Sharp curves in freeways are known to be unsafe design elements since drivers do not expect them. It is difficult for drivers to estimate the radius of a curve. Therefore, drivers are believed to use other cues to decelerate when approaching a curve. Based on previous successful experiences of driven speeds in curves, drivers are thought to have built expectations of safe speeds given certain cues, minimalising risks. This research employs a Bayesian Belief Network to model driver expectations using measured speeds in 153 curves and data on the characteristics of the curve approaches. This model mimics expectations as the probability of measured speeds given certain cues. Using Bayes theorem, prior beliefs on safe speeds are updated towards a posterior belief when a new cue is observed during curve approach. We refer to this posterior belief as expected safe speed. Drivers are assumed to adjust their operating speed if it does not match their expected safe speed. The model shows that the visible deflection angle has a large influence in setting the expectations of a safe speed for an upcoming curve. In addition, the preceding type of roadway and the number of lanes are both important cues to set a driver's expectations of a safe speed. Speed and warning signs are shown to be interdependent on the road scene and hence have less influence in setting expectations. This research shows that design and safety assessment of freeway curves should be considered aligned with the road scene upstream of the curve.

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This dissertation explores what road characteristics trigger drivers’ speed adjustments when approaching freeway curves. It combines speed prediction modelling and human factors research methods. The results show that drivers primarily consider visible cues such as the preceding roadway, deflection angle, and the number of lanes, as opposed to traditional factors like horizontal radius or speed signs, when starting to decelerate. The study advocates for integrating driver perspectives into road design.@en

Driver anticipation plays a crucial role in crashes along horizontal curves. Anticipation is related to road predictability and can be influenced by roadway geometric design. Therefore, it is essential to understand which geometric design elements can influence anticipation and cause the road to be (un)predictable. This exercise, however, is not straightforward because anticipation is individual-specific whereas road geometric design is location-specific; anticipation is latent and measuring it may not be trivial; anticipation may have several stages from the preceding tangent until the midst of the curve; and not all drivers anticipate in the same way and thus there may well be unobserved heterogeneity in the effect of anticipation on crash risk. Despite methodological advancements in crash risk modelling, there is no econometric model that can adequately explain the above complexities. This study aims to fill this gap by developing an econometric model with a new latent variable, named ‘predictability’ that is measured by individual-specific driving behaviour indicators and predicted by location-specific road geometric factors. The model is specified with random parameters to account for unobserved heterogeneity and is empirically tested by a unique dataset including detailed geometric design and driver behaviour data obtained for 156 curves in the Netherlands. Results indicate that higher exposure and uphill vertical grade are associated with increased likelihood of vehicle crashes along horizontal curves, whereas adequate superelevation and higher predictability are associated with decreased likelihood of those crashes. Pavement friction influences this likelihood too but it has varied effects. Road predictability is influenced by the differences in angle of horizontal curves, vertical grades, and width of consecutive road segments.@en

Although much research is done on speed and gaze behaviour inside curves, there is little understanding of which cues drivers use to anticipate and slow down while approaching curves. Therefore, an on road experiment was conducted in which 31 participants drove through six freeway curves in their own car. During the experiment, look-ahead fixations and speed were recorded using an eye-tracker and a GPS tracker, respectively. In addition to these measurements, the participants verbalised their reasons for changing speed. The distribution of fixations over various areas of interest was investigated around the start of deceleration before each curve and around the start of each curve. Verbalisation data were analysed to infer the number and types of reasons for changing speed and when these were mentioned together with mentions of deceleration before a curve. The results showed that before starting to decelerate, the participants fixated mostly on the Focus of Expansion and edges parallel to the curve trajectory, whereas most fixations on warning or speed signs were recorded mostly after participants started to decelerate. These findings suggest that drivers use information from the Focus of Expansion, be it a change in optical flow or the presence of a kink in the alignment, as the main cue to start decelerating. Parallel edges are also important cues, whereas warning and speed signs are primarily used to confirm that a speed change is needed.

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Road designers need to have insights where deceleration and acceleration are expected related to the position of the curve, and in in which amount so that drivers are able to safely decelerate and accelerate respectively into and out of a freeway curve. For this, empirical speed data is needed. Therefore, Floating Car Data in 153 curves in The Netherlands were collected at a resolution of 1 Hz and were filtered on free-flow periods, to analyse over 800 thousand unique continuous free-flow speed observations on these curves. Regression models were developed to predict speed development, including deceleration and acceleration behaviour upon entering and exiting freeway curves. The models rely on easy to generate geometric design variables, including the start and end position of the horizontal curve, the horizontal radius and the number of lanes. Using these variables, the designer can predict the speed development based on the 85^th percentile of speed and acceleration, relative to the position of the curve. The regression models reveal strong goodness-of-fit of the predicted 85^th percentiles of speed in a curve, showing acceleration and deceleration inside the curve, and higher predicted 85^th percentile speeds than the design speeds. The models also show satisfying results in speed development prediction in sets of consecutive curves with different characteristics, as well as deceleration when entering a first curve and acceleration when exiting a last curve. These insights are valuable in evaluating road design in relation to traffic safety based on its predicted use.

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In the Dutch freeway geometric design guidelines, there is a rule that in connector roads, the second curve should not be smaller than the first curve in a connector road, so there is no need to decelerate further inside the connector road. By this it is assumed to match the expectation of the driver. Based on speed profiles in free flow situations and accident data, this research compares speed behaviour and accident risk in second curves which do or do not adhere to this rule and compare those to single curves as a baseline. In general, it can be concluded that the first curve does set expectations for the second curve which is seen in speed behaviour the curve approach phase of the second curve. Furthermore, the ratio of first and second radius is of influence to the speed at curve start of the second curve. The speed inside the curves is not different by using different radii for the first curve and comparable to single curves. The different speed behaviour in second curves for adhering to the design rules or not is however relatively small and does not seem to have an influence on accident risks.@en

The actual speed behaviour when drivers approach a curve is very relevant to assess the road design and safety but is mostly overlooked in the scientific literature. Most research into curve driving behaviour is focussed at the behaviour inside the curve, although the speed selection is done before curve entry. The main objective of this research is to identify which freeway characteristics play a role in driving speed selection. High Frequency Floating Car Data, detailed reconstruction of the curves and their surroundings, as well as three dimensional sight distance analysis, were used to analyse individual speed profiles on 153 Dutch freeway curves. By defining the positions where the acceleration approaches 0 m/s² before and after a curve starts, the positions when the driver started and stopped decelerating upon curve entry were defined. Further correlation and regression analysis of those positions revealed that the radius of the curve is indeed a main explaining variable, as well as the speed driven before deceleration starts. Sight distances and cross section characteristics play a further role in determining the position where deceleration starts. Deceleration ends at approximately 135 m after curve start, and the speed in a curve is also correlated with the deflection angle and length of a curve. Sight distances do not play a role in selecting the speed in a curve based on this research. Overall, the findings indicate a non-constant nature and variability of speed behaviour upon curve entry. This can be used for safer freeway curve design and to assess traffic safety based on actual speed behaviour.

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Operating speeds in Dutch freeway curves differ often by 20 km/h compared to their design speeds. Operating speed is thought to be influenced by how drivers perceive curves when approaching a curve. This explorative research explores which curve cues and other variables influence drivers’ speed choice in curves. For this purpose, a survey was designed with 28 sets of curve comparisons. The curves were chosen from interchanges in the Netherlands and were compared to each other. To avoid direction bias, the curves were right turning only. In each set illustrations of two different curves out of a total of 8 curves were shown, and the participants were asked in which curve they would drive faster. In total 819 participants in the age range of 18 and 78 (mean=41.3; Std.=11.9) completed the survey. The survey data showed four common categories of curve cues and variables influencing the decision to drive faster, of which those in the category of the road environment and its surroundings were mentioned the most. The top three variables influencing speed choice are visibility of curve characteristics, “overview” as a holistic but as such hard to measure variable, and number of lanes. Variables such as presence of signage and trees were also mentioned frequently by the respondents. Geometric road characteristics such as curve radius and deflection angle were identified by the respondents as influencing variables, but only showing to affect speed selection when these are visible to the driver and not obscured by trees or other elements. This suggests combinations of geometric and surrounding elements are needed to get a better understanding of speed selection by drivers.

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