Time-to-passage judgments on circular trajectories are based on relative optical acceleration

Current theories of arrival time have difficulty explaining performance in the common but neglected case of nonlinear approach. Global tau, a variable supposed to guide time-to-passage (TTP) judgments of objects approaching o n linear trajectories, does not apply to circular movement. However, TTP ju dgments are surprisingly accurate in such cases. We simulated movement thro ugh a three-dimensional cloud of point-lights on various circular trajector ies. Arrival-time judgments were found to be above chance when observers ha d to determine which of two expansionless targets would pass them first. Si milar to the inside bias observed in heading studies on circular trajectori es, observers showed a strong bias to select the target on the inside of th eir own curved motion path as passing by first. Analysis of the projected t arget motion revealed that targets on the inside had lower optical velociti es and relatively high optical acceleration rates. Empirical TTP judgments agreed best with a strategy based on relative optical velocity changes.