Effect of inter-string friction on tennis ball rebound

Abstract

Tennis players report anecdotally that the choice of string material affects the amount of spin applied to the ball by the racket. Previous research on the effect of the coefficient of friction of tennis strings has concluded that ball rebound is mostly, but not always, independent of the string friction. To understand this better, tennis balls were projected at a fixed racket at 25 m·s⁻¹ with backspin varying from 0 to 400 rad·s⁻¹ at an angle of 40° and 60° to the normal with strings made from either nylon or polyester. Each string type was modified by lubricating it to give low friction or sanding it to give high friction. It was shown that the inter-string friction μ_s had different consequences depending upon whether the strings slid across each other during contact. The ball tended to roll at high μ_s, unless the inbound backspin was high enough to induce slipping. A decrease in μ_s allowed slipping of the strings over each other which reduced the horizontal impulse applied to the ball. At very low μ_s the ball was induced to overspin at steep impacts or slip at shallow angles. It was concluded that the dominant effect of a change in inter-string friction was in the string movement rather than the coefficient of friction between the ball and strings, and that the effect was dependent upon impact angle and spin.