Friday, 3 January 2014

The A - Z of Sports Vision - Tau

Hofsten (1983) videotaped infants between 34 and 36 weeks as they reached out towards a brightly-coloured object travelling in a circle. In 144 reaches, they only missed 17 times, and the mean timing error was just 4.4ms when the object travelled at 45cm/second. McLeod, McLaughlin & Nimmo-Smith (1986) asked non-games players to hit vertically-dropping squash balls towards a target with a bat. They were extraordinarily consistent, with standard deviations of just 10ms in 90% of trials, and only 5ms in 50% of trials. So “ordinary people” can demonstrate fine timing even without any particular practice. How do we manage these extraordinary calculations? The answer is that we don’t calculate them. Suppose you are a fielding on the boundary in cricket and the ball has been hit in the air towards you. To calculate the balls arrival (Time-to-Contact or Tc), you’d have to estimate the distance the ball has to travel and its speed, and then divide one by the other. This doesn’t seem a likely method for adults, let alone infants. Lee (1976) proposed that the time to contact could be assessed by using changes to the size of the image that an object creates on retina as it approaches. For our fielder in the deep, the ball approaches him at a fairly constant speed. But when it’s far away, the size of image it forms on the retina doesn’t change much. As it gets nearer, however, the image size gets larger at an increasing rate. The ratio between the image size and the rate of expansion of that image size is known as tau (it’s actually the ratio of visual angle of rate of change of visual angle, but you get the idea). Tau can be used to predict the time at which an object travelling at a constant speed will reach us, and therefore the time at which we need to instigate a movement to intercept it. In a brilliant experiment, Savelsbergh et al (1991) got subjects to catch a ball one-handed. But the ball actually consisted of a small ball 5.5cm in diameter surrounded by an inflatable balloon 7.5cm in diameter. As the balloon approached the catcher it was mechanically deflated without he catcher’s knowledge, so by the time it reached the catcher’s hand it was the same diameter as the small ball. The ball was travelling at a constant velocity, so if the catchers were using that velocity to judge when the ball would arrive, they should still catch it. But because the ball was deflating, the ball’s image on the retina did not expand at the expected rate, so the catchers were late in their attempts to intercept the ball. This proved that the catchers were using tau when catching. Of course for the fielder on the boundary the ball isn’t coming in a straight line, it’s in a parabola, and the fielder may well have to run laterally to get to it. There are other visual strategies that can be used for successful catching, but that’s for another blog. David Donner