How Does a Curveball Curve? Spin, Air and the Magnus Effect
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In 1997 Roberto Carlos took a free kick for Brazil from 35 metres that flew a metre outside the goalpost, curved back in the last few metres and went in, and the physics that explains it also explains why a baseball pitcher's curveball drops out of the strike zone, why a topspin forehand dips, why a golf slice goes right and why a bowler's swing turns a cricket ball in the air. All of them are one effect, described by a German physicist in 1852 to explain why cannonballs missed, and it comes down to a spinning ball dragging the air round with it.
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.
In each sport
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
Seams, roughness and the knuckleball
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.
The numbers
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.
Why it fools the eye
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 takeaway
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.