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Impact and damage. (Read 2921 times)
Mersa
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Impact and damage.
Dec 6th, 2017 at 4:12pm
 
So I've been looking into the complex theory of collisions and strait away I'm in too deep, I understand the principles in place but have trouble when trying to quantify it.

So the question in my head.
Are you always best throwing a small dense projectile.??????

I know that the properties of a smaller dense object are much better in flight for saving energy and have a better penetration.

But With projectile weight, hardness and strength all hypothetically the same but size changing is there a point were bring small is decreasing damage.

So how I've thought about it hypothetically

You have a ball of something like silicon
Projectile weight stays the same ( so does KE in flight) but size of projectile changes. Let's make them all spheres for ease
So a very small diameter will have best penetration.
A very large diameter will have more chance of pushing the whole ball of silicon.

So what I'm wondering is is there a point that if you were aiming to kill a person or a game animal that At some point the diameter is too small and a certain diameter is too big
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Colton
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Re: Impact and damage.
Reply #1 - Dec 6th, 2017 at 4:43pm
 
I think it matters. A very small ball may be able to penetrate through much but there wouldn't be much damage, at least bruising wise. A very large ball wouldn't do much either. Too much surface area being pushed back on by the target, and with too little weaight it will stop like a big styrofoam ball.
There is probably a minimum size of shot you've gotta use or I would think the slinger's effectiveness would fall. Maximum size and weight would be determined by the size and strength of the sling and the slinger's, right?
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JudoP
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Reply #2 - Dec 6th, 2017 at 5:04pm
 
If you put the KE of a bullet in a rugby tackle it wouldn't do a whole lot to you.

If you put it in a single proton, it would go straight through and you wouldn't even notice it.

If you put it in a bullet you are gonna do some damage.

If penetration is too high you risk disappearing through the target without depositing all that much energy or causing any disruption, if it's too low the energy deposited is too spread out to cause any damage.

It may depend quite a lot on the target too. Think how little energy a bullet deposits as it's shot through a layer of tissue paper.
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Mersa
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Re: Impact and damage.
Reply #3 - Dec 6th, 2017 at 5:33pm
 
Ok so let's say hypothetically that the target is a boar.

3 different points that you hit it broadside.
The head , the vitals (shoulder ribs) and the rear(back bum shoulder).

Let's say there are 5  sizes of ammo and the 5 effects are
Completely pass through (smallest diameter) , embedded halfway in pig, half diameter of projectile embedded, projectile hit and drop no penetration and bounce back off pig(largest diameter.

Now what is the best given we don't know the diameters ??

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Teg
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Reply #4 - Dec 6th, 2017 at 5:54pm
 
Mersa wrote on Dec 6th, 2017 at 5:33pm:
Now what is the best given we don't know the diameters ??


Difficult question because too many undefined variables Wink Define a figure of merit (FOM) to measure your success. Then we can make a model to optimize this FOM. If your FOM is death = true, then you have different possible answers depending on your initial parameters (how much energy available).

A lot of energy available: all answers = death
not much energy available then most probably  halfway embedded.

More detailed answers will depend on your (mathematical) pig model.

(I'll post a little mathematical "game" once I'm done writing it down.)
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Thearos
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Reply #5 - Dec 6th, 2017 at 5:59pm
 
I had a discussion once with Aussie, of blessed memory, about the stone which some ancient sources mention as used in war, the "hand-filler", say about egg-sized or a bit more, 150-200g stone. I find these daunting to sling, but they really preserve energy-- and presumably pack a lot of punch at the other end.
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Mersa
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Reply #6 - Dec 6th, 2017 at 6:30pm
 
So for the FOM let's say 2 different goals death on impact in 1 or more zones and best overall likely hood of damage resulting in you being able to recover or kill the pig.

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Teg
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Reply #7 - Dec 6th, 2017 at 6:45pm
 
Ok, here we go. The following is a little game for illustration.
It is very simplified and does not represent reality very good.

My figure of merit (FOM) is: Volume of displaced tissue (e.g. how "big" is the bullet tunnel)
This is distance traveled * cross section (FOM = s_p * A)


Model: The projectile comes. For penetration you need a bit of energy to get through the skin. This energy is proportional to the cross section of the projectile (delta_E = A * k). This energy is lost there.
Then it travels through the body (size: d_body). In the body, the projectile is decelerated proportional to its cross section (F = - k_tilde * A)

If it has enough initial energy, it will come out on the other side. Otherwise it will stop.

For the math see the appended picture. (You'll have to deal with my handwriting  Tongue )

Result: your FOM is maximized if the projectile is just small enough to completely penetrate. If it is larger it loses more energy when initially penetrating, if it is smaller it goes through and creates a smaller tunnel.
---

The FOM's (yes you defined two Wink ) that you defined are very difficult to translate into math and to model. I can't do it within a reasonable time frame. The FOM I defined above would most probably correspond to something like
"caused blood loss" or "percentage of muscle in limb destroyed". It does not take pure shock (e.g. hitting it with a club), cavitation (bullet) and all these other effects into account. Also, the boar is just an unstructured lump of meat and nothing more (no brain, lungs, etc.).

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FOM_sketch_V2.JPG (229 KB | 29 )
FOM_sketch_V2.JPG
 
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Teg
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Re: Impact and damage.
Reply #8 - Dec 6th, 2017 at 6:58pm
 
Mersa wrote on Dec 6th, 2017 at 6:30pm:
So for the FOM let's say 2 different goals death on impact in 1 or more zones and best overall likely hood of damage resulting in you being able to recover or kill the pig.


To clarify: That FOM would be very good for field testing. However, I'd say it's nearly impossible to model as there are too many factors.
Now you have to specify your model a bit more.
Say e.g. only hit to head allowed.
Then the model would include the combination of:
- simulation of momentum transfer required for knockout (or the probability of knockout)
- simulation of energy transfer to break the skull (or the probability of breaking the skull)
- simulation of penetrating the skull to the  brain.

Depending on your initial projectile mass and available energy you will obtain different answers for good or optimal FOM.


Edit: Thinking again, the relation you want is stopping power vs. projectile diameter?
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Mersa
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Re: Impact and damage.
Reply #9 - Dec 6th, 2017 at 7:17pm
 
I think your FOM is good for the intended discussion.
Works well for my first example of a silicon ball.
So basically if your not getting penetration go smaller and if your getting full pass through with momentum go bigger.
Also where full penetration isn't necessary. If you only need to go into half way or not even penetrate to do the job.




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Teg
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Re: Impact and damage.
Reply #10 - Dec 6th, 2017 at 7:28pm
 
Mersa wrote on Dec 6th, 2017 at 7:17pm:
So basically if your not getting penetration go smaller and if your getting full pass through with momentum go bigger.


Yes, that's exactly what this simple FOM says in combination with the very coarse model.
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Mersa
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Re: Impact and damage.
Reply #11 - Dec 6th, 2017 at 7:50pm
 
Thanks Teg .
The variables in the pig scenario are complex. I get that.
Makes  a lot of sense that small and dense is best. But I wonder where the relationship with lethality lies in slingers capabilities
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Colton
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Re: Impact and damage.
Reply #12 - Dec 6th, 2017 at 8:11pm
 
Also, would you want to kill it outright, or would causing concussion and finishing the job up close do the trick? That would also affect the size, density, etc of the bullet you want to use, as well as where you hit it. If you want to kill it quickly, then use a stone that would penetrate lungs, heart, any vital really. Concussion? You'd want a heavy stone to the head. Hitting the back legs might cripple it's rear end but it probably won't die or be knocked out. It'll just be really mad.
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Re: Impact and damage.
Reply #13 - Dec 7th, 2017 at 11:00am
 
Once you begin trying to extrapolate lethality out of the easier to quantify physical properties of the projectile and throw (not easy, but easier) everything becomes a bit more murky. You can read hundreds of pages of online forums of people arguing about which size broadhead and how many blades etc work best in real world conditions. Tests have been attempted to prove something one way or another but I'm not sure that's really possible.

Given the options I would choose a projectile that penetrates halfway through the body. Big enough to damage organs or major blood vessels, small, sharp and dense enough to achieve the penetration nessecary to get it fairly deep.


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Re: Impact and damage.
Reply #14 - Dec 14th, 2017 at 3:37pm
 
The most commonly used ammunition size throughout history depends on the type of ammunition being used.

If you're using stones, the optimal size seems to be somewhere between the size of a golf ball to medium sized chicken egg. Much smaller than a golf ball, and it won't have enough momentum to cause much more than a little bruise. Realistically, much larger than a chicken egg, and it you will not be able to sling it at a reasonable speed, and it will also not cause very much damage.

There are other factors though that are very unique to slings that limit ammunition size. If the stone is too small, it will be difficult to be accurate, since the stone will be too light to properly feel it as you spin the sling around. In addition, it won't have enough momentum to promptly pull open the pouch when released, resulting in an unintentionally delayed release.
Too big, and the ammunition will risk being released too early from most slings as the pouch won't be big enough to handle the ammunition properly. Very large ammunition will also increase the risk of spraining or pulling a muscle as it's being thrown.
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