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How does it change safety margins if overtaking is prohibited: A pilot study
4ccid. Anal. & Prey. Vol. 12, pp. 95-103 Pergamon Press Ltd., I~0. Printed in Great Britain
HOW DOES IT CHANGE SAFETY MARGINS IF OVERTAKING IS PROHIBITED: A PILOT STUDY HEIKKI SUMMALA Department of Psychology,Universityof Helsinki, Ritarikatu 5, SF-00170Helsinki 17, Finland (Received31 January 1979;in revisedform 14 August 1979) Abstraet--Overtaking was temporarily prohibited on a 1.2km long stretch of two-lane road and the time headway for every car, passing the site in a certain direction, was measured at two points between which the prohibition sign was posted. Additionally, the lateral position of every car was recorded. Due to the prohibition, some favorable effects on safety margins were found. When passing the prohibition sign the drivers followinganother car very closelyincreased their followingdistance; no such change was found in the control condition. Furthermore, when overtakingprohibited, the closelyfollowingdrivers reserved a bit greater safety margin with respect to the oncoming vehicles. The results suggest that waiting for an opportunity of overtakingincreases the accident risk by inducingvery short followingdistances and driving near the center line. This implies that the total accident loss due to overtakingis not whollyincluded in the category "overtakingacidents" but, in fact, a part of rear-end accidents should be counted on overtaking, too. This should be taken into account when estimating the pay-offof overtakingon two-laneroads. iln 1977, only 4% of road casualties were classified as "overtaking accidents" in Finland and the respective figures are low in other countries, too [Finnish National Board of Public Roads and Waterways, 1978; Fasler, 1973; Jeffcoate, Skelton and Smeed, 1973]. There is, however, good reason to believe that this is not the total accident loss due to overtaking. It is suggested that 1he accident risk is increased because of the aim at overtaking even before the maneuver proper is started. When waiting for an opportunity of overtaking a driver is, supposedly, inclined to follow just behind the lead car in order not to miss his chances; it is known that merely giving a driver an instruction to follow another car as if prepared t o overtake produces very short following distances [Rockwell, 1972, p. 145], Braking abruptly by the lead car may, then, result in unhappy consequences which cannot be seen in the category "overtaking accidents" but, instead, in the category "rear-end accidents". Additionally, when waiting for an opportunity of overtaking a driver probably chooses a driving path closer to the center line--and closer to the oncoming vehicles--than normally in order to have better sight ahead of the lead car. This, ,,.upposedly, increases the probability of any exceptional maneuvers or occurrences to have ,.erious consequences. The present study was carried out to test whether waiting for an opportunity of overtaking really induces short safety margins. If this were the case, the prohibition of overtaking should lengthen short safety margins in car following. METHOD Procedure Overtaking was temporarily prohibited on a heavily-trafficked highway by erecting a traffic sign involving quite a long (1.2 km) stretch of road. The time headway for every car, passing the site in a certain direction, was measured at two points, 440m apart, at the halfway point between which the prohibition sign was posted. At their actual speed of about 80 km/hr, therefore, drivers had about 10 sec time to adjust their headway from the sign to the latter point cf measurement. Additionally, the lateral poition of every car and the time distance to the next encoming vehicle were recorded at the latter point. The measurements were carried out in seven related one-hour periods on four consecutive days. The first and fourth day were control conditions (the sign was not posted) and the second and third one were experimental conditions (the sign was posted). Apparatus A time recorder with pneumatic tube detectors, one for each point and direction, was used in measuring headways. (Deviating from its usual definition the headway was defined as a time 95
96
H. SUMMALA
distance from the back axle of the lead vehicle to the front axle of the following vehicle.) The lateral position of the vehicles (the distance of the left tire from the center line) was observed by means of painted markings in the pavement. The prohibition sign (see Fig. l) was a standard one: symbolic, round, 65 cm in diameter, with a red and a black car on a yellow background which was surrounded by a red edge of the width of 7 cm. Below the sign, attached to the same leg, there was a smaller, rectangle, yellow additional plate with black figures "1.2 kin" indicating that the overtaking prohibition was valid for the next 1.2 kin. The height of the figures was 7 cm. When posted, the sign was located on the nearside, at the distance of 3 m from the edgeline and at the height of 2 m above the pavement level. Measurement site The measurements were carried out for uphill-going vehicles on a long, gently-sloping stretch of road. It was a 10-m wide, two-lane (each of them 3.75 m in width), single-carriageway road with heavy traffic. The great flow in the opposite direction and the long ascent substantially reduced chances of overtaking between the two points of measurement. Hence, overtakings did not disturb data collection, and drivers waiting for an opportunity of overtaking in "steady-state" car following--the primary object of the study--could be better observed. It is to be noted that, from the point of view of the drivers, the prohibition of overtaking was not arbitrary because there was a tiny crossing for a temporary road maintenance station about 100 m after the experimental sign and it was used at the time of the study (see Fig. 1). The disturbing effect of this lorry traffic was, of course, carefully removed from the data.
/ "Observer
210
m
/
Measurement
point 2
[rossing for the ro maintenance station
Location of the experimental s
\ J
g
\
eJ N3
Observer
•
Measurement
point
cu :E
Fig. 1. The measurementsite with the experimentalsignon the roadside.
How does it change safety margins if overtaking is prohibited
97
RESULTS
H,'adway In Figs. 2 and 3, the cumulative time headway distributions are presented at the two points of measurement for each day, separately for the five off-peak hours and for the two peak hours. Due to technical failures the peak hours of the third day were missed and, therefore, the results are presented for the peak hours of only three days. Both figures show that, as was expected, the proportion of short headways (about 1 sec or less) decreased from the former point to the latter on the experimental days but not on the coatrol days. (It is to be noted that, except for these shortest ones, the headways generally tended to shorten because of the long ascent which reduced the speed of heavy or underpowered vehicles.) For a statistical test of this general experimental effect, it was first calculated the relative change, from the former point to the latter, in the proportion of drivers who followed another vehicle with a headway equal to or less than 1 sec. (The criterion was selected ex post facto but cala be justified as being a critical value close to the median brake reaction time [Johansson and Ru mar, 1971]). This measure was calculated for each day and hour, and the Friedman two-way analysis of variance by ranks [Siegel, 1956, pp. 166-172] was applied to these data. Hence, the I Control
]1 Experimental
25
25 - -
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- -
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/
P2 20
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10
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--PI
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0/.
P2
P2
20
x'
20
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// 15
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15
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/ Headway (see)
Fig. 2. The cumulative headway distribution for each day of measurement: the off-peak hours. P1 refers to the former point of measurement (overtaking permitted); P2 refers to the latter point of measurement (overtaking prohibited in the experimental condition). AAF Vol. I I , No. 2--B
98
H. SUMMALA II Expenmentat
I Control
3S
%
/ ///fJ/
/
- - P 2
30
25
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25
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0
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5 / 2
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2
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1
2 Headway(sac)
Fig. 3. The cumulativeheadwaydistributionfor three days of measurement:the peak hours. observations made during a given one-hour period, say from eight o'clock up to nine o'clock, on different days, were treated as if they were made from the same group of subjects in different experimental conditions. This procedure, aimed at reducing the confounding effect of dependent observations, is based on the assumption that many people drive regularly along the same road at about the same time on different days. Consequently, the number of drivers passing the measurement site during a given one-hour period on two consecutive days is probably greater than the number of drivers passing the site during a given one-hour period on one day and, say, during the next one-hour period on another day. Furthermore, the traffic flow is generally more homogenous during the related hours of day. Based on the procedure presented above, the differences between the first, second, and fourth day, for which all the seven one-hour periods were available and included in the analysis, were found to be of a marginal statistical significance (X7 -- 5.21; df = 2; p < 0.10). This was the case, too, with the differences between all the four days when only the five off-peak one-hour periods were included in the analysis (X7 = 6.54; df = 3; p < 0.10). Another analysis was made to reveal the effect of the overtaking prohibition specifically in "steady-state" following, i.e. when excluding the cars catching up the lead car or overtaking it between the two points of measurement. The change in headway between the two points (the headway at the latter minus the headway at the former) was calculated for every car which drove at the former point with a headway smaller than 1.3 sec and which did not overtake the lead car before the latter point. The criterion value was the mode of the overall headway distribution, indicating drivers' normal behavior in car following, and it was used instead of the former criterion of 1 sec in order to provide enough data for this more restrictive analysis. Figure 4 shows the median change in headway. It can be seen that the close-following drivers increased the headway to the lead car about 0.1-0.15 sec (about 2-3 m) more on the experimental days than on the control days during the off-peak hours. During the peak hours, instead, the median increase in headway was greater on the first (control) day than on the second (experimental) day. The respective change distribution was clearly bimodal on Day I, however, and the proportion of the close-following drivers who increased the headway was higher on Day II (70.2%) than on Day I (61.5%) or on Day IV (51.1%). For a statistical test, the percentage of drivers who increased the headway between the two points was calculated for each day and hour, and the Friedman analysis of variance was applied to the data. The differences between the first, second, and fourth day, with the seven one-hour periods included in the analysis, were statistically significant (X~ = ll.14; d r = 2 ; p<0.01). The experimental condition differed from each control day at the level of significance of 1% (the
How does it change safety margins if overtaking is prohibited
99
OL,
0.3
/
)c
0.2
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g
= 0.1 ro
c.J
/
0.0
-01 I (rainy confrot)
11 ( sunny
experimental)
Tn ( rainy
(sunny
experimental) control) Experimental condition
Fig. 4. The median change in headway from the former point of measurement to the latter one for the cars whose headway at the former point was less than 1.3 sec. The circles refer to the off-peak hours and the squares to the peak hours.
lcinomial test): on the control days, 53.8% (Day I) and 47.4% (Day IV) of the drivers with a small headway at the former point increased the headway before the latter point whereas the respective figure in the experimental condition (Day II) was 70.5%. The differences between the four days, calculated over the five off-peak hours, were significant at the level of 5% (X7 = 8.83; c~ = 3). On the control days, 58.3% (Day I) and 50.0% (Day IV) of the close-following drivers increased the headway before the latter point and the respective figures on the experimental days were 67.8% (Day II) and 65.9% (Day III). Day II consistently differed from each control eay (p = 0.03; the binomial test) but Day III did not (p = 0.06 and 0.19, respectively).t
l.ateral safety margin Figure 5 shows the mean distance of the left-hand tire of cars from the center line, at the latter point of measurement, as a function of the time distance to the lead vehicle and to the ~ext oncoming vehicle. The data are only presented for Day II (experimental conditions) and Day IV (control condition) because they were the only--sunny--days that the lateral position ef vehicles was observed. In an analysis of variance (see Table 1), the headway as well as the time distance to the next ~ncoming vehicle but not the experimental condition as such were found to have a significant effect on the lateral position. Instead, the interaction effect of the experimental condition and the headway was significant at the level of 5%.~: When overtaking prohibited, the closefallowing drivers seem to reserve a bit greater safety margin with respect to the oncoming ~ehicles than in case overtaking is permitted. The opposite is true, however, when drivers with a long headway are considered indicating that, overtaking being prohibited, slower drivers l:ossibly try to prevent following drivers from overtaking or, at least, do not give way to them. DISCUSSION
The results, although partly of marginal significance, were in accordance with the hypotheses presented: small safety margins, with respect to the lead vehicle and to the oncoming vehicles,
fWhen the headway change distributions, all the five off-peak hours together, were compared with the Mann-Whitney test, each experimental day differed from each control day at the risk level of 10% or smaller in a two-tailed test and, accordingly, at the risk level of 5% or smaller in a one-tailed test the use of which is well motivated. The experimental days d d not, instead, differ from each other and so did the control days, neither. The Kruskal-Wallis test showed that the ocerall differences between the four days were significant at the risk level of 1% (H = 12.9; df = 3). It is to be noted, h)wever, that both the Mann-Whitney U and the Kruskal-Wallis H may be somewhat inflated because of repeated o 3servations on different days. :Ht is to be noted that the test may be somewhat inflated because of the dependent observations.
100
H. SUMMALA
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------Headway<
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\
Exp
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Fig. 5. The lateralpositionof the cars (the distanceof the left-handtire fromthe centerline) as a function of the time distance to the next oncomingvehicle and of the headway, separatelyfor the experimental and controlcondition. were found to be less frequent when a temporary prohibition of overtaking was introduced. It is to be noted that, first, the weather conditions varied with the day of measurement and, accordingly, with the experimental condition. The effect of prohibition was consistent, however, during the off-peak hours for which there was one rainy and one sunny day both in the control and experimental condition. Another factor having potential effects on drivers' following behavior is the traffic flow. The great flow probably reduces drivers' desire of overtaking because they gain less from each overtaking maneuver in heavy traffic and, furthermore, there are less opportunities for overtakings. In this study the data were collected at the same time each day resulting in very similar flows to be analyzed. The only period during which a somewhat smaller flow--compared to the respective periods on the other days--may have induced differences in following behavior is the peak-hour period on the second day. It can be seen from Fig. 3 that, in spite of a somewhat smaller flow, there are as many short headways at the first measurement point on Day II as on the control days. It is possible that the short headways are really due to waiting for an opportunity of overtaking on Day II but, instead, due to the greater flow on the control days. If this is the case the experimental effect may be somewhat inflated over the peak hours. However, it should be noted that the proportion of drivers who maintained a headway equal to or less than 1 sec dropped from 15% in the former point to 10% in the latter although rather the opposite would be expected because of the ascent. Therefore, the prohibition is the plausible explanation to this change anyway. As far as the lateral safety margin is concerned, the experiment was not very well controlled because the lateral position of vehicles was only observed at the latter point of measurement. Furthermore, observation cannot be regarded as a fully satisfactory method of measuring the lateral position of vehicles on the road (for a more advanced method see Summala and Merisalo [1978]). This study suggests, however, that the prohibition of overtaking has favorable effects on the lateral safety margins, too, although an opposite effect was found among drivers with a long headway who drove a bit closer to the center line when overtaking being prohibited; so they possibly tried to prevent other drivers from overtaking or, at least, did not give way to them. It is to be noted that the temporary prohibition of overtaking had an influence on small safety margins although, in light of research on perception of traffic signs [H~kkinen, 1%5; Johansson and Backlund, 1970; Johansson and Rumar, I%6; for a review, see Nfifit~inen and Summala, 1976, pp. 115-139], it can be estimated that a part of drivers did not perceive the
I01
How does it change safety margins if overtaking is prohibited Table 1. Analysisof variance for the lateral position data
Source
SS
df
MS
F
A (Prohibition)
5.50
I
5.50
B (Distance to the oncoming vehicle)
120.10
3
40.03
10.94 ++
C (Headway)
51.30
I
51.30
14.02 ++
A5
10. 10
3
3.37
O. 92
AC
14.09
I
14.09
3.85
BC
5.30
3
i. 77
o. 48
ABC
io. 09
3
3.36
Within
4317. I0
1180
3.66
Total
4533.60
1195
++ +
I. 50
+
p <.01 p <.05
prohibition sign. In fact, there may be a positive correlation between missing the sign and very close following. The closely following drivers may be attending to the lead car or to the oncoming cars to such a degree that they miss the sign, and drivers following a lorry or a large van very closely can even be physically prevented from seeing the sign. It is not known how many drivers actually missed the sign but, due to no substantial differences prevailing in the number of short headways at the former point, there is no reason to believe that some differences would occur between the measurement days in this respect (except for the rain but, as was stated earlier, the effect of the prohibition was not dependent on it). Therefore, this is not a crucial point: missing the sign by some drivers only decreased chances of the experimental effect to show up. But it showed up, nevertheless. CONCLUSIONS The present results suggest that a temporary prohibition of overtaking on a two-lane road has some favorable effects on the critical safety margins in car following. Such effects imply that, in addition to the maneuver proper, merely aiming at overtaking increases the accident risk by inducing very close car-following and driving near the center line.t" (It is expected that small ,,afety margins, such as those dealt with, are really hazardous although definitive evidence is ,,.till missing.) Hence, this study supports the hypothesis according to which the accident loss due to overtaking is not wholly included in the category "overtaking accidents" but, in fact, a part of "real" rear-end accidents should be counted on overtaking. This point clearly deserves turther attention and, if valid, it should be taken into account when estimating the pay-off of overtaking on two-lane roads. Acknowledgements--This study was conducted as a part of a contract with the Finnish National Board of Public Roads ~nd Waterways. Writingthis paper was financed by the Academy of Finland. The author is indebted to the anonymous referees for their invaluablecomments.
REFERENCES Colbourn C. J., Brown I. D. and Copeman A. K., Drivers' judgmentsof safe distances in vehiclefollowing.Human Factors 20, [-11, 1978. Fasler S., Die 0berholunf~ille in der Schweiz. Paper presented at the Ist Int. Conf. on Driver Behavior, Zurich, Switzerland, Oct. 1973. fAnother reason to follow closely the car in front, as suggestedby Colbourn, Brown and Copeman [1978], and even to drive closer to the center line, may be drivers' desire to prevent the followingdriver from overtaking.The accident loss cue to such behavior is, in fact, to be counted on overtaking,too.
102
H. SUMMALA
Finnish National Board of Public Roads and Waterways, Traffic accidents on public roads in 1977. Rep. No. 742634-77, Helsinki, Finland, 1978 (In Finnish). H/ikkinen S., Perception of highway traffic signs. Reps. from TALJA, No. 1, Helsinki, Finland, 1965. Jeffcoate G. O., Skelton N. and Smeed R., Analysis of national statistics of overtaking road accidents. Paper presented at the 1st Int. Conf. on Driver Behavior, Zurich, Switzerland, Oct. 1973. Johansson G. and Backlund F., Drivers and road signs. Ergonomics 13, 749-759, 1970. Johansson G. and Rumar K., Drivers and road signs: a preliminary investigation of the capacity of car drivers to get information from road signs. Ergonomics 9, 57-62, 1966. Johansson G. and Rumar K., Drivers' brake reaction times. Human Factors 13, 23-27, 1971. N~i/it~inen R. and Summala H., Road-User Behavior and Traffic Accidents. North-Holland, Amsterdam, 1976. Rockwell T., Skills, judgment and information acquisition in driving. In Human Factors in Highway Traffic Safety Research T. W. Forbes (Editor) pp. 133-164. Wiley, New York, 1972. Siegel S., Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill, New York, 1956. Summala H. and Merisalo A., Measuring the lateral position of vehicles on the road: system and preliminary results. Traffic Engng & Control 19, 328-330, 1978. Winer B. J., Statistical Principles in Experimental Design. McGraw-Hill, New York, 1%2. APPENDIX
Testing daily differences in driver behavior at the same stretch of road When studying driver behavior outside the car, i.e. as measured from the traffic flow at a given stretch of road, experimental treatment is sometimes varied daily. Consequently, the samples at different treatment levels are not independent because of drivers who daily pass the experimental site. In the optimum case, each regular driver should be identified and the relevant features in his behavior should be daily recorded. This is not feasible, however, when considering a small subset of drivers, e.g. those following another car very closely: the sample consisting of drivers doing it every day would be too small. In such a case, the related periods (e.g. hours) of day, during several days, can be treated as if they were, say, subjects in different experimental conditions. Within such related periods both the driver population and the traffic flow are generally more homogenous than between such periods. In case the assumptions associated with it are fulfilled the analysis of variance (the model of repeated measures; see Winer [1%2]) can be used to test whether the treatment effect is statistically significant or not or, whether the samples are drawn from identical populations. Table AI. The experimental design: the scores
Day of measurement (=treatment level) xi,1
Xl,k
xn, t
Xn,k
Hour of day (="subject m)
Table A2. The experimental design: the ranks
Day of measurement (=treatment level) ri,1
rl,k
rn,1
rn,k
Hour of day (=Nsubject")
How does it changesafetymarginsif overtakingis prohibited
103
V,.~ry often, however, the underlying assumptions are to be treated as too strict, and nonp~rametric tests should be used. Among them, the Friedman two-way analysis of variance by ranks [Siegel, 1956, pp. 166-172] is probably the most powerful one. It applies when the data from k matched samples are in at least an ordinal scale. Methodically, the scores (Table A1) in e6 ch row are first ranked (Table A2): The Friedman test then determines whether the column rank totals (Rj = ~ ri,j) differ i-I
sil;nificantly. The statistic 12_ "~ (Ri) z - 3 n ( k + 1) X] - n k ( k + 1)/_-~
waere n = number of rows; k = number of columns; and Rj = sum of ranks in jth column, is distributed approximately as chi square with d f = k - 1. For paired comparisons between the treatment levels, or days, the binomial test or the V~ilcoxon matched-pairs signed-ranks test [Siegel, 1956, pp. 75-83] is useful.
HOW DOES IT CHANGE SAFETY MARGINS IF OVERTAKING IS PROHIBITED: A PILOT STUDY HEIKKI SUMMALA Department of Psychology,Universityof Helsinki, Ritarikatu 5, SF-00170Helsinki 17, Finland (Received31 January 1979;in revisedform 14 August 1979) Abstraet--Overtaking was temporarily prohibited on a 1.2km long stretch of two-lane road and the time headway for every car, passing the site in a certain direction, was measured at two points between which the prohibition sign was posted. Additionally, the lateral position of every car was recorded. Due to the prohibition, some favorable effects on safety margins were found. When passing the prohibition sign the drivers followinganother car very closelyincreased their followingdistance; no such change was found in the control condition. Furthermore, when overtakingprohibited, the closelyfollowingdrivers reserved a bit greater safety margin with respect to the oncoming vehicles. The results suggest that waiting for an opportunity of overtakingincreases the accident risk by inducingvery short followingdistances and driving near the center line. This implies that the total accident loss due to overtakingis not whollyincluded in the category "overtakingacidents" but, in fact, a part of rear-end accidents should be counted on overtaking, too. This should be taken into account when estimating the pay-offof overtakingon two-laneroads. iln 1977, only 4% of road casualties were classified as "overtaking accidents" in Finland and the respective figures are low in other countries, too [Finnish National Board of Public Roads and Waterways, 1978; Fasler, 1973; Jeffcoate, Skelton and Smeed, 1973]. There is, however, good reason to believe that this is not the total accident loss due to overtaking. It is suggested that 1he accident risk is increased because of the aim at overtaking even before the maneuver proper is started. When waiting for an opportunity of overtaking a driver is, supposedly, inclined to follow just behind the lead car in order not to miss his chances; it is known that merely giving a driver an instruction to follow another car as if prepared t o overtake produces very short following distances [Rockwell, 1972, p. 145], Braking abruptly by the lead car may, then, result in unhappy consequences which cannot be seen in the category "overtaking accidents" but, instead, in the category "rear-end accidents". Additionally, when waiting for an opportunity of overtaking a driver probably chooses a driving path closer to the center line--and closer to the oncoming vehicles--than normally in order to have better sight ahead of the lead car. This, ,,.upposedly, increases the probability of any exceptional maneuvers or occurrences to have ,.erious consequences. The present study was carried out to test whether waiting for an opportunity of overtaking really induces short safety margins. If this were the case, the prohibition of overtaking should lengthen short safety margins in car following. METHOD Procedure Overtaking was temporarily prohibited on a heavily-trafficked highway by erecting a traffic sign involving quite a long (1.2 km) stretch of road. The time headway for every car, passing the site in a certain direction, was measured at two points, 440m apart, at the halfway point between which the prohibition sign was posted. At their actual speed of about 80 km/hr, therefore, drivers had about 10 sec time to adjust their headway from the sign to the latter point cf measurement. Additionally, the lateral poition of every car and the time distance to the next encoming vehicle were recorded at the latter point. The measurements were carried out in seven related one-hour periods on four consecutive days. The first and fourth day were control conditions (the sign was not posted) and the second and third one were experimental conditions (the sign was posted). Apparatus A time recorder with pneumatic tube detectors, one for each point and direction, was used in measuring headways. (Deviating from its usual definition the headway was defined as a time 95
96
H. SUMMALA
distance from the back axle of the lead vehicle to the front axle of the following vehicle.) The lateral position of the vehicles (the distance of the left tire from the center line) was observed by means of painted markings in the pavement. The prohibition sign (see Fig. l) was a standard one: symbolic, round, 65 cm in diameter, with a red and a black car on a yellow background which was surrounded by a red edge of the width of 7 cm. Below the sign, attached to the same leg, there was a smaller, rectangle, yellow additional plate with black figures "1.2 kin" indicating that the overtaking prohibition was valid for the next 1.2 kin. The height of the figures was 7 cm. When posted, the sign was located on the nearside, at the distance of 3 m from the edgeline and at the height of 2 m above the pavement level. Measurement site The measurements were carried out for uphill-going vehicles on a long, gently-sloping stretch of road. It was a 10-m wide, two-lane (each of them 3.75 m in width), single-carriageway road with heavy traffic. The great flow in the opposite direction and the long ascent substantially reduced chances of overtaking between the two points of measurement. Hence, overtakings did not disturb data collection, and drivers waiting for an opportunity of overtaking in "steady-state" car following--the primary object of the study--could be better observed. It is to be noted that, from the point of view of the drivers, the prohibition of overtaking was not arbitrary because there was a tiny crossing for a temporary road maintenance station about 100 m after the experimental sign and it was used at the time of the study (see Fig. 1). The disturbing effect of this lorry traffic was, of course, carefully removed from the data.
/ "Observer
210
m
/
Measurement
point 2
[rossing for the ro maintenance station
Location of the experimental s
\ J
g
\
eJ N3
Observer
•
Measurement
point
cu :E
Fig. 1. The measurementsite with the experimentalsignon the roadside.
How does it change safety margins if overtaking is prohibited
97
RESULTS
H,'adway In Figs. 2 and 3, the cumulative time headway distributions are presented at the two points of measurement for each day, separately for the five off-peak hours and for the two peak hours. Due to technical failures the peak hours of the third day were missed and, therefore, the results are presented for the peak hours of only three days. Both figures show that, as was expected, the proportion of short headways (about 1 sec or less) decreased from the former point to the latter on the experimental days but not on the coatrol days. (It is to be noted that, except for these shortest ones, the headways generally tended to shorten because of the long ascent which reduced the speed of heavy or underpowered vehicles.) For a statistical test of this general experimental effect, it was first calculated the relative change, from the former point to the latter, in the proportion of drivers who followed another vehicle with a headway equal to or less than 1 sec. (The criterion was selected ex post facto but cala be justified as being a critical value close to the median brake reaction time [Johansson and Ru mar, 1971]). This measure was calculated for each day and hour, and the Friedman two-way analysis of variance by ranks [Siegel, 1956, pp. 166-172] was applied to these data. Hence, the I Control
]1 Experimental
25
25 - -
%
- -
- -
P1
/
P2 20
/
15
10
- -
%
- -
--Pl / f
P2 r,
20
/
15
10
/ /
/
_ _ . . J J
TIT Experimentat
Controt
25
25 --Pl
--PI
%
0/.
P2
P2
20
x'
20
/
// 15
.I
15
/ // 10
10
/ Headway (see)
Fig. 2. The cumulative headway distribution for each day of measurement: the off-peak hours. P1 refers to the former point of measurement (overtaking permitted); P2 refers to the latter point of measurement (overtaking prohibited in the experimental condition). AAF Vol. I I , No. 2--B
98
H. SUMMALA II Expenmentat
I Control
3S
%
/ ///fJ/
/
- - P 2
30
25
20
15
~ Contrc4
35 ------PI
/
//
5
o/o
---- --Pl
-- ----PI
'°
- -
- - P 2
P2
/1
//
20
' //~/
15 lo
10
f
/
,y'
25
!
0
/
/
/
]l
,/
5 / 2
3
0
5
I
2
3
1
2 Headway(sac)
Fig. 3. The cumulativeheadwaydistributionfor three days of measurement:the peak hours. observations made during a given one-hour period, say from eight o'clock up to nine o'clock, on different days, were treated as if they were made from the same group of subjects in different experimental conditions. This procedure, aimed at reducing the confounding effect of dependent observations, is based on the assumption that many people drive regularly along the same road at about the same time on different days. Consequently, the number of drivers passing the measurement site during a given one-hour period on two consecutive days is probably greater than the number of drivers passing the site during a given one-hour period on one day and, say, during the next one-hour period on another day. Furthermore, the traffic flow is generally more homogenous during the related hours of day. Based on the procedure presented above, the differences between the first, second, and fourth day, for which all the seven one-hour periods were available and included in the analysis, were found to be of a marginal statistical significance (X7 -- 5.21; df = 2; p < 0.10). This was the case, too, with the differences between all the four days when only the five off-peak one-hour periods were included in the analysis (X7 = 6.54; df = 3; p < 0.10). Another analysis was made to reveal the effect of the overtaking prohibition specifically in "steady-state" following, i.e. when excluding the cars catching up the lead car or overtaking it between the two points of measurement. The change in headway between the two points (the headway at the latter minus the headway at the former) was calculated for every car which drove at the former point with a headway smaller than 1.3 sec and which did not overtake the lead car before the latter point. The criterion value was the mode of the overall headway distribution, indicating drivers' normal behavior in car following, and it was used instead of the former criterion of 1 sec in order to provide enough data for this more restrictive analysis. Figure 4 shows the median change in headway. It can be seen that the close-following drivers increased the headway to the lead car about 0.1-0.15 sec (about 2-3 m) more on the experimental days than on the control days during the off-peak hours. During the peak hours, instead, the median increase in headway was greater on the first (control) day than on the second (experimental) day. The respective change distribution was clearly bimodal on Day I, however, and the proportion of the close-following drivers who increased the headway was higher on Day II (70.2%) than on Day I (61.5%) or on Day IV (51.1%). For a statistical test, the percentage of drivers who increased the headway between the two points was calculated for each day and hour, and the Friedman analysis of variance was applied to the data. The differences between the first, second, and fourth day, with the seven one-hour periods included in the analysis, were statistically significant (X~ = ll.14; d r = 2 ; p<0.01). The experimental condition differed from each control day at the level of significance of 1% (the
How does it change safety margins if overtaking is prohibited
99
OL,
0.3
/
)c
0.2
\\
_m
g
= 0.1 ro
c.J
/
0.0
-01 I (rainy confrot)
11 ( sunny
experimental)
Tn ( rainy
(sunny
experimental) control) Experimental condition
Fig. 4. The median change in headway from the former point of measurement to the latter one for the cars whose headway at the former point was less than 1.3 sec. The circles refer to the off-peak hours and the squares to the peak hours.
lcinomial test): on the control days, 53.8% (Day I) and 47.4% (Day IV) of the drivers with a small headway at the former point increased the headway before the latter point whereas the respective figure in the experimental condition (Day II) was 70.5%. The differences between the four days, calculated over the five off-peak hours, were significant at the level of 5% (X7 = 8.83; c~ = 3). On the control days, 58.3% (Day I) and 50.0% (Day IV) of the close-following drivers increased the headway before the latter point and the respective figures on the experimental days were 67.8% (Day II) and 65.9% (Day III). Day II consistently differed from each control eay (p = 0.03; the binomial test) but Day III did not (p = 0.06 and 0.19, respectively).t
l.ateral safety margin Figure 5 shows the mean distance of the left-hand tire of cars from the center line, at the latter point of measurement, as a function of the time distance to the lead vehicle and to the ~ext oncoming vehicle. The data are only presented for Day II (experimental conditions) and Day IV (control condition) because they were the only--sunny--days that the lateral position ef vehicles was observed. In an analysis of variance (see Table 1), the headway as well as the time distance to the next ~ncoming vehicle but not the experimental condition as such were found to have a significant effect on the lateral position. Instead, the interaction effect of the experimental condition and the headway was significant at the level of 5%.~: When overtaking prohibited, the closefallowing drivers seem to reserve a bit greater safety margin with respect to the oncoming ~ehicles than in case overtaking is permitted. The opposite is true, however, when drivers with a long headway are considered indicating that, overtaking being prohibited, slower drivers l:ossibly try to prevent following drivers from overtaking or, at least, do not give way to them. DISCUSSION
The results, although partly of marginal significance, were in accordance with the hypotheses presented: small safety margins, with respect to the lead vehicle and to the oncoming vehicles,
fWhen the headway change distributions, all the five off-peak hours together, were compared with the Mann-Whitney test, each experimental day differed from each control day at the risk level of 10% or smaller in a two-tailed test and, accordingly, at the risk level of 5% or smaller in a one-tailed test the use of which is well motivated. The experimental days d d not, instead, differ from each other and so did the control days, neither. The Kruskal-Wallis test showed that the ocerall differences between the four days were significant at the risk level of 1% (H = 12.9; df = 3). It is to be noted, h)wever, that both the Mann-Whitney U and the Kruskal-Wallis H may be somewhat inflated because of repeated o 3servations on different days. :Ht is to be noted that the test may be somewhat inflated because of the dependent observations.
100
H. SUMMALA
1.5 1 sec
------Headway<
i=
Headway> 5 sec u L
~1.3 m
Control
E×p
l:3
\
Exp
\\ \
\ N\
1.1
Eonfro[
<2
2125-5
5,125-15
>I Oisfance
to oncoming
sec
car
Fig. 5. The lateralpositionof the cars (the distanceof the left-handtire fromthe centerline) as a function of the time distance to the next oncomingvehicle and of the headway, separatelyfor the experimental and controlcondition. were found to be less frequent when a temporary prohibition of overtaking was introduced. It is to be noted that, first, the weather conditions varied with the day of measurement and, accordingly, with the experimental condition. The effect of prohibition was consistent, however, during the off-peak hours for which there was one rainy and one sunny day both in the control and experimental condition. Another factor having potential effects on drivers' following behavior is the traffic flow. The great flow probably reduces drivers' desire of overtaking because they gain less from each overtaking maneuver in heavy traffic and, furthermore, there are less opportunities for overtakings. In this study the data were collected at the same time each day resulting in very similar flows to be analyzed. The only period during which a somewhat smaller flow--compared to the respective periods on the other days--may have induced differences in following behavior is the peak-hour period on the second day. It can be seen from Fig. 3 that, in spite of a somewhat smaller flow, there are as many short headways at the first measurement point on Day II as on the control days. It is possible that the short headways are really due to waiting for an opportunity of overtaking on Day II but, instead, due to the greater flow on the control days. If this is the case the experimental effect may be somewhat inflated over the peak hours. However, it should be noted that the proportion of drivers who maintained a headway equal to or less than 1 sec dropped from 15% in the former point to 10% in the latter although rather the opposite would be expected because of the ascent. Therefore, the prohibition is the plausible explanation to this change anyway. As far as the lateral safety margin is concerned, the experiment was not very well controlled because the lateral position of vehicles was only observed at the latter point of measurement. Furthermore, observation cannot be regarded as a fully satisfactory method of measuring the lateral position of vehicles on the road (for a more advanced method see Summala and Merisalo [1978]). This study suggests, however, that the prohibition of overtaking has favorable effects on the lateral safety margins, too, although an opposite effect was found among drivers with a long headway who drove a bit closer to the center line when overtaking being prohibited; so they possibly tried to prevent other drivers from overtaking or, at least, did not give way to them. It is to be noted that the temporary prohibition of overtaking had an influence on small safety margins although, in light of research on perception of traffic signs [H~kkinen, 1%5; Johansson and Backlund, 1970; Johansson and Rumar, I%6; for a review, see Nfifit~inen and Summala, 1976, pp. 115-139], it can be estimated that a part of drivers did not perceive the
I01
How does it change safety margins if overtaking is prohibited Table 1. Analysisof variance for the lateral position data
Source
SS
df
MS
F
A (Prohibition)
5.50
I
5.50
B (Distance to the oncoming vehicle)
120.10
3
40.03
10.94 ++
C (Headway)
51.30
I
51.30
14.02 ++
A5
10. 10
3
3.37
O. 92
AC
14.09
I
14.09
3.85
BC
5.30
3
i. 77
o. 48
ABC
io. 09
3
3.36
Within
4317. I0
1180
3.66
Total
4533.60
1195
++ +
I. 50
+
p <.01 p <.05
prohibition sign. In fact, there may be a positive correlation between missing the sign and very close following. The closely following drivers may be attending to the lead car or to the oncoming cars to such a degree that they miss the sign, and drivers following a lorry or a large van very closely can even be physically prevented from seeing the sign. It is not known how many drivers actually missed the sign but, due to no substantial differences prevailing in the number of short headways at the former point, there is no reason to believe that some differences would occur between the measurement days in this respect (except for the rain but, as was stated earlier, the effect of the prohibition was not dependent on it). Therefore, this is not a crucial point: missing the sign by some drivers only decreased chances of the experimental effect to show up. But it showed up, nevertheless. CONCLUSIONS The present results suggest that a temporary prohibition of overtaking on a two-lane road has some favorable effects on the critical safety margins in car following. Such effects imply that, in addition to the maneuver proper, merely aiming at overtaking increases the accident risk by inducing very close car-following and driving near the center line.t" (It is expected that small ,,afety margins, such as those dealt with, are really hazardous although definitive evidence is ,,.till missing.) Hence, this study supports the hypothesis according to which the accident loss due to overtaking is not wholly included in the category "overtaking accidents" but, in fact, a part of "real" rear-end accidents should be counted on overtaking. This point clearly deserves turther attention and, if valid, it should be taken into account when estimating the pay-off of overtaking on two-lane roads. Acknowledgements--This study was conducted as a part of a contract with the Finnish National Board of Public Roads ~nd Waterways. Writingthis paper was financed by the Academy of Finland. The author is indebted to the anonymous referees for their invaluablecomments.
REFERENCES Colbourn C. J., Brown I. D. and Copeman A. K., Drivers' judgmentsof safe distances in vehiclefollowing.Human Factors 20, [-11, 1978. Fasler S., Die 0berholunf~ille in der Schweiz. Paper presented at the Ist Int. Conf. on Driver Behavior, Zurich, Switzerland, Oct. 1973. fAnother reason to follow closely the car in front, as suggestedby Colbourn, Brown and Copeman [1978], and even to drive closer to the center line, may be drivers' desire to prevent the followingdriver from overtaking.The accident loss cue to such behavior is, in fact, to be counted on overtaking,too.
102
H. SUMMALA
Finnish National Board of Public Roads and Waterways, Traffic accidents on public roads in 1977. Rep. No. 742634-77, Helsinki, Finland, 1978 (In Finnish). H/ikkinen S., Perception of highway traffic signs. Reps. from TALJA, No. 1, Helsinki, Finland, 1965. Jeffcoate G. O., Skelton N. and Smeed R., Analysis of national statistics of overtaking road accidents. Paper presented at the 1st Int. Conf. on Driver Behavior, Zurich, Switzerland, Oct. 1973. Johansson G. and Backlund F., Drivers and road signs. Ergonomics 13, 749-759, 1970. Johansson G. and Rumar K., Drivers and road signs: a preliminary investigation of the capacity of car drivers to get information from road signs. Ergonomics 9, 57-62, 1966. Johansson G. and Rumar K., Drivers' brake reaction times. Human Factors 13, 23-27, 1971. N~i/it~inen R. and Summala H., Road-User Behavior and Traffic Accidents. North-Holland, Amsterdam, 1976. Rockwell T., Skills, judgment and information acquisition in driving. In Human Factors in Highway Traffic Safety Research T. W. Forbes (Editor) pp. 133-164. Wiley, New York, 1972. Siegel S., Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill, New York, 1956. Summala H. and Merisalo A., Measuring the lateral position of vehicles on the road: system and preliminary results. Traffic Engng & Control 19, 328-330, 1978. Winer B. J., Statistical Principles in Experimental Design. McGraw-Hill, New York, 1%2. APPENDIX
Testing daily differences in driver behavior at the same stretch of road When studying driver behavior outside the car, i.e. as measured from the traffic flow at a given stretch of road, experimental treatment is sometimes varied daily. Consequently, the samples at different treatment levels are not independent because of drivers who daily pass the experimental site. In the optimum case, each regular driver should be identified and the relevant features in his behavior should be daily recorded. This is not feasible, however, when considering a small subset of drivers, e.g. those following another car very closely: the sample consisting of drivers doing it every day would be too small. In such a case, the related periods (e.g. hours) of day, during several days, can be treated as if they were, say, subjects in different experimental conditions. Within such related periods both the driver population and the traffic flow are generally more homogenous than between such periods. In case the assumptions associated with it are fulfilled the analysis of variance (the model of repeated measures; see Winer [1%2]) can be used to test whether the treatment effect is statistically significant or not or, whether the samples are drawn from identical populations. Table AI. The experimental design: the scores
Day of measurement (=treatment level) xi,1
Xl,k
xn, t
Xn,k
Hour of day (="subject m)
Table A2. The experimental design: the ranks
Day of measurement (=treatment level) ri,1
rl,k
rn,1
rn,k
Hour of day (=Nsubject")
How does it changesafetymarginsif overtakingis prohibited
103
V,.~ry often, however, the underlying assumptions are to be treated as too strict, and nonp~rametric tests should be used. Among them, the Friedman two-way analysis of variance by ranks [Siegel, 1956, pp. 166-172] is probably the most powerful one. It applies when the data from k matched samples are in at least an ordinal scale. Methodically, the scores (Table A1) in e6 ch row are first ranked (Table A2): The Friedman test then determines whether the column rank totals (Rj = ~ ri,j) differ i-I
sil;nificantly. The statistic 12_ "~ (Ri) z - 3 n ( k + 1) X] - n k ( k + 1)/_-~
waere n = number of rows; k = number of columns; and Rj = sum of ranks in jth column, is distributed approximately as chi square with d f = k - 1. For paired comparisons between the treatment levels, or days, the binomial test or the V~ilcoxon matched-pairs signed-ranks test [Siegel, 1956, pp. 75-83] is useful.