Visual Expert Human Factors: Rear End Collision

The Psychology of Rear End Collisions: Looming

Marc Green

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.

Looming simply reveals the TTC, but it does not specifically say whether or not response is necessary. The driver still must interpret the TTC in terms of the overall situation. After all, drivers commonly travel behind a lead vehicle with a 1.5 seconds or less temporal headway (Taieb-Maimon, & Shinar, 2001), which is just the instantaneous TTC. They do this because they do not expect the lead vehicle to suddenly brake hard. There is more to deciding whether to brake than merely perceiving the TTC. Moreover, our brains evolved prior to the development of motorized vehicles. At foot speed, an object even 150-200 feet away is not an immediate threat. We don't have a strong innate sense that an object at that distance constitutes a collision affordance.

The entire scenario described above is based on the "

hypothesis," which posits that drivers use

to judge TTC and to avoid collision. However, much research (e.g., Bootsma & Craig, 2003) challenges the hypothesis. While drivers certainly incorporate optical image growth into judgments about when to brake, the judgment is not necessarily based on

either alone or with other variables. A common finding is that braking behavior is better predicted by a weighted combination of expansion rate and image size. Other research suggests that drivers use the temporal derivative of

("tau dot"), rather than

or perhaps use the temporal derivative of the expansion rate. All of these optical variables change systematically with TTC.

There is also ample evidence that drivers judge TTC based on some other variables from the optic flow field, e .g., edge rates, and global optic flow rate (GOFR). These provide information about egospeed.

There is good evidence that driver TTC judgments are also influenced by spatial variables such as depth and distance cues, e .g., size, linear perspective, occlusion, height in the visual field, etc. Viewers also experience "motion adaptation," which causes the looming to slow. (See Green, et al, 2008 for more discussion).

Humans are satisficers. Time and again I have seen reports and heard testimony that blame a person for failure to act in some idealized, optimal way - a way in which absolutely no real person behaves. Most drivers have approached trucks on the highway thousands of times. At the normal speed differentials, the driver can look in his mirror, scan the scenery, think of dinner, etc. for a few seconds without any substantial danger or risk. Since this is almost always the existing state-of-affairs, the driver adapts and relies on this degree of fault tolerance as the norm. This is human nature and what people do: 1) they adapt their behavior to requirements of the situation and 2) they economize their effort to be efficient. Nobel Prize winner Herbert Simon coined the term "satisficing" (Simon, 1956) to summarize the strong innate human tendency to seek satisfactory solutions that are reasonable tradeoffs between efficiency and outcome. Humans are not optimizers who attempt unnecessary perfection for its own sake. They learn the system tolerance and determine a satisficing solution that is a good tradeoff between effort and outcome. They don't stare fixedly at the road because such close attention extracts a high mental cost of stress and fatigue and because it is simply not necessary. The person who encounters the stopped truck and fails to avoid is often simply unlucky.

The decision to brake also depends on the vehicle capabilities, possible response alternatives and the possible consequences of sharp braking or turning, etc. (Green, 2009).

This last point deserves some amplification. Once the driver discovers that he has 4 seconds to avoid a collision while traveling at 60 mph, he must decide what to do. His actions depend on several factors. First, he must know the stopping capability of his vehicle. How much distance does he require to stop? Unfortunately, the driver has likely never had to slam on the brakes while traveling at 60 mph, so he has no direct experience. In fact, few drivers ever exceed .5g braking, about 2/3 of the maximum normally achievable, under any circumstances. In sum, the driver is likely faced with a situation that he has never encountered before, so he has no learned response or even mental schema or script to cover the situation.

If he has hit the brakes hard in the past, it was probably at a low speed. However, stopping distance increases with the square of speed. That is, braking at 60 mph requires 4 times the distance of braking at 30 mph. Since people tend to extrapolate linearly (stopping distance at 60 mph should be twice that at 30 mph), the driver is likely to underestimate the stopping distance. The underestimation will likely be even greater if traveling downhill or on wet or icy roads, both conditions that reduce tire friction with the road.

Moreover, collision avoidance is not the driver's only immediate problem. Drivers do not want to make extreme responses while traveling at high speed. A sudden hard brake or steer risks loss of control, leaving him in a ditch, colliding with some roadside object, crashing head-on into oncoming traffic, rolling over, etc. The driver will likely want to gather more information and increase certainty before deciding on such an extreme action. Gathering information, however, requires time, which shortens the available stopping distance. Alternatively, the driver may temporize by taking his foot off the accelerator or by lightly stepping on the brake. The result is a tradeoff uncertain value. It slows the vehicle and buys time at the cost of distance. It may or may not be helpful, depending on the degree of slowing and the length of time required to assess the situation.

Lastly, the driver may simply have no feasible response. This scenario occurs most often when there is a tractor-trailer blocking all lanes of the roadway. The driver is faced with an avoidance-avoidance conflict (Lewin, 1935), where the response alternatives are all unfavorable. In such cases, PRT is often very long. "Should I steer right into the ditch or left into oncoming traffic?" It's like asking your child whether he'd prefer broccoli or spinach for dinner. Expect a very long pause.

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

¹There 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.

References

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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.

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.