Q:

Hi. I had a football punted into the left side of my head giving me a brain injury. I've read studies that show 15 year old soccer players and first grade rugby players punt the football between 80Kph to 100kph. So if that's the velocity I was hit with can you tell me how much force I was hit with in newtons and G force and can you give me some equivalent activities of that force? Our football in Aus weighs 400grams

- Leanne Cox (age 42)

BLACKALLS PARK

- Leanne Cox (age 42)

BLACKALLS PARK

A:

That's terrible, I hope that you're recovering well.

We can give a reasonably precise value for the impact, the total momentum transfer. Our estimate for the force will be more of a guess, because the force is the impact divided by the time of the collision, which we don't know.

The football had momentum 0.4kg *90 Kph = 0.4 kg*25 m/s =10 kg-m/s.

It probably bounced back the other way with roughly half that momentum of the opposite sign. So the impact was about 15 kg-m/s =15 N-s.

The mass of a head is about 4-5 kg (10x the football mass), so, if it gets 3/2 the ball’s initial momentum, its speed is about 3 m/s. How long did the impact take? Let's say that your head moved about 0.1 m during the impact at about half its final speed. That means the impact lasted about 0.07 s. The acceleration then was about ~ 50 m/s^{2 }or ~ 5 g. The force would then be about 200 N. The big uncertainty here is in our guess as to how far the ball and your head moved during the main part of the collision.

I can't think of much of any events like this in ordinary life. Brain damage can’t be easily estimated from the acceleration, which depends on the mechanical properties of brain tissue.

Mike W. (w help from JJT)

(Leanne- The first version accidentally got posted, with errors, before we checked it, This version is correct.)

*(published on 04/21/2020)*