# Bicycle Helmet Physics - Momentum Calculations

1. Jul 28, 2009

### yowatup

edit

Last edited: Jul 29, 2009
2. Jul 28, 2009

### mgb_phys

Energy is force x distance, so that force acting over the distance of the thickness of the helmet isn't very much. Remember also that KE is velocity^2 so 30->40km/h is almost a doubling of en ergy.

3. Jul 28, 2009

### yowatup

Right, the wikipedia statement regards energy.

That aside, my calculations of force are sound? That with a helmet, hitting the the ground (or another object) at 20km/h, is roughly equivalent to hitting the ground at 2.8km/h without a helmet?

4. Jul 28, 2009

### mgb_phys

Seems reasonable, it's hard to know the time an the force isn't necessarily linear as the helmet distorts - but I wear one!

5. Jul 28, 2009

### yowatup

I'm glad that the calculations appear to be in order, despite the baffling conclusion that 20km/h(w helmet)=2.8km/h(w.o helmet).

You're right about the force not being necessarily linear, but I think I just need something simple to illustrate the effectiveness of helmets.

While I can reliably source the time figure of 6ms afforded by helmets, I think the arbitrary time value I added of 1ms probably skews the data quite a bit. I just don't know how else the comparative analysis would work. I can't calculate the acceleration if I just use the 6ms figure (since t=0 w/o helmet then). The obvious solution is to increase the time that the skull affords, but I really am not sure what number to decide on.

6. Jul 28, 2009

### yowatup

Okay, so I did some research and have found that the human skull is roughly 1/4" = 6.35mm thick. Helmet foam on the other hand is 20mm. So I think I can reasonably conclude that the time allowance afforded by the skull is 1/3 of the helmet foam. That is, if it's distance that is the operative variable here that extends time of deceleration; since the human skull is surely stronger, that just means it absorbs more force but doesnt really affect the time.