[abeppu]

That's a very specific application.

Isn't there a bound on the efficacy of a helmet based on its size / thickness? I.e. your head's initial velocity and the thickness of the helmet constrain the distance over which your head's velocity must drop to zero, so there's some minimum force that must be applied to your head no matter what the helmet's material is?

[kbelder]

Conclusion: The helmets must be bigger, much bigger.

I don't know their current thickness; maybe 2 cm? If we expand that to a cushioned 10-20cm all the way around their head, the force would be reduced by a factor of five to ten. I'd imagine they could head-butt all day long without damage, and football games would be much more entertaining.