How Does a Curveball Curve? Spin, Air and the Magnus Effect

A ball moving through air has air flowing past it, and if the ball is spinning, the surface on one side is moving with the flow and on the other side against it. The side moving with the flow carries the air along faster and further round the ball before it separates; the side moving against it slows the air and makes it separate early. The result is that the wake behind the ball is deflected to one side, and by Newton's third law the ball is pushed the other way: the air goes one way, the ball goes the other. The force is at right angles to both the direction of travel and the spin axis, so a ball spinning with its top moving forward, topspin, is pushed down, one spinning the other way, backspin, is pushed up, and one spinning about a vertical axis is pushed sideways. Heinrich Magnus measured it on spinning cylinders in 1852; Newton had noticed it in tennis balls in 1672.

The same push produces different results depending on the spin the game allows:

• •Baseball: a curveball is thrown with topspin and drops sharply, up to 40 centimetres more than gravity alone would take it; a fastball has backspin and falls less than the batter expects, which is why it appears to rise; a slider spins about a tilted axis and breaks sideways and down
• •Football: a free kick struck off-centre with the inside of the foot spins about a vertical axis and swerves; Carlos's kick was hit so hard that it flew almost straight while the air was too turbulent for the spin to bite, and curved late as it slowed, which is why it looked impossible
• •Tennis and table tennis: topspin makes the ball dip and lets it be hit hard and still land in; backspin makes it float and skid
• •Golf: backspin from the lofted clubface gives lift and doubles the carry of a drive, and any tilt of the spin axis produces the slice or hook
• •Cricket: a spinning delivery drifts in the air before it turns off the pitch, and a fast bowler's swing is a different effect, from the seam and the roughness of one side

Spin is not the only thing that bends a ball. The stitched seam of a baseball and a cricket ball, the panels of a football and the dimples of a golf ball all change where the air separates from the surface, and a ball that is rough on one side and smooth on the other will swerve without spinning, which is what a cricket bowler achieves by polishing one side. A ball thrown with almost no spin, a baseball knuckleball or a football struck dead centre, has its seams drift slowly through the flow as it goes, so that the separation point wanders and the ball wobbles unpredictably, which is worse for the batter than a curve. The dimples on a golf ball exist because a smooth ball's air separates early and leaves a wide wake; the dimples trip the flow into turbulence that clings to the surface and halves the drag, and a dimpled ball flies about twice as far as a smooth one of the same weight.

A major-league curveball leaves the hand at around 130 kilometres an hour with 2,500 revolutions a minute of topspin, and the Magnus force on it is about a quarter of its weight, enough to move it the length of a bat's width across the 18 metres to the plate. A struck football at 100 kilometres an hour with ten revolutions a second swerves about a metre over 30 metres. The force rises with the spin and with the speed, up to a point; at the highest speeds the flow around a smooth ball goes turbulent, the Magnus force weakens or even reverses briefly, and the ball flies straighter until it slows, which is the physics of the late swerve. Wind tunnel measurements and, since 2015, ball-tracking radar in stadiums have replaced argument with data, and the spin rate of every pitch in a season is now public.

A curveball does not curve suddenly; its path is a smooth arc from the moment it leaves the hand. It looks as if it breaks because the batter's eye tracks it for the first half of its flight, when the curve is small, and then loses it in the last hundredth of a second, when most of the deflection accumulates; the brain fills the gap with a straight line and reports a jump. The same illusion sends goalkeepers the wrong way and makes a topspin lob look like it accelerated downward. The physics is steady and the perception is not, which is why the players who hit and catch these balls are not calculating anything; they are running a prediction built from thousands of previous arcs and adjusting when the arc surprises them.

The Magnus effect works on any spinning object in a moving fluid, not just balls, and engineers have tried to harness it. In the 1920s the German engineer Anton Flettner replaced the sails of a ship with tall vertical cylinders driven round by small motors. When the wind blew across the spinning cylinders, the Magnus force pushed the ship sideways to the wind, much as a sail does, and his rotor ship crossed the Atlantic in 1926. The idea faded because cheap oil made engines simpler, but it never quite disappeared.

In recent years rotor sails have returned on some cargo ships and ferries as a way to cut fuel use, because the motor that turns the cylinder uses far less energy than the thrust the wind supplies. You can see the same principle at home with a simple experiment: wrap string around a light cardboard tube, hold the loose end and pull it so that the tube spins as it falls forward, and it will swoop or loop rather than drop in a straight line. The direction it curves tells you which way it is spinning, and it follows exactly the rule a pitcher uses on a baseball.

For decades many people, including some scientists, doubted that a baseball really curved, and argued that batters were simply fooled. The pitcher usually credited with inventing the curveball in the 1860s, Candy Cummings, was eventually elected to baseball's Hall of Fame, yet popular magazines in the mid twentieth century still published sequences of photographs that claimed to show the ball travelling in a straight line. Measurement settled the argument. In 1959 the American physicist Lyman Briggs tested spinning baseballs in a wind tunnel and showed that spin alone could push a ball sideways by tens of centimetres over the distance to the plate.

The Magnus force depends on the density of the air as well as on spin and speed, and that matters in at least one stadium. Denver's major-league ground sits about 1,600 metres above sea level, where the air is roughly a sixth thinner than at the coast. Pitchers there find that curveballs and sliders break noticeably less, while batted balls meet less drag and carry further, and it has long been one of the easiest parks in which to hit a home run. Since 2002 the home team has stored its baseballs in a humidity-controlled room, partly to stop them drying out and becoming bouncier in the dry mountain air.

One of the most famous curving shots in football was taken by the Brazilian defender Roberto Carlos against France in 1997. From around thirty-five metres out, he struck the ball with the outside of his left foot, sending it so far to the right of the wall that a ball boy near the corner flag ducked, before it swerved back sharply and went in off the post.

Physicists later studied the kick and explained it as a combination of the Magnus effect, from the strong spin, and the shot's speed and distance. As a fast spinning ball slows, the curve tightens, so the path is not a simple arc but a spiral, bending more and more towards the end. That late, sharp swerve is what made the goal look as if it defied physics.

A spinning ball curves because its surface drags air with it, so that the air separates late on the side moving with the flow and early on the other, deflecting the wake and pushing the ball the opposite way, a force at right angles to spin and travel called the Magnus effect. Topspin makes baseballs and tennis balls drop, backspin lifts golf drives and fastballs, sideways spin swerves free kicks, and seams, roughness and dimples bend or straighten the flight further; the ball's arc is smooth and the eye's tracking is what makes it seem to break.