The Magnus effect in volleyball service by video analysis

In general, undergraduate laboratories of experimental physics do not usually have experiments designed to address Magnus effect and to measure the value of the lift coefficient. This work explores some experiments outdoors, which has the potential to arouse students' curiosity about Magnus force by addressing three different types of volleyball services, performed by a professional beach volleyball player: spinning clockwise, counterclockwise, and low clockwise spin. In fact, due to the difference in these three ways of the volleyball service, the trajectory and the time of the travel can differ quite a lot from the movement of an oblique launch in vacuum. These differences can be predicted theoretically, although the complete solution can be obtained only numerically. However, in this work, two simplifications were adopted to provide an analytical solution: to consider only the drag force along the horizontal direction, and just weight and the Magnus force in the vertical direction. These simplifications can be justified because the oblique launches (the volleyball service) performed are close to small angles with respect to the horizontal direction. Thereby, the horizontal and vertical components of the motion equation could be solved as a function of time. The validity domain of this approach was established a posteriori by comparing the position data obtained by video analysis with the curves predicted by this simplified theoretical model. Furthermore, the drag and lift coefficients for the ball were extracted as adjusted parameters from these mathematical fits. These parameters are in good agreement with the literature.