Ballistic formulas

[boilingleadbath]

So, I've been messing around with modeling the terminal ballistics of bullets in flesh.

I've got a spreadsheet which accurately predicts penetration distance in ballistics gel for all sorts of bullet designs.

...things are looking good for the the shotgun-slug and 45-70 people.

But I don't feel that the formulas I have are very good right now; I feel I have a fairly good description of the hemorrhage-type effects of firearm munitions. I feel that I accurately account for tissue directly crushed by the bullet crushed tissue and make a fairly good approximation of permanent stretch cavity.

But what about temporary cavitation? How important is this? Any ideas on how to treat it?

Oh, and (generally) how many times the bullet diameter is the permanent cavity in muscle, if the bullet is an expanded softpoint at 2800 fps?
Or if you got data for any other shape/velocity, that would be just as useful.
(right now, I'm using "3")

**********

Here is what I'm finding right now:

1) Penetration depth is roughly equal to (Velocity*Mass)/(Cd*Diameter^2)
This means two things:
a) Bullet momentum is a WAY better indicator of performance potential than energy. That is, if the gun kicks, it's powerful.
b) Small/pointy bullets penetrate very well. But you already knew that.

2) The area (length*average width) of the permanent cavity is roughly equal to (Velocity*Mass), so long as the Cd and diameter of the bullet are fairly typical. (doesn't hold so true with FMJ stuffs)
This would tend to indicate that expanded diameter of the bullet can change so long as the bullet penetrates as deep as you want/need it to (to reach organs).

 

[rcmodel]

b) Small/pointy bullets penetrate very well. But you already knew that.

Unless they are varmint bullets, Then they just blow up.

Sectional density is the determining factor on how deep a bullet will penetrate. But even that does not account for the bullets construction.

I actually don't know how you can account for bullet construction in your formulas.

Two identical weight & shape bullets can have different jacket thickness, jacket taper, bonded, not bonded, core hardness, etc., and give totally different penetration, and results on game.

I fear you are tilting at windmills!

rcmodel

 

[boilingleadbath]

Oh, I don't try to calculate how the bullet will deform when it hits stuff. I (let other people) determine that empirically.

Bullets do change shape when they hit stuff, but only penetrate a couple inches while doing so, so you cat get pretty damn close by just telling the sheet the Cd and diameter of the expanded bullet.

Yeah, it ends up being a little bit off, because the bullet is assumed to smack into the block already expanded, but it's close enough. Real critters are variable density and hardness anyways.

******

Formula is like this:
Velocity = Velocity-((.5*Cd*diameter^2*Velocity^2 + constant)/(time_step*mass))

Pretty much standard drag formula stuff with a bit of extra friction added to account for the fact that tissue isn't a pure fluid.

 

[GunTech]

Take a look at the book "Bullet penetration" by Duncan McPherson

http://www.firearmstactical.com/bulletpenetration.htm

 

[MCgunner]

I don't think terminal ballistics are quite as simple as exterior ballistics. Dr Michael Courtney on this very site posted links to his research into pressure wave effects and then there are the Facklerites than just can't believe in physics at all. They probably call Einstein and Newton stupid. Whatever. I know what works for me and the best thing I can do is TEST it in animal flesh to find out. For me, that might be a trapped hog, just do the animal doesn't get away. Maybe that's unsportsman like, but the truth is in the flesh, not the computer.