Thread: Is there any formula that may show whether a bullet will penetrate a material or not?

I'm curious as to whether or not mathematics can show this or if experimentation is the only way.

Well yes. I think there is.

Take into account,
- The bullet does not change shape, or shatter. Setting the standards.
- The amount of energy the material can have until bending. joule
- The amount of bending before breaking. mm
- The thickness of the material. mm
- The energy of the bullet. 1/2 mass * speed^2

I don't know the exact formulae though.

Then, if it reaches a certain threshold in bending, the material will puncture.

Anyone else wants to give his 2 cents?

Let’s say I have a 35 grain bullet shot at 1000 fps. I want to know whether it can penetrate and break through ½ inch Oak or Quercus.

How would you solve that problem through math?

Note: This is not a homework problem or anything school related. It is just my inquisitive nature.

I doubt there is a "formula" for that. But it can probably be solved by simulation

Here you go: http://hsrlab.gatech.edu/AUTODYN/papers/paper156.pdf.
And: http://www.eng.hawaii.edu/~nejhad/BALLISTICS/bul.html

Originally Posted by Strange

I doubt there is a "formula" for that. But it can probably be solved by simulation

Here you go: http://hsrlab.gatech.edu/AUTODYN/papers/paper156.pdf.
And: http://www.eng.hawaii.edu/~nejhad/BALLISTICS/bul.html

Do they have simulators such as this open to the public?

Originally Posted by idontknowanything

Let’s say I have a 35 grain bullet shot at 1000 fps. I want to know whether it can penetrate and break through ½ inch Oak or Quercus.

How would you solve that problem through math?

Note: This is not a homework problem or anything school related. It is just my inquisitive nature.

If there is a formula, it is not a simple formula. The penetration of a bullet depends on its energy, momentum, and cross-sectional area. The larger in diameter the bullet is, the bigger the hole it has to make in your oak board. If it expands, its effective diameter is larger than the caliber. A frangible bullet may break apart and spread its energy over a wide area. There will also be some variability in the characteristics of the oak board, since it is a natural product and may vary from sample to sample.

Originally Posted by idontknowanything

Do they have simulators such as this open to the public?

Most of them are commercial products (and probably pretty expensive) but there are free/open source products as well:
List of finite element software packages - Wikipedia, the free encyclopedia

Harold has the right of it... The formula would need the mass of the round, its velocity, the surface area and density of the material it is made of and then we would need the mass and density of the material being fired at. At some point the velocity will always defeat the resistance of the object being fired upon. An example is if we launch 1oz of iron at an equal size ounce of iron we will not see penetration. However, if we continue to increase the velocity of the first ounce it will eventually penetrate the second ounce. Then you get into density. A 1oz slug of iron fired at a 1oz sheet of iron that is only 1/8th of an inch thick is going to require significantly less velocity then if it were trying to penetrate a 1oz cube of iron. I wish I knew the actuall formula... I know there is one, it is used by munition developers. I just do not know where to find it

Sorry… I didn’t get back to this thread because Harold14370 and his post on how difficult it would be. I just threw the idea out the window at that point.

I guess the question is if you want a formula or an equation - you can write out the deformation equations for the material in question and then model the shock of the bullet. Rarely do you get formulas this way but for nice symmetrical problems you can extract a lot of information this way.