Magnus effect: spinning ball trajectory

What you are seeing: a baseball-like ball (m = 0.15 kg) launched at angle and speed with adjustable spin. The Magnus force $\mathbf{F}_M \propto \boldsymbol{\omega} \times \mathbf{v}$ acts perpendicular to the velocity. With positive spin (top-spin, ball rotates in flight direction) the force pushes down, shortening the range. With negative spin (back-spin) the force pushes up, extending the range. Drag opposes velocity.

The lines show trajectories at three spin values for the current speed and angle. The orange dashed line is the spin-free reference. Adjust the spin slider to see the curvature dramatically change. Back-spinning fly balls travel about 20 percent farther than spin-free balls; top-spinners die fast (hooked pitches, etc.).