The physics of Magnus gliders

Abstract

Magnus gliders are spinning toys displaying spectacular looped trajectories when launched at large velocity. These trajectories originate from the large amplitude of the Magnus force due to translational velocities of a few meters per second combined with a backspin of a few hundred radians per seconds. In this article, we analyse the trajectories of Magnus gliders built from paper cups, easily reproducible in the laboratory. We highlight an analogy between the trajectory of the glider and the trajectory of charged particles in crossed electric and magnetic fields. The influence of the initial velocity and the initial backspin on the trajectories is analyzed using high speed imaging. The features of these trajectories are captured by a simple model of the evolution of the Magnus and drag forces as a function of the spin of the gliders. The experimental data and the modeling show that the type of trajectory—for instance, the occurrence of loops—depends mostly on the value and orientation of the initial translational velocity regardless of the value of the backspin, while the maximum height of the apex depends on both the initial translational velocity and initial backspin.

Analytic solutions for drag and Magnus forces

“…However, since the equations of motion of such an object are nonlinear, finding analytic solutions can be challenging. Numerical solutions using computers are often preferred [3][4][5][6][7].…”

Inverse Magnus Effect Induced by Dilute Water Fog

“…Understanding the motion of a spinning projectile is very important for ball games [2][3][4] as well as for aeronautics [5][6][7], particle saltation [8], and passing time on a riverbank [9][10][11]. The Magnus effect has therefore attracted much interest and it is still an active area of research [12,13]. However, less known is that, at a certain condition, the direction of the force is reversed relative to the conventional Magnus effect.…”