In this blog post, we’ll analyze the flow around a spin-free ball and examine why it oscillates up and down from a fluid dynamics perspective.

Spinless Balls and Flow Visualization

Whenever Ronaldo’s spinless free kick narrowly clears the defensive wall and finds the back of the net, the goalkeeper’s bewildered expression is often caught on camera. The goalkeeper’s look of frustration directly illustrates how the ball moves unpredictably up and down. But did Ronaldo really kick the ball exactly as he intended?
In fluid dynamics, since we cannot directly observe the flow around an object—such as a ball—moving through a fluid, flow visualization techniques are widely used to make these invisible flows visible. A common method involves using smoke to visually reveal airflow. In laboratories, researchers sometimes introduce small particles into a fluid to track their movement or analyze shadows created by differences in gas density to observe flow patterns.
The lines visible through flow visualization are called streamlines. A streamline is a line connecting the tangential directions of the fluid’s velocity vectors at a specific point at a given moment; simply put, it connects the trajectories followed by fluid particles. By observing these streamlines, we can infer the distribution of invisible pressures and forces.

Kármán Vortices and the Oscillation of a Ball Caused by Pressure Distributions

When observing the flow around a non-spinning ball using flow visualization, one can see small vortices periodically forming behind the ball. While this pattern changes or disappears in a spinning ball, distinct vortex flows appear when the ball is nearly non-rotating. This phenomenon is called a Kármán vortex street and is closely related to the peculiar trajectory of a non-rotating ball.
An object moving in a curved path experiences a force directed toward its center. This is easy to understand if you recall the experience from childhood of spinning an eraser on a string and having to pull the string to keep it centered. In the case of a fluid, if a streamline is curved, a force acts toward the center to maintain that curvature. However, since a fluid has nothing holding it from the outside like a string, the source of this force is ultimately the pressure distribution.
Around a curved streamline, the pressure on the outside tends to be higher than the pressure on the inside. This creates relatively lower pressure on the side of the streamline with greater curvature, and as a result, the flow is drawn toward the center of curvature. Take a hurricane as an example: due to the spiral streamlines, the pressure at the center is lower than on the outside, causing air to be sucked toward the center and reinforcing the rotation—the same principle applies here.
The Karman vortices that form behind a spin-free ball periodically create weak low-pressure areas on either side of the ball’s rear. Since the center of the vortex has relatively low pressure, the ball is pulled in that direction and wobbles from side to side or up and down. Crucially, the location and direction of these vortices are highly sensitive to minor variables—such as wind, the ball’s surface condition, and flow velocity—and thus occur randomly.
Therefore, the trajectory of a spin-free ball is inherently unpredictable. Even the player cannot guide the ball exactly as intended, and the goalkeeper cannot foresee its path in advance. This uncertainty is precisely why a spin-free free kick poses such a significant threat to the goalkeeper and why fans refer to it mysteriously as a “wild shot.”
Ultimately, a spin-free kick can be described as a feat created by the combination of a player’s skilled technique and physical chance. While the player attempts a well-balanced kick, the ball’s subtle wobbles are ultimately created by fluid phenomena such as Karman vortices. That’s why it’s natural to feel a sense of “let’s just kick it and see what happens” before taking the shot.