# What causes a soccer ball to follow a curved path?

Soccer players kick the ball in a linear kick, though you find it to turn sideways, not even in one direction. Just mid air it changes that curve's direction, i.e., it swings, as footballers say. Is there any physical explanation?

Maybe this video will better emphasize this phenomenon: http://www.youtube.com/watch?feature=player_detailpage&v=ZEv7QEFNVq0#t=265s

• It's because of gravitation. It follows a parabolic path because of projectile motion. – newera Apr 10 '13 at 18:31
• Could you clarify? I assume you mean left or right motion as opposed to the arc due to gravity. – tpg2114 Apr 10 '13 at 18:36
• Yes the curve side ways. Actually good footballers master this kind of skill. Although they follow their instinct, some of them do it almost every time. – Sam William Apr 10 '13 at 18:46
• Probably you are refering to changes in direction away form the usual parabolic path?. Interaction between spin and the air. – iiqof Apr 10 '13 at 18:48
• – Qmechanic Apr 11 '13 at 23:16

There's an interesting paper that discusses some of the physics/maths involved in the spiral path of a football. Here's Roberto Carlos' goal against France (discussed in comments to question).

This is the way we interpret a famous goal by the Brazilian player Roberto Carlos against France in 1997. This free kick was shot from a distance of $$35~\text{m}$$. Roberto Carlos strongly hits the ball
($$U_0 = 38~\text{m}/\text{s}$$) with an angle of about $$12^\circ$$ relative to the direction of the goal; due to the rotation
($$\omega_0 \approx 88~\text{rad}/\text{s}$$, a value difﬁcult to extract from the movies, yet plausible), it sidestepped the wall, bent toward the goal, hit the goal post and entered (Fig. 11). The goalkeeper Fabien Barthez did not move: without rotation, the ball would have left the ﬁeld $$4~\text{m}$$ away from the goal! If the trajectory had been simple circle and not a spiral, the ball would have been still $$1~\text{m}$$ away[.]

Update:

Another article "Gaining insight about the unpredictable movement of knuckleballs by dropping beads into water" describes the so-called Knuckleball shot popularised by Ronaldo.

"When a sphere is in a flow, there is a critical velocity at which the wake behind the sphere and the drag force acting on the ball sharply decrease," explained hydrodynamics graduate student Caroline Cohen of France's Ecole Polytechnique. The decrease in the size of the wake can lead to a sideways force that increases the ball’s deviation from a straight-line path. Fluid physicists call this the "drag crisis."

Thrown relatively slowly and with minimum spin, compared with that of Major League fastballs, the knuckleball confuses batters by changing direction in an apparently random fashion late in flight.

But knuckleballs aren't restricted to baseball. In cricket, Indian fast bowler Zaheer Khan has been known to use a knuckler for his slower ball. Volleyball players experience knuckling as a spiked ball closes on them. And, most important to the French scientists, top players such as Spanish league Real Madrid star Cristiano Ronaldo can kick a soccer ball in such a way that it zigzags unpredictably en route to an opposing goalkeeper.

If the ball has some spin, there's a differential drag force on either side of the ball, which is what causes "curveballs": the edge moving in the direction of the ball's travel "feels" the air moving past at a higher speed than the edge moving opposite the ball's direction of travel, so there's a greater aerodynamic drag on the fast side than the slow side. This is called the Magnus effect.

This is in addition to gravity, which will naturally give you a parabolic path curving downwards, but I assume you meant that funny left-right deflection.

EDIT: I may as well take the opportunity to point out the connection to lift and circulation as well: both Lift and the Magnus force can be understood as being due to the air flowing faster on one side of the object than another, the flow having a relative circulation around the object. In the case of the curveball, this circulation is due to the air being accelerated by aerodynamic drag at the surface of the ball.

• What about the midair change of curve direction ? – Sam William Apr 10 '13 at 19:32
• @Sam: Soccer shots curve, there isn't a mid-air discontinuity in the curvature of the path - unless the ball deflects from a player. See typical video compilation – RedGrittyBrick Apr 10 '13 at 20:04
• @Red The ball curves to the left then midair to the right in some free kicks, it's like the center of gravity shifts or something – Sam William Apr 10 '13 at 20:07
• @Sam: Abrupt changes in direction must be due to impact with players or ground. Can you provide a link to a clear video with time offset showing what you describe? – RedGrittyBrick Apr 10 '13 at 20:09
• @Gugg: OK, it looks weird but the knuckleball path is relatively smooth. I'm not sure if the main factor that causes goalies problems isn't the fact that the pattern on the ball isn't rotating much, knuckleball path deviation is said to be "roughly the diameter of a ball (0.2 m)" which isn't a lot. Still, I'm glad I'm not a goalie facing Carlos or Ronaldo. – RedGrittyBrick Apr 10 '13 at 21:37

The answer is the well-known Magnus effect which says that when a ball spins in a fluid it feels a force. A soccer ball's spin is most noticeable when it's spinning left-right (giving it the strong curve in either direction). This is the dominant kind of spin since soccer balls are kicked from the ground, making top-(or back-)spin difficult to achieve.

This is the reason curveballs exist in baseball. In this case they're thrown, so it's easier to give them topspin or backspin.

I will quote a paragraph from this article http://www.soccerballworld.com/Physics.htm which also explains the phenomenon:

Consider a ball that is spinning about an axis perpendicular to the flow of air across it. The air travels faster relative to the center of the ball where the periphery of the ball is moving in the same direction as the airflow. This reduces the pressure, according to Bernouilli's principle. The opposite effect happens on the other side of the ball, where the air travels slower relative to the center of the ball. There is therefore an imbalance in the forces and the ball deflects - or, as Sir J J Thomson put it in 1910, "the ball follows its nose". This lateral deflection of a ball in flight is generally known as the "Magnus effect".

The forces on a spinning ball that is flying through the air are generally divided into two types: a lift force and a drag force. The lift force is the upwards or sidewards force that is responsible for the Magnus effect. The drag force acts in the opposite direction to the path of the ball.

Let us calculate the forces at work in a well taken free kick. Assuming that the velocity of the ball is 25-30 ms-1 (about 70 mph) and that the spin is about 8-10 revolutions per second, then the lift force turns out to be about 3.5 N. The regulations state that a professional football must have a mass of 410-450 g, which means that it accelerates by about 8 ms-2. And since the ball would be in flight for 1 s over its 30 m trajectory, the lift force could make the ball deviate by as much as 4 m from its normal straight-line course. Enough to trouble any goalkeeper!

It's a very interesting article which explains this effect in detail it's very long though, so I didn't find the use to copy all of it here.

You will also find images there, defining the aerodynamics behind the effect.

This effect also is mentioned in this blog http://scienceblogs.com/dotphysics/2010/09/07/the-curving-soccer-ball

• It appears that any mention of the Magnus effect collects upvotes, but I don't think that effect straightforwardly applies to the knuckleball, which hardly rotates. The OP's question (although not very clear) is about balls curving one way and then another way. (I didn't check your links, so please correct me if I got this wrong.) – Řídící Apr 11 '13 at 21:31
• @Gugg I've read the comments below the OP's question, and the Magnus effect applies to Roberto carlos' ball, which is rotating, how it will curve then if it's not rotating? – Nick Apr 11 '13 at 22:53
• By knuckling. :) See the Update section to the accepted answer. – Řídící Apr 12 '13 at 7:25
• I might agree with you that Cristiano Ronaldo's ball falls more into the knuckle ball territory, who uses a different technique than Carlos'. But I will still hold to my analysis that Roberto Carlos' ball is Magnus Effect in play. I sought to cover all aspects in the OP's question.. – Nick Apr 12 '13 at 11:14

Rotating soccer ball will change air flow direction in one of ball sides, which according to Bernoulli's principle, will induce pressure differences between ball sides, and that will be Magnus Lift force, which for a sphere roughly is : $$F = 4 \pi \,r^3 \rho\, v\, \omega$$

where $$\rho$$ density of air; $$r$$ ball radius ; $$v$$ is airflow speed and $$\omega$$ - ball rotation angular velocity.