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. In particular, I examine the role of looming in vehicle guidance. Like perception-reaction time, the concept is far too frequently used by "experts" with no understanding of the underlying science, "ecological optics".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 can use spatial cues such as headway to determine the sign of relative motion, i.e., whether they are closing, falling farther behind or staying a constant distance. However, they cannot tell anything about the rate of closing or the imminence of collision. This is not a problem in normal driving, since the closing speeds are relatively low. If the vehicle ahead is unexpected stopped or very slow, then the situation changes because closing rate is fast, and the crude spatial information is no longer adequate. The drivers must determine that they are rapidly closing on a lead vehicle and that the time-to-collision (TTC) is short. This requires a different type of visual information, optical information which is contained in the retinal image transformations that occur with movement through the environment. For collision avoidance, the most important information is contained in the retinal image dilation of approaching objects, 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. Psychophysics is the discipline that relates the physical world to the psychological world. The physics here is the description of the optical events, the image projection on to the retina, that occur when a driver closes on a lead vehicle. The psychological world is the drivers motion detection ability. The outline presented below 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)1:
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 Comparison of TTC from spatiotemporal variables and tau from optical 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 time-to-collision2. 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 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). However, it should be remembered that these thresholds come from "car following" studies where a driver trail another vehicle and responds when the lead vehicle brakes. There are absolutely no studies of looming that involve drivers traveling at high speed on a freeway when they encounter stopped or slow moving vehicle. 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 object. 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.
Table 3. Angular velocities, TTC and distance for three different percepts. At 12 seconds prior to collision, the angular velocity is far too low to perceived looming, which is why the tractor-tanker appears to be moving at normal speed. By a TTC of 4.5 seconds, he is just reaching the distance .004 rad/sec limit where the angular velocity is approaching perceptibility. At three seconds, the looming is highly perceptible at .0097 rad/sec and the imminent collision is obvious. In sum, perception of looming is not a sudden, all or none. It grows gradually as distance decreases and angular velocity increases. In sum, the typical rear-end collision with a stopped/slow vehicle on the freeway probably goes something like this: 1. The driver perceives that he is closing on a vehicle relatively far ahead using headway or other spatial information, which is sufficient to perceive the sign of relative motion, closing, falling behind or remaining constant, but says nothing about the rate of closing. He recognizes a situation that he has seen many times and assumes that it is moving a normal freeway speed. He is in operating from "habit" (Trick, Enns, Mills & Vavrik. 2004) controlling the vehicle but with little conscious awareness. Since he knows his vehicle can brake or swerve long before overtaking, there is no need to respond or even to pay particular close attention until he is much closer to the action boundary. This scenario normally works fine, since he overtakes the lead vehicle only very gradually. He doesn't need highly detailed TTC/urgency information; 2. If the lead vehicle is stopped or very slow moving, then the situation changes at an intermediate distance, perhaps 250-400 feet. He reaches the looming perception distance and begins to notice that something is happening, but the angular velocity and impression of looming is not yet strong and the driver tries to figure out what is different. He gathers more information while time and distance are reduced (c.f.,Markkula, Engström, Lodin, Bärgman, & Victor, 2016). He does not initially realize that it is an emergency since he believes that he can slow in time. (Changing lanes at this point would require looking in the mirror, but he doesn't want to take his eyes off the road.) However, he has never had to brake hard at such a high speed before, and does not know physics, i.e., that stopping distance increases with the square of speed. He greatly underestimates the required stopping distance, so he hesitates until he can assess the situation further, especially if he is a cautious driver (Prynne & Martin, 1995); and 3. He reaches a point where the looming is strong and the impression of imminent collision is clear because the angular velocity is increasing at a high rate. By this point, however, he may have come too close to the lead vehicle to avoid. So How Do Rear End Freeway Collisions Occur? In sum, the typical rear-end collision with a stopped/slow vehicle on the freeway probably goes something like this: 1. The driver may perceive that he is closing on a vehicle relatively far ahead using headway or other spatial information (i.e., the ventral system), which is sufficient to perceive the sign of relative motion, closing, falling behind or remaining constant, but which says nothing about the rate of closing. He recognizes a situation that he has seen many times and assumes that it is moving a normal freeway speed. He is in operating from "habit" (Trick, Enns, Mills & Vavrik. 2004) and controlling the vehicle but with little conscious awareness. Since he knows the system tolerance, i.e., that his vehicle can brake or swerve long before overtaking. There is no need to respond or even to pay particular attention until he is much closer to the action boundary. This scenario normally works fine, since he overtakes the lead vehicle only very gradually; 2. If the lead vehicle is stopped or very slow moving, then the situation changes at an intermediate distance, perhaps 250-400 feet, the action/vista space border. He reaches the looming perception distance and the optical information allows him to notice that something is happening, but the impression of an object coming toward him is not yet strong because in the innate looming-avoidance reflex is limited to very short distances well within action space. (Humans have not evolved to travel faster than 8 mph, maximum running speed, so there is no need to worry that an object 300 feet away is an immediate an threat). Instead, the driver tries to figure out what is different. He does not initially realize that it is an emergency since he believes that he can slow in time. (Changing lanes at this point would require looking in the mirror, but he doesn't want to take his eyes off the road.) If he has been driving for some time, he "velocitates". Motion adaptation produces the impression that he going slower than he actually is, so he thinks that stopping distance is correspondingly shorter. Eventually the optical information reveals that there is an emergency. He is jolted from low arousal habit into high arousal and high stress where his mind is racing about what to do4. However, he has never had to brake hard at such a high speed before, and does not know physics, i.e., that stopping distance increases with the square of speed. He greatly underestimates the required stopping distance, so he hesitates until he can assess the situation further before making an extreme response, especially if he is a cautious driver (Prynne & Martin, 1995; Keisewetter, Klinkner, Reichelt & Steiner, 1999). Yes, conservative, not reckless, drivers are more likely to have this collision. 3. He reaches a point where the looming is strong and the impression of imminent collision is clear because the angular velocity is increasing at a high rate. By this point, however, he may have come too close to the lead vehicle to avoid. Conclusion Drivers likely rely heavily on optical information, such as and in judging when to brake. However, calculation of the looming perception distance is only the starting point in analyzing driver behavior. First, drivers incorporate other sensory information in making their judgments about whether to act. Although I have not discussed them here variables, such as edge rates, global optic flow rates, contrast level, motion adaptation and depth cues may play a role (Green, et al, 2008). Second, the sensory information is only grist for the cognitive mill - the driver must interpret the information based largely on experience and expectation. The presence of a stopped vehicle on a freeway is a rare and unexpected event. Studies of accident rates and speed differential suggest that such vehicles constitute an "error trap" (Reason, 2004) that is likely to snare many drivers. Footnotes 1Tau actually give a very close approximation rather than the precise TTC because it relies on the small angle approximation.
2People (myself included) sometimes speak loosely about"closing rate". This is a mistake, as tau provides information about instantaneous time-to-collision and says nothing about closing rate. Tau dot, however, is an indicator of "closing rate". Tau also says nothing about whether the vehicle ahead is stopped or moving at any particular speed.
3There is also a "global " which is useful in calculating time-to-passage (TTP) of a stationary object. For example, it could be used to calculate the time to pass a sign on the roadside.
4I know this because I've been there! References Bootsma, R., & Craig, C. (2003). Information used in detecting upcoming collision. Perception, 32, 525-544. Gibson, J.J. (1979). The ecological approach to visual perception. Boston: Houghton Mifflin. Green, M. et al (2008). Forensic Vision: With Applications To Highway Safety. Tucson: Lawyers And Judges Publishing. Green, M. (2009). Perception-reaction time: Is Olson (& Sivak) all you need to know? Collision, 4, 88-93. Hoffman, E., & Mortimer, R. (1996). Scaling of relative velocity between vehicles. Accident Prevention and Analysis, 28, 415-421. Lee, D. 1976. A theory of visual control of braking based on information about time-to-collision. Perception, 5, 437-459. Lewin, K. (1935). A dynamic theory of personality. New York: McGraw-Hill. Markkula, G., Engström, J., Lodin, J., Bärgman, J., & Victor, T. (2016). A farewell to brake reaction times? Kinematics-dependent brake response in naturalistic rear-end emergencies. Accident Analysis & Prevention, 95, 209-226. Plotkin, S. (1984). Multiple Causation. Automotive Engineering and Litigation, 1, 215-228. New York: Garland Law Publishing. Reason J. (2004) Beyond the organisational accident: the need for "error wisdom" on the frontline. Quality And Safety In Health Care, 13 Suppl 2: ii28-ii33. Simon, H. A. (1956). Rational choice and the structure of the environment. Psychological Review, 63, 129-138. Taieb-Maimon, M. & Shinar, D. (2001). Minimum and comfortable driving headways: Reality versus perception. Human Factors, 43, 159-172. Weinberger, H. (1971). Conjecture on the visual estimation of relative radial motion. Nature 229, 562-562.
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