In the UK there has been dramatic growth in the number of proposed wind farms, and the impact on wildlife of this expansion is largely unknown. Avian collisions with wind turbines have received wide attention but reliable predictions remain elusive. Existing predictive models consider behavioural factors such as group movement only implicitly and require accurate site-specific data to produce predictions, making them difficult to translate between locations. Here we introduce an individual-based modelling approach to describe group interactions with obstacles that incorporates aspects of collective motion to simulate and quantify likely avoidance behaviour. We quantify the effect of group size on the probability of an individual colliding with a fixed obstacle, and investigate the roles of both navigational efficiency and group cohesion. We show that, over a wide range of model assumptions and parameterisations, social interactions have a significant and potentially large effect on collision risk; in contrast to previous models, collision risk is typically a non-linear function of group size. These results show that emergent behaviour induced by social interactions can have important effects on the metrics used to inform management and policy decisions.