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

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?

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.

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 ??

Mersa wrote on Dec 6^th, 2017 at 5:33pm:

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

Difficult question because too many undefined variables ;) 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.)

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.

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.

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  :P )

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.
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The FOM's (yes you defined two ;) ) 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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Mersa wrote on Dec 6^th, 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?

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.

Mersa wrote on Dec 6^th, 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.

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

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.

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.

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.

if the target is a boar - then you need a boar spear or a rifle - NOT a sling.

In reality, you can't have a too dense projectile for a sling. Osmium, which currently is the most dense metal known, would be optimal. however, it would be like 800 USD for a good gland. Affordable wise lead is the best option, which is definitely not that dense, to be a problem. Not even close. Osmium glans might just overpenetrate ,if they plow through only soft tissue.. but even that would be relatively rare.

Curious Aardvark wrote on Dec 15^th, 2017 at 7:45am:

if the target is a boar - then you need a boar spear or a rifle - NOT a sling.

For best results I agree.. a shotgun and some kinds of handguns would work in a pinch.. slinging stones at swine is not advised even with the best aim and ammo.

Ouch. Sounds like a lot of rifle and pistol caliber debates I hear from friends in the Army. 9mm V .45ACP, 7.62x51mm V 5.56x45mm, and so on.

My argument would be to use the models to get a range that will put your shot through the ribs and intercostal musculature, because there's a good chance of causing a Pneumothorax and collapsed lung, but without the resistance of the skull factoring in as armor with angles and penetration, deflection, etc.

Slings, like many projectile weapons, kill primarily by Exsanguination and Shock, so going through the lungs and just past the half-way mark would likely be your best bet, due to collapsing the lung and damage to high-pressure, high-volume blood vessels.

Figure out the depth of penetration necessary to get this, and you'll have a formula for energy required of any diameter of projectile, after that, it's just balancing mass and speed over that threshold, though I am willing to say you'd need to set a minimum for each to achieve you goal. I'm willing to say that larger cavitation is going to be more deadly every time, and at the speeds a slingstone travels at, you'll need to have a wider projectile. They just aren't going fast enough to induce the kind of temporary shock-cavitation a rifle or modern pistol bullet induces.

So, with possible energy a sling can dispense, you could get to a really complex model here. If you set the range based on a Sling's possible power output, you could give a table of weights and diameters that are viable for such purposes. But, that seems a lot of effort for not a lot of gain. Historic models should give us what we're going to learn, and I bet we'll learn that Boars aren't something the Sling can take on effectively.

Also, don't hunt boars without a .450 Nitro Express, .357 magnum, a spear, and a sword. Those things are mean.

(Edited for horrid spelling and clarity)

I have no doubt that a sling has enough power.
It's the other attributes that may make it less proficient in hunting. The boar was just an example I could have said duck or bear. My question is more to do with transfer of energy.
I can't say that a projectile needs to penetrate to do efficient damage. The answer I've received all have good points.

Someone needs to get a dead boar and try out some razor glandes on it. My money is on the sling. Blunt ammo I think would be a mistake.

A nice point would help!!

When I chased off momma pig with all her little ones, the little ones ranged from around 25-30 pounds, (10-15 kg) down to maybe 10 pounds (5 kg).  I have no doubt that an egg sized rock that connected anywhere on the smaller and on the head or shoulder area on the larger would have incapacitated it by breaking bones and possibly rupturing internal organs.

I didn't try it because I also figured that the little piggys' screams of pain would have also triggered an attack by momma pig and that I would have lost that fight.

Somehow, the thought of momma pig eating my guts was enough to make sure I didn't do anything particularly stupid. 

This time. 

This paper deals with your question. It compares different projectile sizes, densities etc.
https://www.ncbi.nlm.nih.gov/pubmed/28088089

The traumatic potential of a projectile shot from a sling.
Borovsky I, Lankovsky Z, Kalichman L, Belkin V.
Forensic Sci Int. 2017 Mar;272:10-15. doi: 10.1016/j.forsciint.2016.10.006. Epub 2016 Oct 26.

This is a great article Teg! Thanks for providing the link.

bear in mind that with a glande shaped projectile, impact is just one aspect.

The missile will be spinning at a serious rpm - so you also get a substantial drilling effect as well.

One reason you get so many oval or 'rough' historical lead glandes. The rough edges help it drill and cause even more damage.

It's also one of the reasons battlefields yield so many glandes. The opposition didn't pick them up and sling them back because they drill themselves into the ground.

I've been about 6 feet away from  alead glande hitting glrund after about 250metres flight - heard it in flight, saw it land. Didn't have a shovel so zero chance of recovery. That thing buried itself deep !

I like to sling smooth 120-150 gram stones against an old brick wall from about 20 meters using balearic style with a balearic sling. The first time I did that I thought I would be able to recover my stones as I thought the stones would simply bounce.
Turns out they completely shatter on impact. Doesn't matter what mineral stone I've used.
The power of a sling is very much dependent on its user. I see many beginning slingers sling with the wrong form with sidearm style. They take their back foot too high off the ground. I believe Luis Livermore's form is the most powerful practical slinging form and I've become quite good at imitating that.

LPL's style is the best combination of power, speed and accuracy I've ever seen. That's not to say it's the most accurate style ever, but as a combination of those three factors he's hard to beat.