## Time to contact

We saw earlier that people moving through an environment (e.g., long-jumpers) seem to make use of information about the rate of expansion of an object's retinal image to predict the time to contact. The measure generally used is tau, which is the inverse of the rate of object expansion (Lee, 1980). There has been much research interest in trying to see whether the same is true when an object moves towards a more or less motionless observer.

Schiff and Detwiler (1979) obtained evidence that tau, rather than perceived distance or perceived velocity, is used to calculate time to contact. Adults were reasonably accurate at predicting when an object on a film would have hit them. Their accuracy was little affected by whether the object was filmed against a blank or a textured background, suggesting that information about the rate of expansion of the retinal image is sufficient to decide when an object will arrive.

Lee et al. (1983) studied the relevance of tau to performance in a situation in which participants had to jump up and punch balls dropped from various heights above them. The speed of a dropping ball increases over time, but the calculation of tau ignores such changes in velocity. It follows that the actual time to contact will be less than tau. The key finding was that the participants' leg and arm movements were determined more closely by tau than by the actual time to contact. However, tau was still useful, because its value predicts time to contact reasonably well in the last 250 milliseconds prior to contact.

Lee (1980) assumed that the rate of expansion of an object's retinal image is the crucial factor influencing judgements of time to contact. It would thus be valuable to manipulate the rate of expansion as directly as possible. Savelsbergh, Whiting, and Bootsma (1991) achieved this by requiring participants to catch a deflating ball that was swinging towards them on a pendulum. The rate of expansion of the retinal image is less for a deflating than for a non-deflating ball. Thus, on Lee's theory, participants should assume that the deflating ball would take longer to reach them than was actually the case. The peak grasp closure was 5 milliseconds later with the deflating ball, which is in line with prediction. Similar findings were reported by Savelsbergh et al. (1993).

The findings of Savelsbergh et al. (1991, 1993) have been regarded as the most convincing evidence that tau is used to calculate time to contact. However, Wann (1996) argued persuasively that this is not the case. Strict application of the tau hypothesis to the data of Savelsbergh et al. (1993) indicated that the peak grasp closure should have occurred about 230 milliseconds later to the deflating ball than to the non-deflating ball. In fact, the average difference was only about 30 milliseconds. As Wann (1996, p. 1043) concluded, "The results of Savelsbergh et al. point to it [tau] being only one component in a multiple-source evaluation process."

Tau provides a measure of the time to contact with the observer's eyes, and does not indicate accurately when an object will reach his or her outstretched hand. It would seem to follow that interception of a rolling ball would be more accurate if the ball were moving directly towards participants rather than off to one side. However, Tresilian (1994a) obtained precisely the opposite findings, suggesting that other factors (e.g., angular position and velocity of the ball relative to the participant) influence performance.

### Evaluation

Tau is not the only source of information used by observers. For example, Peper et al. (1994) had participants judge whether a ball had passed within arm's reach. The judgements were usually accurate, except when the ball was larger or smaller than expected. In those circumstances, the observers systematically misjudged the distance between themselves and the ball. Thus, familiar size can influence judgements of object motion relevant to an individual observer.

Convincing evidence that tau is not the only variable used in catching a ball was obtained by Wann and Rushton (1995). They used a virtual reality setup, which allowed them to manipulate tau and binocular disparity separately. The participants' task was to grasp a moving virtual ball with their hand. Tau and binocular disparity were both used to determine the timing of the participants' grasping movements. Whichever variable predicted an earlier arrival of the ball had more influence on grasping behaviour.

Another problem was identified by Cumming (1994). He pointed out that the value of tau would be the same for two different objects provided that their size, distance, and approach velocity were all in a fixed

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