Physics of a Bike Helmet: HELP!

[KShan5[PrFC]]

Last year for my science I asked for help, and recieved a lot of it....I am asking for some more again. I know there are many people on the board who have a strong physics background. So if anyone can help me formulate the equation I am looking from this hypothesis, it would be much appreciated.

Hypothesis: One can formulate an equation, which includes for any given angle of impact, x, with two other variables, the velocity of the bike rider, and the mass of the rider; that determines the breaking point of the helmet.

Thank you in advance.

[neevel]

You need to talk with some materials science people, and you'll require some fairly detailed information about the precise shape and composition of the helmet. This is the sort of problem where the "assume a spherical, frictionless chicken" aspects of elementary-level physics courses become untenable.

Not to say that, after everything, an single equation might not be derived. The formula for whether or not a capped AP naval shell would be decapped passing through an outer hull plate turned out to simply be that if the plate thickness was equal or greater to 0.08*(shell diameter), the shell would have it's AP cap knocked away.

-Dave

[KShan5[PrFC]]

So, email a few physics professors at local universities for the answer?

[Artisan]

Originally posted by KShan5[PrFC]

Hypothesis: One can formulate an equation, which includes for any given angle of impact, x, with two other variables, the velocity of the bike rider, and the mass of the rider; that determines the breaking point of the helmet.

Thank you in advance.

Flawed hypothesis:
you need an additional variable, the compressive strength (how much force for it to give or deform) of the helmet, and the rupture strength (material failure). If you have that, and can calculate force required to break a helmet with a straight on impact (90 degrees), then the force required at a given angle X impact is simply= force to break x (SIN X)^2.

Modern helmets (bicycle, motorcycle) are designed much like modern cars. They are intended to deform - and self destruct - upon impact to reduce the deceleration force. Automotive engineers have designed "crumple zones" which absorb the energy of impact by letting the chassis, engine and other components smash in for a certain distance before penetrating the passenger space.

In a helmet this is accomplished by the styrofoam shell of the helmet, which compresses upon impact and absorbs the energy. Stryofoam is just the right stuff to help prevent brain from sloshing too badly. In terms of hardness: brain < styrofoam < Skull < pavement, however:
styrofoam < brain inside skull < pavement

Assuming Neevel's "frictionless chicken," the basis for your equation is simply:
F=ma , the value of "(a" (the de-acceleration) varies directly with F. The helmet increases the distance and time during which the impact occurs, recucing the apparent F that the occupant of the helmet observes
Further "frictionless chicken" assumptions:
- Straight on impact: angle = 90 degrees, like head first into a wall.
- Suppose the helmet lining compresses D inches during the impact, which lasts T seconds - the relationship of D and T are tied to F and m by the properies of the material ; "k".
- Softer material; D increases and T decreases. Harder material; D decreases and T increases ; Therefore k~TxD, but D depends on the surface area (A) overwhich the force (F) is being applied; D~F/A

Since:
a=V/T and T=k/D and D=F/A then T=kA/F
so:
a=VF/kA, plugging into F=ma gives:
F=m(Vma)/kA; or F=aV(m^2)/kA

And for an angle of impact x;
F=[(sin x)^2][aV(m^2)/kA]

problem solved.....

[KShan5[PrFC]]

Thank you so much, lol. This project was supossed to take us a couple months, but our physics teacher doesn't care about it, another chem teacher hijacked the science department and is forcing all classes to do it. SO we figured it looked relatively complex but could be done easily enough. You have saved me a lot of time and grief thanks.