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Target Strengths

A place to ask general spud cannon related questions.
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Target Strengths

Unread postAuthor: kenbo0422 » Tue Oct 20, 2009 10:34 am

Since everyone typically will use plywood for a target, especially to measure the force of a projectile, does anyone know the max loading weight of a typical 3/4" piece of plywood, at say 2ft x 2ft? The idea is, if a 1/4" slug has 50 ft-lb of energy, when it hits, would it go through? Or for that matter, what size slug (blunt tipped) and at what energy/velocity would it take to pierce a piece of plywood that size?

I guess I'm wondering what plywood and other materials have as far as resistance to a concentrated force of a projectile. Anybody have any data for this stuff?
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Re: Target Strengths

Unread postAuthor: jackssmirkingrevenge » Tue Oct 20, 2009 10:48 am

kenbo0422 wrote:Since everyone typically will use plywood for a target, especially to measure the force of a projectile


I think most serious builders here use a chrony and a good pair of scales.

Penetration of a given medium is too subjective, projectile hardness, density, shape and velocity are all variables which will affect your result significantly.

As an extreme example, a 7 gram marble travelling at 100 feet per second with an energy of 3.4 ft/lbs will not penetrate 1/2" of ply. A 0.25 gram pin travelling at 600 feet per second has much less energy at 2.1 ft/lbs, but it will go through like a hot knife through butter.
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Unread postAuthor: kenbo0422 » Tue Oct 20, 2009 11:00 am

OK, then let me rephrase that:

The standard projectile is steel, 1/4" dia. 1" length, it is blunt tipped, like a rod just cut off. This will be the standard to measure all penetrations or failures to penetrate.

So, my question is at what energy/velocity will these materials fail? For one example, 3/4" plywood, or even 1/4" aluminum.

I don't know how much the total area of the target matters, either. Like, would a 1ft x 1ft piece hold up better than a 2ft x 2ft, since materials have an elastic quality to them no matter how rigid they are.
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Unread postAuthor: btrettel » Tue Oct 20, 2009 11:02 am

In general, estimating penetration distance or if a projectile will go through a material requires computer simulation. However, estimating if the projectile will be deflected is rather simple.

Look at how much energy the material can absorb before yielding (deforming permanently). The energy per unit volume a material can absorb is called the modulus of resilience: http://en.wikipedia.org/wiki/Resilience

If the projectile's energy is less than the yield energy, then the projectile is deflected without deforming the material. Doing the math assuming that the projectile hits normal to the plane of the material...

energy = (pi * d ^ 2 * t * Sy ^ 2) / (8 * E)

where
pi is 3.141592...
d is the projectile diameter (for sloping projectiles, this will vary obviously, indicating that the projectile faces less resistance at first and more the further it gets in)
t is the barrier thickness
Sy is the yield strength of the material
E is the modulus of elasticity of the material

I do not know what the yield strength and modulus for plywood is but I am confident Google can find these.

A little more useful result is some critical velocity at which the material will yield. If the projectile velocity is less than this the projectile is defeated. Doing the math...

v_c = d * Sy * sqrt((pi * t) / (4 * E * m))

where
m is the projectile mass
and everything else is the same as before

It's worth noting that this theory will predict that smaller but highly dense objects penetrate better... as you would expect in reality.

This could be useful to see approximately how much energy the projectile requires to begin to defeat a barrier. More energy obviously will be required but this will give you a good idea where to start.

As a note, this analysis assumes that the material doesn't bend such that all of the energy is absorbed by the material in the normal direction (so the dimensions of the material don't matter much as long as it's bigger than the projectile). If you want to take into account bending you could use the plate equation... but that's a PDE and while I could solve it and post the solution, I don't care to and bet the difference would be negligible in most situations and very annoying to take into account.
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Unread postAuthor: kenbo0422 » Tue Oct 20, 2009 12:16 pm

As a note, this analysis assumes that the material doesn't bend such that all of the energy is absorbed by the material in the normal direction (so the dimensions of the material don't matter much as long as it's bigger than the projectile). If you want to take into account bending you could use the plate equation... but that's a PDE and while I could solve it and post the solution, I don't care to and bet the difference would be negligible in most situations and very annoying to take into account.


Well, I think you pretty well answered the question ( I needed a mathematical formula), and you're right, in most all cases the flex will be negligible.

Oh, and thanks for the LARGE TEXT on your site... :D Getting old sux...
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Unread postAuthor: jackssmirkingrevenge » Wed Oct 21, 2009 12:03 am

I would still recommend getting your hands on a chrony if you're concerned with performance, there are several reliable methods of measuring velocity on the forum and if you don't want to improvise you can get an F1 for less than 100 bucks. If you're only concerned with projectiles less than 0.25" in diameter, the Combro is also a good investment ;)
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Unread postAuthor: Moonbogg » Wed Oct 21, 2009 12:27 am

OK I can say from experience with air rifles that if you have a 1/4" slug shot at 50ft/lbs that it will go through the plywood. I am comparing it to high powered air rifles and 50 ft/lbs is quite a lot for the average pcp air rifle and they will totally shoot through 3/4" plywood easy.
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Unread postAuthor: jackssmirkingrevenge » Wed Oct 21, 2009 1:22 am

Moonbogg wrote:OK I can say from experience with air rifles that if you have a 1/4" slug shot at 50ft/lbs that it will go through the plywood. I am comparing it to high powered air rifles and 50 ft/lbs is quite a lot for the average pcp air rifle and they will totally shoot through 3/4" plywood easy.


My 30-odd ft/lb 0.22" air rifles will penetrate that thickness of ply easily, as will my 12 ft/lbs 0.177" rifle.
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Unread postAuthor: kenbo0422 » Wed Oct 21, 2009 6:09 am

Those are helpful evaluations.

The actual destructive test results of different materials would be helpful. Probably would find those on some scientific/engineering site, though. My gas gun easily penetrates the 3/4 ply at 1x, so I was wondering just what it took to penetrate certain materials, using the 1/4 inch projectile as a standard for measurement. My projectiles aren't blunt tipped, but I was going for more of a 'hammer' effect with the blunt tip. I think it would be interesting and helpful if that information were available here to be used as a guideline for the destructive / penetration benefits of a design. Using the chronies of course would be needed to find the actual speed, but with the possibility of someone else already having done these experiments, we could all benefit from that info. Well, at least I think so.

Thanks for the info, guys, it is appreciated.
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Unread postAuthor: jackssmirkingrevenge » Wed Oct 21, 2009 6:49 am

Are you suggesting a more hardcore version of the coke can chrony?
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Unread postAuthor: kenbo0422 » Wed Oct 21, 2009 6:55 am

Well, I was going for something a little more sophisticated... :roll:

That, and a bunch of materials destructive testing data...
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Unread postAuthor: jackssmirkingrevenge » Wed Oct 21, 2009 7:18 am

If we could decide on a standard projectile, say a 6mm steel bearing, someone with a high pressure launcher, chrony and several sheets of ply to spare could up the pressure incrementally - measuring the corresponding velocity - and in an afternoon come up with a muzzle energy vs N<sup>o.</sup> of sheets penetrated charts.

I would volunteer but I don't have enough ply to waste :P
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Unread postAuthor: jeepkahn » Wed Oct 21, 2009 8:46 am

kenbo0422 wrote:Those are helpful evaluations.

The actual destructive test results of different materials would be helpful. Probably would find those on some scientific/engineering site, though. My gas gun easily penetrates the 3/4 ply at 1x, so I was wondering just what it took to penetrate certain materials, using the 1/4 inch projectile as a standard for measurement. My projectiles aren't blunt tipped, but I was going for more of a 'hammer' effect with the blunt tip. I think it would be interesting and helpful if that information were available here to be used as a guideline for the destructive / penetration benefits of a design. Using the chronies of course would be needed to find the actual speed, but with the possibility of someone else already having done these experiments, we could all benefit from that info. Well, at least I think so.

Thanks for the info, guys, it is appreciated.


This site has different materials being tested... http://www.theboxotruth.com/

I can't believe I beat JSR to it...
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Unread postAuthor: POLAND_SPUD » Wed Oct 21, 2009 9:00 am

@jeepkahn
yeah but first of all, JSR knows about the site and he often provides links to it.. and secondly, so far they tested firearms only
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Unread postAuthor: jackssmirkingrevenge » Wed Oct 21, 2009 9:49 am

jeepkahn wrote:I can't believe I beat JSR to it...


Had you bothered to check JSR's profile :)
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