For a moving observer it is essential to foresee the locomotor course with respect to structures in the environment. Optical flows that are available to a moving observer contain powerful information for visual kinesthesis. In general, optical flows consist of separable translational and rotational components. The information examined here is contained completely in the translational component and its time derivatives. Curved paths of observation are specified by different orientations of the translational components of optical velocity and acceleration fields. Obstacles and their temporal separation from a curvilinearly moving observer are specified in the optical flow, as is the angle of collision.