowing time headway was increased after the installation of the transverse line markings with reverse perspective information. And a greater degree of the divergence of the reverse linear perspective information could result in a greater increase in time headway. The effects of the transverse line markings were further discussed considering the influences of edge rate and reverse linear perspective information. The findings of this study suggest that the direct visual intervention on drivers’ distance perception could also be a prominent countermeasure for rear-end crashes and the other safety issues on roadways.

1. Introduction Road traffic crashes pose a serious threat to our daily life. According to the World Health Organization (World Health Organization, 2015), over 1.2 million people were killed in road traffic crashes worldwide annually. In particular, road traffic crashes are a leading cause of death among young people, and the number one cause of death among those aged 15–29 years. In China, there were 63,093 deaths and 226,430 injuries reported in over 8.6 million road traffic crashes in 2016 (Traffic Management Bureau of the Public Security Ministry, 2017). Among these, rear-end crashes are the most common accident type throughout the world. NHSTA reported that rear-end crashes accounted for 33.4% of all road traffic crashes, which led to 2203 deaths and 556,000 injures in U.S. in 2015 (NHTSA, 2017). In China, 6108 people died and 17,933 injured for the same reason in 2016, and more specifically, rear-end crashes contributed 35.7% of all crashes and 33.9% of all fatalities on freeways (Traffic Management Bureau of the Public Security Ministry, 2017). Confronted with this issue, researchers have examined various factors leading to rear-end crashes, which can

⁎

normally be categorized into human factors, roadway environmental factors, and traffic flow factors. The most common human factors are biased visual perception (Dewar and Olson, 2007), fatigue (Liu and Wu, 2009; Zhang and Chan, 2014), distraction by cell phone (BackerGrondahl and Sagberg, 2011) and/or other internal or external stimuli, mental impairments by alcohol and/or drugs (Waller et al., 1997), and aggressive driving or risk-taking driving (Dahlen et al., 2012). The most typical roadway environmental factor would be poor sight distance (Harwood and Bauer, 2015). Other than these factors, the quantity and composition (vehicle type/size) of traffic flow (Golob et al., 2004; Nagatani, 2015) and operating speed (Islam, 2016; Li et al., 2014) of vehicles can also play a role in the causation of rear-end crashes, and which all can be regarded as the traffic flow factors. Among these three kinds of factors, the human factors are the predominant one as the vast majority of the rear-end crashes can occur if the following driver errs in judging closing speed and headway to the leading vehicle. Corresponding to these contributing factors, numerous countermeasures are taken into practice to be expected to have positive effects on the crash issues. The most common one would be speed reduction

Corresponding author. E-mail address: [email protected] (N. Ding).

https://doi.org/10.1016/j.ssci.2018.08.021 Received 30 December 2017; Received in revised form 21 July 2018; Accepted 27 August 2018 0925-7535/ © 2018 Elsevier Ltd. All rights reserved.

Please cite this article as: Ding, N., Safety Science (2018), https://doi.org/10.1016/j.ssci.2018.08.021

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predicted that the visual system was unable to establish a reliable reference frame with result of failure to obtain correct absolute distance, when the common ground surface disrupted (discontinued). Based on Gibson’s fundamental contributions, Sinai et al. (1998), Yarbrough et al. (2002), and Wu et al. (2004) verified that the “discontinuous” ground surface visual information was able to lead to a phenomenon of distance underestimation among observers, which was also referred to as the “discontinuity effect” by Feria et al. (2003). By absorbing the results and thoughts from the above research, Ding et al. (2017a, 2017b) designed a kind of discontinuous longitudinal edge line markings and installed it on the road surface of a freeway to visually intervene drivers’ car-following behavior, and the filed observations revealed that the car-following time headway increased after the installation of the longitudinal edge line markings. In addition, a considerable body of research has extensively proved that linear perspective information provided drivers with an effective depth cue and a basis for distance perception to judge the vehicle gap (Gibson, 1950; Vogel and Teghtsoonian, 1972; Sedgwick, 1983; Cutting et al., 1995; Wu et al., 2007). Linear perspective is a depth cue that is related to both relative size and texture gradient (another depth cue concerning the density variation of textures on ground surface), which can create an illusion of depth on a flat surface. In linear perspective parallel lines that recede into the distance appear to get closer together, and finally converge in a single vanishing point on the horizon line. In particular, Wu et al. (2007) found that the convergent linear perspective information, compared with parallel one, could result in distance overestimation of observers. It means that if two lines (with limited length) are intentionally placed in a pattern of convergent in distance, with respect to the observer, on the ground, the observer would normally attribute this “convergence” of lines to as that the far end of the paired lines is distant. Actually, the convergence or divergence of lines cannot be correctly defined unless they are compared with a reference, like the parallel lines (see Fig. 1). So, intuitively, the parallel lines per se could be deemed as divergent when compared with the convergent ones. Based on the study of Wu et al. (2007), a question can naturally be raised. That is, would distance underestimation emerge when observers are exposed with divergent linear perspective information? Yet, prior to reflect on this question, it was notable that the above research concerning linear perspective information mainly developed in static scenarios or in virtual settings. In addition, the actual distances the participants needed to judge were less than 15 m. Therefore, the effect of linear perspective information on distance judgement needs to be further explored in a real-word situation. Here in this paper, we referred to the divergent linear perspective information as the reverse linear perspective information to distinguish it from the regular one (convergent in distance). Considering the above question and the existing limitations of the research on linear perspective, here we proposed the following two hypotheses with respect to the car-following headway:

treatments, for speeding is one of the major reasons for crashes. The typical engineering countermeasures for reducing speed include stereoscopic surface treatments, for instance, the speed humps (Molan and Kordani, 2014); the transverse rumble strips (Persaud et al., 2004); pavement markings, such as the converging chevron marking pattern (Drakopoulos and Vergou, 2003), the transverse markings (Gates et al., 2008; Martindale and Urlich, 2010), and the optical speed bars (Meyer, 2001); and traffic signs, for example, the variable speed limit signs (Chaurand et al., 2015). It can be found that these countermeasures may introduce a sensation of vibration to drivers while the wheels roll over the humps or alike, or may create the illusion of travelling faster or the impression of a narrower lane. Actually, it was reported that 90% information that drivers obtains and uses was visual (Sivak, 1996). So the pavement markings are of great importance as to speed reduction, which can also be called the “visual intervention” to driving behaviors. Compare to its practical usage, the functional theory of these visual interventions for speed reduction are inadequately developed. The most valuable and prevalent interpretations could be explored from the research of some cognitive psychologists. Gibson (1950) is just the most representative one, who interpreted the observers’ visual perception as that there was continuous light entering and “flowing” through its retina, when the observer was seeing moving objects. And that was the socalled “optic flow”. Optic flows can be produced by motions of objects with respect to the background or by motions of the perceiver per se. In particular, edge rate (ER) is a kind of optical variable that is homologous with the optic flow, which relates to the speed perception of observers. It was defined as the rate at which local discontinuities cross a fixed point of reference in the observer’s field of view (Warren, 1982). Generally, edge rate can be measured by the unit of Hz. By employing the virtual-reality experiments, Francois et al. (2011) found that edge rate could cause overestimation in self-speed of drivers, which in turn led to a speed reduction. Larish and Flach (1990) discovered that the estimated speed rose along the increase of edge rate. Retting et al. (2000) installed a series of transverse markings on the upstream of the exit ramp of a low-grade road, and found that the speeds of the small cars and large trucks were significantly decreased before they entered the ramp. Godley et al. (2000) conducted a similar field observation and found that both the transverse markings and the longitudinal ones could lead to a certain effect of speed reduction, if the markings were spacedly installed in a certain gap. Rakha et al. (2006) designed a kind of transverse bars with a constant gap, and its analyses of data from field observations showed a 6 km/h reduction on the mean speed and an 8 km/h reduction on the 85% speed. Similarly, based on on-road experiments, Liu et al. (2013) found that all the drivers decelerated when the edge rate of edge line markings varied from 8 Hz to 18 Hz, at which there was an approximate linear relationship between the edge rate and the deceleration. In addition to speeding, the headway is another vital important factor influencing rear-end crashes. Actually, the distance to the leading vehicle would be a direct stimulus to the drivers in perceiving the possible pending crash risk. And an insufficient headway in car-following could be a major reason for rear-end crashes since the following driver may not have enough time to react to a sudden break from the leading vehicle. In the traffic engineering domain, time headway (TH), the time interval between two vehicles, just incorporates the relative distance and the speed of the following vehicle, which is the most important variable for traffic safety evaluation. However, there is rare seen a direct distance or headway control countermeasure, let alone any visual interventions for headway control. The most common relevant one would be the traffic signs or alike to warn the drivers to be in a safe following distance, which are of limited usefulness. So, in this paper, we attempt to fill the gap by intervening drivers’ distance perception to influence the car-following headway. Similar to the speed reduction, the visual intervention on headway (distance) control could also derive from the visual information on road surface. Gibson (1950) put forward the “Ground Theory”, and it

Convergent

Divergent

Near

Far

Parallel

Fig. 1. The schematic of convergent and divergent lines compared with the parallel ones. 2

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(1) The reverse linear perspective information could result in an increase in car-following headway, as it may lead to distance underestimation among drivers. (2) Different degrees of the divergence of the reverse linear perspective information would lead to variations in car-following headway.

Table 1 Design parameters of the transverse line markings.

To verify these hypotheses, an experiment was conducted on a realworld freeway in China. In the experiment, a series of transverse line markings was placed aside the original white markings of a lane to produce the reverse linear perspective effect. Naturalistic vehicle flow data like speed, distance headway (DH), and time headway were collected via video cameras set at consecutive observation sections. The remainder of the paper is organized as follows. Section 2 describes the process of the experiment. Section 3 presents the statistical analyses of the experimental results, and the subsequent discussions are appeared in Section 4. Section 5 concludes the research findings.

Section range

SR = 20 m

SR = 50 m

SR = 100 m

Interval of markings Length of markingi

200 cm

200 cm

200 cm

0.5 ·(20−2i)·100 20

0.5 ·(50−2i)·100 50

0.5 ·(100−2i)·100 100

Quantity of sections

15

6

3

reflected three levels of divergence (see Table 1 and Fig. 2). 2.3. Data collection and treatments In the experiment, the speed (V), distance headway (DH) and time headway (TH) of each vehicle were obtained indirectly by recording the very moments when the vehicle passed through two close sections. Fig. 3 demonstrates a sketch map of the way the data collection worked. As shown in Fig. 3, six video cameras (Sony HDR-PJ510E, 50 frames of images with a resolution of 1920 × 1080 recorded per second) were consecutively mounted outside of the crash barrier on the hard shoulder with a constant interval of 100 m in depth. Moreover, to avoid the impact from drivers who would take those cameras as traffic violation surveillance and adjust driving behavior, the cameras were sheltered with shrubs and invisible from the lanes. Accordingly, the position of these cameras represented six observation sections (numbered at the bottom of Fig. 3). In addition, in order to minimize the observation error, a total length of 500 m area was artificially scaled like a “ruler” with red tick marks (see Fig. 3). Thus, the speeds, distance headways, and time headways of a vehicle at observation section #1 to #6 could be calculated as follows. Take observation section #2 as an example, Vi2 = (x iB −x iA) (tiB−tiA) , where Vi2 is the speed of vehicle i when it just passes through observation section #2, x iA and x iB are the positions of vehicle i at minor section A and B, tiA and tiB are the time (or moment) of vehicle i at minor section A and B. In particular, in this experiment the minor section A and B were set five meters away from its corresponding major section. It means x iB −x iA = 10 m. The corresponding distance headway of vehicle i can be calculated as DHi2 = x ir− 1−x i2 , where DHi2 is the distance headway of vehicle i when it passes through observation section #2, x i2 is the position of vehicle i (the following vehicle) at observation section #2, x ir− 1 is the position of vehicle i−1 (the leading vehicle) when vehicle i just arrived at observation section #2. Moreover, the moments that a vehicle passed through the major section #1 to #6 were also recorded, then the time headway of vehicle i could be calculated as THi2 = ti2−ti2- 1, where THi2 is the time headway when vehicle i passes through the major section #2, ti2- 1 and ti2 are the moments when vehicle i - 1 (the leading vehicle) and vehicle i (the following vehicle) pass through the major section #2. Similar calculations concerning V, DH, and TH were applied to the other five major sections. All the data were collected during 8:30–11:30a.m. or 14:00–17:00p.m.

2. Experiment 2.1. Test site The segment of Daijiashan and Huangpi freeway (coded S1) at Wuhan, Hubei Province, P.R. China was selected as the test site. It was a two-way-four-lane freeway with a design speed of 100 km/h, a landwidth of 3.75 m. Its Annual Average Daily Traffic (AADT) was 18,061vehicles per day. The precise location of the test site was between 6.9 km and 8 km of S1, at which it was a flat and straight segment. Along the direction of mileage increment, the test site was connected with a flat and straight segment in upstream and with a rightturn curve in downstream. In addition, in the very middle part of 6.9 km to 8 km of S1, a 300 m-long slow lane was installed with the transverse line markings. There was no tunnel or overpass within the experimental area, nor any exposed surveillance system for violation capture. 2.2. Design of the transverse line markings

SR=100m

200cm

…

…

In order to make the transverse line markings have effects on drivers’ speed perception as well as distance perception, according to the studies introduced above, the transverse line markings should generate both edge rate and reverse linear perspective information. The edge rate could be produced if there was a gap between two adjacent line markings, and when the gap was fixed to 200 cm, as recommended by Liu et al. (2013), the drivers’ would experience a stable edge rate that led to speed overestimation. Then, combine the fixed gap with the proposed hypotheses concerning distance underestimation due to the reverse linear perspective effect (refer to Fig. 1), three types of the transverse line markings were designed as shown in Fig. 2, which

50cm 15cm Fig. 2. Layout of the transverse line markings (only the condition of SR = 100 m is demonstrated). 3

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Slow lane 100m

100m

100m

100m

100m

Major Minor A B

5m

Camera ##2

#1

#3

#4

#5

#6

Fig. 3. Layout of the cameras (only the condition of SR = 100 m is demonstrated).

generally compare the TH, V, and DH of all conditions (including the control), and (2) to particularly compare the above parameters between observation sections. Take the TH as an example, for the general comparison, the average TH of the six observation sections was calculated in each condition; for the comparison between observation sections, the average TH at observation section #1 and #5 were calculated respectively in each condition. Similar calculations were conducted for the comparisons of V and DH. In statistics, the analysis of variance (ANOVA) was employed to examine the effects of transverse line markings, and the Student’s t test was used for the comparison between observation section #1 and #5.

Table 2 Effective samples and descriptive statistics of each test. Test

(a) Control

(b) SR = 20 m

(c) SR = 50 m

(d) SR = 100 m

Raw sample Effective sample Mean TH (s) Standard deviation of TH (s) Standard error of mean (s) Minimum value (s) Maximum value (s)

2154 406 4.15 0.31

2381 438 4.49 0.26

2188 385 4.42 0.18

2307 383 4.38 0.21

0.24

0.12

0.11

0.11

2.15

2.12

2.20

2.15

6.79

6.88

6.84

6.81

3. Results 3.1. General effects of the transverse line markings

in no precipitation days. In order to meet the request of sample size for statistical analysis, at least one-day observation was conducted for a single test. The raw sample size of each test is shown in Table 2.

3.1.1. Effect on time headway Fig. 4 illustrates the mean time headway (mean ± s.e.m.) of each test. It can be found that the mean time headway increased after the installation of the transverse line markings. Wherein, the corresponding increments were 0.34 s (+8.2%), 0.21 s (+5.0%), and 0.17 s (+4.0%) with regard to the tests of SR = 20 m, SR = 50 m, and SR = 100 m respectively, when compared with the control. In addition, the mean time headways of the three tests and the control were found to be statistically different by a Student's t test (see Fig. 4, where asterisk denotes the significant degree (*p < 0.05). Also, a one-way ANOVA revealed that the transverse line markings influenced the time headway significantly (F(2,1203) = 6.58, p < 0.05).

2.4. Data filtering processes 2.4.1. Filter out free-flow vehicles Free-flow is a status when there is no constraint placed on a driver by other vehicles on the road. To guarantee the data validity used for car-following behavior analysis, the free-flow vehicles were filtered out by the such criterion: if the stopping time was less than its time headway, then the vehicle should be defined as a free-flow vehicle, otherwise, it was in a car-following status. Here, the stopping time was calculated as follows, t = V / a , where t is the stopping time, s; V is the instantaneous speed of a vehicle, m/s; a is the deceleration (a = 2.5 m s2 was suggested by AASHTO (2011). In addition, if the status of free-flow occurred at any observation section of the six, then the vehicle needed to be removed. 2.4.2. Filter out lane-change vehicles Lane-change could happen among vehicles. To avoid the impact of these data, the video clips were reviewed frame by frame to check the trajectory of each vehicle from observation section #1 to #6. If the lane-change appeared between any two consecutive observation sections, the vehicle needed to be removed from the dataset. Based on the above data collecting methodologies and data filtering rules, the effective sample size and the basic descriptive statistics of each test are showed as follows in Table 2. 2.5. Data analysis

Fig. 4. Time headway comparison between the before and after the installation of the transverse line markings.

In general, the influence of the transverse line markings on carfollowing behaviors was analyzed at the following two levels: (1) to 4

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the section rang (SR) of the transverse line markings on distance headway was found to be significant, F(2,711) = 27.3, p < 0.05. The mean distance headways in the tests of SR = 20 m, SR = 50 m, and SR = 100 m were 82.85 m (SE = 1.79), 82.47 m (SE = 1.71), and 81.71 m (SE = 1.63). It can be discovered that the distance headway increased compared with the control (80.14 m (SE = 1.75)), when there were the transverse line markings. And the corresponding increments were 2.71 m (+3.4%), 2.33 m (+2.9%), and 1.57 m (+2.0%) respectively. In addition, the post hoc comparisons (Tukey’s HSD test) showed significant differences of the paired comparisons among the tests of SR = 20 m, SR = 50 m, and SR = 100 m (p < 0.05). Meanwhile, the ANOVA showed a significant main effect of speed intervals on distance headways, F(2,711) = 23.4, p < 0.05. The mean distance headways in the speed intervals of (−∞, 65 km/h), [65 km/h, 80 km/ h], and (80 km/h, +∞) were 80.78 m (SE = 1.77), 82.83 m (SE = 1.67), and 83.45 m (SE = 1.63). Similarly, the post hoc comparisons (Tukey’s HSD test) showed significant differences of the paired comparisons among the three speed intervals (p < 0.05). Also, there was a significant interaction effect between the section rang (SR) and the speed intervals, F(4,711) = 15.9, p < 0.05.

Fig. 5. Speed comparison between the before and after the installation of the transverse line markings.

3.1.2. Effect on speed Fig. 5 presents the mean speed (mean ± s.e.m.) of each test. According to Fig. 5, the mean speed reduced after the installation of the transverse line markings. Wherein, the corresponding reductions were 3.5 km/h (−4.3%), 3.1 km/h (−3.8%), and 3.0 km/h (−3.7%) with regard to the tests of SR = 20 m, SR = 50 m, and SR = 100 m respectively, when compared with the control. In addition, the mean speed of the three tests and the control were found to be statistically different by a Student's t test (see Fig. 5, where asterisk denotes the significant degree (*p < 0.05). Also, a one-way ANOVA revealed that the effect of the transverse line markings on speed was not found to be significant (F (2,1203) = 5.64, p = 0.11).

3.2. Comparisons between observation sections 3.2.1. Time headway comparisons Fig. 7 shows the time headway comparisons between observation section #1 and #5 of each test (including the control). The Student’s t test revealed no significant difference of time headways between observation section #1 (4.14 s (SE = 0.25)) and #5 (4.16 s (SE = 0.21)) in the control (t(4 0 5) = 0.89, p = 0.19). On the contrary, when there were transverse line markings, the time headways at observation section #1 and #5 were found to be significantly different (SR = 20 m: t (4 3 7) = −2.36, p < 0.05; SR = 50 m: t(3 8 4) = −2.25, p < 0.05; SR = 100 m: t(3 8 2) = −2.18, p < 0.05). In addition, it can be discovered that the biggest difference in time headway (0.39 s) appeared in the test of SR = 20 m.

3.1.3. Effect on distance headway In this paper, three speed intervals, (−∞,65 km/h), [65 km/h, 80 km/h], and (80 km/h, +∞), were considered in the comparison of distance headways. Then, a two-way ANOVA with repeated measures of distance headways was conducted under the circumstance of three kinds of transverse line markings (SR = 20 m, SR = 50 m, and SR = 100 m) and three speed intervals. According to the sample size distribution regarding the speed intervals above, and for the sake of convenience in calculation and analysis, the sample size for repeated measures was set to 80 in each combination of the line markings designs and the speed intervals. Fig. 6 demonstrates the distance headways under different tests and different speed intervals. The two-way ANOVA revealed that, the main effect of

3.2.2. Speed comparisons Fig. 8 depicts the speed comparisons between observation section #1 and #5. The Student’s t test revealed no significant difference of speed between observation section #1 (80.3 km/h (SE = 1.16)) and #5 (80.8 km/h (SE = 1.18)) in the control (t(4 0 5)=1.02, p = 0.22). On the contrary, when there were transverse line markings, the speeds at observation section #1 and #5 were found to be significantly different (SR = 20 m: t(4 3 7) = 2.28, p < 0.05; SR = 50 m: t(3 8 4) = 2.29, p < 0.05; SR = 100 m: t(3 8 2) = 2.24, p < 0.05). But, it seemed to be that there was no obvious difference regarding the speed variation

Fig. 6. Distance headways under different tests and different speed intervals.

Fig. 7. Time headway comparisons between observation section #1 and #5. 5

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distance perception of drivers owing to the transverse line markings that produced reverse linear perspective information. 4.1. Influence of speed perception on time headway With the transverse line markings installed on the lane, the speed reduced 3.2 km/h or 3.9% in average when compared with the control. This speed reduction phenomenon was in line with the studies of Francois et al. (2011), Rakha et al. (2006), and Liu et al. (2013). In particular, the studies of Francois et al. (2011) and Liu et al. (2013) both suggested that edge rate could induce speed overestimations of drivers, which eventually gave rise to the reduction in actual speed. Similarly, as depicted in the on-road experiment, the transverse line markings were installed with a constant gap of any two adjacent markings, which enhanced drivers’ perception of speed since edge rate generated due to relative motion. It led to speed overestimation and resulted in reduction in actual speed eventually. However, there was no significant difference with regard to the conditions of SR = 20 m, SR = 50 m, and SR = 100 m. This perhaps because, (1) there was no significant difference in the initial speed when the vehicles passed through the initial observation section (section #1) in all tests, and (2) the transverse line markings were set the same that the gap between two adjacent markings was fixed to 200 cm. As a result, the edge rates that the drivers perceived were basically the same in terms of a similar vehicle speed. It means that the effects of the transverse line markings on driver’s speed control were fairly equivalent in those three conditions. Thus, there was no statistical difference in speed reduction. However, according to Figs. 4 and 7, there existed substantial differences in time headways among the tests of SR = 20 m, SR = 50 m, and SR = 100 m. Thus, the increase in time headway did not derive directly and utterly from a reduction in speed.

Fig. 8. Speed comparisons between observation section #1 and #5.

between observation section #1 and #5 among the tests of SR = 20 m, SR = 50 m, and SR = 100 m. 3.2.3. Distance headway comparisons Fig. 9 presents the distance headway comparisons between observation section #1 and #5. The Student’s t test revealed no significant difference of time headways between observation section #1 (80.1 m (SE = 1.67)) and #5 (80.0 m (SE = 1.85)) in the control (t (4 0 5) = 0.89, p = 0.19). On the contrary, when there are transverse line markings, the distance headways at observation section #1 and #5 were found to be significantly different (SR = 20 m: t(4 3 7) = −2.42, p < 0.05; SR = 50 m: t(3 8 4) = −2.33, p < 0.05; SR = 100 m: t (3 8 2) = −2.21, p < 0.05). Similarly, it can be discovered that the biggest difference in distance headway (4.3 m) appeared in the test of SR = 20 m.

4.2. Effect of distance perception on time headway 4.2.1. Effects of the transverse line markings on time headway Actually, this could be that the reverse linear perspective information, produced by the transverse line markings, induced a distance underestimation of drivers, which in turn affected the time headway. Specifically, the study of Wu et al. (2007) suggested that distance overestimation could occur with convergent linear perspective information on the ground, when compared to the parallel one. For this phenomenon, Wu argued that the convergent linear perspective information descended observer’s perceived eye level, which consequently led to distance overestimation. In reverse, observers would underestimate distance with the parallel linear perspective information demonstrated since its perceived eye level was tilted when compared with the condition with the convergent one. In fact, it is safe to state that parallel is somewhat divergent in comparison with convergence. Analogously, as illustrated in this research, the transverse line markings appeared on the road surface diverged from the original parallel ones in terms of linear perspective. As a consequence, distance underestimation occurred (see Fig. 10). As depicted in Fig. 10b, the relationship between the perceived distance and the actual distance can be written as follows:

4. Discussions It can be discovered from the above experimental results that, there was a slight decrease in speed and a significant increase in time headway after the installation of the specially designed transverse line markings. However, the average time headways differentiated significantly in conditions of SR = 20 m, SR = 50 m, and SR = 100 m regardless of the non-significant difference in speeds. Hence, the variations of time headways in different conditions did not derive directly and utterly from a speed reduction. Perhaps there were differences in

tan α = d=

H H , tan(α + β ) = D d

tan α D tan(α + β )

(1)

(2)

where α is the angular declination below the eye level regarding to a target, β is the angle between the perceived eye level and the actual eye level, H is the observer’s eye height, D is the actual horizontal distance between the observer and the target, and d is the perceived horizontal distance from the target. It can be seen from the above formulas that the distance was

Fig. 9. Distance headway comparisons between observation section #1 and #5. 6

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(a) perceptual space

(b) physical space

Fig. 10. A schematic of the geographic relationship between the perceived eye level and perceived distance.

underestimated due to the reverse linear perspective information produced by the transverse line markings. As far as the car-following situation was concerned, the driver of the very first leading vehicle met no other vehicles in its stopping distance range. It means he/she did not have to focus on the distance between itself and the vehicle (if there was) just ahead of him/her excessively. So, little effect of the reverse linear perspective information would act on the distance perception of him/her, but instead the perceived speed would be mattered. However, the following drivers, on the one hand, would be affected by the very first leading vehicle since its speed reduced. On the other hand, the transverse line markings could have effects on both the perceptions of speed and distance of the following drivers. Consequently, the following vehicles would move forward with a greater deceleration until they matched the speeds of its very leading vehicle. In other words, under the situation of a equivalent initial speed, the leading vehicle would advance with a relatively greater speed compared with the following one, which eventually gave rise to the increase in time headway.

is the section range, m; is the length of the initial marking, m; is the initial speed, m/s;

is the distance a vehicle advanced over a time of , m; is the length of the marking at the time of .

Fig. 11. A schematic of the change of the marking length.

was continuously installed, the change of the marking length can be calculated as follows.

4.2.2. Effects of section range on time headway As showed in Figs. 4 and 7, the average time headways in conditions of SR = 20 m, SR = 50 m, and SR = 100 m were significantly varied, and the magnitude relationship was SR = 20 m > SR = 50 m > SR = 100 m. This relationship could be explained from the following three aspects. On the one hand, there was a substantial variation in the quantities of sections in those three conditions. That was, as described in Table 1, the quantities of sections of SR = 20 m, SR = 50 m, and SR = 100 m were 15, 6, and 3 respectively. So, the drivers experienced different stimuli in different conditions. Besides, according to Stevens’ power law (Stevens, 1957), there was a relationship between the magnitude of a physical stimulus and its perceived intensity or strength, i.e., Ψ(I ) = kI a , wherein, I is the magnitude of the physical stimulus, Ψ is the subjective magnitude of the sensation evoked by the stimulus, a is an exponent that depends on the type of stimulation (a = 1 when concerning visual length), and k is a proportionality constant that depends on the units used. Based on this formula, it can be seen that the drivers experienced the biggest strength of stimulus in the condition of SR = 20 m when compared with the rest two, since a larger quantity of sections was out there. That was the reason that the condition of SR = 20 m met the largest increase in time headway. On the other hand, from a relative microscopic view angle, the drivers experienced different change rates of the marking length in those three conditions. More importantly, based on the studies of Sinai et al. (1998), Yarbrough et al. (2002), Wu et al. (2004), and Feria et al. (2003), it can be deduced that the varied change rates of the length of the markings, to a certain extent, delivered visual information about texture gradient, linear perspective, etc. Fig. 11 illustrates a schematic of the change of the marking length as a vehicle pass by. Then, supposing the deceleration was constant and the markings

1

L(t ) =

2 1 v0 t + 2 at − 2 2L

L(′t ) = −

v0 + at 2L

(3)

(4)

where L(′t ) denotes the change rate of the marking length, a stands for the deceleration. According to formula (4), under the circumstance of an equivalent initial speed, the condition of SR = 20 m could meet the greatest change rate of marking length. This means that the condition of SR = 20 m generated the greatest “discontinuity effect”, named by Feria et al. (2003), which led to the greatest rise in time headway. Finally, the ground based distance perception was also affected by a slant (η) introduced by Yarbrough et al. (2002). Yarbrough argued that the distance underestimation occurred because of an intrinsic bias in the visual system to perceive a ground surface as slanted with its far end upward (see Fig. 12). Therefore, the distance would be further underestimated as d = sin α·D sin(α + β + η) (the variables mean the same as formula (2)). In addition, the effect of this intrinsic bias on distance perception could be aggravated when the visual cue was limited or even absent. In this study, the transverse line markings destroyed the original continuous ground surface visual information with a varied degree in conditions of SR = 20 m, SR = 50 m, and SR = 100 m. Specifically, in the condition of SR = 20 m, there was the greatest number of sections, which formed the maximum intensity of destruction to the original ground surface. Consequently, the greatest rise in time headway was witnessed in the condition of SR = 20 m, in which the greatest effect of distance underestimation occurred. 7

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Fig. 12. A geographic relationship among the eye level, slant, and perceived distance.

5. Conclusions In this study, a kind of transverse line markings were used to alter the drivers’ perception of speed and distance to enlarge the following time headways, by producing the reverse linear perspective information. This, to a certain extent, interprets the roles of perceptual variables in decision and control of the process of car-following. In particular, the on-road experiment was conducted to collect naturalistic vehicle flow data. Besides, considering the factors of edge rate and linear perspective, the influences of speed perception and distance perception on time headways were analyzed. This study makes the speed perception and distance perception progress from a stationary scenario into the car-following process. More importantly, it provides evidence that the direct visual intervention on headway (distance) control is basically feasible, which may be a new solution to the rearend crash issues. However, there are some limitations of this research. Firstly, only three forms of design of the transverse line markings adopted. This might throw out a doubt that if there is a better design that can be more effective in headway control. Secondly, some other visual and/or nonvisual information may take a part, such as the eye height of the drivers, the size of the leading vehicle, the colors of the markings, age, gender, and so forth. Besides, before the transverse line markings could be practically used for applications, the medium and/or long term effects of the transverse line markings on headways need to be further investigated. Also, the effects of road conditions, like the curves, tunnels, long-slopes, and so on, should be taken into consideration to extend the study and the feasibility of the transverse line markings. Therefore, our research in progress is looking forward to diversifying the design of the transverse line markings, to controlling the latent variables, and to examining its long term effect on various road conditions to pave the way for its practical applications. Acknowledgements This work was supported by the National Natural Science of Foundation of China (grant number 71771183); the Ministry of Transport of the People’s Republic of China (grant number 2010353342240); and the Scientific Research Foundation of Wuhan Institute of Technology (grant number K201845). References AASHTO, 2011. A Policy on Geometric Design of Highways and Streets. American Association of State Highway and Transportation Officials (AASHTO), Washington, DC. Backer-Grondahl, A., Sagberg, F., 2011. Driving and telephoning: relative accident risk when using hand-held and hands-free mobile phones. Saf. Sci. 49 (2), 324–330. Chaurand, N., Bossart, F., Delhomme, P., 2015. A naturalistic study of the impact of message framing on highway speeding. Transport. Res. Part F: Traff. Psychol. Behav. 35, 37–44.

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