Aerodynamics of a Curveball in Navier-Stokes Flow

Joey Huang

It is well-known that the trajectory of a spinning ball is not a straight line - specially for baseball fans. This is so-called Magnus effect. Many people had computed the motion of the fluid around a moving 2D ball (cylinder) when the ball's constant velocity and spinning speed are specified to verify the Magnus effect. This approach can only give us the pressure and stress tensor around the ball - but we can not really obtain the trajectory of the ball.

In this research, I consider the motion of a ball and the fluid around it simultaneously. A dynamical system of interaction between a ball and a viscous flow in two-dimensional space is proposed, combining the Navier-Stokes equations for the fluid and Newton's 2nd law for the ball. A moving coordinate method is developed to facilitate numerical simulations. The simulations clearly demonstrate the interaction: the flow changes the motion of the ball and the moving ball changes the behavior of the flow.

The Simulations: (3.43MB)

Paper: Trajectory of a moving curveball in Viscid Flow