A site specific model of avian-turbine collision risk is an important component of assessing environmental impacts from wind power projects. Existing models assume, however, that avian flight paths are either parallel or perpendicular to the turbine orientation and that other orientations do not significantly affect the predicted collision probability. We describe a mathematical model which estimates the probability of a collision between a bird passing through a wind turbine and one of the turbine components. Our model improves significantly upon the reference "Tucker Model", and Band model, by accounting for different angles of avian approach other than perpendicular or parallel to the turbine rotor plane. We demonstrate, using a case study of fall raptor migration data, that the angle of approach between the flight path and the turbine orientation has a significant effect on the collision probability and resulting mortality estimates. We conclude that the angle of approach should be considered when estimating avian-turbine collision risk.