Theoretical Study of the Effect of Ball Properties on Impact Force in Soccer Heading

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Abstract
The objective of this study was to theoretically model, based on the Hertz contact theory, the impact force and contact time, as well as the linear and angular head accelerations during heading in children using two neck stiffness conditions (infinite and negligible stiffness). The following mathematical model inputs were obtained: elastic modulus and mass of size three, four, and five balls at inflation pressures of 10, 12, and 14 psi, head modulus, head mass, head length, head and trunk moment of inertia, and the precontact ball velocity. The model outputs consisted of linear and angular head acceleration, impact force, contact time between the ball and head, and head impact criteria (HIC) all at the point of impact. Head mass and length were obtained as a percentage of body weight and height, respectively, based on age. With an increase in head mass, there is a decrease in the linear and angular head acceleration. With an increase in ball size, for the same head mass, there is an increase in the contact time between the head and the ball. Changing ball inflation pressure has little effect on the impact characteristics. Infinite neck stiffness decreased linear and angular head acceleration and HIC. Head mass and ball size have an effect on linear and angular head acceleration and contact time, respectively, whereas ball inflation pressure has a minimal effect on the impact characteristics. These results indicate that children should be restricted to using the appropriate ball for their age. Smaller head size within an age group is an underemphasized though important identifier of a player’s injury risk.