# Football physics

Gold Member
A 12 yearold asked me to explain to him some of the physics involved with a football. I wrote him a letter but i wanted you guys to look it over before i sent it. I'd like to check that 1-i'm not writing nonsense and 2-i'm making myself clear to a 12 yearold. Here it is:
[EDIT: Don't be daunted by the block of text - it's trivial stuff]
First lets pretend that the football isn't spinning and that there's no air resistance. In that case the ball would fly in a simple parabola (sort of an arch shape - like a rainbow), depending on the angle and the velocity that the ball was thrown with. The initial velocity of the ball can be broken into 2 parts - the part going up = vertical and the part horizontal to the ground. The amount of vertical speed determines how much time the ball will be in the air - because the harder you throw it up the longer it takes to fall back down. The amount of horizontal speed determines the distance the ball will go since this is the part of the speed that causes the ball to move forwards.
-So if the ball was thrown with a big angle most of the velocity is vertical so the ball will be in the air for a lot of time, but since the velocity in the horizontal direction - which is the part that moves the ball forward - is very small , so the ball won't be able to go far.
-But if the ball has a small angle then the amount of velocity going up is small so the ball will only be airborne for a short time causing it to go a short distance - even though the horizontal speed is big.
How can the QB make the ball go far?
The answer is that he has to throw it at about a 45deg angle - this means that the velocity is distributed evenly in the vertical and horizontal directions, so it will have enough time in the air and enough horizontal speed to go far.
Now lets see what happens with a football shape and air resistance but without the ball spinning:
When a ball flies through the air it gets slowed down by the air that's rubbing against it; this is known as air resistance. If the ball is pointy at the ends like a football then there's less air resistance than with a regular ball because the air can flow around the point instead pushing the ball back. As an example of this you can put you hand in a pool and try to move it - if you move it in the direction of the side of your hand it's easier than if you push your palm. So the football can go further than a regular ball if it always moves in the direction of its tip. But here's the problem, as we said in the beginning, the football doesn't go in a straight line, it goes in a parabola (curved) shape, so how can the QB throw it so that the tip of the football always points in the direction that the ball is moving? How can he throw it so that at the beginning the tip points up (because the ball is pointing up) and at the end it point down? This is the most interesting part...
The solution is that the QB has to spin the ball. It's a little complicated to understand how the spinning helps, but it basically goes like this:
When the ball isn't spinning the air on right pushes against the ball with the same force as the air on the right. The force that the air pushes is relative (to a good aproximation) to the speed of the ball through the air. So if the ball is spinning, one side is spinning into the air while the other side is spinning away from the air. This means that the ball is getting pushed either left or right depending if it's tip is pointing to high or to low, this force to the right or left moves the axis of rotation -which is the direction of the point- up or down. This is an important phenomanon called percusion. You can see an example of this in a spinning top - gravity is pulling it down but that makes the top move to the side, that's why the top doesn't fall down as long as it's spinning, instead it "wabbles" to the side. Here it's the same thing, if the ball is pointing too high then there's a bigger force on the right side (assuming a clockwise spin) which makes the ball turn down and if the ball is pointing too low then there's a bigger force on the left side which makes the ball turn up. Only when the tip is exactly in the direction that the ball is going in there's an equal push to the left an the right so the tip doesn't turn.
The spin also prevents the ball from shaking and turning - just like a top that's spinning quickly doesn't shake as much as one that's spinning slowly.

Could you tell me if i made any mistakes, worded things badly...
Thanks.