How to calculate impact/stopping power energies

[jack616]

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 that's a good
starting point or where to go from there. I have the DuPont PDF for the kevlar
but don't 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 modeled 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

 

[MrCedgy]

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!

 

[jack616]

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

 

[MrCedgy]

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!

 

[alphy]

I would recommend the following steps to calculate impact/stopping power energies:

1. Understand the basic principles of energy and momentum. In order to accurately model the performance of an object in stopping a high velocity projectile, it is important to have a good understanding of energy and momentum. This will help you understand the calculations involved and make informed decisions about which variables to consider in your model.

2. Determine the initial kinetic energy of the projectile. As you mentioned, this can be calculated using the equation KE = 1/2 mv^2, where m is the mass of the projectile and v is its velocity.

3. Consider the properties of the kevlar material. Kevlar is a synthetic material known for its high strength and durability. It is important to understand the specific properties of the kevlar you are using, such as its density, thickness, and tensile strength.

4. Use the DuPont PDF to determine the stopping power of kevlar. The DuPont PDF should provide information on the energy absorption capabilities of kevlar. This can help you determine how much energy the material can absorb before failing.

5. Account for different weaves and materials. As you mentioned, different weaves and materials may be employed in kevlar vests. It is important to consider these variables in your model and understand how they may affect the material's stopping power.

6. Consider the rigidity of the target. The rigidity of the target can greatly affect the impact and stopping power energies. For example, a free-floating net will have different properties than a fully rigid solid vest. It is important to account for this in your model.

7. Use a spreadsheet program such as Excel to create your model. You can input the variables you have gathered and use equations to calculate the impact and stopping power energies for different scenarios.

8. Validate your model with experimental data. It is important to validate your model by comparing its results with real-life experiments. This will help ensure the accuracy of your calculations and allow you to make any necessary adjustments to your model.

In conclusion, calculating impact/stopping power energies involves understanding the basic principles of energy and momentum, considering the properties of the material being used, and accounting for different variables such as weaves, materials, and target rigidity. By following these steps and using a spreadsheet program, you can create a model that can be used to approximate design for different impacts. I hope this helps in your research. Best