The Psychology of Rear End Collisions: Looming
To understand the causes of rear end collisions, and all other accidents, the first step is to determine how a person normally and successfully performs the task. The second step is to determine why the person failed to perform the task successfully in the particular situation. This article explains how people normally use optical information in the avoidance of rear end collisions.The key perceptual issue in most rear-end collisions is motion perception rather than visibility. In daylight, the lead vehicle is usually visible. At night, there may be instances where the lead vehicle is dark or difficult to see. Generally, however, taillights and sometimes reflective tape make the lead vehicle visible, if not necessarily recognizable, at a relatively long distance. Drivers see many vehicles on the roadway ahead, so the mere presence of a lead vehicle does not necessarily imply the need to respond. They must determine that they are closing on a lead vehicle and that the time-to-collision (TTC) is short given the current situation. In theory, a driver can see that he is closing on a lead vehicle by noting changes in the headway, the amount of road between his vehicle and the lead vehicle. However, headway is a crude, slow and inexact way to determine whether a collision is imminent (e .g., Green, et al, 2008). Drivers probably do not use it. Instead, they use optical image transformation, information is contained in the dilation of the retinal image, a perceptual phenomenon called "looming motion." The analysis of driver looming/motion perception and behavior consists of two sets of factors, sensory and cognitive. The sensory, "psychophysical" factors are the eye's ability to sense object contrast, motion, etc. These limitations are hard-wired into our species. Sensory factors bound what is humanly possible. That is obviously a good place to start a collision analysis. The sensory information by itself, however, has little significance. To behave intelligently, drivers must interpret the sensory information, and assess the situation. This requires cognitive processing that is largely based on experience and expectation. Lastly, there is much more to collision avoidance than just perception. The decision on whether, when and how to respond depends on the available response alternatives and their consequences. This article provides a bare bones introduction to the psychophysical aspects of collision avoidance. This is just the tip-of-the-iceberg of the entire perceptual psychology field of "ecological optics" (e .g., Gibson, 1979), which is critical for understanding visually guided behavior such as driving. Finally, I briefly touch on some cognitive and response factors, but these are discussed more fully elsewhere (Green et al, 2008; Green, 2009). Sensory Analysis The optical transformation that the visual image undergoes as the driver travels forward is the primary sensory information that drivers use to judge whether a rear-end collision is imminent. When a driver views an object such as a truck (Figure 1), it creates an image on the eye's "film," a light sensitive layer called the "retina." As the driver approaches the truck, the retinal image expands, and the edges move outward. Figure 1 shows an object's image at time T and then the same image a moment later (time T+1) as the driver nears. On the retina, the truck's edges have moved outward, creating a motion cue called "looming." The faster the closing rate, the faster the expansion, the faster the edge motion and the greater the looming.
Figure 1 Schematic depiction of retinal image expansion and of looming. It is possible to use optical expansion rate, combined with the instantaneous image size, to perceive the time-to-collision (TTC), signified by the variable (tau):
where = time-to-collision (seconds)
= retinal image size (radians)
= expansion rate of retinal image growth (radians/second) This relationship between image growth and TTC was first noted by Astronomer Fred Hoyle in his 1957 book The Black Cloud and subsequently rediscovered by Weinberger (1971). However, Lee (1976) first appreciated its relevance to driver behavior. According to the " hypothesis," (Lee, 1976) a driver can use this retinal image growth for collision avoidance by directly perceiving the time-to-collision. To see this, just take any object, hold it at a distance and move it toward your eye. The image grows until it fills the entire visual field as it strikes the eye. There is no doubt that the calculation (size)/(expansion rate) empirically gives the TTC. The role that this information plays in collision avoidance, however, is still debated, and I shall return to the issue later. However, there is no dispute on one point: when an object is distant, the expansion rate is so slow that the driver cannot detect the motion and could not use this looming cue or any similar optical variable to perceive closure. As the driver approaches the lead vehicle, the expansion rate increases until it reaches motion detection threshold. At this point, there is theoretically sufficient sensory information to precisely determine the TTC. (The driver can also use an optical variable, , the temporal derivative of to determine the ideal braking deceleration, but that's beyond the scope of this article.) This critical point requires some explanation. Thinking in terms of optical variables is unintuitive to most people, so it is often better to express them as their spatiotemporal equivalents. Figure 2 shows the conversions:
Figure 2 Calculating TTC from optical and spatial variables. The graph shows the effects of closing velocity and distance. The dashed line is the mean looming threshold found in research studies. The yellow area is the best estimate for real driver looming thresholds. The TTC is simply distance/velocity (D/V) and using the small angle approximation, the retinal image angle is size/distance (W/D). Table 1 demonstrates that TTC calculated by spatiotemporal and by optical variables produces the same result. According to Gibson (1979), however, drivers cannot use the spatiotemporal variables because they are "extrinsic," not represented directly in the visual array while optical variables are "intrinsic." This presumably explains why drivers are so poor at estimating distance and speed - they do not actually use such variables to guide their vehicles.
Table 2 TTC calculated by spatial and optical variables. The expansion rate is: where W= object width (feet)
D = distance (feet)
V = closing velocity in (feet/sec) From this formula, it is apparent that the expansion rate grows with increased size and closing speed, but declines with distance. Note that the distance variable is squared, making it the most important factor. Figure 2 also illustrates the importance of the distance variable. The most salient aspect of the figure is that expansion rate is low when the distance between the driver and the lead vehicle is large. As the driver approaches, the rates grows slowly at first but then explodes at short distances. Perceptually, expansion goes from undetectable to highly obvious within a short and dramatic transition period. In contrast, speed and size are less critical. In the analysis of a specific collision, the important factor is the position on the curve, the distance where the looming is perceptible. At longer distances, the driver cannot see the looming and cannot accurately judge the closing rate. Once the driver reaches a distance where the looming is perceptible, then he theoretically can perceive the TTC. Whether this tells him to respond immediately is a different question that I discuss later. But it is certain that until looming is perceptible, the driver has no accurate information about closing rate or TTC. The distance at which looming is detectable (the point of the curves in Figure 2) depends on the motion threshold, the minimum rate of expansion that is perceptible. This motion rate is usually expressed as angular velocity, degrees/second or more often as radians/second. Estimates range from .0030 radian/second in highly optimized research experiments (e. g., Hoffman & Mortimer, 1996) to .0275 radian/second (Plotkin, 1984) based on road accident data. There are reasons to discount both of these extreme values and to put a reasonable range estimate for normal drivers under good daylight conditions at about .004 to .008 radian/second (Green, et al, 2008). Table 2 shows distance and time-to-collision (TTC) at which looming is perceptible as a function of looming threshold for a driver traveling 60 mph (88.02 ft/sec). I have assumed that width is 8 feet, the width of a typical tractor-trailer.
Table 2 Looming threshold, distance of looming perceptibility and TTC. Assumed speed is 60 mph, and lead vehicle is assumed 8 feet wide. The table shows that the driver has from 3.37 to 4.77 seconds to avoid collision. This range is valid for perfect conditions. The driver must be looking directly at the lead vehicle's center under good visibility. Low contrasts are known to raise motion thresholds, so dim light, fog, etc. can shorten the looming distances. Moreover, all threshold data apply only to "local , Type 2," the dilation of a single object such as a vehicle's rear. There are almost no data for "local , Type 1," the spread of points on the object1. For example, as a driver approaches a vehicle that has only taillights visible, the lights will spread, providing a looming cue. There are reasons to believe that threshold for this Type 1 looming will be higher. See Green et al (2008) for more explanation. Lastly, Table 2 does not take into account driver perception-reaction time (PRT) or the time required to depress the brake pedal. For example, a 1.5 seconds PRT and 0.4 second pedal depression time subtracts 1.9 seconds and 167 feet from the table. What Does It All Mean? Many analyses assume that a normal driver would and should respond as soon as looming is perceptible. Is that a good assumption? There are several reasons why it probably is not.
|| Home | Experience | Services | Contact Us | Seminars/CLE | Attorney's Guide | Resources ||
Copyright © 2009 Marc Green, Phd
Home Page: http://www.visualexpert.com