Did you know that most drivers swing left before taking a right curve? In fact, this is a given for all race car drivers and a rule for efficient curve negotiation. This distinct way of approaching a curve is called prepositioning. In a recent study it is found that incorporating knowledge of this prepositioning phase is crucial for the reliability and acceptance of some trajectory-guiding advanced-driver-assistance-systems. Unfortunately, our understanding of prepositioning behaviour is still limited, with most driver models unable to account for this phenomenon. In an attempt to improve our understanding, the effects of changing velocity and road radius on prepositioning behaviour are studied experimentally in a fixed-base driving simulator. Twenty-four participants drove four conditions comprising two different fixed-speed velocities (50 and 80 km/h) and two different curve radii (204 and 350 m). The results show that the drivers' maximum prepositioning position significantly increases with increasing velocity and significantly decreases with increasing radius. With 88% of the runs exhibiting a significant displacement, i.e. larger than 0.05 m relative to a constant road bias. The findings suggest that drivers adjust their prepositioning behaviour to the Time-to-Line-Crossing (TLC) of the road environment, in an attempt to maximise TLC. Incorporating these findings in future driver modelling will bridge the gap between straight road and in-curve driving behaviour, thereby bolstering the descriptive capacity of these models.