Bend it like Bernoulli
Even if you’re not a soccer fan, you are likely to have been aware of the festivities that transpired in Russia this summer, the event that comes once every four years—the Men’s World Cup.
Definitely a soccer fan, I lived for the fanfare and the drama. This world cup brought us a group-stage elimination of the previous champions, Germany, and early goodbyes to two of the world’s best, Christiano Ronaldo and Lionel Messi. The English team, unexpectedly, made it to the semi-finals, besting teams of higher rank.
Unfortunately for the nation from which football came, Croatia sent them packing in the semi-finals, but even with a loss it was in that game that England’s Kieran Trippier scored a tournament-defining goal.
Trippier’s strike managed to rise over the wall of Croatian players and dip back down to make it into the goal, but how?
This skill is called “bending the ball” which requires the player to strike the ball in a specific place, with a specific part of their foot, and follow through with the kick across their body. The ball will spin as it travels towards the goal and begins to take a curved trajectory away from its initial direction.
While glued to your TV screen goals like these may look and feel like miracles, but physicists and engineers alike can assure you that it’s not. It’s a matter of fluid dynamics, specifically it’s caused by a combination of the Mangus and Wake effects.
To start, in order to address the Magnus effect we must take a step back to the basics: Bernoulli’s theorem. Bernoulli’s theorem relates pressure, velocity, and elevation in a specific streamline of fluid. The equation essentially states that the sum of these values at any given point on the streamline is equal to the sum of the values at any other point on the same streamline. For example, if on a streamline pressure were to increase from one point to another, another term (elevation or velocity) would have to decrease to keep a constant value.
The Magnus effect specifically refers to when a spherical object spins and induces velocity changes, generating a sideways force. As the ball spins it affects air flow, increasing the pressure on the side that is spinning into the air and, by Bernoulli’s theorem, causes a decrease in velocity on that same side. The pressure increase experienced on one side of the ball creates a pressure decrease on the other side. This environment of unbalanced pressure pulls the ball toward the low-pressure area and in turn causes the ball’s trajectory to change.
The Wake effect, although acting in the same direction as the Magnus effect, works quite differently. As the ball moves through the air it causes flow to separate around it, creating a wake. The spinning motion of the ball complicates this further by asymmetrically altering the airflow, resulting in a deflection of the wake to one side, pushing the ball in the opposite direction.
The two effects acting together cause the ball to change direction, sometimes drastically, and causes goalkeepers everywhere to sweat.
If soccer isn’t your bag, I guess that’s okay. If you must watch other sports, you can observe a similar effect in a volleyball serve or a curveball in baseball.
My recommendation though, as a spokesperson for the beautiful game, is to watch out for next summer’s event, the Women’s World Cup. Not only will it bring upsets, passion, and athleticism, but it’ll bring plenty of opportunities to observe fluid dynamics in action.
To finish off, for your viewing pleasure: this beautifully bent ball by USA player Rose Lavelle to equalize against Brazil in the 2018 Tournament of Nations.