Paper prepared for the First Japan-Finland Joint Meeting on Traffic Safety.
August 27-29, 1996, Finnish Psychological Association, Turku, Finland.
Insufficient headway and unforeseen greater
stopping distance as combined factors in traffic
accidents
Katsuya Matsunaga, Ph.D.
Professor
Department of Intelligent Informatics
Faculty of Information Science
Kyushu Sangyo University
2-3-1 Matsukadai, Higashi-ku,
Fukuoka 813-8503, Japan
E-mail: matsnaga@is.kyusan-u.ac.jp
Abstract
Most traffic accidents come of collisions between two objects in the road transport system.
It was assumed that the driver's failure to stop before a collision is caused by a combination
of insufficient headway and unforeseen greater stopping distance, and that the human
factors which lead to accidents comprise both the driver's tendency to exhibit an unusual
delayed reaction or cognition, and a tendency to maintain an insufficient headway. On the
basis of this hypothesis, the driver's choice reaction times and the tendency to hasten were
measured. Accident-prone drivers showed higher scores on the hastening test than
non-accident-prone drivers, and/or accident-prone drivers showed more irregular reaction
times than non-accident-prone drivers. It can be concluded that the human factors leading to
collisions while driving are the driver's irregularity in reaction times, which can result in a
sudden delay in reaction and a stopping distance than usual, and the driver's tendency to
hasten, which can result in a shorter headway being maintained.
1 Mechanism Involved in the Occurrence of Traffic Accidents
or Collisions
Most traffic accidents come of collisions between two objects in the road transport system.
The collisions occur when the stopping distance is greater than the headway (Fig. 1). This
condition is a result of an unexpected lengthening of the stopping distance or a sudden
shortening of the headway. If drivers frequently experience an increase in their stopping
distances, they will maintain sufficient headway to avoid collisions. If drivers often do not
maintain sufficient headway, they will cause frequent collisions and will lose their driving
licenses. Therefore, it can be surmised that collisions are
ACCIDENT (COLLISION)
↑
STOPPING DISTANCE > HEADWAY DISTANCE
↑
↑
-SUDDEN GREATER STOPPING
-SUDDEN INSUFFICIENT HEADWAY
DISTANCE
IN RELATION TO SUDDEN
↑-SUDDEN GREATER
GREATER STOPPING DISTANCE
｜ BRAKING DISTANCE
↑-IMPULSE TO BE AHEAD
｜ ↑-SUDDEN DROP OF
OF OTHER CAR
｜ ｜ FRICTION BETWEEN
↑-PSYCHOLOGICAL FACTORS
｜ ｜ THE TIRES AND THE ROAD
｜ ↑-HASTY PERSONALITY
｜ ↑-SUDDEN DROP OF
｜ ↑-INSUFFICIENT
｜ ｜ BRAKE POWER
｜ ｜ INTELLIGENCE
｜ ↑-SUDDEN HIGHER SPEED
｜ ｜ (INSUFFICIENT MEMORY
↑-SUDDEN GREATER
｜ ｜ OF EXPERIENCES)
THINKING DISTANCE
｜-ENVIRONMENTAL FACTORS
↑-DRIVER’S SUDDEN GREATER
｜ ↑-DELAY FROM EXPECTED
DELAY OF COGNITION OR
｜ ｜ TIME OF ARRIVAL
REACTION
｜ ↑-TRAFFIC JAMS
↑-PHYSIOLOGICAL FACTORS
↑-KNOWLEDGE FACTORS
｜ ↑-FLUCTUATION OF
↑-INSUFFICIENT
｜ ｜ AWARENESS
｜ KNOWLEDGE IN
｜ ｜ ↑-BIOLOGICAL
｜ RELATION TO
｜ ｜ ｜ RHYTHM
｜ EFFICIENT DRIVING
｜ ｜ ↑-FATIGUE
↑-INSUFFICIENT KNOWLEDGE
｜ ｜ ↑-DISEASE
OF DEFENSIVE DRIVING
｜ ｜ ↑-DRINKING
｜ ↑-MALFUNCTION
｜ OF THE EYES
↑-ENVIRONMENTAL FACTORS
｜ ↑-LOW VISIBILITY OF OBJECTS
↑-PSYCHOLOGICAL FACTORS
↑-MENTAL DISPERSION
｜ ↑-MULTIPLE TASKS
｜ ↑-DIVORCE
｜ ↑-FAMILY TROUBLE
｜ ↑-FRICTION WITH
｜ OTHER PEOPLE
↑-LOW MOTIVATION
Fig. 1. Factors in relation to accidents or collisions which occur while driving.
The stopping distance comprises the latency distance (the distance
covered by a vehicle from the time of the first appearance of an obstacle or
a sudden change in the surroundings to the time when the driver hits the
brakes), and the braking distance (from the initial braking action to the
actual stopping of the vehicle).
caused by the combination of a sporadically greater stopping distance, and the driver's
failure to maintain sufficient headway.
2 The Stopping Distance, the Latency Distance, and the
Braking Distance
The stopping distance comprises the latency distance and the braking distance. The latency
distance is the distance covered by a vehicle from the time of the first appearance of an
obstacle or a sudden change in the surroundings and the time when the driver initiates the
braking action. The braking distance is the distance covered by a vehicle from the time of
the initial braking action to the time when the vehicle actually stops. An unexpected greater
stopping distance is caused by a sudden lengthening of the reaction distance and/or a sudden
lengthening of the braking distance.
3 Factors Leading to a Sudden Greater Braking Distance
Sudden lengthening of the braking distance is caused by a sudden drop in friction between
the tires and the road or a sudden drop in the braking power. It is reported by the Police
Bureau of Japan that more collisions occur at the beginning of the rainy season and the
snowy season.
4 Factors Leading to a Sudden Greater Latency Distance
A sudden greater latency distance is caused by an unusually greater delay in reaction to the
obstacles or changes in the surroundings. The cognition and/or reaction time is affected by an
individual driver’s physiological characteristics, psychological characteristics, and low
visibility within the environment (Matsunaga, 1985).
Matsunaga (1988) reported that a group of accident-prone drivers showed a greater
variation (standard deviation) in choice reaction times than non-accident-prone drivers
(Fig.2), although the two groups did not have significantly different mean reaction times
(Fig.3). Accident-prone drivers therefore will encounter situations in which their normal
awareness of changes in their surroundings is suddenly delayed (Fig.4).
Using the values of the standard deviation of the reaction time test and the scores of the
hastening tendency test, eighty-four percent of accident-prone drivers and eighty-one percent
of non-accident-prone drivers were identified by the discrimination analysis (Matsunaga,
1988).
Fig. 2. Individual subjects’ standard deviations of reaction times (left bars)
against the number of accidents (right bars) which they experienced
during a 2-year period (Matsunaga, et al., 1985).
Fig. 3. Individual subjects’ mean reaction times (left bars)against the number of
accidents (right bars) which they experienced during a 2-year period
(Matsunaga, et al., 1985).
Fig. 4. Examples of measurements of reaction time for an accident-prone driver
(left) and for a non-accident-prone driver (right). The reaction times from
the time of the appearance of the red disc or the yellow disc to the time
the foot was removed from the accelerator pedal (the left side bars in both
figures), and the time the foot was transferred from the accelerator pedal
to the brake pedal (the right side bars in both figures) are shown. The
stimulus presentation and the choice reaction time measurements were
both under the control of a personal computer (NEC: PC-9801EX) using
the KM choice reaction time measuring software (the KM system;
Matsunaga, 1989). The red disc, the yellow disc, and the green disc were
displayed on the CRT screen for 3 seconds under the control of a personal
computer, in random order, and at random intervals. The red disc and the
yellow disk appeared 20 times, while the green disc appeared 11 times
during each session. Two foot switches which were similar to the
accelerator pedal and the brake pedal of a traditional car, served as the
response keys of the computer. The accelerator pedal was held in a
depressed position by the subject’s right foot prior to the initiation of each
trial. When a red disc appeared, the subject was required to remove his/her foot from
the accelerator pedal and to press down the brake pedal with the same foot. When a
yellow disc appeared, the subject was required only to remove his/her foot from the
accelerator pedal. The subject was instructed to do this as quickly as possible. When
the green disc appeared, the subject was required to continue pressing the accelerator
pedal down (Matsunaga, 1988).
Effect of an Individual’s Physiological Characteristics: Cognition and reaction time are
affected by a fluctuating awareness level. It is supposed that this fluctuation of awareness in
humans is an evolutionary survival trait to save energy, that is suitable to the pedestrian
world, but in the world of automobiles this fluctuation of awareness level is now one of the
causes of loss of human life.
When drivers drink alcohol, their reaction time fluctuates, especially 30 minutes after
drinking (Fig. 5; Matsunaga, 1988).
Fig. 5. The fluctuation (SD) in reaction times became greater, especially 30
minutes after drinking 60 cc of whisky. In this figure A-1,A0,A30, and A60
refer to the results measured just before drinking, just after drinking, 30
minutes after drinking, and 60 minutes after drinking, respectively.
Effect of Individual’s Psychological Characteristics: Delays in cognition and reaction occur
when drivers do not concentrate on their driving. It can be assumed that drivers who have an
unstable personality, in addition to those drivers who are experiencing difficulty in human
relations (e.g. divorce, problems at work etc. ) are not able to concentrate on their driving.
The drivers who have unstable personalities will share their capacity of information
processing (a dual task) with something not related with the driving. Therefore, their
cognition and reaction times will fluctuate more than those of drivers with stable
personalities, who can concentrate on their driving.
Effect of Low Visibility of Objects (Environmental factors): When illumination is
insufficient, the cognition and reaction times fluctuate (Fig. 6). Similarly, when the contrast
between the objects and background is small, cognition and reaction times also fluctuate.
Therefore, a low contrast environment is conducive to sudden greater reaction times.
Fig. 6. When illumination is insufficient, the reaction time of objects fluctuates.
The fluctuation in reaction times became large when a stimulus was
displayed in the peripheral area of the retina (Matsunaga, 1985 ).
5 Factors Leading to a Shortened Headway (Hastening)
Factors such as those described above, or the driving environment cannot be easily controlled
or modified by an individual driver. However, in cases where there are problems involving a
delay in reaction time, drivers can avoid collisions simply by maintaining sufficient headway.
In Japan, around 44% of collisions happen at intersections or near intersections, 34% on
straight roads, and 19% on the curves of roads (Facts of Traffic Accidents of Japan in 1995).
Collisions at intersections could be avoided if the drivers would stop their cars and wait
yielding right of way to oncoming vehicles in the opposite lane, allowing them to turn or to
go through the intersection. If, on straight roads, they would keep sufficient headway to
allow for a sudden greater stopping distance, they could stop without collision.
It has been reported that the modal length of headway time is around 1 second
(Wasielewski,1979; Nakajima et al., 1983: Fig. 7), while the modal headway distance is
around 20 meters (Nakajima et al, 1981: Fig. 8). These headways are too short to avoid a
collision if the car ahead were to suddenly stop. Why do so many drivers fail to maintain
sufficient headway?
Fig. 7. Distribution of time headways measured at the Tomei motorway. Mode of
the time headway is 1 second (Nakajima et al., 1983).
Fig. 8. Distribution of distance headway of passenger cars measured at the
Tomei Motorway (Nakajima et al, 1981).
It has been reported that almost half the drivers who have had accidents were hastening
(i.e., decreasing headway distance) at that moment (Maruyama, 1982; Fig.9). The idea that a
drivers' headway should tend to be shorter when driving in rushing situations, which force
drivers to hasten, may be modified by some of the factors mentioned below.
54.2
23.1
18.9
17
16
15.6
12.7
1.9
1.4
0.9
0.5
0
10
20
30
40
50
60
IN HASTE
ABSORBED
ABSENT MINDED
LOOK ASIDE
%
ig. 9. Drivers’ mental state just before accidents (Maruyama, 1989).
Delay in Travelling: The tendency of drivers to hasten could be intensified if they found
that their journey was taking longer than they had expected, or if they predicted that their
journey would be delayed by traffic jams, etc.
Psychological Factors: It is assumed that humans have the impulse to be ahead of other
people. People have to have food to survive. When provisions are short, people want to be
ahead of others to get food first. Humans have repeated the struggle for existence for many
generations. Now we continue to try to be ahead of other people every time without
consciously being aware of it.
Nevertheless, a driver's propensity to drive hastily varies from individual to individual. It
is known that those drivers who maintain a shorter headway display a more active
personality than those who maintain a longer headway (Matsunaga,1986). Drivers who have
insufficient intelligence and drivers with insufficient knowledge of efficient driving may also
drive more hastily.
6 Relationship between Subjects' Ages and the Rate of
Subjects Exceeding the Discriminant Levels of the Reaction
Time Test and the Hastening Tendency Test
Figure 10 and Figure 11 show the relationship between subjects' ages and the percentage of
subjects exceeding the discriminant levels of the reaction time test and the hastening
tendency test. A large number of younger subjects showed greater fluctuations in reaction
time and also an increased tendency to hasten than those of other ages. These tendencies
may resemble the accident-rate tendency in relation to the subjects' ages.
Fig. 10. Relationship between subjects’ ages and the rate of subjects whose
standard deviations are over the discrimination level of the standard
deviation of the reaction time test (Matsunaga, 1994).
Fig. 11. Relationship between subjects’ ages and the rate of subjects whose
values are over the discrimination level of the hastening tendency test
(Matsunaga, 1994).
7 Is fast driving an effective mode of driving?
The intrinsic tendency of humans to hasten may make it difficult for them to maintain
sufficient headway while driving. The original purpose of such a tendency was to ensure that
humans could compete with other humans. Would hastening while driving bestow any
advantage to either the drivers or their passengers? Table 1 shows some differences between
driving fast and driving at an ordinary pace (Cohen and Preston, 1984). Fast drivers arrived
at their destinations 2 hours and 48 minutes earlier.
Table 1. Differential effects of normal and fast driving (Swiss experiment; Cohen
& Preston, 1968).
VEHICLE
VEHICLE
TRAVELLING
TRAVELLING
AT NORMAL AT FAST
SPEED
SPEED
DIFFERENCE
Duration of journey
47 hours,
45 hours,
2 hours,
(excluding pause on route) 53 min.
5 min.
48 min.
No. of times a vehicle was
overtaken:
lorry
262
616
51
private car
230
531
301
tractor
42
54
12
No. of times brake was
sharply applied
(unexpectedly)
7
184
177
Petrol consumption
49 gal.
61 gal .
12 gal.
Wear on tires
1 mm
2 mm
1 mm
(approx.)
(approx.)
(approx.)
Average speed
36 m.p.h.
38 m.p.h.
1.9m.p.h.
The shortening of travelling time by driving fast is not significantly large on ordinary
roads or motorways. Drivers have to stop at traffic lights and at four-way-stop intersections
on ordinary roads. Drivers cannot commit traffic violations if another car has stopped at an
intersection for a red light.
Drivers are more tired and need more rest when driving fast because, during such driving,
they drive with greater tension, thus expending more energy, than drivers driving at normal
speeds. Therefore, even on motorways, the difference in travelling time between driving fast
and driving at normal speeds is not significantly large.
Moreover, fast drivers experienced sharp braking 177 more times, consumed 12 more
gallons of fuel, and wasted 1 more millimeter of tire than ordinary drivers did (Cohen &
Preston, 1968) . Fast drivers make their headway shorter than the ordinary drivers, and the
probability of collision becomes larger. According to these results, it can be said that hasty
driving is clearly not an efficient mode of driving. It is apparent that this behavioral
mechanism that drives us to overtake others is adaptive in the pedestrian world, but it is not
advantageous in the automobile world.
8 Conclusions
As a result, accident-prone drivers showed higher scores on the hastening test than
non-accident-prone drivers, and/or more irregular reaction times than non-accident-prone
drivers. Accident-prone drivers could be detected by their irregular reaction times and by
their scores on the hastening test with a probability of around 84%.
Around 89% of younger drivers 18 or 19 years old and 64.7% of drivers over 65 showed a
higher irregularity in reaction time than the threshold, above which around 80% of all
drivers were accident-prone. Around 78% of 18 or 19 years old drivers and around 65% of
drivers over 65 showed higher scores on the hastening test than the threshold. The degree of
tendency to hasten and the fluctuation in reaction times were the lowest among drivers
between 25-39 years of age.
It can be concluded that the human factors leading to collisions while driving are the
driver's irregularity in reaction times, which can result in a sudden delay in reaction and a
stopping distance greater than usual, and the driver's tendency to hasten, which can result
in a shorter headway being maintained.
To reduce the number of accidents, drivers should be taught to maintain sufficient
headway in order to allow for any unexpected delay in reaction or for an unusually greater
stopping distance due to road conditions.
Acknowledgment
I wish to thank Mr. Victor Garbarino for proofreading the English used in this manuscript.
References
［1］Cohen, J., and Preston, B.(1968) Causes and Prevention of Road
Accidents. Faber, P. 65.
［2］Maruyama, Y.(1982) Human Science of Safe Driving 1. Kigyoukaihatu Center
Ltd., Tokyo, P. 230. (in Japanese)
［3］Matsunaga, K. (1986) A Report of the Research and Development of Aptitude Test
for Traffic Accident Prevention. Jidosya-jiko Taisaku Center, Pp.75-98. (in
Japanese)
［4］Matsunaga, K. (1988) The Research Report of Kyushu University Vol. 1, Pp. 2-4.
(in Japanese)
［5］Matsunaga, K., Haraguchi, M., and Suenaga, K. (1985) Japanese Journal of EEG
and EMG Vol. 13, Pp. 169-177. (in Japanese)
［6］Matsunaga, K., Kito, T., Kitamura, F., Shidoji, K., and Yanagida, T. (1990) Paper
presented at the 22nd International Congress of Applied Psychology, Kyoto,
Japan. (Abstract, P311).
［7］Nakajima, M., Suenaga, K., Suzumura, A., Funatsu, T., and Matsunaga, K. (1980)
IATSS REVIEW Vol. 6. Extra edition, Pp. 49-57. (in Japanese)
［8］Nakajima, M., Suenaga, K., Suzumura, A., Funatsu, T., and Matsunaga, K. (1981)
IATSS REVIEW Vol. 7. Extra edition, Pp. 49-59. (in Japanese)
［9］Waselewski, P. (1979) Transportation Science Vol. 1., Pp. 36-55.
