### FLUID MECHANICS ANALYSIS IN VOLLEYBALL SERVICES

#### Abstract

The service is considered the first attack action in volleyball games. Erratic behavior also appears along the trajectory, hindering reception. We suspect that these effects can be related to the ‘drag crisis’ phenomenon described in fluid mechanics. Thus, we decided to quantify the trajectories of four types of services (underhand, floater, floater with jump, overhand with jump). Altogether, twenty-six real trajectories of service balls were recorded and 3D reconstructed with the DVIDEOW system. Polynomials of the 4th degree of time were adjusted to the coordinates of each trajectory, obtaining the speed and acceleration of the balls.

We compared, in the horizontal and vertical planes, the real trajectories with simulated ones in which the ball was submitted to the same initial conditions but without any aerodynamic drag forces. We calculated the Reynolds Number (Re), the drag coefficient (CD) and the drag force (FD), applying the model presented at the XVI ISB Congress (Deprá et al., 1997). We observed that all services are placed in the region of the so-called drag crisis (1.105 < Re < 3.105) and present great variations of drag coefficient (Fig. 1). We also observed that the four types of services analyzed can be ordered in an increasing sequence of Reynolds numbers. The first three types presented a decreasing sequence of median values of CD, accompanying the CD(Re) literature curve (line in Fig. 1). Even so, we observed the growth of the drag force (FD) as a function of Re (Fig. 2). Comparing the magnitude of the two forces that act on the ball, we estimated that in the case of the overhand service with jump the drag force becomes up to 1.4 times larger than the weight force (mg = 2.55 N). All these kind of quantification may also be used to compare characteristics of different players.

We compared, in the horizontal and vertical planes, the real trajectories with simulated ones in which the ball was submitted to the same initial conditions but without any aerodynamic drag forces. We calculated the Reynolds Number (Re), the drag coefficient (CD) and the drag force (FD), applying the model presented at the XVI ISB Congress (Deprá et al., 1997). We observed that all services are placed in the region of the so-called drag crisis (1.105 < Re < 3.105) and present great variations of drag coefficient (Fig. 1). We also observed that the four types of services analyzed can be ordered in an increasing sequence of Reynolds numbers. The first three types presented a decreasing sequence of median values of CD, accompanying the CD(Re) literature curve (line in Fig. 1). Even so, we observed the growth of the drag force (FD) as a function of Re (Fig. 2). Comparing the magnitude of the two forces that act on the ball, we estimated that in the case of the overhand service with jump the drag force becomes up to 1.4 times larger than the weight force (mg = 2.55 N). All these kind of quantification may also be used to compare characteristics of different players.

#### Keywords

biomechanics, drag forces, three-dimensional reconstruction, volleyball

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