Automobile driving as psychophysical discrimination

Abstract

The driver tries to keep the car in the center of the lane. If the car is too near the left edge, this causes the driver to make a “corrective” right turn. If the car is near the right edge, a “corrective” left turn is made. Therefore, a quantity which decreases with increasing distance Δ _L from the left edge may be considered as a stimulusS _R producing the reactionR _R of turning to the right. A similar situation holds for the distance Δ _R from the right edge. When the car is in the center of the lane, Δ _L = Δ _R andS _R =S _L , the stimuli are equal. We thus have here a situation analogous to the one studied by H. D. Landahl in his theory of psychophysical discrimination. In general a reactionR _R (resp.R _L ) will occur only ifR _R −R _L ≥h ^* (resp.R _L −R _R ≥h ^*) whereh ^* is a threshold. Applying Landahl’s theory to this situation, we find thath ^* determines the distance from the edge, at which a corrective turn is made. This distance is not constant, but a function of the speedv of the car. The requirement that a corrective turn should be madebeforre the car runs off the road leads to an expression for the maximum safe speed. Because of the transcendency of the equations involved, closed solutions cannot be obtained. It is, however, shown that the expression for maximum safe speed, given in a previous paper (Bull. Math. Biophysics,21, 299–308, 1959), is a rough first approximation to the expressions found now.