The trajectory of a soccer ball, kicked with a spin to curve it into the goal, is strongly influenced by aerodynamic factors such as the Magnus force. Several studies using a wind-tunnel and high-speed cameras have investigated the Magnus force acting on a spinning soccer ball. However, the exact effect of the Magnus force on the trajectory of a spinning soccer ball in free flight remains unclear. This study set out to use an optical three-dimensional motion-capture system to record the details of the flight of such a spinning soccer ball. The maximum curvature of the ball’s trajectory occurred in the middle of its flight. The sideways-directed Magnus force acting on the ball decreased as the ball’s speed decreased during the entire flight. Thus, it was concluded that the deflection of the trajectory of the ball decreases as the sideways-acting force decreases throughout the flight.

This paper presents a high-fidelity model to simulate the three-dimensional full-flight aerodynamics of a spinning soccer ball during a free kick. The simulation accounts for the Magnus effect–an aerodynamic phenomenon where spin induces lateral forces–by solving Navier–Stokes equations of incompressible flows and rigid-body motion in a fully coupled fluid-object interaction setting. A monolithic overset approach, which combines a boundary-fitted moving mesh around the ball with a stationary background mesh, is developed to accurately capture near-ball flow features while allowing unrestricted ball motion in 3D space. The monolithic approach solves the flow equations on overlapping domains without using subdomain iterations. A series of simulations is performed across varying initial kick speed and spin rate to quantify their effects on the ball trajectories systematically. The results reveal that the spin rate has a significant influence on lateral deviation due to the Magnus effect, while the initial kick speed has a substantial impact on overall flight range and flight time. Comparisons between a realistic soccer ball and an idealized smooth ball highlight the aerodynamic role of surface features, with smoother balls exhibiting a more substantial Magnus effect and greater lateral deviation. Furthermore, we compare the CFD results with predictions from a conventional ordinary differential equation (ODE) model using empirical drag coefficients. These comparisons show clear limitations in the ODE-based model, particularly under high-Reynolds-number flow regimes.

The Magnus effect is a phenomenon that occurs when a spinning object is moving through a fluid. A lift force acts on the spinning object and its path The Magnus effect is a phenomenon that occurs when a spinning object is moving through a fluid. A lift force acts on the spinning object and its path may be deflected in a manner not present when it is not spinning. The strength and direction of the Magnus force is dependent on the speed and direction of the rotation of the object. The Magnus effect is named after Heinrich Gustav Magnus, the Germa The Magnus effect explains commonly observed deviations from the typical trajectories or paths of spinning balls in sport, notably association football, table tennis, tennis, volleyball, golf, baseball, and cricket. The curved path of a golf ball known as slice or hook is largely due to the ball's spin axis being tilted away from the horizontal due to the combined effects of club face angle and swing path, causing the Magnus effect to act at an angle, moving the ball away from a straight line in its trajectory. Backspin (upper surface rotating backwards from the direction of movement) on a golf ball causes a vertical force that counteracts the force of gravity slightly, and enables the ball to remain airborne a little longer than it would were the ball not spinning: this allows the ball to travel farther than a ball not spinning about its horizontal axis. In table tennis, the Magnus effect is easily observed, because of the small mass and low density of the ball. An experienced player can place a wide variety of spins on the ball. Table tennis rackets usually have a surface made of rubber to give the racket maximum grip on the ball to impart a spin. In cricket, the Magnus effect contributes to the types of motion known as drift, dip and lift in spin bowling, depending on the axis of rotation of the spin applied to the ball. The Magnus effect is not responsible for the movement seen in conventional swing bowling, in which the pressure gradient is not caused by the ball's spin, but rather by its raised seam, and the asymmetric roughness or smoothness of its two halves; however, the Magnus effect may be responsible for so-called "Malinga Swing", as observed in the bowling of the swing bowler Lasith Malinga. In airsoft, a system known as hop-up is used to create a backspin on a fired BB, which greatly increases its range, using the Magnus effect in a similar manner as in golf. In baseball, pitchers often impart different spins on the ball, causing it to curve in the desired direction due to the Magnus effect. The PITCHf/x system measures the change in trajectory caused by Magnus in all pitches thrown in Major League Baseball. The match ball for the 2010 FIFA World…

consecutive instants. This restraining effect causes the ball to be accelerated toward the center of the circle … of angular momentum, means that a spinning body will continue spinning in- definitely (and with the same … resultant force causes the ball to deviate from a straight-line path. While the Magnus effect produces embarrassing

consecutive instants. This restraining effect causes the ball to be accelerated toward the center of the circle … angular momentum, means that a body spinning will continue spinning indefinitely (and with the same angular … force causes the ball to deviate from a straight-line path. While in some sports the Magnus effect produces

to be taken into account by players in sports such as golf. The spin of the ball will affect its trajectory through the Magnus effect. According to the The physics of a bouncing ball concerns the physical behaviour of bouncing balls, particularly its motion before, during, and after impact against the surface of another body. Several aspects of a bouncing ball's behaviour serve as an introduction to mechanics in high school or undergraduate level physics courses. However, the exact modelling of the behaviour is complex and of interest in sports e T…