Correction: An earlier version of this story described the trajectory of a ball that is launched and is pulled down by gravity as hyperbolic instead of parabolic.

William Carvalho of the Portuguese national soccer team trains with the Brazuca ball outside Lisbon. (Mario Cruz/European Pressphoto Agency)

As soccer’s World Cup gets set to begin Thursday, many fans are focused on the surprising star of the last tournament: the ball. Adidas’s Jabulani ball, designed for the 2010 World Cup in South Africa, was supposed to be aerodynamically superior to other soccer balls. Many players, however, complained that its flight wasn’t true. Brazilian goalie Julio Cesar called the Jabulani “terrible” and said it looked as though it had come from a grocery store. This time, the Jabulani has been retired in favor of the Adidas Brazuca, and early reviews have been positive.

But all the fuss raises an important question: What governs the flight of a soccer ball?

Of course there are the obvious factors: a player’s foot and gravity. The player’s foot applies a force to the ball, launching it forward and, usually, upward. Gravity drags the ball toward the ground. If that were all that happened, the ball would follow the parabolic trajectory that all of us studied in high school physics: up, forward and down. But there’s much more to it than that.

Drag is what makes the flight of a ball interesting. Drag is what soccer players use to add the dips and curve that fool goalkeepers, and it’s what soccer ball designers manipulate to make their inventions unique.

There are many forms of drag, but one of the more important kinds in the flight of a ball is known as pressure drag, or form drag. As the ball moves forward, the front of the ball separates air particles, which don’t immediately come back together as the ball passes. This leaves a negative pressure directly behind the ball, which slows the ball down and creates turbulence, making the flight unpredictable.

Argentina’s forward Lionel Messi drives the ball during a training session at the squad’s Buenos Aires training complex. (Juan Mabromata/AFP/Getty Images)

Another kind of drag that affects trajectory is called skin friction drag — the interaction of air particles with the particles on the surface of the ball. The rubbing of those particles also creates turbulence. It’s of a lower magnitude than the turbulence created by pressure drag, though.

The Jabulani ball was supposed to remedy some of the unpredictability created by skin friction and pressure drag. One of its innovations was fewer panels — eight instead of the 32 on many soccer balls. Fewer panels means fewer stitches. Fewer stitches means a smoother, rounder ball. In theory, that should create less friction and reduce turbulence.

But that’s not what happened. A couple of problems caused the Jabulani to fly every which way but straight. First, even though stitches contribute to turbulence, they create a somewhat regular turbulence all around the surface of the ball. In many cases, those bumps seem to balance each other out, making the ball fly in a more predictable path. Because large surfaces on the Jabulani lacked stitches while others were rough with seams, the unbalanced turbulence created a bumpy ride between foot and goalkeeper. The engineers’ attempts to offset the stitching problem by building grooves into the ball failed to ameliorate the problem.

More important, the Jabulani dipped and swerved at different points in its flight than a normal ball. An ordinary soccer ball dips and curves the most when it is flying between 20 and 30 mph. Since a good free kick can be launched at around 70 mph, the ball spends a significant amount of its flight traveling in a predictable path, allowing the goalkeeper to get a good sense of where he can meet the ball. The Jabulani, in contrast, swerved and dipped significantly between 45 and 50 mph, according to NASA scientists who examined the problem. This is a critical period for a goalkeeper. If the ball isn’t flying predictably in this speed range, there is a good chance he will position himself at the wrong place.

The Brazuca has only six panels, but the initial laboratory tests suggest that it flies truer than its predecessor. The key innovation appears to be an intentional roughing of the ball’s surface. The Brazuca is covered with little polyurethane nubs that imitate the effect that stitches create on a traditional 32-panel ball. They are there to even out turbulence, cutting down on what experts refer to as knuckleballing. They can be compared to the dimples that help a golf ball fly straight. The Brazuca’s designers also changed the layout of the panels, which distributed the seams differently, further smoothing the flight path.

More important than laboratory tests, however, will be how the players react to the ball. Anyone who watches soccer knows that the players and managers will use virtually any excuse — the referee, the weather, the playing surface, the crowd, the kickoff time — after a loss. So far, the world’s top players seem to be satisfied with the Brazuca. Argentine Lionel Messi has called the ball “great,” as has Spanish goalkeeper Iker Casillas. Of course, both players are on Adidas’s payroll. We’ll see how they feel about the ball if and when their teams exit the tournament.

More from The Washington Post:

Players will compete with a new ball at the 2014 World Cup in Brazil. Named the Brazuca, adidas spent three years developing it. Here's what you should know about it. (Tom LeGro/The Washington Post)

U.S. soccer team sets up camp in Sao Paulo

Soccer star confronts concussion that killed her career

First kick at World Cup may be delivered by disabled teen