Motorway safety depends largely on curve geometry and driver behaviour, a relationship that has implications for research and practice. This paper introduces a novel approach to quantifying geometric design consistency, defined as the degree to which drivers’ expectations of curve radii match actual road geometries. The hypothesis is that if a driver expects a larger curve than that actually present, an accident might occur because of an excessively high approach speed. To test this hypothesis, this study uses Dutch motorway data, including ramp and curve characteristics, as well as crash frequencies. The data were employed in three steps: 1) constructing a Bayesian model that mimics drivers’ expectations, 2) testing the predictions of this model against real curve characteristics, and 3) examining the relationship between disparities in expectations, reality, and crash frequency. The results indicated a positive correlation between disparities in expectations, reality, and crash frequency. This finding suggests that the crash frequency is higher when drivers expect a larger curve than what is present. The Tree Augmented Naïve Bayesian Network (TAN) reveals the complexity of curve expectations, demonstrating that drivers anticipate larger radii in connector ramps and higher speeds with gentler curve angles. Applying this research to motorway design involves using TAN predictions and crash frequency models to assess safety in motorway curve design, which could proactively improve road safety.

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.

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.

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.

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.

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.