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 THW_pref (preferred time head­way).

Evans and Wasie­lewski (1982) found that drivers with a larger THW_pref 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 THW_pref 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 THW_pref 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 THW_pref. Fuller (1981) stu­died THW of truck drivers in convoy situations. During the late shift, cove­ring a large period of driving in the dark, THW_pref 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 THW_pref; fatig­ue and marijuana increase THW_pref which may be a reflecti­on of an adaptation of THW to adverse effects on the brake reaction, whereas alcohol decreases THW_pref, 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 THW_pref 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, THW_pref must be consis­tent within the individual driver, while it differs between drivers as a function of operational skill. Since THW_pref represents the ultimate reaction time in case of a deceleration by the lead ­ve­hicle, THW_pref 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 THW_pref, 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 THW_pref is constant over different speeds.

In the present study, an important hypothesis is that THW_pref is constant over speed and consistent within the driver. In order to test consistency of THW_pref 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/V_r, where V_r 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 (TTC_t0) and BRT. Since TTC_t0 is an index for criti­cality, it is expected that BRT is faster if criticality is higher, i.e. when TTC_t0 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 TTC_t0 than BRT of less skil­led drivers. This is because better skilled dri­vers are more sensitive to varia­tions in TTC_t0. A hypo­thesis in the present study is that THW_pref 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 THW_pref 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 (DEC_­max), the mini­mum TTC reached during braking (TTC_mi­n), and the time differen­ce be­tween the moment of TTC_min (t_TTCmin) and the moment of DEC_max (t_DECmax). TTC_min des­cribes how immi­nent a colli­sion has been during the braking process. According to Van der Horst, t_DEC­max gives an indi­cation of the moment the driver knows a collision will be avoided. During the time before t_TTCmin is reached, TTC is still decreasing resulting in increasing criticality. If t_DECmax occurs some time before t_TTCmin, critica­lity is still incre­asing at the moment the driver already relaxes the dece­lerati­on. If t_DECmax occurs some time after t_TTCmin is reached the driver keeps increasing the deceleration when it is no longer necessary. A close relation in time between t_DECmax and t_TTCmin 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 THW_pref 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 TTC_t0 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 t_TTCmin and t_DECmax.

 

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 TTC_t0.

 

Data registration and analysis. Speed of the simu­lator car (V) and lead vehicle (V_lead) 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-V_lead). 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. THW_pref 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. TTC_t0 repre­sents the TTC on t₀. BRT was compu­ted as t_br – t₀, where t_br refers to the moment the brake ­pe­dal was pres­sed more than 5%. TTC_br repre­sents TTC on t_br. On t_maxbr the maximum brake pressu­re, MAXBR, was reached. TTC_maxbr represents TTC on t_maxbr. Brake control move­ment time, (BCMT) was calcu­la­ted as t_maxbr-t_br. The moment the maxi­mum dece­lerati­on, DEC_max, was reached is indica­ted as t_DECmax. The moment the minimum TTC, TTC_min, was reached is indicated as t_TTCmin. The abso­lute time difference between the moment of maximum dece­le­ration and the moment of minimum TTC was computed as ABS(t_DEC­max-t_TTCmin) and is referred to as t_dif. 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 THW_pref. For this, diffe­rences between the two braking conditions were studied to test whe­ther braking-related variables covaried with TTC. The diffe­ren­ce in TTC_t0 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 dTTC_t0. 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 THW_pref.

 

 

Figure 1. Time-history of braking and dependent varia­bles.

 

Effects of THW_pref 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 THW_pref. 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 THW_pref.

 

 

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 THW_pref. Based on the frequency distribution of THW_pref, three groups of equal size were created. These groups are referred to as ‘THW_pref 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 THW_pref groups.

 

Table 2. Size, mean THW and sd of THW for THW_pref groups

 

THW_pref 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 THW_pref groups in both braking conditions. Four data­points are dis­played. The first point represents TTC_t0, the second TTC_br, the third TTC_min and the fourth TTC_maxbr. The time interval between TTC_t0 and TTC_br repre­sents BRT, while the time inter­val between TTC_br and TTC_maxbr repre­sents brake control movement time (BCMT).

 

The initiation of braking. Table 3 gives the MANOVA effects of THW_pref group and braking condition on variables related to the initiation of braking.

TTC_t0 and TTC_br were significantly smaller, while the relative speed (Vr) at t₀ and t_br was signi­ficantly larger for subjects with a smaller THW_pref. 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 THW_pref group and braking condition on variables related to the

initiation of braking (F-sta­tis­tics)

 

Effect

Dependent               THW_pref group           Braking con.               interac­tion

 

TTC_t0                          8.57**                      0.16                           0.52

TTC_br                        18.05**                      0.59                           1.14

Vr_t0                           15.83**                      6.79**                       1.90

Vr_br                           24.72**                      8.07**                       1.26

BRT                            0.62                          20.57**                      1.01

 

THW_pref 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 THW_pref 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 t_br in this condi­ti­on. None of the interac­tions were signi­ficant.

Table 4 presents the correlations of BRT with TTC_t0 and TTC_br.

 

Table 4. Correlation of BRT with TTC in braking conditi­on 50 and 60

 

Condition 50     Condition 60

 

TTC_t0            0.66**               0.61**

TTC_br            0.01                   -0.21

 

** = p < 0.01

 

The correlations of BRT with TTC_t0 were highly signifi­cant. The correlations of BRT with TTC_br were not signi­ficant. Thus, BRT decreased as TTC_t0 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 THW_pref group on TTC_t0 and the absen­ce of a significant effect of THW_pref 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 TTC_t0. Analysis of covariance revealed that dBRT was depen­dent on dTTC_t0 (F(42,1) = 14.77, p<0.001). This means that, within Ss, a smaller TTC_t0 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 TTC_t0. 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 dTTC_t0 repre­sents the sensi­tivity of BRT for TTC_t0. The magnitu­de of the slope as well as the correlation coeffi­cients are shown in table 5 for the three THW_pref 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 THW_pref 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

 

THW_pref 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 THW_pref group and braking condi­tion on variables rela­ted to the control of braking.

 

Table 6. Effects of THW_pref group and braking condition on variables related to

the control of braking (F-statis­tics)

 

Effect

Dependent               THW_pref group           Braking con.               interac­tion

 

TTC_min                      18.78**                      0.30                            1.23

TTC_maxbr                   16.13**                      0.01                            0.51

BCMT                        0.86                          2.01                            2.19

MAXBR                    6.24**                      7.12**                        0.33

DEC_max                     4.54*                         2.49                            0.02

t_dif                              3.88*                         0.75                            0.09

 

THW_pref 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 (TTC_min) was signi­ficantly smaller for short followers, as was the TTC at the mo­ment the brake was pressed to the maximum (TTC_maxbr). Short followers generated a more intense brake reaction than long followers : MAXBR was signifi­cantly larger for short followers. Also DEC_max 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 THW_pref groups.

The absolute time difference between t_DECmax and t_TTCmin, t_dif, was seen as an indicator for the effi­ciency of bra­king con­trol. There was a significant effect of THW_pref group on this measure. T_dif 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 dTTC_t0 (diffe­rences in TTC_t0 between the two braking conditi­ons), with THW_pref group as a between-sub­jects factor. A smaller TTC_t0 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 TTC_t0. The inter­acti­on with THW_pref 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 TTC_t0 for short followers compared to long followers. The differen­ces in slope indicate that the intensity of the bra­king res­ponse is more sen­si­tive to TTC_t0 for drivers with a smaller THW_pref, 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 t_TTCmin and t_DECmax as a functi­on of THW_pref group­s

and braking condi­tion.

 

 

Table 7. Correlation and sensitivity of MAXBR to TTCt0

 

THW_pref 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 THW_pref is consistent within the driver and the hypothesis of constancy of THW_pref 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 THW_pref 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 (TTC_t­0 ) 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 THW_pref 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 TTC_t0. Thus, the hypothesis that diffe­rences in THW_pref 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 (t_DECmax) was assumed to indicate when the driver knows a collisi­on will be avoi­ded. A closer corres­pondence in time with the moment of minimal TTC (t_TTCmin) 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 t_DECmax and t_TTCmin 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 TTC_t0 were different between THW_pref 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 TTC_t0 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.