LoaderSave StorySave this storyCommentLoaderSave StorySave this storyWith the talent on tap, World Cup 2026 is sure to serve up plenty of jaw-dropping kicks, like a ball that curves in midair to go around a defender, or a shot on goal that swerves away from where the keeper thought it was headed. How is this possible? What wizardry enables a striker to change the ball’s trajectory after it leaves their foot?
It’s not magic, it’s fluid dynamics, the behavior of objects in a fluid—and air is considered a fluid, since it flows. (Kids, want to be a real-life FIFA hero? Take physics.) To really understand what’s going on, let’s model the motion of a ball, starting with the simplest and silliest scenario, then adding back elements of reality one at a time.
Why would you play soccer in space? Well, if you’ve seen the ticket prices for this year’s tournament, you might think it’s cheaper to go off planet. Anyway, say we’re way out yonder where there’s no air or gravity. The ball is at rest, and then a player in a space suit gives it a kick.
While the foot is in contact with the ball, it exerts a pushing force. The ball compresses and then rebounds, launching off the foot; all of this takes about a hundredth of a second, and a pro can easily fire the ball at 80 miles per hour.
So the applied force changes the velocity of the ball, but the thing to know is that once the ball loses contact with the foot, there is no longer any force acting on it. Which means the ball will keep moving in a straight line at a constant speed … er, till the end of time. You might recognize this as Newton’s first law.
Of course, you’d lose a lot of balls this way in space, so maybe it isn’t very practical. Let’s move the action back to Earth, but to keep it simple we’ll first assume there’s no atmosphere. Back into your space suits!
Now there’s a new interaction involved—the planet’s gravitational pull. We can calculate this downward force as Fg = m × g, where m is the mass of the ball and g is the gravitational field on Earth (9.8 newtons per kilogram). By the way, Fg is what normies call an object’s “weight.”
What’s different about this force is that it's still there after the ball is kicked. The ball is moving with some velocity, and the gravitational force continuously alters its motion. The rate of change in velocity is called acceleration (a).
Courtesy of Rhett AllainWe need one more thing—how about Newton's second law? This says the acceleration depends on the net force (Fnet) and the mass (m) of an object. It’s usually written as Fnet = m × a, but we can rearrange it like this: a = Fnet/m. Combining this with our gravitational force, we get something pretty interesting:
Courtesy of Rhett AllainSince both gravity and acceleration depend on the mass of the ball, the mass cancels. We find that any object on Earth has a downward acceleration of 9.8 meters per second per second (m/s2). This means that if you drop a bowling ball and a marble at the same time, they’ll hit the ground at the same time—even though the gravitational force on the bowling ball is thousands of times higher. Weird, right?
Anyway, now, in the presence of gravity, if you kicked a ball at an upward angle, it’s vertical velocity would slow, halt, and reverse, with the speed increasing as it falls. In other words, it starts accelerating in the downward direction as soon as it’s kicked, even while it’s moving upward.
What about the horizontal motion? Ah, since there’s no horizontal force after the initial kick, the ball continues traveling forward at the same speed, just like in space. People tend to think a ball falls because its forward motion slows, but actually it’s the opposite. Without air drag it doesn’t slow down at all. It only stops because the ground gets in the way.
So what we get for a trajectory is that familiar upside-down parabola, often called a ballistic trajectory because it’s the path of any unpowered projectile, like a cannon ball, a bullet, or a basketball. Any flying object for which gravity is the only (significant) force acting on it will move this way.
Happily, the Earth does have air. But it drastically changes the game. Now there is a continuous force acting horizontally, which we call air resistance, or drag, and it pushes in the direction opposite to the ball’s motion.
Think of air molecules as a bunch of tiny ping-pong balls. As a soccer ball moves through the air it collides with gazillions of these little air balls, and each collision exerts a backward-pushing force; all combined, this creates the total air-resistance force. The bigger the object, the more collisions it has to fight through.
You also have more collisions with a faster-moving object. This means that if you’re just throwing a soccer ball in from the sideline, air resistance isn’t a factor, but on a hard kick, you can’t ignore it. In fact, doubling the ball’s speed quadruples the air resistance. Without air resistance, a goalie could kick a ball the length of the field and over the stands beyond.
But there's another way a soccer ball is affected by air. If the ball is spinning, the tiny air balls don’t just bounce off; they also get dragged along in the direction of rotation. Here’s your fluid dynamics. This causes the path of the soccer ball to curve. In the picture below, the ball is moving to the right but spinning counterclockwise, which means it has a horizontal axis of rotation.
Courtesy of Rhett AllainAs it spins, it drags some of the air from above the ball and pushes it back and under. But if the ball is pushing the air down, the air must push the ball up. Remember, forces always result from an interaction between two things—so the ball pushing on the air and the air pushing on the ball are equal and opposite forces. (Hat trick! Newton's third law.)
We call this the Magnus force, and its magnitude depends on the size of the ball, the type of surface (rough or smooth), the rotation rate, and the velocity. Yes, it's complicated.
With backspin, like in the diagram above, the Magnus force pushes up on the object, partially offsetting gravity. That means the ball carries farther. This is why baseball players try to create backspin to hit home runs.
Here’s a super fun experiment you can do yourself. Get two paper cups and tape the bottoms together (in other words, with the open ends pointing outward). Next, loop three of four rubber bands together to make a chain, and wrap it around the middle. Use the end of the chain as a slingshot to shoot the cup-thingy forward. With backspin, you can see how it curves upward:
Just for fun, I programmed the physics for our last three scenarios into a Python model and generated the animation below. It shows three balls kicked at the same upward angle and initial velocity. The red ball has only gravity acting on it, and it follows a parabolic trajectory. The blue ball has gravity along with air resistance, which slows its horizontal velocity, causing it to fall short of the red ball.
Courtesy of Rhett AllainFinally, the magenta ball has both of those forces, but it’s also spinning, so there’s a Magnus force. And there’s your sideways curve. That’s how you bend it like Beckham—or mash it like Messi. Olé, olé, olé!
