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Article Excerpt
INTRODUCTION
On U.S. roads, 41,821 individuals were killed and 3.2 million injured during the year 2000 (National Highway Traffic Safety Administration [NHTSA], 2000). Accident analyses implicate errors in perception and decision making as the probable cause of the majority of these accidents (Groeger, 2000). One of the more dangerous judgments a driver must make is whether there is sufficient time to complete a driving maneuver before colliding with an oncoming car--for example, in overtaking or in executing a left turn at an intersection. In the study reported here, we investigated visual-motor control and decision making during overtaking maneuvers.
Perception and Decision Making During Overtaking
Accident analyses indicate that overtaking a more slowly moving vehicle can be one of the more dangerous situations a driver faces. In the United States, overtaking accidents account for 2.1% of all fatal crashes and 1.1% of injury crashes (NHTSA, 2000). Although at first glance these numbers may seem small, it is important to note that overtaking maneuvers are performed relatively infrequently during normal driving. The situation is even worse in the United Kingdom, where two-lane rural roads make up a larger proportion of the roadway system, left-coat, Skelton, and Smeed (1973) reported that on British roads in 1972 about 15% of injury-causing automobile accidents involved an overtaking vehicle. More recently Clarke, Ward, and Jones (1998) reported that overtaking accidents accounted for nearly 10% of fatal road accidents in Nottinghamshire, England. From these analyses, Clarke et al. concluded that "the majority [of these accidents] arose from a decision to start the overtake in unsuitable circumstances" (Clarke, Ward, & Jones, 1999, p. 849) and that "the problem stems from faulty choices of timing and speed for the overtaking maneuver, not a lack of vehicle control skills as such" (Clarke et al., 1998, p. 465).
Laboratory and field studies on overtaking have reached similar conclusions. In a closed-track driving study, Jones and Heimstra (1964) reported that drivers made as many overestimates (i.e., that there was more than enough time to pass safely) as underestimates when judging the last safe moment to pass another vehicle. There was also considerable intersubject variability in the ability to make this judgment. From their findings, Jones and Heimstra (1964) concluded that drivers are unable to make accurate judgments about the temporal gap that is necessary for safe overtaking and passing. Similarly, Gordon and Mast (1970) reported that drivers were not able to accurately estimate the distance required to pass: Estimation errors ranged from 20% to 50%. Underestimations of the required distance increased with driving speed; at 50 miles/hr (mph; 80.4 km/hr) drivers were underestimating the minimum safe distance on 68% of trials.
Wilson and Best (1982) monitored vehicles on a stretch of public road in England. More than 400 overtaking maneuvers were classified into different categories, such as "cutting in" and "piggy backing" (i.e., tailgating). The main finding was that drivers often engaged in dangerous behaviors such as flying overtaking (overtaking without a pause) and lane sharing (not going completely out of the lead car's lane). These behaviors were often used to compensate for small temporal gaps with the oncoming vehicles. It was also reported that 14% of overtaking drivers used a gap size that was too small for a safe overtaking maneuver to be completed.
Visual Information Available for Overtaking
One reason for the high level of driver error involved in overtaking is the complexity of the visual judgments involved (Hills, 1980). The driver must simultaneously estimate the time to collision (TTC) with an oncoming car, monitor the TTC with the lead vehicle so as to avoid a rear-end collision, and estimate the time required to complete the overtake based on the current speed, road conditions, and knowledge of the capabilities of his or her own vehicle. As we will discuss, the sources of information used by drivers to make these estimates and control their vehicle during the overtaking maneuver are largely unknown. We will next turn to a discussion of visual information that the driver could use to perform this dangerous task.
Accurate information about the TTC with the lead vehicle and oncoming cars is theoretically available to the driver under most conditions (the cases in which it is not are described in detail later). The time to collision with an approaching car is given by
TTC [approximately equal to] [theta]/(d[theta]/dt), (1)
in which [theta] is the lead (or oncoming) vehicle's instantaneous angular subtense and d[theta]/dt is its instantaneous rate of increase of angular subtense (Hoyle, 1957). Research on how accurately observers can estimate TTC on the basis of Equation 1 has yielded mixed results. A large number of studies (including some that have involved judgments made while traveling in a moving car) have shown that observers make large (20%-40%) underestimates of TTC, with the magnitude of underestimation depending on a variety of factors, including approach speed, gender, age, and driving experience (reviewed in Gray & Regan, 1999b; Groeger, 2000). However, more recently we have shown that these large errors may be an artifact of the experimental methodology used (discussed in Gray & Regan, 2003). When the procedure was designed so that Equation 1 provided the only reliable information to perform the experimental task, estimation errors ranged from only 2% to 10%. In driving, TTC information appears to be particularly important for the initiation and control of braking (van Winsum & Heino, 1996; Yilmaz & Warren, 1995).
In some driving situations it has been found that the time headway (TH) appears to be a more important control variable than is TTC (Lee, 1976; van Winsum, 1998; van Winsum & Heino, 1996). The distinction between TTC and TH can be best understood by considering a car-following situation. If the follower maintains a constant distance behind the lead vehicle, the TTC (i.e., the time until the front bumper of the follower's car contacts the rear bumper of the lead car) is infinite. However, the TH, defined as the time until the front bumper of the follower's car reaches the location on the roadway currently occupied by the rear bumper of the lead vehicle (Lee, 1976), is finite and will depend on the follower's speed. Van Winsum and Heino (1996) have reported that when following another vehicle, drivers regulate their speed to maintain a fixed value of TH that varies from driver to driver depending on skill level (i.e., more skilled drivers prefer a shorter TH). We have previously discussed the optical specification of TH and how it can be computed by the human motion-in-depth processing system (Gray & Regan, 2000); however, we are unaware of any research that has examined how accurately observers can estimate this quantity.
It has been demonstrated that the perception of the relative speed of self-motion is influenced by the visual information provided by the global optic flow rate and the edge rate (Larish & Flach, 1990); however, these visual cues do not provide accurate information about absolute speed. (In order to estimate absolute speed on the basis of the global optic flow rate or the edge rate, the driver would need to know the absolute distances of the objects that are creating the optical flow.) Field studies have consistently demonstrated that drivers cannot accurately estimate their speed of travel: "errors in subjectively estimating speed are sufficiently great that drivers should consult speedometers" (Evans, 1991, p. 128). Studies using verbal estimates of speed (reviewed in Groeger, 2000) and studies using a procedure that requires drivers to adjust their speed to a specified level (e.g., halve their current speed; Denton, 1976, 1977) have shown that speed estimates are highly inaccurate (errors range from 10 to 60 km/hr) and are easily biased by factors such as the driving speed on the previous trial.
There are two primary sources of information that a driver could use to estimate the absolute distance of another vehicle on the roadway, although both sources of information are very limited. The vergence angle of the eyes provides accurate distance information for an object that is fixated; however, because this source of information is effective only for objects nearer than about 10 m, it would not be useful for most driving situations. It also been suggested that drivers could use the angular size of the retinal image as a cue to absolute depth for familiar-sized objects such as cars and pedestrians (Stewart, Cudworth, & Lishman, 1993). However, usage of this cue could lead to dangerous estimation errors if the driver incorrectly identifies the object that is being approached (e.g., mistake a child pedestrian for an adult or mistake the type of car). Consistent with this theoretical analysis, empirical studies have demonstrated that drivers are quite inaccurate when estimating absolute distance. Observers consistently underestimate absolute distance: Estimated distance was a power law function of the absolute distance with an exponent of roughly 0.8 (Groeger, 2000; Teghtsoonian & Teghtsoonian, 1969).
The research reviewed so far has primarily examined performance in conditions in which visual information is accurate and reliable. Another possible source of errors of judgment is that in some situations the information provided by the human visual system is inaccurate. For example, a driver's estimates of speed, TTC, and distance can be distorted by fog (Snowden, Stimpson, & Ruddle, 1998). For objects with a small angular size (e.g., a motorcycle viewed from a distance of 300 m), observers cannot accurately estimate TTC from Equation 1 because the object's rate of expansion is near the detection threshold. Hoffmann and Mortimer (1996) have estimated the threshold value of d[theta]/dt for driving to be roughly 0.005 rad/s and have shown that d[theta]/dt can be well below this value in many driving situations. We have previously shown that staring straight ahead during simulated driving on a straight open road can give the driver the illusion that the TTC (and TH) with other vehicles is longer than it really is (Gray & Regan, 2000). This closing speed aftereffect is quite distinct from the well-known adaptation of the perceived speed of self-motion that is caused by the expanding retinal flow pattern (Denton, 1976; i.e., drivers underestimate their driving speed following adaptation).
To summarize, accurate visual information for TTC is available to the driver, whereas information about absolute driving speed and the absolute distance of other vehicles is lacking in most driving situations. Laboratory and field research has shown that under optimal conditions drivers can accurately estimate TTC but cannot accurately judge their own speed of travel. Under nonoptimal conditions (e.g., closing speed adaptation or for small objects), TTC estimation can also be highly inaccurate.
Aims of the Present Study
From this brief review it is clear that overtaking is a dangerous maneuver in which driver judgment errors can occur and that there are numerous potential sources of these errors. A limitation of previous research in this area is that behavioral models of overtaking (like those developed for other driving tasks such as curve negotiation [Godthelp, 1986] and braking [Yilmaz & Warren, 1995]) are lacking. In order to reduce the number of accidents in these situations it is crucial to understand the perceptual-motor control and decision-making processes involved in overtaking so that these areas can be addressed in...
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