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EXPERIMENT 4: Time-headway in car-following and operational performance during unexpected braking

EXPERIMENT 4: Time-headway in car-following and operational performance during unexpected braking

This is chapter 7 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:


The relation between choice of time-headway during car-follo­wing and the quality of braking skills was studied in a driving simulator. The theoreti­cal perspective was that individual differen­ces in behaviour on the tactical level may be related to skills on the operational level of the driving task via a process of adaptation. In a sample of 16 young and middle-aged experienced drivers independent asses­sments were made of preferred time-headway and braking skill. Starting from modern theories of visual-motor learning, braking skill was analyzed in terms of a reaction time component, an open-loop visual-motor component, and a closed-loop visual-motor component involving the precise adjustment of braking (timing and force) to the situation. The efficiency of the visual-motor component of braking was a strong and significant predictor of time-headway in such a way that more efficient braking indicated a shorter preferred time-headway. This result appears to support the adaptation theory on an individual level.


7.1 Introduction

For many years it has been realized that individuals who have very good driving skills in the sense of great fluency and agility in performing the basic driving tasks of visual orientation and vehicular control, are not necessarily safe drivers (Williams and O’Neill, 1974; Evans, 1991). Traf­fic safety de­pends on what the driver will do in a given situa­tion and not on the maximum level of performance (Nääta­nen and Summala, 197­6) or, as Evans (1991) puts it, what is cruci­al is not how the driver can drive but how the driver does drive. The failure of driver skill models in explaining accident involvement has been attribu­ted to various adaptive mechanisms. For example, drivers with poor skills might compensate by driving slower, or, the other way around, very skilled drivers might tend to drive very fast. Because traditional skill models do not incorporate such compensatory mechanisms they are not suitable for assessing and understanding individual differences in the safety of traffic behaviour.

A solution to this problem may be the application of the hierarchical framework discussed by Michon (1985) to driving behaviour (Ranney, 1994). In this framework driving is viewed as a hierarchically organized set of tasks on the strategic, tactical and operational level. On the strategic level trip planning and the selection of trip goals and route occur. The tactical level includes, for in­stance, choice of speed on straight roads and in curves and choice of headway in car-follo­wing. Steering and control­ling the timing and intensity of braking are activities on the operational level. Traditionally the study of driving skill was aimed as the efficiency of performance on the operational level. However, in this article the importance of the interrelation between behaviour on the operational and the tactical level is stressed.  In this framework the adaptation problem may be understood as a compensation on the tactical and strategic levels of the driving task for individual differences in skills on the operational level (Brouwer et al., 1988). This adaptation theory has been used as an explanati­on for the relatively safe driving records of functionally impaired drivers. The link with driver safety now becomes clear. Driver safety may be defined in terms of the relationship between operational level skills and choices and preferences on the tactical level.

Recently, Van Winsum and Heino (1996) found some evidence with regard to the relationship between individual differences in operational level skills and tactical behaviour which appears to fit an adaptation theory on the individual level. In a study on time-headway in car-following, they found evidence for a relationship between braking skill and choice of time-headway. Since time-headway (THW), defined as the time interval between two vehicles in car-following, represents the time availa­ble to reach the same level of deceleration as the lead vehi­cle in case it brakes, they studied whether choice of THW is related to time-critical skills underlying braking performance. THW was constant over the range of speeds studied. Drivers were con­sis­tent in their choice of THW, evidencing systematic individual diffe­rences in choice of THW during car-following. The results sugge­sted differen­ces in skills related to the motor control of braking as a function of preferred time-headway. What was lacking in this study was a specific model of the braking skills so that it was difficult to pinpoint in which respect drivers with short THW differed from those with long THW. In the present study a model for the decomposition of perceptual-motor processes in braking is proposed and individual differen­ces in the effi­ciency of such processes are related to the choice of time-headway in a free field situation.

Braking for a decelerating lead vehicle requires substan­tial perceptu­al-motor skills because of the dynamic task environ­ment. Lee and his co-workers have shown in a number of publications that a perceptu­al varia­ble, named tau, which is the inver­se of the expansion of the retinal image, is used in action. This variable directly specifies time-to-contact in dynamic situations. Thus, perception is assumed to guide action and this relation between tau and action has been established in a number of different tasks such as long jum­pers running up to a take-off board (Lee et al., 1982) and jum­ping up to hit a falling ball (Lee et al., 1983). Also, Bootsma and Van Wieringen (1988) found that time-to-contact plays an important role in the guidance of actions of an experienced table tennis player. In car driving and braking the equivalent of time-to-contact is time-to-collision (TTC). Lee (1976) suggested that TTC information is used by the driver in the initia­tion and control of braking. Van Winsum and Heino found that the initiation and control of braking for a decele­rating lead vehicle was very sensitive to TTC information. The timing of the initiation of the braking response was equally sensitive to TTC for short follo­wers and long follo­wers. However, short followers were more efficient in the control of braking, braked harder and adju­sted the inten­sity of braking better to the critica­li­ty (as measured by TTC) at the moment the lead vehicle started to decelerate, compared to long followers. So, it appeared that the difference between the short and long followers was in the execution of the motor response.

­   Substantial individu­al differen­ces in the ability to accu­rate­ly estimate TTC have been reported in the literature (for instance see Schiff and Detwiler, 1979). A general finding is that TTC is unde­res­timated with a constant proporti­on. TTC esti­mation is more accurate for smaller TTC’s, see for in­stance, McLeod and Ross (1983), Cavallo et. al (1986), Hoffm­ann and Mortimer (1994). Given this evidence, the re­sults of Van Winsum and Heino could have been af­fected by the fact that the TTC at the moment the lead vehicle started to brake (t0) was smaller for short follo­wers alt­hough the distan­ce at t0 was the same for all subjects. This was caused by a higher speed on average for short follo­wers on t0. Theoreti­cally, short followers were thus in a positi­on to estima­te TTC more accurately. In additi­on, since TTC was smaller for short follo­wers they may have been forced to brake harder and more accu­ra­tely. In order to control for effects of diffe­rential criti­cality and accu­racy of TTC estimation, all dri­vers will be subjec­ted to the same high level of criticali­ty in the present study.

In dynamic situations such as braking for a decele­rating lead vehicle, following the initial reaction of releasing the accelerator, the motor response is assumed to consist of two phases, i.e. an open-loop and a closed-loop phase. We attempt to separately assess these three processes by analyzing the braking response in terms of Reaction time (RT), the Brake Initiation Movement Time (BIMT) and the Brake Control Movement Time (BCMT) (see Figure 1). Starting from the adaptation theory we expect that the quality of these processes is related to preferred time-headway: specifically we hypothesize that preferred time-headway (behaviour on the tactical level) can be predicted from the BIMT and the BCMT (performance on the operational level). To be able to assess the reliability of preferred THW as an indicator of a stable individual characteristic, it is measured at four different speeds. It is expected that the results of Van Winsum and Heino concer­ning the con­sistency of THW and the constancy of THW over speed will be replica­ted.

Reaction time (RT) represents the interval between stimulus presentation and movement initiation. Several information processing stages including response selection and response preparation, together called motor program­ming, occur within this interval. Motor programming time, as a part of RT, is assumed to be related to temporal complexity and organization of the movement to be executed, but not with physical task dimensions such as distance (Kerr, 1978). This suggests that the time associated with parameter setting for a generalized motor program does not vary for different parameter values. Thus, TTC is not expected to affect RT because TTC is assumed to determine the speed parameter value for the generalized motor program.

The Brake Initiation Movement Time (BIMT) is used to operationally define the open-loop phase under the control of the genera­lized motor program for braking of which the speed parameter is set by TTC informa­tion. During this phase the influence of feedback is absent. Because of the time charac­teristics of the braking response the open-loop phase is defined here as the interval between the moment the driver withdraws the foot from the accele­rator pedal and the moment the brake pedal is touched. The duration of this phase is then assumed to be depen­dent on TTC at the moment the driver de­tects the deceleration of the lead vehicle or at the moment the driver decides to brake.

Error detection and error cor­rection are assumed to take place during the closed-loop phase, operationally defined here as the Brake Control Movement Time (BCMT). This is the inter­val between the moment the brake pedal is touched and the moment the brake maximum is reached. Since the environmen­tal goal of the movement is to avoid a collision and to keep sufficient dis­tance to the lead vehicle, TTC infor­mation is possibly used during this feedback process. Accor­ding to Hayes and Marteni­uk (1976) movement control complexity can be viewed as the informa­tion load imposed on the performer by the necessity to detect and correct movement errors. For more skilled operators movement time decreases because of a decrease in the number of movement corrections (Keele, 1968). During the closed-loop phase of the braking response, movement time is then expected to be related to the number of movement correcti­ons.


7.2 Method


Subjects. Sixteen (8 male, 8 female) subjects participated in the experi­ment. The average age was 33.6 years (sd. 6.1, range 22-47). They had held a driving license on average for 11.6 years (range 2-27). The average annual kilometrage was ap­proximately 10083 kilometers (range 1500-30000).

Apparatus. The experiment was performed in the Traffic Research Centre (TRC) fixed-based driving simulator. It consists of a car (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 in space. On a 2 x 2.5 meter projection s­creen, 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 3D-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 artificially intelligent traffic. The sound of the engine, wind and tires is presented by means of a digital soundsampler recei­ving input from the simulator computer. The simula­tor is described in more detail elsewhere (Van Wolffe­laar & Van Winsum, 1992 and Van Winsum & Van Wolf­felaar, 1993).

Procedure. A circuit of two-lane roads (lane-width 3 meters) with broken center lines and continuous edge lines was used. Since the subjects had participated in another simulator experiment not involving car-follo­wing prior to the present experiment, they were already sufficiently practi­ced. First, preferred time-headway was measured as a function of different speeds. Subjects were instructed not to overtake other vehicles, to respect the speed limit of 80 km/h and to follow other vehicles at a safe distance. While driving, the sub­jects approached vehicles that were parked on the right shoulder. At a distance of 200 meter these vehicles accelerated to a fixed cruising speed and merged in front of the simulator car. There were four of these trials that differed in the cruising speed of the lead vehi­cles. The order of speeds was 60, 40, 70 and 50 km/h for all subjects (speed condition). In every trial, time-headway was measured during 5 minutes.

After this, a vehicle, driving with a speed of 60 km/h, was approached. Prompted by the experi­menter the subjects were asked to rate the danger of the present headway on a scale from 1 to 5. Then they were requested to drive a bit closer and again asked to give a rating. This continued until a time-headway of 0.6 seconds was reached. At that moment the lead vehi­cle suddenly decelerated unexpectedly from 60 km/h to 30 km/h with a decelera­tion of 6 m/s². This constitutes the braking condition. The aim of this procedure was to ascertain a fixed time headway at the moment the lead vehicle started to brake for all subjects.

Data registration and analysis. Speed, brake and accele­rator pedal signal (percenta­ge pres­sed), distance-headway, time-headway and time-to-collision were sampled with a fre­quency of 10 Hz. Average THW was computed, for the four trials in the speed condition, from the moment the simula­tor car reached the same velocity as the lead vehicle until the lead vehicle left the road. THW’s were averaged over the four speed trials to compute preferred time-headway (THWpref). The effect of speed on THW was tested with multiva­riate analysis of variance with repeated measurements.

Figure 1 shows the time-history of braking together with a number of dependent variables. In the braking condition, t0 represents the moment a THW of 0.6 was reached. On t0 the lead vehicle started to brake. The moment the acce­lerator pedal was 5% less than the position on t0 represents tacc. Reaction time (RT) was calculated as the interval between t0 and tacc. The moment the brake pedal was pressed more than 5% is indicated as tbr. The interval between tacc and tbr represents the open-loop phase of the movement and is referred to as brake initiation movement time (BIMT). The moment the maximum brake position was reached is indicated by tmaxbr. The duration of the closed-loop phase, brake con­trol movement time (BCMT), was computed as the inter­val between tbr and tmaxbr. Move­ment time (MT) was compu­ted as the sum of BIMT and BCMT. TTC on tacc is referred to as TTCacc.

During the closed-loop phase the brake pedal is pressed. A typical time-history of this is presented in figure 2. It shows the percentage at which the brake pedal is pressed toge­ther with the velocity of pressing the brake pedal and accelera­tion of brake pedal signal as a function of time. The number of decelerations in this signal reflect the number of movement (speed) corrections. The effect of driver reactions to braking by the lead vehicle on THWpref were tested with multiple regression analysis.


Figure 1. Time-history of the braking maneuver. Vlead represents speed of lead vehicle in m/s, accel represents accelerator pedal position.



Figure 2. Brake pedal signal, velocity and acceleration of bra­king as a function of time during the closed-loop phase.


7.3 Results

Before testing the main hypothesis a preliminary assessment is made of the reliability of THWpref.

Reliability of preferred THW. THW was not significantly affected by the speed of the lead vehicle (F(3,15)=1.20, p>=0.352), where­as distance headway significantly increased with speed (F(3,15)=­20.20, p<0.00­01). This means that THW was constant over speed. The test’s reliability index (Cron­bach’s alpha) for the four measurements of THW over different speeds was 0.89, while the standardized alpha was 0.90. This was taken as eviden­ce that all THW’s are an expression of a subjects’ general preferred THW. THWpref was computed as the average THW over the four speed trials.

The correlations of THWpref with annual kilometrage and number of years licensed were not statistically significant (R=0.13 resp. -0.02). This means that preferred time-headway was not related to driving experience. Also, none of the braking-related variables correlated significantly with driving experience.


The relationship between preferred THW and braking skill. It is first tested whether the duration of the open-loop phase is determined by TTC after the RT interval and whether the duration of the closed-loop phase is affected by the number of movement corrections as predicted by the braking model presented in the introduction. The regression coefficients (Beta weights) are presented in table 1.


Table 1. Effects of regression analyses of TTCacc and movement corrections on

the duration of the open-loop (BIMT) and closed-loop (BCMT) phases.


Dependent   Independent       R(=Beta)  F      


BIMT           TTCacc                0.81          27.11 **

BCMT          nr corr               0.83          30.09 **


nr corr = number of movement corrections

** = p < 0.01;


From inspection of table 1 it appears that the duration of the open-loop phase was strongly determined by TTC at the moment the accelerator was released. The duration of the closed-loop phase was strongly determined by the number of movement corrections. This confirms the model of braking discussed in the introduction.

It was then tested whether operational braking performance affected choice of time-headway. For this the regressions of RT, BIMT and BCMT on THWpref were analyzed, controlling for the effects of TTCacc and number of movement corrections. In this way the direct effects the independent variables on THWpref could be established. Table 2 lists the effects of RT, BIMT and BCMT on THWpref. This table should be read as follows. The first column lists the dependent variable. The second column lists the indepen­dent variables in order of inclusion in the regressi­on equati­on. R represents multiple correlation after addition of the independent variable, and F represents the accompany­ing F statistic for the whole regression equation. Beta and T represent the Beta weight and t value when all dependent variables are included in the equation.


Table 2. Effects of multiple regression analyses of brake-related times on THWpref.


Dep              Indep         R                F               Beta         T           


THWpref       RT             0.31         1.50          -0.31                  -1.23N.S.


THWpref       BIMT        0.53         5.37          1.12                  3.25**

TTCacc       0.68         5.64          -0.74                  -2.13*


THWpref       BCMT       0.49         4.39          0.49                  2.09*

nr corr      additional contribution too small

for inclusion

THWpref       MT            0.67          11.24         0.67                  3.35**


* = p < 0.05; ** = p < 0.01; N.S. = not significant


Figure 3. Path diagram with partial regression coefficients.

*=p< 0.05, **=p< 0.01, ns=not significant.


There was no significant effect of RT on THWpref. The effect of BIMT on THWpref, with TTCacc controlled for, was statistically significant. This means that subjects with a faster open-loop motor reaction preferred a smaller THW. This was not simply caused by a smaller TTCacc for subjects with a smaller THWpref, since there also was a significant direct effect of TTCacc on THWpref indicating that drivers with a larger TTCacc tended to have a smaller preferred time-headway. The effect of BCMT on THWpref also was statistically significant. There was no significant direct effect of number of movement corrections on preferred time-headway. This means that the faster closed-loop motor response of drivers with a smaller preferred time-headway was caused by a smaller number of movement corrections. The effects of total movement time (MT) on THWpref also was statistically significant. The path diagram of dependent variables on preferred time-headway is presented in figure 3.


7.4 Discussion and conclusions

The hypothesis that preferred time-headway is consistent within the driver and constant over different speeds during steady-state car-following was confirmed for the range of speeds (40, 50, 60, 70 km/h) examined in the present experi­ment. This replicates the results of Van Winsum and Heino (1996).

Reaction time, i.e. the difference between the moment the lead vehicle started braking and the moment the accelerator was released, was not related to preferred time-headway. This confirms the results of Van Winsum and Heino that short follo­wers do not differ from long followers in perceptual mechanisms related to time-to-collision (TTC) detecti­on. The open-loop phase of the motor response was very sensitive to TTC, and especially to TTC at the moment the foot was released from the accelerator pedal. This suggests that as soon as the driver detects the deceleration of the lead vehicle, the speed parameter of the generalized motor program is set as a function of TTC. Drivers who moved their foot faster to the brake pedal had a smaller preferred time-headway. The direct effect of TTC at the moment the accelerator was released on preferred time-headway indicates that the effect of the duration of the open-loop phase on preferred time-headway was not caused by a smaller TTC for short followers. This suggests that drivers with a smaller preferred time-headway program the movement speed of the foot to a higher level than drivers with a longer preferred time-headway. This suggests differences in the transfor­mation of perceptual information into the adjustment of the speed parame­ter.

The duration of the closed-loop phase of the motor response was strongly related to the number of movement corrections. This confirms the expectations, discussed in the introduction, of separate influences on the duration of the open-loop and the closed-loop phases. Subjects who moved their foot faster to the maximum during the closed-loop phase and who exhibited fewer movement corrections had a smaller preferred time-headway. This suggests a higher skill level in these subjects. Subjects with a larger preferred time-headway appear to be more uncertain about the requi­red braking response.

An important result in the present experi­ment was the strong effect of total movement time on preferred time-headway. This strengthens the conclusion that short and long followers differ in both the open- and closed-loop phases of movement. Short follo­wers may be more sensitive to the task requirements in emergency braking situations. Short and long followers differ in the efficiency of the control of braking. This was also found in Van Winsum and Heino, but there results could have been affected by differences in absolute levels of TTC between drivers with different preferred time-headway.

Together, the results suggest that individual differences in choice of time-headway are related to individual difference in braking performance. This supports the hypothesis that drivers adapt their tactical level behaviour to their opera­tional skill level. However, the mechanism could also be the other way around: Short followers may have had more opportunities to acquire emergency braking skills, simply because they had to brake hard more often. It can be argued that this would be particularly the case in relatively inexperienced drivers. A very experien­ced driver, even when being a long follower, will probably have experienced a substantial number of emergency stops anyway. Also experience in other situations may count, e.g. for stationary objects such as traffic lights. Braking for stationary objects also requires a tuning of the braking response to perceptual information. In the present study, none of the braking related variables were affected by driving experience. This does not support the idea that short followers have learned to brake more efficient­ly because they have been exposed to critical encoun­ters more often. However, this is not enough evidence to rule out the alternative hypothesis and this issue will have to return in future research.