RealLifePhysics#1: Football (How They Made It Bend)

Final of the world cup 2018 coming soon. The battle between Croatia and France gonna be epic. In Malaysia, everybody talks about it, either at school or "mamak" restaurant. And today I would like to make a post about physics and football.

One of the term that we gonna use is Magnus effect.

So guys, what is Magnus effect? Magnus effect is the when it being kicked not at the centre, the ball tends to curve during the flight. When the football player kicks the ball at a certain point(not at the centre) it will cause the ball to spin. How much the ball curves is depend on the force and the speed of the ball.





The banana kick or the curve ball, everyone knows about Brazillian star, Ronaldo, who make a goal from the freekick using this technique. The goal is so popular until now and also a Malaysian footballer named Mohd Faiz Subri managed to score a goal using this technique in 2016.

Now I,m gonna explain to you what is in that diagram. This is how footballer makes the ball curves. When the ball being kicked at the red point it will transfer the energy or force from the footballer leg. When the ball start to move from it static point, it will spin on the air. Then, the air resistance or friction(the black arrow from the first diagram) will collide with the ball. As the ball spin that way, the velocity at point A is much higher than the velocity at point B. Because velocity and pressure are inversely proportional, so the pressure at point B is high enough to push the ball slightly to the left side.

Knuckleball

I think this type of kick is the most difficult. This is just my assumption, I'm not a footballer. After the ball being kicked, it is not spinning. And the ball moves unpredictable, I not sure if this case the footballer kicked it co-incidentally at a certain point. But for me, to master this technique is almost impossible. While the ball on the air, it looks like the ball is so slow because of the air resistance and the friction did not follow the ball spinning like the "banana kick". Then after it hit the far-post or anything, it will reflect on the other way. You can see the ball move so fast.

Based on my opinion, I think the ball just follow the air resistance and after it hit something, it starts to spin. That is why the ball look slower before it hit something. If you have another idea or an explanation about this knuckleball, you can leave a comment.

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Calculating the velocity of the ball after collision.

To calculate the kick between the ball and foot, there is an equation for inelastic collision. The equation is related to the initial and the final velocity. Here is the equation :

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e is the coefficient of restitution. The coefficient of restitution is the ratio of the final to initial relative velocity between two objects after they collide. It normally ranges from 0 to 1 where 1 would be a perfectly elastic collision.(wikipedia)

V(a1) = velocity of the foot before the kick
V(a2) = velocity of the foot after the kick
V(b1) = velocity of the ball before the kick
V(b2) = velocity of the ball after the kick

Then, the conservation of linear momentum equation :

m(a)V(a1) + m(b)V(b1) = m(a)V(a2) + m(b)V(b2)

m(b) is the mass of the soccer ball
m(a) is effective mass for the foot or stand-alone mass

Now combine this equation to the first equation in term of V(b2) :

V(b2) = m(a)V(a1)[ 1 + e ] + V(b1)[m(b) - em(a)] / m(total)*

Neglect the V(b1) because ball at static point which is equivalent to zero.
Effective mass for the foot is approximately four times that of the ball (m(a) = 4m(b))

So the final equation is :

V(b2) = 0.8( 1 + e )V(a1)

Now we can calculate the velocity of the ball after the collision. Based on experimental results, the value of e for soccer kicks is between 0.46-0.68. here.

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Reference :

For further reading
1.The biomechanics of soccer
2.Collisions in Soccer Kicking
3.The Physics behind Soccer Kicks
4.Collision

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Disclaimer: I am not an expert. I wrote based on my understanding and my experience. Maybe some of it is not accurate from the fact. If I make something wrong, feel free to drop a comment.