# How to calculate impact/stopping power energies

## Main Question or Discussion Point

I hope this is a good place to ask this:

I'm trying to model how an object such as a kevlar vest performs in stopping
a high velocity projectile such as a bullet.

I have only basic knowledge of energy and momentum etc. but can learn if directed.

I can calculate the Ke of the bullet (half mv squared) but don't know if thats a good
starting point or where to go from there. I have the DuPont PDF for the kevlar
but dont really know how to apply the data. Especially since different weaves and
materials may be employed.
A starting point would be helpful though.

Eventually I want the model (in excel if I can) to be able to substitute variables
such as types of materials and different impact energies etc.

I'd especially like to know how to calculate the consequences of different levels
of rigidity of the target (from free floating net to fully rigid solid vest) The idea of this
being to enable different types of impact to be modelled to the point where an approximation
of design can be suggested for different impacts.

(Yes I know ceramics etc are used also - but I'm not designing actual body armour)
I'm interested in the energies involved in deflecting the projectile - kevlar being my
first (and obvious) test material.

Any pointers or indications of existing methods full or partial would be very welcome.
I know its a bit of a tall order.
Thanks for any assistance.

jack

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I am not an expert, but if you are strictly interested in the amount of energy, you may want to use the Work-Energy method, which is what you referred to when talking about Ke. The method is quite simple: you evaluate the different types of energy (elastic, potential and kinetic) at a point A, then at a Point B.

Depending on the assumptions you make (no heat loss, no friction with air, etc) you will find a good estimate of the energy involved in the phenomenon, since energy does not simply vanish. ( 1st law of thermodynamics).

If you are more interested in the damage the bullet would do on the vest, it becomes a lot more tricky. There is a thing called Finite Element Method, where you split a body into multiple, finite elements. These elements are then analysed one by one to give the final result (displacement, strain, etc).
I am not sure how complicated it is to implement when both objects's shape is defined, but if you replaced the bullet with a force or an equivalent pressure, it should once again give you a good enough estimate to appreciate the magnitude of the energy.

Disclaimer: I am not an expert in ballistics, nor have I studied the FEM a lot so my answer may have to taken with a grain of salt. A senior engineer might want to clarify/correct some points.

Have a nice day!

Hi MrCedgy - thanks for the response.

You are right in that I can ignore the more intricate data such as friction etc. Put simply the final goal is to be able to point at a material and say something like "An english longbow arrow should be deflected by X cm thickness of Y material hanging across goalposts" or "X thickness of standard kevlar weave should deflect an
object of Ke 10Kjoules when pasted to a wall" or something like that. Just approximations for various scenarios. (Would it be more helpful to work with Newtons maybe?)

I've heard of finite element analysis - I'll do some browsing on that.

Any more pointers on what I have to do from anyone would be welcome.

thanks
jack

If you want to do that, I am afraid I don't have the know-how to help you step by step. However, I think you should try and look for graduate papers on the matter, they are usually very helpful when you take the time to read and understand them.

I can recommend you to start easy and then gradually add more effects in your analysis. For example, start with the energy involved. Assume the kevlar is a thin sheet and see how much it is deformed, then start playing with it's thickness. You might want to pick up some books on material resistance. Sure, it will take more time to achieve your goal, but you learn much more this way as you each parameter's impact on the phenomenon.

I do not know how much you know about engineering and a little info on your knowledge background would help.

Hope this helped!