Many a pub crawler has engaged in the time-honored tradition of throwing beer mats—those round cardboard coasters that are ubiquitous in bars—as if the mats were frisbees, often competing to see who can throw one the farthest. But unlike frisbees, beer mats tend to flip in the air and fly with a backspin. Now physicists at the University of Bonn have come up with a theoretical model to explain the phenomenon, according to a new paper submitted to the physics arXiv preprint server.

Thanks to their natural curiosity, physicists are fascinated by the physics of beer, and lead author Johann Ostmeyer is no exception. A couple of years ago, he became intrigued by the physics of so-called "beer tapping": a common prank where the perpetrator, holding an open bottle of beer, finds a target in the bar holding another open bottle. The prankster strikes the top of the target's bottle with the bottom of their own, then savors the sight of beer explosively foaming all over the target's hands and clothes.

Back in 2013, Javier Rodríguez-Rodríguez, a physicist at Carlos III University of Madrid, and several colleagues presented experimental and computer-simulation findings of why beer cans foam up so much after being shaken. They concluded that the foaming-over stemmed from a series of waves. Apparently the physics is similar to the development of the cloud in an atomic bomb, although the source of the "explosion" is very different.

The initial tap creates a shockwave that travels from the top to the bottom of the target's bottle. That shockwave's energy is transferred to the beer, sending a second shockwave bouncing back and forth between the bottom of the bottle and the beer's surface. All that activity releases tiny pockets of gas trapped in small imperfections in the bottle's glass, creating clouds of smaller bubbles from the beer's dissolved CO2. As they rise to the surface, those bubbles get bigger and speed up, eventually creating the shower of foam that makes beer tapping such a popular pub prank.

Ostmeyer submitted his own analysis on the beer tapping issue to the arXiv last year, specifically focusing on why the lower beer bottle foams over and the upper one does not. The initial tap creates a low pressure in the lower bottle, and the CO2 bubbles expand and collapse into fragments.

More gas gets diffused into the cluster of bubbles, rising up to create the foam. Something different happens in the top bottle. There is a higher initial pressure, so there are only moderate oscillations in the bubbles, and the eventual bubble collapse doesn't happen—or at least not to the same extent. Thus, you don't get the same rapid growth cloud turning your entire beer into foam. "The prankster leaves the scene dry," Ostmeyer wrote.

Now Ostmeyer, inspired by a 2017 trip to Munich for a German physics outreach demonstration show, has turned his attention to the pressing question of beer-mat flight trajectories. Beer mats (at least the round variety) are basically thin, flat disks with a given radius and mass. A frisbee is also a thin flat disk, and the physics surrounding its flight is well-known.

A frisbee's distinctive curved upper surface is essentially the same shape (when viewed from the side) as an airfoil. Throw it with sufficient force to overcome the downward pull of gravity, and it will generate lift. Of course, there is also air resistance, or drag, acting on the frisbee as it flies through the air. The resistance depends on the angle of attack. If the angle is negative, it pushes the air up and forces the frisbee down, while a positive angle will push the frisbee up. To keep wobbling to a minimum, professional frisbee players know to add a spin when they throw, ensuring their frisbees stay on a single plane as they travel.