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EXPERIMENT 1: Speed Choice and Steering Behaviour in Curve Driving

EXPERIMENT 1: Speed Choice and Steering Behaviour in Curve  Driving

This is chapter 4 of 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 speed choice and steering performance during curve negotiation was studied in a driving simulator. The hypothesis was that curve radius and steering competence both affect steering error during curve driving resulting in compensatory speed choice. In this, the control of safety margins was assumed to operate as a regulatory mechanism. Smaller curve radii resulted in a larger required steering wheel angle while steering error increased linearly with required steering wheel angle. This was compensated for by choosing a lower speed, such that the time-to-line crossing to the inner-lane boundary was constant over all curve radii examined. Steering competence was measured during straight road driving. Poorer steering competence also resulted in larger steering errors that were compensated for by choosing a lower speed such that the safety margin to the inner-lane boundary was unaffected by steering competence.

4.1 Introduction


Car driving behaviour in curves may be regarded as an interesting case where steering, as an example of operational performance, is intimately related to behaviour on the tactical level, in this case the choice of speed as a function of curve radius. The distinction between the operational and the tactical level of car driving behaviour has been made by several authors (c.f. Michon, 1985) and might form a fruitful basis for the development of modern driver behaviour theories (see c.f. Ranney, 1994). Until now, studies of car driving behaviour in curves have focused either exclusively on speed choice or on steering behaviour while no attempts have been made to integrate these two lines of research.

A consistent finding in studies on speed choice in curves is that speed has a curvilinear relation with curve radius (see c.f. Kanellaidis et al., 1990) and an inverse relation with lateral acceleration. This means that with smaller radii speed is lower but lateral acceleration is higher compared to larger radii (c.f. McLean, 1981). Sometimes an inverse linear relation is reported (Ritchie et al., 1968) while other studies have found an inverse non-linear relation between speed and lateral acceleration (Herrin and Neuhardt,1974; Macura, 1984). These results have encouraged the idea that lateral acceleration is used by drivers as a cue in speed choice in which a smaller lateral acceleration is accepted as a safety margin at higher speeds (and thus larger radii).

In studies of steering behaviour during curve negotiation, speed is usually held constant. Donges (1978) presented a two-level steering control model that incorporated negotiating curves. Anticipatory open-loop control starts with a steering action some time before the curve is entered followed by a steering-wheel angle maximum, dsa, in the curve. Then a period of stationary curve driving begins during which the driver generates correcting steering actions in a compensatory closed-loop mode. In a survey of models of steering behaviour Reid (1983) argued that driver models should incorporate both lane tracking and speed control. In Donges’ model the parameters estimated to fit the model on experimental data were influenced by vehicle speed and confounded with road curvature. Curve radius and speed during curve negotiation affect required operational performance because both factors affect the required steering-wheel angle. Godthelp (1986) described this phenomenon as follows: the required steering-wheel angle for a particular curve can roughly be characterized as dsr = GL(1+Ku²)/Rr. In this, dsr represents required steering-wheel angle, Rr the road radius in meters, G the steer-to-wheel ratio, L the wheel base, K a vehicle related stability factor and u represents longitudinal speed in m/s. For any given speed, required steering-wheel angle then increases with smaller radii, but for a given radius it increases with higher speed, if K is larger than zero, which is the case for a normal understeered car.

If the steering-wheel angle during curve negotiation matches the required steering-wheel angle perfectly, speed is only restricted by an upper limit where the vehicle starts skidding. The speed at which this occurs is generally much higher than actual speed in curves. The hypothesis of the present study is that steering errors play an important role in speed choice, such that speed is adapted to operational performance. There is some evidence that steering errors increase linearly with required steering-wheel angle, see c.f. Godthelp (1985, 1986). Since negotiating curves with a smaller radius requires a larger steering-wheel angle, the implication is that steering error is larger in curves with smaller radii compared to wider curves. If steering error is a linear function of required steering-wheel angle, the fraction defined as steering error divided by required steering-wheel angle should be constant over radii.

There is also evidence that steering error is affected by steering competence. Cavallo et al. (1988) found that, under visual occlusion, experienced drivers estimated the correct required steering-wheel angle better than inexperienced drivers. Also, experienced drivers exhibited less variation in steering-wheel amplitude during closed-loop control compared to inexperienced drivers. These results suggest that experienced drivers generate smaller steering errors.

If the driver compensates for larger steering errors induced by smaller radii or poorer steering competence by choosing a lower speed, some regulating mechanism or safety margin is required that determines how speed is adapted. It is suggested here that the time-to-line crossing (TLC), developed by Godthelp et al. (1984), is such a safety margin. TLC represents the time available for a driver until the moment at which any part of the vehicle reaches one of the lane boundaries. In a study of Godthelp (1988) drivers were instructed to generate correcting steering actions when vehicle heading could still comfortably be corrected to prevent a crossing of the lane boundary. Drivers made a corrective steering action at a constant TLC irrespective of vehicle speed.

The model on the relation between speed choice and steering performance may then be summarized as follows. Required steering-wheel angle is determined by curve radius and speed, while steering error is determined by required steering-wheel angle and steering competence. It is assumed that the driver has learned the effect of curve radius and speed on required steering-wheel angle and on steering error from previous experiences. Also, it is assumed that steering error is consistent and the driver is aware of his or her steering competence. When the driver approaches a curve, both radius and steering competence cause an anticipatory adjustment of speed, much like the anticipatory avoidance response in the threat avoidance model of Fuller (1984), in which the effects of radius and steering competence on steering error are traded off with speed such that the safety margin TLC remains constant and independent of radius and steering competence. Although mathematically TLC is determined by steering error as well as speed, the higher steering errors associated with smaller radii and poorer steering competence are assumed to result in lower speeds because of the constancy of preferred TLC as a guiding principle. This principle will then result in low or non-significant correlations of speed and steering error with TLC. The relation between lateral acceleration and speed is then assumed to be a by-product of this mechanism.

In the experiment steering competence was measured separately during straight road driving. Road radius was manipulated within-subjects with radii of 40, 80, 120 and 160 meters. Originally, lane-width was manipulated within-subjects as well, since lane-width was expected to affect TLC. However, the effects of lane-width are not reported since these are not of crucial importance to the issue addressed here. Also, subjects used only a part of the lane-width because they drove relatively close to the inner lane boundary. This counteracted possible effects of lane-width on TLC and speed choice. There is also evidence in the literature that drivers use the inner lane boundary as a reference for vehicle guidance, see c.f. Shinar et al. (1980), McDonald and Ellis (1975), Cohen and Studach (1977). Therefore, only TLC and steering behaviour data towards the inner lane boundary are reported in the present article.


4.2 Method


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 with a lane-width of either 3.0, 3.5 or 4.0 meters was used. Roads had deline­ation with broken center lines and continuous edge lines. Four left-turning curves with 90 degrees angle and radii of 40, 80, 120 and 160 meters were separated by straight road segments. After completing a questionnaire on driving experience and age, subjects practiced driving in the simulator for ten minutes. They were instructed to choose their own preferred speed but to adapt the speed for curves as they normally would and to stay in the right lane. There were three trials, one for every lane-width. Each trial consisted of five roundtrips. This means that in every trial all four curves were negotiated five times. The three trials are treated as multiple measurements here.


Data registration and analysis. Sample measurements (10 Hz) were taken on speed (m/s), lateral position, steering-wheel angle (degrees), TLC (seconds), and steering error (degrees).

The steering integral (Ids) during straight road driving was used as a measure for steering competence. This was computed as follows. The steering-wheel signal was divided into periods where the steering wheel was turned to left and periods where it was turned to right (relative to the zero angle). For every period the amplitude was integrated over time and these integrals were averaged resulting in Ids. Thus, this measure is affected by both steering-wheel amplitude and frequency. A smaller steering integral represents better steering performance. Steering error in curves, dse, was defined as the difference between the actual steering-wheel angle and required steering-wheel angle (ds – dsr).

Figure 1 presents a time-history of steering error and TLC during curve negotiation. The curve is entered at time 0. Positive values of steering error and TLC represent steering to the inner lane boundary (left) while negative values represent steering to the outer lane boundary (right). The steering error fluctuates around zero. If steering error is zero then the steering-wheel angle equals the required steering-wheel angle. The open-loop phase ends when the maximum steering-wheel angle, dsa is reached. In Figure 1 this is indicated by the first maximum for dse. This is followed by closed-loop steering control during which deviations from the required steering error are minimized by the driver.

The following variables were analyzed:

– The steering error dse on the moment dsa is reached. This represents the steering error during the open-loop phase.

– The required steering-wheel angle dsr. This was measured as the steering-wheel angle on the moment that steering error was zero just before dsa was reached.

– The steering error ratio, computed as dse/dsr. This ratio is a measure for the relative steering error.

– The steering error integral, Idse, during the closed-loop phase. This was computed as the average integral of all periods where the steering error was directed toward the inner lane boundary.

– The minimum TLC’s to the inner lane boundary, TLCmin during the closed-loop phase. These were determined and averaged for every radius/trial combination.

– The minimum speed during curve negotiation. This was determined and averaged for every radius/trial combination.

The effects of radius were analyzed with repeated measurements analysis of variance. The effects of steering competence were analyzed with correlation and regression analyses. The confidence level for significance was set at p£0.05.

Figure 1. Steering error and TLC time-history during curve negotiation.

Subjects. 16 subjects, 8 male and 8 female, participated in the experiment. The average age was 34 years (sd. 6.3, range 22-47). They were licensed drivers for 12 years on average (sd. 6.3, range 2-27). The average annual kilometrage was 10594 (sd. 8267, range 1500-30000).


4.3 Results


The correlation between steering integral Ids and drivers’ total kilometrage was -0.62 (p<0.01). This means that more experienced drivers steered more accurately on straight road segments.

The minimum speed during curve negotiation was significantly affected by radius (F(3,15)= 58.17, p<0.01). Required steering-wheel angle (dsr) was significantly affected by radius (F(3,15)=188.24, p<0.01) as was the steering error (dse) during the open-loop phase (F(3,15)=28.28, p<0.01) and the steering error integral (Idse) during the closed-loop phase (F(3.15)=14.29, p<0.01). The effect of radius on steering error ratio was not statistically significant. Also, the effect of radius on the minimum TLC (TLCmin) during the closed-loop phase was not significant. The averages of these dependent variables as a function of radius are presented in Table 1.

Table 1. Averages of dependent variables as a function of radius


Radius (m)

Dependent variable                40              80                120             160


speed (m/s)                            11.23        14.92        17.58              17.99

required angle (degrees)     121.44        74.64       56.56             43.47

steering error:

-open loop (degrees)           14.20         7.47           5.54              4.75

-closed loop (integral)        14.02         6.55           5.26              4.67

steering error ratio                 0.12         0.10           0.10           0.11

minimum TLC (s)                   2.52         2.70           2.89           2.79



It can be seen that a smaller radius resulted in a larger required steering-wheel angle, larger steering errors and a lower speed. However, TLC and the steering error ratio were constant over all radii. Both steering errors during the open and closed-loop phases were affected by radius in the same manner.


Table 2. Standardized alpha coefficients of dependent variables


Dependent variable              standardized alpha


Speed                                    0.93

required angle                      0.91

steering error:

-open loop                            0.88

-closed loop                         0.86

steering error ratio              0.91

minimum TLC                      0.90


In order to test effects of individual differences in steering competence on dependent variables it is required that these variables are consistent within the driver. In that case, it is justified to average over all measurements (4 radii x 3 repetitions). In that way, the effect of radius is canceled while the effect of individual differences is preserved. The reliability, or consistency, of the dependent variables was tested with the standardized alpha coefficient. This represents the estimated square of the correlation of scores on a collection of items, in this case the 12 measurements, with true scores (Nunnally, 1978). For basic research a reliability of 0.80 is generally regarded as a satisfactory level.

Table 2 presents the standardized alpha coefficients for all dependent variables. It can be seen that all variables are reliable and most alpha’s are higher than 0.90. The minimum speed, TLC, steering errors, required steering-wheel angle and steering error ratio were averaged over radii and repetitions. Figure 2 presents the results of multiple regression analyses. Only significant partial regression coefficients are displayed.


Figure 2. Path diagram with partial regression coefficients.

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


It can be seen that the measures for steering errors in the open-loop and the closed-loop phase are strongly intercorrelated, indicating that they measure the same phenomenon. Steering error is determined by required steering-wheel angle, while there is no direct path from speed to steering error. Required steering-wheel angle is strongly determined by speed. In addition to this, steering error is strongly determined by steering competence (Ids). But while a higher steering competence results in lower steering error it also results in higher speed. Because steering competence is an intermediary factor, there is no effect of speed or steering error on TLC. Also, there is no path from steering competence to TLC. This suggests that subjects with poorer steering performance maintain the same safety margin as subjects with better steering performance, and that they choose a lower speed in order to maintain that safety margin. The correlation between Ids and the steering error ratio was 0.74 (p<0.01).


4.4 Discussion and conclusions

The effects of curve radius as a road design factor and steering competence as an individual driver characteristic on speed choice in curves were studied from the perspective that effects on operational performance are compensated for on the tactical level. The implied mechanism in the case of curve negotiation is that both curve radius and steering competence affect steering errors on the operational level. In this, the preferred TLC was assumed to be a regulating mechanism that determines how speed is controlled in order to compensate for larger steering errors. Since TLC is mathematically determined by speed and steering error, higher steering errors can be compensated for by choosing a lower speed such that TLC is unaffected by radius or steering competence. The results supported this model. It was found that both required steering-wheel angle and steering error during the open and closed-loop phases increase with smaller radii, but that the relative steering error, defined as steering error divided by required steering-wheel angle, is constant over radii. This strongly suggests that steering error is linearly related to required steering-wheel angle and is consistent with the results of Godthelp (1985, 1986). Smaller radii resulted in the choice of a lower speed, but the minimum TLC’s during curve negotiation were not affected by radius. This suggests that larger steering errors are compensated for by choosing a lower speed such that a constant minimum TLC is maintained. This finding confirms the ideas of Summala (1988) and Rumar (1988) that drivers control safety margins that can be operationalized as distance or time related measures. The TLC as a safety margin then is controlled by the drivers’ speed choice. The results suggest that speed choice and steering performance are both intimately related in negotiating curves.

In this study, individual differences in steering competence strongly determined speed choice and steering performance in curves. Steering competence was measured with the steering integral during straight road driving. A larger steering integral is an indication of poorer steering performance. The quality of steering performance was related to driving experience. Steering performance, speed choice and minimum TLC were consistent within drivers during curve negotiation. Steering error was determined both by steering competence and by required steering-wheel angle while required steering-wheel angle was determined by speed. This confirms the model discussed in the introduction. Because drivers with poorer steering performance drove slower, while their steering errors were larger, no significant relations of speed and steering errors with TLC were found. This suggests that drivers with poorer steering competence compensated their larger steering errors, which decreased TLC, by choosing a lower speed, which increased TLC. Since steering competence did not affect TLC, it can not be concluded that drivers with poorer steering competence were less safe drivers. Steering error ratio correlated significantly with steering-competence as measured by the steering integral. The strong effect of steering competence on the steering errors during curve negotiation suggests that the steering integral is a good indicator for the quality of steering performance and that steering performance is consistent within the driver.

Based on the finding that steering error is a linear function of required steering-wheel angle and on the constancy of the minimum TLC to the inner lane boundary, the speed in curves as a function of radius was calculated using a mathematical model. From this, lateral acceleration was computed. Lateral acceleration proved to be an inverse function of speed as a by-product of the presented driver strategy.

Thus it appears that both radius as a road design element and steering competence as a driver characteristic exercise their influence on driving behaviour in the same manner. Both affect operational performance resulting in an adaptation of behaviour on the tactical level in an attempt to control safety margins. This is of theoretical significance for driving modeling in general since it suggests that effects of various factors related to the vehicle, weather, road, traffic, temporary states and the driver on behaviour on the tactical level (c.f. speed choice) may exercise their influence via an effect on operational performance. Most driver models are exclusively directed at either the operational or the tactical level. However, it is suggested that the relation between operational performance and behaviour on the tactical level should be a fundamental element in driver modeling.



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