EXPERIMENT 3: Choice of time-headway in car-following and the role of time-to-collision information in braking

This is chapter 6 from the thesis “From adaptive control to adaptive traffic behaviour” about traffic psychology and behavioural adaptation of drivers, by Wim van Winsum. The thesis is from 1996. It describes a number of behavioural experiments into car driving that were performed in a research driving simulator.
Other chapters of this thesis can be found here:
- Chapter 1: Introduction.
- Chapter 2: Models of driver behaviour.
- Chapter 3: Instrumentation: The driving simulator.
- Chapter 4: EXPERIMENT 1: Speed Choice and Steering Behaviour in Curve Driving
- Chapter 5: EXPERIMENT 2: Preferred time-headway in car-following and operational skills in expected braking reactions
- Chapter 6: EXPERIMENT 3: Choice of time-headway in car-following and the role of time-to-collision information in braking
- Chapter 7: EXPERIMENT 4: Time-headway in car-following and operational performance during unexpected braking
- Chapter 8: EXPERIMENT 5: The effects of deceleration on braking reactions as a function of preferred time-headway
- Chapter 9: EXPERIMENT 6: Perceptual-motor skills and sensitivity to TTC as a function of preferred time-headway in car-following
- Chapter 10: General discussion and conclusions.
Time-headway (THW) during car-following and braking response were studied in a driving simulator from the perspective that behaviour on the tactical level (e.g. choice of THW) may be linked to operational competence of vehicle control (e.g. braking) via a process of adaptation. Time-headway was consistent within drivers and constant over a range of speeds. Since time-headway represents the time available to the driver to reach the same level of deceleration as the lead vehicle in case it brakes, it was studied whether choice of time-headway was related to skills underlying braking performance. The initiation and control of braking were both affected by time-to-collision (TTC) at the moment the lead vehicle started to brake. This strongly supported the idea that time-to-collision information is used for judging the moment to start braking and in the control of braking. No evidence was found that short followers differ from long followers in the ability to accurately perceive TTC. There was however evidence that short followers are better able to program the intensity of braking to required levels. Also, short followers tuned the control of braking better to the development of criticality in time during the braking process. It was concluded that short followers may differ from long followers in programming and execution of the braking response.
6.1 Introduction
Close car-following has been associated with traffic accident involvement. Rear-end collisions accounted for about 24% of all accidents involving two or more vehicles in the U.S.A in 1990 (McGehee et al., 1992). These accidents are usually attributed to maintaining insufficiently long headways and/or to inattentive driving resulting in responding too late to a deceleration of a vehicle in front. In the literature, headway is expressed either as distance headway (DHW) or as time headway (THW) (Fuller, 1981). DHW is the bumper to bumper distance between the lead vehicle and the following vehicle. THW is the time interval between two vehicles in car-following, calculated as DHW divided by the speed (in m/s) of the following vehicle. When the following and the lead vehicle drive at the same speed (steady-state following), THW represents the time available to the driver of the following vehicle to reach the same level of deceleration as the lead vehicle in case it brakes. This available time is independent of speed. A faster braking response is then required with a smaller THW. Also, the control of braking is more critical in that case. In this article, the THW during steady-state car-following will be referred to as THWpref (preferred time headway).
Evans and Wasielewski (1982) found that drivers with a larger THWpref had a history of fewer traffic violations and traffic accidents. However, the same authors also argued that accident involvement did not have a reliable relation with THWpref by itself (Evans and Wasielewski, 1983). Especially younger drivers employed smaller THW’s, as did drivers of newer cars and of vehicles with medium mass.
Several factors have been identified that influence choice of THW. Choice of THW has been associated with personality factors by some authors. Sensation seeking as a personality trait is assumed to be related to risky behaviour (Zuckerman, 1979). For example, Zuckerman and Neeb (1980) found a positive correlation between the sensation seeking score and reported driving speed, whereas Heino et al. (1992), using a realistic car-following task, reported a smaller THWpref for sensation seekers than for sensation avoiders. Ota (1994) studied car-following behaviour in relation to personality traits. He suggested social maladjustment as an important factor in choice of THW, although correlations between THW and personality test scores were not significant.
Other authors have stressed the importance of task-related factors with regard to THWpref. Fuller (1981) studied THW of truck drivers in convoy situations. During the late shift, covering a large period of driving in the dark, THWpref was significantly larger than during daytime driving. This was explained as an effect of visual conditions. Brookhuis et al. (1991) reported an increase in THW when using a car telephone while driving, which can be regarded as an additional task competing for attention. This suggests the driver is aware of effects of task demands on the ability to detect a deceleration of a lead vehicle and adapts THW accordingly.
Choice of THW also has been associated with temporary state-related factors. Fuller (1984) reported a time-on-task effect on THW for older truck drivers in the late shift. After seven hours of driving, THW increased quite strongly, accompanied by verbal reports of performance decrements, drowsiness and exhaustion. In an experiment reported by Smiley et al. (1981) in an interactive driving simulator, marijuana resulted in increased headways during car-following. Smiley et al. (1986) studied the effect of marijuana on several car-driving tasks on the road. Again marijuana significantly increased headway in a car-following task. In another simulator study, Smiley et al. (1985) found that marijuana increased headway while alcohol decreased headway. These results strongly suggest effects of temporary states such as fatigue or states induced by marijuana and alcohol on THWpref; fatigue and marijuana increase THWpref which may be a reflection of an adaptation of THW to adverse effects on the brake reaction, whereas alcohol decreases THWpref, possibly because drivers overestimate their braking competence under alcohol.
The effects of task-related factors and transient states refer to intra-individual differences. The results strongly suggest a process of adaptation of THW to changes in operational level competence which is influenced by task-related and state-related factors. From the same perspective, inter-individual differences in following behaviour, may be related to inter-individual differences in operational level competence, such that THWpref is adapted to limitations in braking-related competence. These limitations in braking competence may then be determined by specific skills required for optimal braking performance. For this to be the case, THWpref must be consistent within the individual driver, while it differs between drivers as a function of operational skill. Since THWpref represents the ultimate reaction time in case of a deceleration by the lead vehicle, THWpref must be invariant over speed. However, in spite of years of research into car-following it is still not clear whether this time headway constancy holds over speed and whether it is consistent within drivers.
Fuller (1986) reanalyzed the results of previous car-following experiments and found negative correlations between speed and THW. Following distance increased with speed but not enough to maintain THW at a constant level. However, the conditions resulting in different speeds varied widely. High speeds were associated with rural open-road conditions with low traffic density and the absence of junctions, pedestrians and other hazards. Low speeds, on the other hand were associated with opposite conditions. Conditions that resulted in lower speeds, and an accompanying larger THWpref, were characterized by multiple tasks competing for attention, possibly resulting in performance decrements in braking. Ota (1994) studied THW while drivers were required to drive with a speed of 50, 60 or 80 km/h and follow under different instructions such as ‘follow at a comfortable distance’ and ‘follow at a minimum safe distance’. No effects of speed on THW were found while instruction significantly affected choice of THW. This suggests that THWpref is constant over different speeds.
In the present study, an important hypothesis is that THWpref is constant over speed and consistent within the driver. In order to test consistency of THWpref and constancy over speed, it is required that, besides speed, all other factors that might affect braking performance are constant.
According to Lee (1976) drivers are able to control braking based on time-to-collision (TTC) information from the optic flow field (visual angle divided by the angular velocity). This would enable the driver to judge the moment to start braking and to control the braking process. The initiation of braking includes the timing of releasing the accelerator pedal after a deceleration of the lead vehicle has been detected as well as the interval between release of the accelerator pedal and the moment the foot touches the brake pedal. The control of braking includes braking intensity and the interval between the moment the brake is touched and the moment the maximum brake pressure is reached. Brake reaction time (BRT) is usually measured as the interval between the onset of the stimulus, such as the brake lights of the lead vehicle, and the moment the brake is touched. Therefore, BRT is an important measure for the initiation of braking. BRT to anticipated events is faster than to unexpected events (Johansson and Rumar, 1971) and the DHW at the moment the lead vehicle brakes has a strong effect on BRT (Brookhuis and De Waard, 1994; McKnight and Shinar, 1992;, Sivak et al., 1981). An important skill that has been associated with the initiation of braking relates to the perception of time-to-collision (TTC). TTC is defined as the time required for two vehicles to collide if they continue at their present speed and on the same path (see Van der Horst, 1990). TTC is computed as DHW/Vr, where Vr is the relative velocity or speed difference which must be larger than zero. While the ability to accurately perceive TTC is often mentioned as an important factor for judging the moment to start braking, studies that related TTC to actual braking are scarce. However, Van der Horst (1990) reported evidence that both the decision to start braking and the control of braking are based on TTC information available from the optic flow field. If TTC is an important factor in the initiation of braking, a relation is expected between the TTC at the moment the lead vehicles starts to brake (TTCt0) and BRT. Since TTCt0 is an index for criticality, it is expected that BRT is faster if criticality is higher, i.e. when TTCt0 is smaller. A consistent finding in the literature is an underestimation of TTC, especially at higher TTC’s. Schiff and Detwiler (1979) found substantial individual differences in the ability to give accurate judgments of TTC and an average underestimation of TTC of 39%. McLeod and Ross (1983) found that men gave higher and more accurate judgments than women. They reported an underestimation of TTC of 42%. Cavallo et al. (1986) found that experienced drivers produced better estimates of TTC than inexperienced drivers. They reported a general underestimation of 35%. Hoffmann and Mortimer (1994) found that both estimated TTC and standard deviation of estimated TTC were linearly related to actual TTC. They reported an underestimation of TTC of 20% on average, while other studies typically report an underestimation of around 40%. This better performance in TTC estimation was attributed by Hoffmann and Mortimer to the fact that in their experiment both vehicles were in motion, while other experiments typically measured estimated TTC to a static object. The studies on TTC estimation give substantive evidence for underestimation of TTC and for individual differences in the ability to accurately estimate TTC. Differences in ability to accurately estimate TTC are assumed to be expressed in the initiation of braking. BRT of drivers with better TTC estimation skills is assumed to covary more with TTCt0 than BRT of less skilled drivers. This is because better skilled drivers are more sensitive to variations in TTCt0. A hypothesis in the present study is that THWpref is related to sensitivity of the initiation of braking to TTC information. Drivers who are more sensitive to TTC are then better able to judge the moment to start braking, while drivers who are less sensitive to TTC information run a higher risk of starting to brake too late. This might result in a larger safety margin and thus a higher THWpref for these drivers.
Drivers may not only differ in the initiation of the braking response but also in the control of braking. Van der Horst (1990) studied the control of braking by the maximum deceleration reached by the driver (DECmax), the minimum TTC reached during braking (TTCmin), and the time difference between the moment of TTCmin (tTTCmin) and the moment of DECmax (tDECmax). TTCmin describes how imminent a collision has been during the braking process. According to Van der Horst, tDECmax gives an indication of the moment the driver knows a collision will be avoided. During the time before tTTCmin is reached, TTC is still decreasing resulting in increasing criticality. If tDECmax occurs some time before tTTCmin, criticality is still increasing at the moment the driver already relaxes the deceleration. If tDECmax occurs some time after tTTCmin is reached the driver keeps increasing the deceleration when it is no longer necessary. A close relation in time between tDECmax and tTTCmin then suggests a more efficient control of braking, where the control of braking is better tuned to the development of criticality in time. In the present experiment it will be examined whether THWpref is related to braking control as indicated by these measures. In addition to this, the maximum percentage brake pressed (MAXBR), and the interval between touching the brakepedal and the moment the brake pedal is pressed to the maximum value are measured. Furthermore, it will be examined whether the intensity of the braking reaction, measured by MAXBR, is more sensitive to TTC at the moment the lead vehicle starts to brake for short followers compared to long followers. A higher sensitivity of the intensity of braking to TTCt0 suggests that the braking response is more adapted to criticality at the moment the driver detects the braking of the lead vehicle.
In summary, the following hypotheses will be tested in the present experiment.
1) Preferred time-headway is constant over different speeds.
2) Preferred time-headway is consistent within individual drivers, but differs between drivers.
3) The initiation of braking, measured by BRT, is more strongly related to TTC at the moment the lead vehicle starts to brake for short followers compared to long followers. This is assumed to be related to differences in the ability to perceive TTC information.
4) Preferred time-headway is related to the intensity of braking and quality of braking control. The intensity of braking is measured by MAXBR while the quality of braking control is measured by the sensitivity of the braking intensity to criticality (as measured by TTC) and by the time difference between tTTCmin and tDECmax.
6.2 Method
Apparatus. The driving simulator of the Traffic Research Centre (TRC) was used for the present experiment. This fixed-based simulator consists of two integrated subsystems. The first subsystem is a conventional simulator composed of a car (a BMW 518) with a steering wheel, clutch, gear, accelerator, brake and indicators connected to a Silicon Graphics Skywriter 340VGXT computer. A car model converts driver control actions into a displacement is space. On a 2 x 2.5 meter projectionscreen, placed in front of the car mockup, an image of the outside world with a horizontal angle of 50 degrees is projected by a graphical videoprojector, controlled by the graphics software. Images are presented with a rate of 15 to 20 frames per second, resulting in a suggestion of smooth movement. The visual objects are buildings, roads, traffic signs, traffic lights and other vehicles. The sound of the engine, wind and tires is presented by means of a digital soundsampler receiving input from the simulator computer.
The second subsystem consists of a dynamic traffic simulation with interacting artificially intelligent cars. For experimental purposes different traffic situations can be simulated. The simulator is described in more detail elsewhere (Van Wolffelaar & Van Winsum, 1992 and Van Winsum & Van Wolffelaar, 1993). De Waard et al. (1994) reported a significant correlation (r=0.67) between THW measured in this simulator and ratings of preferred headway on a photo-preference test. In this test subjects rated preferred headway from a series of photographs with a view of a lead vehicle through the windscreen on a motorway. This supports the validity of this simulator for measuring car-following behaviour. Also, TTC has been reported to be directly available from the optic flow field without requiring speed and distance estimation. Since visual angle and angular velocity are identical in the simulator and in real world driving, this simulator was assumed to be a valid instrument for estimation of TTC.
Procedure. The circuit was made of two-lane roads with a lane-width of 3 meters. All roads had delineation with broken center lines and closed edge lines. Sideroads connected with an angle of 45 degrees to the main road, allowing other vehicle to merge in front of the simulator car and leave the main road. The length of the circuit was 7600 meter.
Before the experiment started, subjects completed a questionnaire on driving experience and age. After this, subjects were instructed to drive as if they had to reach their destination as soon as possible, without overtaking other vehicles, to drive safely and to respect the speed limit of 80 km/h. The experiment started after a ten minutes practice drive.
The experiment consisted of two parts, separated by a 15 minutes break. During the first part choice of headway was measured as a function of speed. Lead vehicles drove with a constant velocity of either 40, 50, 60 or 70 km/h. These different speeds are referred to as ‘speed conditions’. Subjects were required to drive around the circuit twice. The first drive around the circuit was used to familiarize subjects with other traffic. Vehicles merged in front of the simulator car, controlling their speed such that when the simulator car was 50 meter from the intersection, the lead vehicle was 100 meters in front of the simulator car.
During the second part of the experiment braking behaviour was measured. Vehicles merged in front of the simulator car in the same way as described above. Lead vehicles drove with a constant speed of either 60 or 50 km/h, resulting in two ‘braking conditions’. As soon as the lead vehicle was 50 meter in front of the simulator car (t0), it decelerated with -2 m/s², with its brakelights on, to a speed 20 km/h below the initial cruise speed. As soon as the simulator car reached this speed (40 of 30 km/h) the lead vehicle pulled up again. The two braking conditions (50 vs 60 km/h) were used to study within-subjects differences in braking as a function of TTCt0.
Data registration and analysis. Speed of the simulator car (V) and lead vehicle (Vlead) in m/s, distance headway (DHW) in meters, acceleration in m/s² and brake pedal signal expressed as percentage pressed were sampled with a frequency of 10 Hz. THW was calculated as DHW/V. TTC was calculated as DHW/Vr, with Vr being the relative speed (V-Vlead). Average THW was computed from the moment the simulator car and the lead vehicle drove with the same speed until the lead vehicle left the main road. THWpref was computed as the average THW over the four speed conditions.
In the second part of the experiment t0 represents the moment a DHW of 50 meters was reached. On t0 the lead vehicle started to brake. TTCt0 represents the TTC on t0. BRT was computed as tbr – t0, where tbr refers to the moment the brake pedal was pressed more than 5%. TTCbr represents TTC on tbr. On tmaxbr the maximum brake pressure, MAXBR, was reached. TTCmaxbr represents TTC on tmaxbr. Brake control movement time, (BCMT) was calculated as tmaxbr-tbr. The moment the maximum deceleration, DECmax, was reached is indicated as tDECmax. The moment the minimum TTC, TTCmin, was reached is indicated as tTTCmin. The absolute time difference between the moment of maximum deceleration and the moment of minimum TTC was computed as ABS(tDECmax-tTTCmin) and is referred to as tdif. Figure 1 shows a time history of braking, together with a number of dependent variables.
Analysis of covariance was applied to test differences in sensitivity to TTC as a function of THWpref. For this, differences between the two braking conditions were studied to test whether braking-related variables covaried with TTC. The difference in TTCt0 between braking condition 60 (lead vehicle braked from 60 to 40 km/h) and braking condition 50 (lead vehicle braked from 50 to 30 km/h) is expressed as dTTCt0. The differences in MAXBR and BRT between these two conditions are expressed as dMAXBR and dBRT. The regression coefficient of dBRT and dMAXBR on dTTCt0 is an indicator for the sensitivity of BRT and MAXBR to TTCt0. Higher sensitivity is expressed as a steeper slope (larger coefficient of regression). Analysis of covariance was used to test differences in slope as a function of THWpref.
Figure 1. Time-history of braking and dependent variables.
Effects of THWpref and braking conditions on dependent variables were tested with repeated measurements multivariate analysis of variance (MANOVA) with braking condition as a within-subjects factor.
Subjects. Fifty-four male subjects participated in the experiment. The average age was 29 years (sd. 8.12, range 19-48) with 65% of the subjects being younger than 30 years of ages. They had held a driving license for 9 years on average (range 1-29).
6.3 Results
Stability of THWpref. THW was not significantly affected by speed of the lead vehicle (F(135,3)= 1.27, p>=0.25), see figure 2. This supported the hypothesis that THW is constant over speed.
Figure 2. THW as a function of speed.
A high correlation between THW’s in the four speed conditions suggests consistent following behaviour. THW’s in all speed conditions were significantly correlated (p < 0.001), as shown in table 1. Additional evidence for consistency in following behaviour was obtained by considering each THW as an “item” in a (4-item) “following behaviour” test (Hendrickx, 1991). The test’s reliability index (Cronbach’s alpha) was found to be as high as 0.91. This was taken as evidence that all THW’s were an expression of a subjects’ general THWpref.
Table 1. Correlation matrix for THW’s in the four speed conditions
THW50 THW60 THW70
THW50 0.69**
THW60 0.76** 0.63**
THW70 0.67** 0.69** 0.60**
(** indicates p < 0.001).
THWxx : THW = time headway, xx = speed (km/h) of lead vehicle
These results supported the hypothesis that THW is consistent within drivers, but differs between drivers. For further analysis, the average THW over the four speed conditions was computed as THWpref. Based on the frequency distribution of THWpref, three groups of equal size were created. These groups are referred to as ‘THWpref groups’. These groups served as a between-subjects factor in subsequent analyses. Four subjects were not included because they failed to reach a stable THW in the 70 km/h condition. Table 2 shows number of subjects, average THW and standard deviation of THW for the THWpref groups.
Table 2. Size, mean THW and sd of THW for THWpref groups
THWpref group N mean THW(s) sd of THW
short 17 0.67 0.19
medium 16 1.08 0.09
long 17 1.52 0.27
Braking responses. Two additional subjects failed to display a clear brake response in one of the two braking conditions. Therefore, the total number of subjects in the analyses was 48.
Figure 3 shows the time history of TTC for the three THWpref groups in both braking conditions. Four datapoints are displayed. The first point represents TTCt0, the second TTCbr, the third TTCmin and the fourth TTCmaxbr. The time interval between TTCt0 and TTCbr represents BRT, while the time interval between TTCbr and TTCmaxbr represents brake control movement time (BCMT).
The initiation of braking. Table 3 gives the MANOVA effects of THWpref group and braking condition on variables related to the initiation of braking.
TTCt0 and TTCbr were significantly smaller, while the relative speed (Vr) at t0 and tbr was significantly larger for subjects with a smaller THWpref. At t0 long followers already had lowered their speed to a greater extent than short followers. BRT was not significantly different for short followers compared to long followers.
Table 3. Effects of THWpref group and braking condition on variables related to the
initiation of braking (F-statistics)
Effect
Dependent THWpref group Braking con. interaction
TTCt0 8.57** 0.16 0.52
TTCbr 18.05** 0.59 1.14
Vrt0 15.83** 6.79** 1.90
Vrbr 24.72** 8.07** 1.26
BRT 0.62 20.57** 1.01
THWpref group effect : df = 45,2;
Braking condition effect : df = 45,1;
Interaction effect: df= 45,2
** = p < 0.01
Figure 3. Time history of TTC as a function of THWpref groups for braking
condition 50 (left) and braking condition 60 (right).
Braking condition had a significant effect on BRT. BRT was faster in the condition where the lead vehicle decelerated from 50 to 30 km/h. This was accompanied by a larger relative velocity on t0 and tbr in this condition. None of the interactions were significant.
Table 4 presents the correlations of BRT with TTCt0 and TTCbr.
Table 4. Correlation of BRT with TTC in braking condition 50 and 60
Condition 50 Condition 60
TTCt0 0.66** 0.61**
TTCbr 0.01 -0.21
** = p < 0.01
The correlations of BRT with TTCt0 were highly significant. The correlations of BRT with TTCbr were not significant. Thus, BRT decreased as TTCt0 decreased for both braking conditions. This was taken as evidence that the initiation of braking, indicated by BRT, was sensitive to TTC information as an index for criticality. The significant effect of THWpref group on TTCt0 and the absence of a significant effect of THWpref on BRT suggests the TTC criterion for initiating the braking response is lower for short followers.
One of the hypotheses was that the initiation of braking was more sensitive to TTC for short followers compared to long followers. Sensitivity was expressed as the extent to which BRT covaries with TTCt0. Analysis of covariance revealed that dBRT was dependent on dTTCt0 (F(42,1) = 14.77, p<0.001). This means that, within Ss, a smaller TTCt0 resulted in a faster BRT. Since dBRT was computed as the difference between BRT’s in the two braking conditions, the effect of braking condition on BRT is partly explained by within-subjects differences in TTCt0. Thus, the initiation of the braking response was very sensitive to between-subjects as well as within-subjects variations of TTC at t0. The slope of the regression of dBRT on dTTCt0 represents the sensitivity of BRT for TTCt0. The magnitude of the slope as well as the correlation coefficients are shown in table 5 for the three THWpref groups. Although the correlation and regression coefficients suggest a stronger relation between dBRT and dTTCt0 for short followers, this was not confirmed by analysis of covariance because the interaction with THWpref groups was not significant (F(42,2)=1.62, p=0.210). Thus, the hypothesis that short followers are more sensitive to TTC information in the initiation of the braking response was not confirmed.
Table 5. Correlation and sensitivity of BRT to TTCt0
THWpref group R coefficient of regression
short 0.72** 0.19
medium 0.63** 0.12
long 0.51* 0.06
** = p < 0.01; * = p < 0.05
The control of braking. Table 6 shows the effects of THWpref group and braking condition on variables related to the control of braking.
Table 6. Effects of THWpref group and braking condition on variables related to
the control of braking (F-statistics)
Effect
Dependent THWpref group Braking con. interaction
TTCmin 18.78** 0.30 1.23
TTCmaxbr 16.13** 0.01 0.51
BCMT 0.86 2.01 2.19
MAXBR 6.24** 7.12** 0.33
DECmax 4.54* 2.49 0.02
tdif 3.88* 0.75 0.09
THWpref group effect : df = 45,2
Braking con. effect : df = 45,1
interaction effect : df = 45,2
** = p < 0.01; * = p < 0.05
The minimum TTC during braking (TTCmin) was significantly smaller for short followers, as was the TTC at the moment the brake was pressed to the maximum (TTCmaxbr). Short followers generated a more intense brake reaction than long followers : MAXBR was significantly larger for short followers. Also DECmax was larger for short followers. This supported the hypothesis that short followers differ from long followers in the intensity of the braking response. BCMT, the time within which the brake maximum was reached, was not affected by THWpref groups.
The absolute time difference between tDECmax and tTTCmin, tdif, was seen as an indicator for the efficiency of braking control. There was a significant effect of THWpref group on this measure. Tdif was smaller for short followers compared to long followers, see figure 4. This supported the hypothesis that short followers differ from long followers in the quality of braking control.
In order to test the sensitivity of the intensity of braking to criticality, an analysis of covariance was performed on dMAXBR (differences in MAXBR between the two braking conditions) as a function of dTTCt0 (differences in TTCt0 between the two braking conditions), with THWpref group as a between-subjects factor. A smaller TTCt0 generally resulted in a larger MAXBR (F(42,1)=22.37, p=0.000). This means that the intensity of the braking reaction strongly depended on TTCt0. The interaction with THWpref group was significant as well (F(42,2) = 4.63, p=0.015). In table 7 it can be seen that MAXBR decreases more as a function of TTCt0 for short followers compared to long followers. The differences in slope indicate that the intensity of the braking response is more sensitive to TTCt0 for drivers with a smaller THWpref, although the correlations between dMAXBR and dTTCt0 are comparable for the three groups.
This again supported the hypothesis that short followers differ from long followers in the quality of braking control.
Figure 4. Difference between tTTCmin and tDECmax as a function of THWpref groups
and braking condition.
Table 7. Correlation and sensitivity of MAXBR to TTCt0
THWpref group R coefficient of regression
short -0.69** -6.52
medium -0.57* -3.13
long -0.58* -1.13
** = p < 0.01; * = p < 0.05
6.4 Discussion and conclusions
The hypothesis that THWpref is consistent within the driver and the hypothesis of constancy of THWpref over speed during steady-state car-following were confirmed for the range of speeds examined in the present experiment. The brake reaction of drivers was analyzed in order to investigate whether differences in THWpref during steady-state car-following are related to differences in braking performance and underlying skills. Since THW during steady-state following represents the time available to the driver to give an appropriate braking response in case the lead vehicle decelerates, THW may be the result of an adaptation of the driver to individual differences in braking competence. Braking performance was assumed to be related to the ability to perceive time-to-collision (TTC) and the ability to generate an efficient braking response, depending on the criticality of the situation. The initiation of braking, as measured by brake-reaction time (BRT) was strongly related to TTC at the moment the lead vehicle started to brake (TTCt0 ) and thus to criticality. This strong relation was apparent between subjects as well as within subjects. This conforms with the suggestion in the literature that TTC information is used by the driver to judge the moment to start braking. However, drivers with a smaller THWpref during steady-state following start to brake at a lower TTC, i.e. when the criticality is higher. This suggests a different TTC criterion for the initiation of braking, depending on preferred time-headway. Although the initiation of braking was very sensitive to TTC information, there were no differences between short followers and long followers in sensitivity of BRT to TTCt0. Thus, the hypothesis that differences in THWpref during steady-state following are related to the ability to accurately perceive TTC was not confirmed since a differential ability related to TTC perception was assumed to be expressed in BRT.
The minimum TTC during braking was smaller for short followers. This indicates that a collision was more imminent for short followers than for long followers. There were however differences in the control of braking. Firstly, short followers pressed the brake pedal to a higher maximum, resulting in a larger deceleration. Secondly, for short followers the intensity of the braking response was more strongly dependent on the criticality at the moment the lead vehicle started to brake. This suggests that the intensity of braking is at least partly programmed before response execution and confirms the suggestion in the literature that TTC information is used in the control of braking. Short followers are then better able to program this response to the appropriate level, depending on criticality. However, at the moment the lead vehicle starts to decelerate, the driver does not know how strong it will decelerate and for how long. Therefore, visual feedback during the braking maneuver is important for continuously adapting the braking response to the required level. The programmed braking intensity may then have to be adjusted to another level depending on the development of criticality in time. The moment of maximum deceleration (tDECmax) was assumed to indicate when the driver knows a collision will be avoided. A closer correspondence in time with the moment of minimal TTC (tTTCmin) suggests a better ability to adjust the control of braking to requirements. In this respect, the third difference was found between short en long followers. For short followers the absolute difference between tDECmax and tTTCmin was smaller, indicating a more efficient braking control where the timing and intensity of braking is better tuned to the development of criticality in time during the braking process.
These results suggest differences in skills related to the response programming and response execution of braking between short and long followers. On the other hand, the absolute levels of TTCt0 were different between THWpref groups. An alternative explanation may then be that short followers had to generate more efficient braking responses that were better tuned to criticality because criticality was higher for them to begin with. In other words, they may have been forced to perform better. Also, since TTC during the braking process was lower for short followers, and, as discussed in the introduction, the estimation of TTC is more accurate for smaller TTC’s, the differences between short and long followers in braking control may have been caused by a more accurate estimation of TTC by short followers. In both cases, however, the sensitivity of BRT to TTCt0 is expected to be higher too for short followers. Since this was not the case, the evidence presented suggests differences in skills related to the programming of the intensity of braking and the control of braking between short and long followers.