2005-01-0427 Relationship Between Relative ...

8 downloads 321362 Views 406KB Size Report
measuring responses of subjects using a laptop simulator. ..... on a laptop computer. This simulator has ... screen and nominally positioned 0.5 meters (20 inches) from the ..... showed that when the eccentricity was 17 degrees, the average ...
SAE TECHNICAL PAPER SERIES

2005-01-0427

Relationship Between Relative Velocity Detection and Driver Response Times in Vehicle Following Situations Jeffrey W. Muttart Accident Dynamics Research Center

William F. Messerschmidt Robinson & Associates, LLC

Larry G. Gillen GILLENgineering

Reprinted From: Human Factors in Driving, Telematics, and Seating Comfort 2005 (SP-1934)

2005 SAE World Congress Detroit, Michigan April 11-14, 2005 400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A. Tel: (724) 776-4841 Fax: (724) 776-5760 Web: www.sae.org

The Engineering Meetings Board has approved this paper for publication. It has successfully completed SAE’s peer review process under the supervision of the session organizer. This process requires a minimum of three (3) reviews by industry experts. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE. For permission and licensing requests contact: SAE Permissions 400 Commonwealth Drive Warrendale, PA 15096-0001-USA Email: [email protected] Tel: 724-772-4028 Fax: 724-772-4891

For multiple print copies contact: SAE Customer Service Tel: 877-606-7323 (inside USA and Canada) Tel: 724-776-4970 (outside USA) Fax: 724-776-1615 Email: [email protected] ISSN 0148-7191 Copyright © 2005 SAE International Positions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE. The author is solely responsible for the content of the paper. A process is available by which discussions will be printed with the paper if it is published in SAE Transactions. Persons wishing to submit papers to be considered for presentation or publication by SAE should send the manuscript or a 300 word abstract to Secretary, Engineering Meetings Board, SAE. Printed in USA

2005-01-0427

Relationship Between Relative Velocity Detection and Driver Response Times in Vehicle Following Situations Jeffrey W. Muttart Accident Dynamics Research Center

William F. Messerschmidt Robinson & Associates, LLC

Larry G. Gillen GILLENgineering

Copyright © 2005 SAE International

ABSTRACT Several previous studies report driver response times when responding to a lead vehicle. There have also been other studies that examined and measured the ability of drivers to detect the relative velocity of a lead vehicle. This study attempts to determine how the relative velocity detection threshold and driver response times fit together. There may be a significant difference between the times at which a lead vehicle is visible versus when it is perceivable as an immediate hazard. This research involved two parts; the first analyzes the raw data reported in previous research. The second part involved measuring responses of subjects using a laptop simulator. The goal of both parts of this research was to compare the subtended angular velocity [SAV] with the response times of drivers to determine if there is a point (threshold) at which response times level off at a fast rate. As theorized, driver response times remained high until the SAV of the lead vehicle increased to over 0.006 radians per second (in Part I) and to 0.0066 r/s (Part II), after which response times remained relatively fast. An in-depth analysis of driver response to a lead vehicle is discussed.

INTRODUCTION Several studies show stopped and slow-moving lead vehicles represent more than 70% of all rear end crashes (1, 2). This result is contrary to the perception that rear end collisions are primarily caused by drivers following too closely while the two vehicles are traveling at similar speeds. Young et al. (3) found when there is a large difference in speed between the lead vehicle and

following vehicle (greater than 15 mph), the potential danger and severity increases. This crash scenario is more difficult to detect and avoid and more serious when it occurs. The depth cues associated with safely judging the relative speed of a vehicle moving in the same direction is a problem for following drivers that has been recognized by numerous authors (4-20). If a lead vehicle (LV) suddenly slows, a driver following a LV at a constant and relatively short distance will see brake lights illuminate in conjunction with an immediate change in following distance and the pitch of the lead vehicle. However, when approaching a stopped or very slow vehicle on a high-speed road, brake lights may be visible, but they are not associated with other cues such as an immediate change in following distance or the pitch of the lead vehicle and the LV may be too far away to be perceived as an immediate hazard in many circumstances. Based upon research, when closely behind a lead vehicle, drivers respond quickly. When headway is much greater, response time increases significantly (10, 18, and 21). If cues are present, for example, a large landmark near a stopped vehicle or a red traffic signal, the following driver will have additional context by which to judge the speed of a LV. For instance, one study (22) showed that the average speed differential when a vehicle enters a high-speed roadway is 9 mph. Because the LV enters at an access ramp or intersection, and because the following driver may see the LV enter his lane, the following driver will have adequate context that will allow him or her to anticipate and perceive the speed difference. Although drivers do not complete their perception and response in a step-by-step manner, the response of a driver to a lead vehicle may be separated into five

phases for better analysis and understanding. The response involves detection, detection of closing, detection of relative velocity rate and the cognitive and motor responses. The first phase involves the detection of the lead vehicle. Obviously, a driver will not respond to a LV if he or she cannot discern it is present. A vehicle must be easily identified as an immediate hazard before most drivers will initiate a response. The last two phases, frequently referred to as perception-response, is addressed in other papers (14, 21, 23, and 24). This study is an attempt to define when a driver can detect there is an immediate hazard when approaching a slowly moving or stopped vehicle.

stated earlier, drivers generally do not and most times should not implement an emergency response yet.

Research has shown that as a driver approaches a stopped or slow-moving LV, there will become a time when they will be able to detect that they are closing on that vehicle (14, 25). Mortimer (12) found that the ability to detect closing occurred at the point that headway changed by 12%. However, rarely do driver slams on their brakes when they first detect that they are closing on another vehicle on a high-speed road. Olson et al (16) found that when a vehicle was 161 and 322 m ahead (528 and 1056 feet) and the following driver was gaining or losing ground at a rate of 13.4 m/s (30 mph), the subjects were only able to determine if the vehicle was closing or not (and were not yet able to detect a hazardous situation). Accuracy of judgments increased as headway decreased. There is a set of eight photographs that follow. Each photograph shows the view from the driver’s seat of a vehicle and shows the same lead trailer at two second intervals when closing at approximately 20 feet per second (6.1 m/s). You may be able to detect that photograph 2 was taken from a position closer to the trailer than photograph 1. The relative size of the slower moving trailer gets larger as the following driver closes on it. Therefore, a following driver may likely be able to determine that they are closing. However, from the distance depicted in photographs 1 through 3, it is unlikely that a following driver would judge that distance to be unsafe. On the other hand, when we close to a distance depicted in photographs 7 and 8, it is apparent that we are closing quickly and have to respond in some way. The reason drivers may not respond earlier is because there is typically nothing perceivable to respond to. Drivers have difficultly perceiving the specific rate of closure. The average driver applies the brakes 50,000 times per year in response to a LV without incident (26). Usually we will remain in our lane until we are closer to the lead vehicle and then slow, or we may choose to pass the slower moving vehicle. If we choose to pass a slower moving vehicle, then we may elect to move closer to the LV so we do not have to drive as long or as far in the higher speed lane. On other occasions we may check our rear view mirrors and prepare to pass when it is necessary. However, as

Photographs were taken of the rear of a trailer taken at 2 second intervals while closing at an average rate of 6.1 m/s. This research attempts to determine the point at which drivers will recognize that they are approaching an immediate hazard. Or if relating this research to the photographs above, which photograph above best depicts the relative size of the lead vehicle at which a driver is likely going to realize that he or she is closing dangerously fast. DEFINITION OF TERMS – ¾

Apperception – the process of understanding something perceived in terms of previous experience (as being an immediate hazard)

¾

Detection – the act of discovering or determining the true character of, or presence of, an object; to be able to state that a particular stimulus is sensed but cannot be (or has not yet been) identified

¾

Discern - the quality of being able to grasp and comprehend what is obscure.

¾

Hazard – (or potential hazard) any object in or near a road, or obstacle to negotiate through or around

¾

Headway – the elapsed time between the front

of the lead vehicle passing a point on the roadway and the front of the following vehicles passing the same point (25, p.313) ¾

Immediate Hazard – a hazard that requires an emergency avoidance response

¾

Normal Driver – a driver who performs within the middle 2/3rds of the driving population (The middle 2/3rds of the driving population would equal the median response plus or minus one standard deviation.)

¾

Perception – to attain awareness or recognize an object [Perception is primarily cognitive rather than emotional or impulsive, although all three aspects are manifested. Perception is vision plus a cognitive component (assessment or categorization.)] For the purposes of an emergency response perception would occur when the hazard is seen and also identified or categorized as an immediate hazard.

b. Perception-response Time – the time interval from the moment when the stimulus is perceived (easily identified as an immediate hazard) until the moment when the vehicle begins to respond [The perception-response time is the perceptionreaction time plus the transition time. Or perception-response time is the perceptionreaction time plus the movement time plus the mechanical latency (21).] ¾

¾

¾

¾

Subtended angular velocity (SAV) – the rate of change of the subtended angle of an object within a driver’s field of view. The SAV Threshold (SAVT) - occurs when 50% of drivers are first able to detect the relative velocity of a lead vehicle as an immediate hazard, without any other cues, based solely on the change in the perspective (subtended arc angle) of the lead vehicle. [Drivers closing at a rate defining an immediate hazard, distinct from drivers’ earliest ability to detect closure]. Drivers will not be able to detect the rate of closure on a lead vehicle without other cues until they are able to determine that the rate of change of the subtended angle of the LV is expanding at a rate that suggests they are closing dangerously fast (5, 6, 8, 9, 13, 14, 18, 19, 20).] Subtended arc angle – The angle that an object encompasses with an observers field of view. The same size object will have a larger subtended arc angle when closer than when further away. Threshold – the point at which a physiological or psychological effect begins to be produced; and, a level, point or value above which something is true and will take place and below which it is not or will not.

There are a number of things that an investigator must consider before evaluating a driver’s response time or

response choice. Basically, there are ten considerations that account for the differences between what the investigator sees and knows and what the driver saw and knew. In essence, an investigator cannot apply a response time, nor will a driver be expected to respond unless or until an object is easily identified as an immediate hazard (apperception). These ten considerations may assist an investigator in his or her determination of when apperception will occur and can be recalled by the IN CAR CREED acronym (14). IN CAR CREED stands for immediacy, neutralized, contrast, anticipation, recall, context, SAV detection, eccentricity, expectancy, and the driving task. Of the terms used in the IN CAR CREED, immediacy, SAV detection and recall have been addressed above. Other factors that must be considered include eccentricity, expectation and the driving task. Eccentricity refers to the angle of the driver’s gaze relative to the location of the immediate hazard. Research has shown that drivers tend to fixate more to the right at night (27). Results from Lee, Olsen and Wierwille (28) show the average single glance times and the probability of a glance in a single direction. Table 1 represents the results of the study by Lee et al. along with the range of eccentricities that were measured by this author using several vehicles. Table 1. Eye glance statistics for slow lead vehicle lane changes, all glance locations for the 3 seconds prior to initiation of maneuver. 295 events. (28)

Glance location

Eccentricity

Mean single glance time (s)

Glance probability during 3 s prior to t0

Forward - any direction

0 to 37.5

0.88

1.00

0 to 20

0.92

0.98

Center forward Left forward

20 to 37.5

0.67

0.26

Right forward

20 to 37.5

0.74

0.07

RV mirror

20 to 35

0.58

0.53

Left mirror

25 to 40

0.66

0.47

Left window

30 to 120

Left blind spot Instrument cluster

0 to 20

Right mirror

35 to 50

0.62

0.30

0.63

0.27

0.52

0.18

0.53

0.04

Right blind spot

0.64

0.01

Other interior

1.50

0.01

0.60

0.01

0.75

1.00

Right window All events

35 to 100

Lee et al. (28) found that there was no difference in eye glance duration or location during the 3 seconds before changing lanes in response to a slow-moving lead vehicle (or other obstacle ahead) for drivers in a sedan or SUV. Therefore, drivers will typically look directly

ahead for only about one of the three seconds before attempting a lane change in response to a slower moving LV. Lee et al. found that the average distance before impact where the lane change began was 124 feet (Median = 96 feet). A driver will be able to detect that they are closing on the lead vehicle from several hundred feet away and frequently begin to prepare for a lane change. However, while preparing to change lanes in response to a slow moving LV, a driver may reach a point that they realize that they are closing at a dangerous rate and not be able to complete the lane change maneuver before a collision. Visual glance duration and the number of glances per task were investigated while performing conventional invehicle and navigation tasks. Tijerina et al. (29) examined eye glance behavior using ride-along observers and participants while driving on public roads. They found that specific eye glance patterns take place before lane change initiation. For example, prior to making a lane change to the left, the likelihood of glancing at the forward view is the highest, followed by a glance to the left mirror or the rear view mirror. Glance data from the current naturalistic lane change field study (28) were analyzed in a similar manner. To understand what drivers do prior to performing lane changes, glance location was evaluated in terms of the proportion of glances to a particular location during the 3 seconds prior to lane change initiation (proportion of times that at least one glance occurred to a particular location was calculated). Out of 295 lane changes in response to a slower LV, each lane change was associated with at least one glance forward in the 3 seconds (or slightly more) prior to lateral vehicle movement. Regardless of the lane change direction, large proportions of glances were allocated for glances to the rear view mirror. Proportions for other glance locations are shown in Table 1. The two most likely glance locations were forward (nearly 100%) and rear view mirror (53%), thirty-five percent of the time a look into the rear view mirror followed a look forward, a pattern similar to that reported by Tijerina et al. (29). Ninety-five percent of the drivers studied maintained a safety envelope of no more than 20 feet per second (6.1 m/s) relative velocity in each direction. Therefore, closure rates of greater than 44 feet per second (13.4 m/s) will represent an unexpected and very low probability event. Dewar and Olson (30) indicated that fixation to a location and attention to a location may be disassociated, which is sometimes referred to as “looked but did not see.” Dewar cited research by Louma (1988) that showed that more than ½ of all subjects did not recall landmarks such as crosswalks, pedestrian crossing signs and pedestrian “crossing ahead” signs, even if the landmarks were fixated upon. Therefore, there may be a great difference between what a driver discerned and what a

post-crash investigator sees; a large part of that difference is due to expectancy. Expectancy is a very subjective term. No driver leaves their house believing they are going to be involved in a collision. The question that should be asked is how the lack of expectancy influences the driver’s response. For example, if a driver does not expect a hazard, he or she may experience some or all of the following: a. Looking in a different direction b. Actions that are contrary to their previous experience c. Not knowing where to look or what to look for d. Expectation of a different hazard e. Belief that a different response is appropriate or not having a prepared (conditioned) response for that hazard f. Not being able to easily distinguish the object when compared to its background and other objects in the area g. Inability to easily weed through all the visual noise and focus specifically upon the hazard h. Focus upon navigating (check for route), controlling (speed) and guiding (lane keeping) the vehicle A driver may face some or all of these issues. Therefore, a single correction factor (30, 31, and 32) to account for expectancy is not scientifically justifiable. Instead an investigator should address the specific issues associated with lack of expectancy and how that would influence the response. Overall, when investigating a case involving a front to rear crash we cannot assume that the following driver is gazing directly ahead at the lead vehicle. Nor can we assume that following driver knows what to look for or that he or she is expecting anything other than a typical slower moving LV and instead may be faced with a LV that is traveling extremely slow or may be stopped.

BACKGROUND If we compare the IN CAR CREED to a vehicle following situation, we know that a vehicle one mile ahead of us is not an immediate hazard, and we know from our experiences that vehicles on high-speed roads typically travel at high speeds and are rarely stopped or traveling very slow. We are unable to detect the relative velocity from one kilometer away, we are making several fixations, only about 1/3rd of which are directly ahead and most of those glances are at locations within 3 seconds of the front of our vehicle based upon the research by Mourant and Rockwell (27) in conjunction with typical following distance research (33, 34, 35). We are also engaged in the tasks of navigating, controlling and guiding our vehicle (36). Since the vehicle one mile ahead of us is not a salient object, it is unlikely that a driver will mentally process its presence and will

therefore also not be able to recall its movements when this distance away. Previous research has attempted to address this problem by examining the subtended angular velocity detection threshold (SAVT). The SAVT refers to the rate at which the subtended arc angle of the LV expands within the following driver’s visual field (See Table 2 for a compilation of previous research results).

Table 2 A compilation of related research. This chart shows when people were first able to judge relative velocity - when the subtended arc angle (perspective) of the LV increases in relative size in their visual field at a rate measured in radians per second. (The studies listed in regular type were cited in the research listed in bold.) RELATIVE VELOCITY DETECTION THRESHOLD Mortimer 1990

Change in Angle (rad/s) 0.0021

Braunstein & Laughery 1964

.0014-.0024

Mortimer 1988

.0028-.0035

Bierly 1963

0.0035 .0022-.0052

Mortimer & Hoffman 1996 Mortimer 1994

0.0027

Farber & Silver 1967 (head on)

0.0030 .002-.0045

Summala, Lamble & Laakso (1998) Lamble, Laakso & Summala (1999)

Plotkin, 1974 Duckstein, Unwin & Boyd 1970 Brown 1960 Michaels & Cozan 1963

Ahead

0.0022 - 0.0038

45 Deg.

.007 - .0095

90 Deg.

.013 - .015 0.0275 .003-.004 .00003-.0061 0.0006

Summala et al. (18) suggested that they believed a figure near 0.002 radians per second (r/s) was the SAVT, but when reviewing their raw data, the average response time for subjects faced with a 0.004 r/s subtended angular rate of change was 2.52 s., while subjects faced with a 0.017 r/s scenario had an average response time of 1.36 s. Clearly, the 0.004 scenarios still involved a significant level of relative complexity. Duckstein et al. (6) found that for relative velocities greater than 3 f/s, recognition of LV closing could be detected relatively quickly. When the subtended arc angles at the relative velocities were calculated, the results showed that when the rate was above 0.003 radians per second, response times were relatively low and when smaller than this figure, the response times increased to as much as 10.6 seconds. It is apparent that the subjects were not burdened with a difficult driving task, nor was leg movement time included in the research by Duckstein et al. The subjects were shown a car-following film in a laboratory. The subjects were told to depress a "throttle" lightly if following at a constant speed, heavily if the lead vehicle was pulling away and to brake if closing. Response

times were an average of more than 2 ½ seconds greater when SAV was less than 0.0035 r/s when compared to SAVs greater than 0.0035 r/s. When examining Whitty's raw response data (cited in 6), response times were much quicker at relative velocities of 0.0031 r/s and above, and they were much greater for relative velocities of 0.0022 r/s and below. When the reported response times and relatively easier task is accounted for, it is apparent that real life drivers will not likely respond until significantly after the 0.003 r/s threshold is met. Hoffman & Mortimer (8) found that the threshold at which 50% of stationary observers were capable of detecting relative velocity exceeds 0.003 radians/second. The results of their three groups averaged between 0.0022 and 0.0052 r/s. Their subjects were allowed 4-second observations and were not burdened with the task of driving. What this means is that a following driver will not be able to detect that a lead vehicle is stopped or traveling very slowly when in fast moving traffic until the stopped vehicle increases in perspective (relative size at the eye) at a rate greater than 0.003 radians (0.17 degrees) each second. This of course is not the case if there is adequate context or priming for the following driver. These studies are corroborated by Brown (cited in 6) who found that the just noticeable difference for alerted subjects who had a binary choice (detected or not detected) was 0.002 radians/second. Hoffman & Mortimer referred to vehicle width, but previous studies (6, 12, and 18) have referred to “size”. Since we are reporting a “threshold” at which most drivers will likely “start” to be able to detect relative velocity, and since height varies more than width on vehicles additional research in this area is appropriate. If only taillights are visible, then naturally the width (from one taillight to the other) would be the appropriate number to use. Further, this research will attempt to determine if drivers assess height more than width or perceptually expanding size (area) of the lead vehicle. Mortimer (11, 12, 13) showed that the rear presence (tail) lamps of motor vehicles should be placed as close as possible to the outboard edges of the vehicle and, in addition, there should be a second pair of presence lamps mounted as high and as far apart as possible, such as in the "C" pillars of passenger cars or in the upper corners of trucks and trailers (much like the retroreflective sheeting or presence lighting that are now required). Mortimer added that the additional pattern information increases driver sensitivity to changing separations between vehicles. Therefore, the additional pattern information will most likely lead to a reduction in the distance threshold for detecting the relative velocity compared with vehicles with closer mounted taillights. This means that drivers should be able to detect relative velocity from a further distance (sooner) if there is additional vehicle pattern information.

Hoffman & Mortimer (8) calculated the absolute threshold is as follows: dș/dt = WVr / D2

(1)

Therefore, D = (WVr / (Ĭ r/s)) 1/2

(2)

Where dș is the change of the subtended arc angle, dt is the change in time, W is the width of the vehicle, Vr is the relative velocity (closing speed), Ĭ is the subtended angular velocity threshold [SAVT] in radians per second and D is the distance from the observer to the rear of the lead vehicle at which the SAVT is met. The first derivative of the subtended arc angle with respect to time is the SAV in radians per second, r/s.

RESEARCH This research will attempt to identify the SAVT in a more real world analogous situation where the driver is required to scan his or her forward field and when the lead vehicle is just one of several potential hazards that he or she may encounter. The hypotheses are: driver response times will remain relatively high until the SAVT is met; and, that when responding to LVs, which are above the SAVT (comparatively close), driver response times should plateau at a relatively fast time. This means that until the SAVT is met, the driver is faced with a hazard that is not easily identified as an immediate hazard. Once the SAVT is met, the hazard should be easily identified as an immediate hazard and could be categorized as a “straightforward” situation – a term used by Olson (30) that is associated with a relatively quick response time. Parts I and II of this research will attempt to identify the SAVT. Part I of the study is a meta-analysis (an analysis of the raw data from previously published studies). The SAV at which the subjects were exposed to the hazard in each study was compared to the average response time. If a driver could easily detect the rate of closure on a lead vehicle, then his or her response time should be relatively quick and remain relatively fast. The goal was to sort the data in ascending order from lowest to highest SAV to determine if response times begin to decrease to a point and then remain constant (at and after the SAVT was met). The Part II of the study was to measure the response times of subjects at various closure rates using a laptop driving simulator. The hypothesis was that response times would plateau at the SAVT at which drivers are able to detect the relative velocity of a LV as an immediate hazard, separate from the basic threshold at which drivers are initially able to detect closure which will likely occur much earlier. Mark Dunn of the University of Nottingham developed a relatively simple yet flexible simulator, designed for use on a laptop computer. This simulator has been used in other published research (37, 38). PART I METHODOLOGY – The research involves two parts. The first is a meta-analysis of the data provided in

previous research (6 including the data from Whitty et al., 8, 18, 33, 34, 35, and 39). We compared the radians per second at which the hazard was displayed to each subject and the reported response times. Furthermore, to assure that we were making a direct comparison, the methodology of each study was examined and adjustments were made to the reported response times to assure that factors such as eccentricity, multiple stimuli, leg movement times, etc were not the cause of the reported response time differences (if any). This helps assure that the differences in response times were due to the change in the radians per second and not by a confounding influence. Adjustments were made in accordance with the procedures outlined in Muttart (14, 23) and these adjustments are listed in Appendix A. If the width of the LV was not given, it was assumed to be 1.8 m. Once adjusted, the numbers were entered into a spreadsheet and sorted by radians per second. If one study reported more than one instance at a single radian per second, those responses were averaged and entered into the spreadsheet. The resulting list can be seen in Appendix B. The radians per second were compared with the adjusted response times to determine the SAVT above which response times plateau and consistently remain relatively fast. There was also an attempt to determine if there was a predictable inverse relationship between SAV measured in radians per second and response times. PART II METHODOLOGY – The driver response time simulator [DRTS] test was carried out on a laptop computer in an area chosen to prevent unwanted reflections. In previous research, the luminance of the bright colored rectangular pedestrians and leading car was 4.8 cdm-2 or greater and these objects appeared in positive contrast against a black background (37, 38). The screen was also programmed to display movements at 4 Hz, which required subjects to use saccadic eye movements. Drivers were allowed to sit comfortably before the screen and nominally positioned 0.5 meters (20 inches) from the screen. At their distance from the computer screen, the height and width of the pedestrians and vehicles were portrayed at their natural subtended angles. The road width was displayed at a subtended angle that would be similar to a 7-meter-wide road that had a 400 m horizon. Pedestrians were displayed so that there were three pedestrians to the left and right for each row, and no more than four rows were displayed at any time. Only the row directly ahead would have a pedestrian move (pedestrians in the second through fourth rows did not move until they were approached and became the first row). Therefore, the driver had 6 pedestrians (3 on each side) that he or she would have to respond to, as well as the LV. The subject would have to respond to

one hazard at a time. The subjects were expected to respond to 21 objects in a 6 ½ minute test or about once every 18 seconds. The speed of the pedestrians was set so they would cross at a speed of 7.5 mph (3.35 m/s) (jogging speed). The lead vehicle would travel the same speed as the subject’s viewing speed until it stopped abruptly. Therefore, the closing speed would be equal to the speed of the observer’s vehicle, which was set at either 65 or 50 mph. The size of the lead vehicle and the SAV (in radians per second) were also randomly adjusted. The DRTS simulator includes an input for headway. For a given vehicle speed (Vr), width of the vehicle (W) and SAV (T), headway was calculated from equation (2) above by substituting V*T for D, where T is the headway, in seconds. Each of the three laptops used had a 15-inch screen.

The subjects were told that their response times and false responses were being recorded by the computer and they were required to respond, by touching the spacebar, to any “pedestrian” that moved toward the road and to the lead vehicle if they believed they were going to collide with it. Figures 1a & 1b. Screen shots of the laptop simulator. Screen 1a represents a ‘car’ at 0.002 radians per second, while 1b shows the following distance behind a 2 m by 2 m ‘box’ when set at 0.01 radians per second. All subjects were following the ‘LV’ at the distances shown or at some distance between the two shown below.

Participants – There were 72 participants comprised of males and females. There was no significant difference between the situations faced by males versus females (p = .294). There was no significant difference in the average age of the participants for each SAV (p = .302). Table 3 shows the average age for each group. Table 3. Average age for each radian/second group Rad/s .0090

16

44.6

12.8

Total

72

44.1

10.7

Procedure – A schedule was developed using a random number generator so that the order and scenario for each subject was random. The subject would get one of three vehicle sizes, and at either 65 or 50 mph closing speeds. Each subject would face one of eight radian/second scenarios (0.002, 0.003, 0.0045, 0.006, 0.0065, 0.007, 0.0075, 0.009), and one of three LVs (passenger car, truck or square box). (See Figures 1a and 1b). The size of the passenger car was 1.4 m tall and 1.7 m wide, the truck was 3.05 m tall and 2.45 m wide and the box was a 2 by 2 m square. The experimenter set up the computer before the next subject entered the testing area and the subject selected one of three laptops to sit at (or one of the remaining laptops). No adjustments were made for gender or age. Therefore, whoever showed up next was exposed to the next randomly assigned scenario for that laptop.

RESULTS PART I - When examining the previous research, we can see that when subjects were required to respond to a lead vehicle with a SAV of 0.0035 radians per second or less, the average adjusted response time was nearly 4 ¼ seconds, compared to 2 ½ seconds when the radians per second were between 0.0035 r/s and 0.007 r/s. The average adjusted reaction time in previous research was slightly more than 1 ¼ second when the radians per second change of the LV was greater than

0.007 r/s. Clearly, the previous research proves that the change in SAV of the LV are negatively related (F30 = 9.33, p = .005) to the response time of the following driver before an SAV of 0.006 r/s. Response times did not change significantly after the SAV of 0.006 r/s (F36 = 1.53, p = 0.224). The compiled list from the metaanalysis can be seen in Appendix B and the overall results can be seen in Table 4 and Figure 2.

Radians second

per

Reported BRT

Adjusted PRT

Percent < 2 s.

< 0.0035

3.52 s

4.28 s

0%

0.0035 to 0.007

2.14 s

2.47 s

46%

> 0.007

1.16 s

1.29 s

94%

Horizontal Subtended Angular Velocity Increases

2400.00

Mean Reaction Time (ms)

Table 4. Results of meta-analysis comparison of driver response times at various radians/second

Figure 3. Average Reaction Time as Relative

2200.00

2000.00

1800.00

1600.00

.0020

.0030

.0045

.0060

.0065

.0070

.0075

.0090

RSAV (r/s)

You may note from the results (in Appendix B) that the reported brake reaction times (BRT) were much higher than the adjusted response times in many instances. This was due to visual eccentricities (looking away from the “hazard”). Also note that brake reaction times do not account for vehicle latencies, or reduced or delayed brake pedal force by a driver. In Figure 2, you can see that response times do not plateau until a SAV of approximately 0.006 r/s. Response times remain relatively high up until that point is met. Figure 2. Adjusted Response Times as RSAV Increases

The SAV in Figure 3 was calculated based upon the width of the vehicle. We examined the influence if the angle was measured based upon the height of the vehicle as well. By varying both the width and height of the vehicles each subject faced, it provides some information regarding the method in which drivers may judge the angular expansion rate. Figure 4 shows how response times varied based upon vertical SAV. Note that the response time of drivers decreased as SAV increased, but it is apparent that SAV based upon height is not quite as predictable as when using width, which is consistent with previous research (40). Also note that response times appear to begin to level off at 0.006 to 0.0065 r/s. However, there was not a significant difference between the responses when faced with different width or height LVs.

6.00 2

5.00

Figure 4. Average Reaction Time as Relative

4.00

Vertical Subtended Angular Velocity Increases

3.00

2600.00

2.00

2400.00

1.00 0.00 0

0.002

0.004

0.006

0.008

0.01

RSAV (r/s)

PART II – The results of the simulator study can be seen in the Figure 3. When the LV was at 0.007 radians per second and above, response times remained relatively quick and remained somewhat constant. As the radians per second were increased, response time decreased significantly (F71 = 20.86) but began to level off as SAV increased (See Figure 3).

Mean Reaction Time (ms)

A d ju sted R e sp o n se T im e s (se co n d s)

3

y = -2E+06x + 88316x - 1199.1x + 6.1285 2 R = 0.9469

2200.00

2000.00

1800.00

1600.00

1400.00 .00200 .00250 .00300 .00400 .00450 .00500 .00600 .00650 .00700 .00750 .00900

RSAV (r/s)

Age (p = .363) and gender (p = .314) were not significant influences on driver response times based upon Analysis of Variance (ANOVA). Speed (p = .255) and vehicle size (p = .932) also failed to reach statistical significance. If speed was not influential, then time to contact, which changes based upon speed, was not a significant influence upon the response of drivers. However, the SAV is clearly a significant influence upon response time.

When the responses from this research were combined with the results from previous research, there was a statistically significant logarithmic relationship (r2 = .38, n = 250) between response times and SAV. This offers face validity for a SAVT in that response times should increase logarithmically as the driver is further away from that threshold and that is what this data suggests.

False responses were also examined. Those who had more false responses did not differ in response times from those who had fewer false responses (p = .519). A false response was a response when one was not necessary.

Part I of our study showed that based upon previous research, response times plateau and remain relatively quick when the SAV was greater than 0.006 r/s (When the methodology requires the subject to devote his or her attention to the lead vehicle). Part II of the study interestingly resulted in a very similar shape line graph and resulted in an average SAV of 0.0066 (SD = 0.0026). Therefore, the average SAVT is this research was approximately 0.006 r/s. This is consistent with the findings of Hoffman & Mortimer (8) who show that alerted observers could scale relative velocities with reasonable accuracy above 0.003 r/s and that one of their groups needed 0.0052 r/s. This is also far less then the SAVT proposed by Plotkin (20) of 0.0275 r/s. Sauer, Anderson and Saidpour (41) suggested that the relative velocity detection threshold model had a problem and that a time to contact based model better explains driver response. Sauer et al. cited an example of a vehicle changing lanes into the path of a following vehicle at the same speed as the following vehicle but at an uncomfortable headway. Previous research (10, 21, 23, and 24) has shown that speed, and therefore time to contact, does not significantly influence driver response time. A model that utilizes a relative velocity detection threshold to locate the start of a perception-response time would account for Sauer’s example because headway would be accounted for in the perception response time estimation (14, 23, and 24).

The primary issue that an investigator is concerned with is to make a comparison of where a driver began his response (skidding or steering) and where a normal driver would have begun their response. Distance to impact (DTI) may be calculated using the following formula. DTI (m) = - (Avg. Speed mph / 2.237) * (PRT ms/1000) + ((Width m * Closing speed mph / 2.237) / (r/s)) ½ (3) We performed a secondary analysis; this time assuming that each of these subjects perceived an immediate hazard when 0.007 r/s threshold was met. The average response time after the 0.007 r/s threshold was met was 1.29 second (SD = 0.46) for all subjects. Subjects were not required to turn away, as they would have to do when looking in the mirrors or if looking at another potential or immediate hazard and there were no other objects that the subject had to respond to at the time. Therefore, a driver’s actual response time could be longer. The ultimate goal was to compare distances from impact. Knowing the average response time (for a relatively easy task compared to driving in real traffic), we determined what the average and range of SAVs were if we assumed the average response time was 1.60 seconds and worked back to determine the SAV. We selected 1.60 seconds because that was the average response time of all subjects once responses began to level off. The 1.6-second number was for responses that involved limited eccentricities and response complexity; real life response times may be much greater (or less if there is greater context). Working back 1.6 seconds from the distance that the responses began, the average SAV of all subjects, regardless of scenario faced (within 0.002 and 0.009 r/s) was 0.0065 r/s and the median was 0.0063 r/s (SD = 0.0026 r/s). Therefore subjects who are approaching a slower moving vehicle from headway of greater than 3 seconds (which is generally the maximum normal following distance) began to respond nominally at a SAV of 0.0065 r/s.

CONCLUSION

The size of the LV and the speed of the closing vehicles did not reach statistical significance. Sullivan and others (42, 43, and 44) found that trucks were much more likely to be involved in a crash at night due to the longer stopping distance for a truck. This over-involvement at night may also be due (in part) to an inability to discriminate the entire size of the truck (only the width of the taillights may be discerned). Leibowitz (45) indicated that large vehicles are perceived to be closing at a slower rate and other research has shown that we perceive taller objects (objects higher in our visual field) as being further away (46). Vecellio (44) found that trucks were more likely to be rear ended on upgrades of high-speed roads. When traveling up a grade, the LV truck may be seen against the background of the sky, which offers very little information from which to judge closing speed. Therefore, predictions of driver response based upon LV width will likely be more accurate than those based upon height. This study involved a response to pedestrians and a single LV. The subjects knew they would have to respond to the LV. The purpose of the study was to

measure the behavior in response to visual angle expansion rate, not brake lights. The influence of brake lights in this single LV situation would change this to a “see the light hit the button” study rather than a measure of visual expansion rate response. There is no doubt that brake light use is better than no brake lights in most real life situations; however, brake lights on a single vehicle among several braking vehicles may not be an intense enough stimulus to alert a following driver that there is an immediate hazard that must be responded to. Furthermore, brake lights indicate that the LV is slowing; they do not offer information related to the speed of the LV. Fisher and Hall (47) found that presence lights result in an insignificant difference when detecting a change in headway. The results by Summala et al (18) showed that vehicles with brake lights illuminated were responded to an average of 0.3 second faster with only one LV in the driver’s forward field (when the results are adjusted to account for eccentricities). Schriener (39) showed that strobe lights had an insignificant effect in vehicle following situations and studies have shown that flashing lights could be more difficult to detect if among other flashing lights (like transient brake lights) (37, 48, 49, 50, 51). Crawford (48, 49) found that flashing lights increase the likelihood of detection if there were no other flashing lights. However, in a real traffic situation, flashing lights may be used to advise a following motorist that the vehicle is traveling slowly, which the following driver will already know based upon what they see. Therefore, additional context of some kind that tells the following driver how slow the LV is traveling will likely increase the effectiveness of flashing lights. For instance, reflective triangles placed in accordance with Federal Motor Carrier Safety Regulations (FMCSR 392.22) are usually conspicuous and have one simple meaning (that the truck ahead is stopped). Ayres et al (5) indicated that it is difficult to demonstrate that enhanced visibility alone is related to a substantial decrease in crash rates because the enhancements may not offer any additional useful information to the following driver. Solomon (51) pointed out that if the outboard lights of a vehicle are flashing on and off, then there is less time for an approaching driver to make depth and location judgments at night and may cause approaching drivers to become de-adapt to the darkness. Even if braking or flashing lights attract a following driver’s attention, and even if the following driver detects that he is closing on the lead vehicle, the following driver still may not perceive an immediate hazard. Once a following driver notices that he or she is closing on the LV, he or she will likely continue to close without concern unless he or she perceives an immediate hazard. In this scenario, a driver may look into their mirrors to check when it is safe to move into another lane to pass. It is unlikely that they will recognize the immediate hazard until the subtended arc angle of the LV increases at a rate of 0.006 r/s or more and, if they

are looking into the rear view mirror at the time they reach the threshold, detection of the immediate hazard could be further delayed. This research strongly supports the notion that drivers will not begin to respond until the lead vehicle is easily identified as an immediate hazard, and that will not occur until they can determine that they are closing on the LV at a dangerous rate while not necessarily looking directly at the lead vehicle. Hoffman and Mortimer (7) found that even when the SAVT is exceeded, drivers continue to underestimate their closing speed at a rate that can be estimated using Steven’s Power Law. Also, Janssen (40) found that a power function could be used to estimate the relationship between sensation of closing speed and actual closing speed in such a way that drivers will underestimate their closing speed to a greater extent as closing speed increased. Along with the dynamics of the visual process, like the rate of closure, the Gestalt (or the sum of what they see) may alert drivers. In head-on collisions, the rate of closure should be detected earlier simply because there is greater context. When following a vehicle, there is an assumption that the lead vehicle is traveling essentially at a speed that is somewhat similar to that of other traffic. The awareness of a grill and/or headlights in the lane ahead will likely be perceived as an immediate hazard earlier than in a vehicle following situation. When faced with a vehicle traveling toward the driver, the unexpectedly high rate of closure should be detected earlier, which would suggest that a SAVT for head on situations will likely be consistent with laboratory research results (6) of 0.003 r/s. The earlier detection is due to the greater context. However, the increased distance between the vehicles (still referred to as the headway term) in a head-on situation will cause the calculated response time to increase in such a way as to account for the increased complexity, difficulty, decision-making, and lack of expectation involved in a head-on collision. A factor that must be considered in a head-on case is that when faced with an on-coming vehicle in their own lane, the response choice is very complex, and when responding to a vehicle riding near the center line, the ability to detect the exact position of the tires is difficult until the resolution is great enough to determine the location of the wheels relative to the centerline. DISCUSSION - Muttart (21, 23, and 24) found that driver response times (in vehicle following situations) could be estimated using the following equation (which has been simplified): PRT = 393H + 509S + 26E – 703Tp + 1335 + Adjustments (+ 40%) (4) Where PRT is the perception response time (up to 1st vehicle response), H is headway in seconds, S is the number of stimuli the driver is mentally responding to (or expected to respond to), E is eccentricity from straight

ahead in degrees, and “Tp” is the topography (1 if on a straight roadway). Previous research that measured PRT usually started the response time when the LV first braked, regardless of its distance or closure rate. Some of the same studies used in Part I of this research was used in Muttart’s (2003) research. After reviewing the results, equation (4) overestimated a driver’s response time by an average of 0.71 seconds if used with an SAVT of 0.006 r/s. Since the ultimate goal is to estimate the distance to impact that a following driver will begin to respond, if equation (4) is used with an SAVT of 0.0045 r/s, it has offered an accurately determination of the initiation of response location. And Mortimer (8) has indicated that the SAV detection distance could be determined using equation (2). Therefore, to determine the point at which a vehicle maneuver would likely begin, the following equation could be used. Individual variance or 40% of the response time, shown in equation (4), should also be considered. Based upon prior research (14, 24), the range of response distances obtained should account for the middle 2/3rd of all drivers. To obtain a distance at which we expect a response to begin, we start from the distance to impact at which the SAVT occurs and subtract the product of the responding vehicle speed multiplied by the mean driver response for that type scenario. The result is the distance to impact that the average driver has started to steer or skid in response to a lead vehicle. DTI = V1 ((D/Vr) - (t – 351225(Ĭ - 0.0045))) (+ 40%) (5) Where DTI is distance to impact, D is the headway (distance) at the point the SAVT is met, V1 is the speed of the responding vehicle, Vr is the closing velocity, W is the discernible width of the LV, t is the PRT in seconds, and Ĭ is the SAVT (0.006 r/s). This model assumes a straight plane and would not apply if there were topography, landmarks or warnings that cued the following driver that the LV was traveling very slowly or was stopped (Please refer to other publications 14, 21, and 23 for methods for estimating response times in other situations). It also assumes a response time up the point the responding vehicle starts to respond (In contrast to when the driver first responds with hand of foot movement). However, in this research, once the 0.006 radians per second angular velocity was reached, it still took over a second for subjects to respond. Therefore, the actual threshold occurs sometime before this. When considering the methodology of this study and the methodologies cited in Part I, detection of SAV in real traffic would likely be more difficult. Therefore, it would not be unreasonable to expect a normal driver to detect the rate of closing of a lead vehicle in traffic when the SAV of the lead vehicle increases at a rate greater than 0.006 radians per second (0.35 degrees per second).

Investigators must understand that vehicle following responses should be ultimately compared using the distance to impact that the following driver’s vehicle maneuver began. The use of a SAVT and PRT that correspond should allow an investigator to determine a distance at which a maneuver is “normally” (mean plus or minus standard deviation) initiated. This research is consistent with the findings by Lee et al. (28) who found that drivers begin a maneuver in response to a slower moving LV when 124 feet behind and when the median distance is 96 feet. That distance choice did not vary significantly due to the relative velocity of the vehicles. Therefore, if closing at 16 km/h (10 mph), a 30 -meter (100 foot) headway is not a problem. However, if the closing speed is greater than 50 km/h (30 mph), the likelihood of a crash increases significantly. This research also corroborates the findings of Lamble, Laakso and Summala (9) who found that during a car following task involving alerted subjects who were told to look directly at a LV, the SAVTs were 0.00215 and 0.00377. They also had the subjects look at one of nine LEDs that were placed within the vehicle and noted that the SAV at which the subjects responded increased significantly as eccentricity increased. Their results showed that when the eccentricity was 17 degrees, the average SAVT was 0.006 r/s, but it resulted in a response delay of 1.2 seconds. Lamble et al examined the influence of visual eccentricities on the SAVT, while equation (5) accounts for eccentricity during the perception-response phases. Either method should produce a reasonable estimate as long as SAVT and PRT are considered in context with one another. When compared to the model proposed in this research, the results are similar. This research did not force the driver to gaze in any particular area; therefore, drivers most likely had a moderate eccentricity on average, which may explain minor differences in the results. On the face, these results seem to be contradicted by Plotkin (20, 52). However, when examining Plotkin’s methodology, we can see that the response distances found in this research and that by Lee et al. (28) are very similar to those reported by Plotkin. Plotkin reconstructed the closing speed of actual crashes and assumed that the response time started 0.75 seconds before the onset of skid marks. From this he concluded that the critical value SAV was 0.0275 r/s. Several studies have shown that response times for similar events are much greater than 0.75 seconds (18, 21, 23, 24, 33, 34, and 35). Therefore, if applying a corrected perception-response time, the start of response distance by Plotkin should be similar to the findings by Lee et al and the SAV should be more in line with the results of this research. The research by Mortimer (11, 12, and 13) showed that the rear presence (tail) lamps of motor vehicles should be placed as close as possible to the outboard edges of the vehicle and that there should be a second pair of presence lamps mounted as high and as far apart as possible. This research corroborates Mortimer’s findings

in that the larger the discernible size of the LV, the earlier the RSAVT will be met. The results from this study also strengthen the theory behind the National Highway Traffic Safety Administration Algorithm for Collision Avoidance Systems [CAS] (53). The NHTSA proposal suggests (p.3-2) that a warning should sound to the driver when the lead vehicle is 70 m ahead if closing on the lead at a rate of 45 mph (72 km/h). On the basis of these figures, if the lead vehicle has a discernible width of 6-feet- (1.89 m), then the closure rate would be 0.0075 r/s, which is similar to the result found in this research. On the basis of Figure 3-1 in their publication, the National Highway Traffic Safety Administration Algorithm calls for an alarm to be sounded at a distance that is based upon the closing speed. We calculated the approximate relationship to be as follows: S = 5.4V – 35.42

(7)

Where S is the distance in meters that the alarm sounds from the rear of the LV and V is the closing velocity in meters per second. Therefore, if the lead vehicle is traveling 11.2 m/s (25 mph) and the following driver is traveling 26.8 m/s (60 mph), the 0.006 r/s threshold will be met when the following driver closes to within 61 metres (202 ft) of the rear of the lead vehicle. An alarm will sound when the following driver closes to within 49 m (161 ft.) of the LV and to within 105 m (346 ft) of impact. If the average driver responds to the audible signal within 1 second and can decelerate at 0.47 gs or better, then a collision can be avoided in this instance by stopping. Despite being only slightly later than the 0.006 r/s threshold found in this study, if drivers are responding to a known audible warning rather than a LV that is more difficult to discriminate as an immediate hazard, their response times should be cut by more than half. Drivers typically respond faster than 1 s. when responding to a known audible stimulus (54, 55). Further, an audible alarm will mitigate the delay in response associated with visual eccentricities that are common when a driver prepares to pass a slower moving vehicle. However, we must learn from history. In the study by Johansson and Rumar (54), a buzzer was placed in the subject’s vehicle. The subject’s first three responses to the buzzer were delayed due to confusion despite their being told earlier to brake when they heard the buzzer. If the warning is audible and can be clearly tied to moderately sharp braking (0.38 gs or more), then the resulting responses (of 1 s. or faster) would allow such a warning device to be a very effective safety tool for drivers closing at speeds less than 30 mph. However, an earlier warning threshold (near 0.0065 r/s) will account for a greater percent of responders, less efficient decelerators and/or higher closing speeds. According to Gray and Regan (56), mitigating adaptation to straight roads with no traffic and varying of visual textures visible

to highway (motorway) drivers may also lead to a decrease in front to rear crashes. Much the same was done to correct a problem faced by pilots at some airports. Kraft (57) found that there were several instances of planes landing short of the runway at night after crossing a dark area (water or nonilluminated ground). In an attempt to replicate the crashes in a flight simulator, Kraft found that Pilots perceived that they had a greater altitude than was true. Without adequate context, pilots had to judge distance based upon linear perspective (the SAV) of the runway lights, which would not expand significantly until the altitude was relatively low. As a correction, airlines had their co-pilots announce the altimeter readings to the pilot during the decent, which resulted in diminished crashes. A similar type verbal notification for drivers may be equally effective (57). Assuming that radar systems offer a warning at the appropriate time and that SAVT, eccentricities and PRT are accounted for, this research offers information regarding how drivers have performed in research in response to slow moving or stopped vehicles. This information may be helpful to understand how drivers will respond to collision avoidance systems. This research may also be helpful to those in working in a forensic setting. The results of this research explain how to mathematically estimate the average distance to impact and range of responses of drivers who responded to slow moving or stopped LVs in research. The distance to impact estimate and range can then be compared to the response of a driver in a collision with a slow moving or stopped LV.

ACKNOWLEDGMENTS We would like to thank the South Carolina Accident Reconstruction Society [SCARS], the Southeast Accident Reconstruction Society [SeARS], the International Association of Accident Reconstruction Specialists [IAARS], the Traffic Response & Safety Research Group and Dominique A. Duvalier for her participant recruitment efforts. We must also thank Heikki Summala of the University of Helsinki for supplying us with his raw data and Nicola Phelps and Mark Dunn for the use of their simulator software. Lastly I would like to thank REC-TEC, LLC for developing a computer program based upon this research.

REFERENCES 1. McGehee, D.V., T. Brown, and T. Wilson (1997). Examination of drivers' collision avoidance behavior in a stationary lead vehicle situation using a front-to-rear-end collision warning system. USDOT/NHTSA Office of Crash

Avoidance Research Technical Report. Contract DTNH22-93-C-07326. 2. Knipling, R., Mironer, M., Hendricks, D., Allen, J., Tijerina, L., Everson, J., & Wilson, C. (1993, May) Assessment of IVHS countermeasures for collision avoidance: Rear-end crashes. Final Report (Report No. DOT HS 807 995). Washington, DC: National Highway Traffic Safety Administration.

13. Mortimer, R., G. (1990). Perceptual factors in rear end crashes, Human Factors Society 34th Annual Meeting, (pp.591-594). Santa Monica, CA: Human Factors & Ergonomics Society. 14. Muttart, J. W. (2004). Estimating driver response times (Ch.14), Handbook for Forensic Human Factors in Litigation, Boca Raton, FL: Taylor & Francis. 15. Meyers, D. G. Psychology (6th Ed). Holland, MI: Worth Publishing.

3. Young, S. K., Eberhard, C. A., & Moffa, P. J. (1995). Development of performance specifications for collision avoidance systems for lane change merging and backing. Task 2: Functional goals establishment. TRW Space and Electronics Group Washington, DC. U.S. Department of Transportation, National Highway Traffic Safety Administration.

17. Sanders, M. S., & McCormick, E. J. (1993). Human Factors in Engineering Design (7th Ed.). New York: McGraw Hill.

4. Allen, M. J., Abrams, B. S., Ginsburg, A. P. & Weintraub, L. (1996). Forensic Aspects of Vision and Highway Safety. Tucson, AZ: Lawyers & Judges Publishing Co

18. Summala, H., Lamble, D., & Laakso, M. (1998). Driving experience and perception of the lead car's braking when looking at in-car targets, Accident Analysis & Prevention, 30, 401-407.

5. Ayres, T. J, Schmidt, R. A.., Steele, B. D., & Bayan, F. P. (1995). Visibility and judgment in car-truck night accidents, Safety Engineering and Risk Analysis, 4, 43-50.

19. Todosiev, E. P. 1965. Velocity thresholds in carfollowing. 23 p. Studies of Driver-Automobiles Interfaces, Appendix III to Final Report on Project EES 202. C.F.S.T.I., Sept 1965, p. 213235. Sponsor: Ohio Department of Highways, Columbus; Bureau of Public Roads, Washington, D.C.

6. Duckstein, L., Unwin, E. A., & Boyd, E. T. (1969). Variable perception time in car following and its effect on model stability, 32nd ORSA National Meeting. Highway Safety Research Institute paper number 15245. University of Michigan 7. Hoffman, E. R., & Mortimer, R. G. (1994). Scaling of relative velocity between vehicles, Proceedings of the Human Factors and Ergonomics Society 38th Annual Meeting, 2, 1-5. 8. Hoffmann, E. R. & Mortimer, R. G. 1996. Scaling of relative velocity between vehicles. Melbourne University, Victoria, Australia/ Illinois University, Champaign. 7 p. Accident Analysis and Prevention, 28, 415-421. 9. Lamble, D., Laasko, M., & Summala, H. (1999). Detection thresholds in car following situations and peripheral vision: implications for positioning of visual demanding in-car displays, Ergonomics, 42, 807-815. 10. Lamble, D., Kauranen, T., Laasko, M., & Summala, H. (1999). Cognitive load and detection thresholds in car following situations: safety implications for using mobile (cellular) telephones while driving. Accident Analysis and Prevention, 31, 617-623. 11. Mortimer, R. G. (1971). The value of an accelerator release signal, Human Factors, 13, 837-841. 12. Mortimer, R. G. (1972). Weber’s Law and Rear End Collisions, Michigan Academian, 4, 99-105.

16. Olson, P. L., Washsler, R. A., Bauer, H. J. (1961). Driver judgments of relative car velocity, Journal of Applied Psychology, 45, 161-164.

20. Plotkin, S. (1976). Accident and Product Failure Analysis; A systems engineering approach, Oakland, CA: California Syllabus. 21. Muttart, J., W. (2003). Development and Evaluation of Driver Response Time Predictors Based upon Meta Analysis. Report #2003-010885, pp 1-21, Warrendale, PA: Society of Automotive Engineers. 22. Reilly, W.R., Pfefer, R.C., Michaels, R.M., Polus, A., & Schoen, J.M. (1989, December). Speed change lanes - Final report (NCHRP Report 335). Washington, DC. 23. Muttart, J., W. (2003). Evaluation of Methods for Estimating Driver Response Times. ITAI / AIRIL 2003 Conference Proceedings, Stratford-uponAvon, England. 24. Muttart, J., W. (2005). Driver Response in various Environments Estimated Empirically: DRIVE3. (In press). 25. Evans, L., (1991). Traffic Safety and the Driver. New York: Von Nostrand Reinhold. 26. Martin, P. G., & Burgett, A. L. (2001). Rear-end collision events: Characterization of impending crashes, Proceedings of the 1st HumanCentered Transportation Simulation Conference. Iowa City, IA: University of Iowa. 27. Mourant, R. R., & Rockwell, T. H. (1972). Strategies of Visual Search by Novice and

Experienced Drivers. Human Factors, 14, 325335.

Systems and Engineering, Blacksburg, VA: Virginia Polytechnic Institute.

28. Lee, S. E., Olsen, E. C. B., Wierwille, W. W. (2003). A comprehensive examination of naturalistic lane-changes. (Technical paper DOT HS 809 702). Washington, DC: National Highway Traffic Safety Administration.

40. Janssen, W. H. (1977). Driver’s inability to judge important parameters of leading vehicle movement at night. (Technical paper # 770129). Warrendale, PA: Society of Automotive Engineers.

29. Tijerina, L., & Hetrick, S. (1997). Analytical evaluation of warning onset rules for lane change crash avoidance systems. Proceedings of the Human Factors and Ergonomics Society 40th Annual Meeting, 949-953.

41. Sauer, C. W., Andersen, G. J., & Saidpour, A. (2003). Linearly changing bearing and collision detection of objects traveling on curved 3D trajectories [Abstract]. Journal of Vision, 3, 793.

30. Dewar, R. R., & Olson, P. L. (2002). Human Factors in Traffic Safety. (Chapter 4. Green. P.) Tucson, AZ: Lawyers & Judges Publishing, Inc. p.101.

42. Sullivan, J., Flannagan, M. J., (2003). Risk of fatal rear end collisions: Is there more to it than attention? Second Driving Assessment Conference Proceedings. Park City, Utah.

31. Farber, E., & Olson, P. L. (2002). Forensic Aspects of Driver Perception and Response 2nd Ed. Tucson, AZ: Lawyers & Judges Publishing, Inc. p.303.

43. Green, P., Kubaki, M., Olson, P. L.., & Sivak, M. (1979). Accident and nighttime conspicuity of trucks. (Technical Report UM-HSRI-79-92), Ann Arbor, MI: University of Michigan Highway Safety Research Institute.

32. Roper, V., J., & Howard, E., A. (1938). Seeing with motor car headlamps. Illuminating Engineering Society, 33, 417-438.

44. Vecellio, R. L. (1967). Ohio Turnpike Accident Analysis, 1960-1965. M.S. thesis, Ohio State University.

33. Kane, M. J., Pearce, K. D., Hancock, P. A., Scallen, S. F., & Heniff, C. B. (1999). Investigating differences in driver accident involvement: the influence of perceptual motor competence, competitive athletics, and gender, University of Minnesota, Human Factors Research Laboratory

45. Leibowitz, H. W. (1985). Grade crossing accidents and human factors engineering, American Scientist, 73, 558-562.

34. McGehee, D. V., & Brown, T. L. (1998). Examination of drivers’ collision avoidance behavior in a lead vehicle stopped scenario using a front-to-rear-end collision warning system. (DTNH22-93-C- 07326). Washington, D.C: Department of Transportation. 35. Van Winsum, W. (1998). Preferred time headway in car-following and individual differences in perceptual motor skills. Perceptual and Motor Skills, 87, 863-873. 36. Alexander, G.J. & Lunenfeld, H. (1986). Driver Expectancy in Highway Design and Traffic Operations. Publication No. FHWA-TO-86-1. Federal Highway Administration, Washington, D.C. 37. Phelps, N. R. & Dunne, M. C. M. (2001). Factors that Influence Driver Reaction Times on a PC-based Test. ITAI 2001 Conference Proceeding, York, England. 38. Phelps N.R. and Dunne M.C.M. (2000) Static or kinetic tests, which are influenced most by age? Investigative Ophthalmology and Visual Science; 41 (4), S433. 39. Schreiner, L. M. (2000). An investigation of the effectiveness of a strobe light as an imminent rear warning signal, Master’s Thesis in Industrial

46. Myers, D. G. (2004). Psychology (6th Ed.). New York: Worth Publishers. 47. Fisher, A. J., & Hall, R. R., (1978). The effect of presence lights on the detection of change of headway, Australian Road Research, 8, 13-16. 48. Crawford, A. (1962). The perception of light signals: The effect of the number of irrelevant lights, Ergonomics, 417-428. 49. Crawford, A. (1963). The perception of light signals: The effect of mixing flashing and steady irrelevant lights, Ergonomics, 287-294. 50. Boff, K. R., & Lincoln, J. E. (1988). Visual warning signals: Effects of flashing, Engineering data compendium: Human perception and performance, Wright-Patterson AFB, 2408. 51. Solomon, S. S. & Hill, P. F. (2002). Emergency Vehicle Accidents: Prevention, Reconstruction and Survey of State Law (2nd Ed) Tucson, AZ: Lawyers & Judges Publishing. 52. Plotkin, S. C. (1991). Multiple causation & human perception limits, Trial Attorney’s Conference Proceedings, 1-5. 53. Brunson, S. J., Kyle, E., M., Phamdo, N., C., & Preziotti, G., R. (2002). Alert algorithm development program NHTSA rear-end collision alert algorithm (DOT HS 809 526). Washington, D.C.: NHTSA

54. Johansson, G., & Rumar, K. (1971). Driver' brake reaction times, Human Factors, 13, 23-27. 55. Lerner, N. D., Harpster, J. L., Huey, R. W., & Steinberg, G. V. (1997). Driver backing-behavior research implications for backup warning devices, In J. Overton (Ed.), Human Performance in Intelligent Transportation Systems, Information Systems, and Highway Design and Older Drivers. (Transportation Research Record No. 1573, pp. 23-29), Washington, D. C.: National Academy Press. 56. Gray, R., & Regan, D. (2000). Risky driving behavior: A consequence of motion adaptation for visually guided motor action, Journal of Experimental Psychology: Human Perception and Performance, 26, 1721 – 1732. 57. Kraft, C. (1978). A psychological approach to air safety: Simulator studies of visual illusions in night approaches, In H. L. Pick, H. W. Leibowitz, J. E. Singer, A. Steinschneider, & H. W. Stevenson (Eds.), Psychology: From Research to Practice, New York: Plenum Press. CONTACT Jeffrey Muttart can be reached at [email protected] or at http://www.accidentdynamics.com, William Messerschmidt can be reached at [email protected] and Larry Gillen can be reached at [email protected].

APPENDIX A Vehicle Following Adjustments (5) Natural Lighting 97.5 ms Day versus Night Brake Lights 583 ms if off Driving -740 ms. (add 740 ms if subject was not driving if comparing with real life) Eccentricity 26 ms. / degree Experiment Location 56.5 ms. / unit Headway 279 ms/second Number of Stimuli 509 ms/stimuli (up to two) Response Complexity -210 ms Topography -703 / unit Transition 375 ms. /unit

APPENDIX B: Driver response times at various radians per second scenarios (6 including the data from Whitty et al., 9, 17, 31, 32, 33, 34, 35)

Ref.

Vc

Meters

On/ off

Trans

Deg.

BRT

R/s

Adj PRT

6

5.4

27.4

1

1

0.0

0.24

0.0128

1.16

35

11.2

31.1

1

3

0.0

0.90

0.0132

0.90

35

12.1

32.1

1

3

0.0

0.90

0.0134

0.90

35

11.2

30.4

1

3

0.0

2.00

0.0139

2.00

6

1.8

15.2

1

1

0.0

0.63

0.0139

1.55

35

12.5

32.1

1

3

0.0

1.00

0.0139

1.00

35

12.3

30.9

1

3

0.0

1.40

0.0147

1.40

16.9

43.9

1

2

27.0

2.53

0.0158

2.32

9

0.5

50.0

1

2

0.0

3.60

0.0003

4.09

33

6

0.4

35.1

1

1

0.0

10.60

0.0007

11.52

17

2.1

15.0

0

2

23.3

1.92

0.0168

1.22

6

0.7

35.1

1

1

0.0

6.98

0.0010

7.90

17

2.1

15.0

1

2

23.3

1.10

0.0168

0.98

17

2.1

60.0

0

2

23.3

4.75

0.0011

4.05

32

3.0

17.9

1

2

0.0

1.20

0.0169

1.69

17

2.1

60.0

1

2

23.3

3.32

0.0011

3.21

35

12.5

28.0

1

3

0.0

1.20

0.0182

1.20

6

0.4

27.4

1

1

0.0

7.12

0.0011

8.04

19.3

1

1

0.0

2.20

0.0013

3.12

3.6

15.2

1

1

0.0

0.22

0.0276

1.14

W(6)

0.3

6 6

5.4

15.2

1

1

0.0

0.16

0.0416

1.07

34 34

3.0 6.0

5.7 5.7

1 1

2 2

0.0 0.0

1.38 1.13

0.1662 0.3324

1.87 1.61

6

0.9

35.1

1

1

0.0

2.61

0.0013

3.53

W(6)

0.3

18.5

1

1

0.0

1.90

0.0014

2.82

W(6)

0.3

18.1

1

1

0.0

1.60

0.0015

2.52

6

0.7

27.4

1

1

0.0

5.33

0.0016

6.25

W(6)

0.3

17.1

1

1

0.0

4.70

0.0016

5.62

W(6)

0.3

16.6

1

1

0.0

2.70

0.0018

3.62

6

1.3

35.1

1

1

0.0

1.77

0.0020

2.69

W(6)

0.3

15.5

1

1

0.0

1.83

0.0020

2.75

6

0.9

27.4

1

1

0.0

1.72

0.0022

2.64

W(6)

0.3

16.3

1

1

0.0

2.80

0.0022

3.72

W(6)

0.3

16.0

1

0.0

1.90

0.0023

2.24

6

1.8

35.1

1

1

0.0

1.27

0.0026

2.19

W(6)

0.3

13.8

1

1

0.0

3.30

0.0030

4.22

W(6)

0.6

18.5

1

1

0.0

4.70

0.0031

5.62

6

1.3

27.4

1

1

0.0

1.35

0.0032

2.27

6

0.4

15.2

1

1

0.0

5.51

0.0035

6.43

6

2.7

35.1

1

1

0.0

0.88

0.0039

1.79

W(6)

0.7

17.9

1

1

0.0

2.50

0.0041

3.42

17

2.1

30.0

0

2

23.3

3.03

0.0042

2.33

17

2.1

30.0

1

2

23.3

1.87

0.0042

1.75

17

2.1

30.0

0

2

23.3

3.02

0.0042

2.32

17

2.1

30.0

1

2

23.3

2.17

0.0042

2.05

6

1.8

27.4

1

1

0.0

0.96

0.0043

1.88

W(6)

0.6

15.5

1

1

0.0

2.80

0.0044

3.72

W(6)

0.3

10.7

1

0.0

1.80

0.0050

2.14

35

10.7

43.8

1

3

0.0

0.90

0.0064

0.90

6

2.7

27.4

1

1

0.0

0.69

0.0064

1.61

35

12.5

45.5

1

3

0.0

1.70

0.0069

1.70

6 ECMWI.00 1

0.9

15.2

1

1

0.0

1.20

0.0071

2.12

25.5

76.3

1

3

0.0

1.20

0.0079

1.20

35

11.2

37.8

1

3

0.0

1.10

0.0089

1.10

35

12.1

39.1

1

3

0.0

1.10

0.0090

1.10

35

11.6

38.0

1

3

0.0

1.55

0.0092

1.55

35

11.6

37.5

1

3

0.0

1.30

0.0094

1.30

35

11.2

36.6

1

3

0.0

1.40

0.0095

1.40

35

12.1

37.8

1

3

0.0

1.50

0.0096

1.50

35

12.5

37.6

1

3

0.0

1.75

0.0101

1.75

35

11.2

35.2

1

3

0.0

1.00

0.0103

1.00

35

10.7

34.1

1

3

0.0

1.10

0.0105

1.10

35

11.6

35.2

1

3

0.0

0.90

0.0108

0.90

32

3.0

22.4

1

2

0.0

1.24

0.0108

1.72

35

11.2

33.4

1

3

0.0

1.00

0.0114

1.00

35

12.5

35.3

1

3

0.0

0.90

0.0115

0.90

35

12.2

33.9

1

3

0.0

0.95

0.0110

0.95

35

12.1

33.4

1

3

0.0

1.05

0.0124

1.05

35

11.2

31.8

1

3

0.0

1.60

0.0126

1.60

35

12.5

33.6

1

3

0.0

0.80

0.0127

0.80