The kick serve in tennis - Cross, R. (Sports Technology, 2011)
A kick serve in tennis is not only the most difficult stroke for players to master but is also the most difficult stroke to understand. The ball must be served by swinging upwards at the ball to generate topspin and the ball must be served down below the horizontal in order to land in the service court. The racquet head is already near the top of its trajectory when the ball is struck, so the angle of approach of the head on impact is much smaller than that needed to generate topspin in a forehand. The ball is almost stationary prior to impact. If a stationary ball is struck by a rising racquet, and if the string plane is vertical on impact, then the ball will rise above the horizontal after the impact. Consequently, several different effects must act simultaneously to generate the necessary spin and launch angle in a kick serve. Three additional effects are identified in this paper, one due to the ball toss, one due to tilt of the racquet head and one due to the fact that the racquet is rotating when it strikes the ball. Additional calculations are presented showing how the bounce height of the ball depends on the serve speed and angle and on the spin and inclination of the spin axis.