# Thread: The physics and physiology of slings and slingers

1. ## The physics and physiology of slings and slingers

So recently I became quite interested in the actual working of the sling in order to reproduce the results that ancient slingers supposedly could achieve (hitting enemies 400 meters away with 1-pound weights). This came about because I was writing a midterm exam on classical mechanics for one of my physics classes (I teach at a local college) and, lacking other inspiration, I had them calculate how many rotations a second a slinger would need for a 400-m shot, and what the tension would be ...

Here's the upshot (no pun intended): Suppose you want to shoot a 1-pound weight 400 meters. And say you do it at a 45-degree angle, which (ignoring air resistance) would give you the greatest range at a given launch speed. Your launch speed would have to be about 63 m/s -- let's say 70 if you take into account air resistance and that you'd probably want a lower launch angle as it gives you better aim and these numbers are supposed to refer to accurate shots. If the cords of your sling are 1 meter long, then that would mean you'd need and angular velocity of 70 radians per second, or a little over 10 revolutions per second. And most images seem to depict slightly shorter slings, so you'd actually need more revolutions per second.

So then the tension in the cords (all together added up) would be mass times velocity squared over radius, or about 2000 N (rounded) -- roughly equivalent to the weight of 400 pounds. For comparison, that is about half the force required by modern Olympic hammer throwers -- however, those use two hands and their own body weight for balance.

A more conservative estimate -- say half a pound weight over a slightly shorter distance would still leave about 500-1000 N. This might be realistic, although it still seems really quite phenomenal to me, and suggests that a great part of the life-long training of Rhodian and Balearic slingers, say, was not just accuracy but also pure strength. Especially since the cords seem to be mostly supported through the motion of the wrist rather than the whole arm. It also means that unless slingers practiced on both sides rather than just their dominant hand they must have had somewhat asymmetrical bodies.

Or am I missing something here in terms of sling techniques?

2. ## Re: The physics and physiology of slings and slingers

I have no input for your question, but would merely like to express my great pleasure and joy on seeing that you got an entire university class to work out the physics of sling use as recorded from antiquity! The hard scientific data will, I am sure, be much appreciated by the EB team and general modding community, as there are lots of people on here hoping to get things that little bit more *right*.

Definitely +rep for you!

3. ## Re: The physics and physiology of slings and slingers

You use pounds when talking about physics? heresy to the metric religion!

4. ## Re: The physics and physiology of slings and slingers

I don't. I use metric or natural units for my purposes. Do you think I'm crazy? (Well, I am, but not that crazy.) The reference I used though refers to pounds and I learned the hard way that in the British and American society reference to such units gives many readers a more intuitive grasp of "how big" something is. Hurts me every time though.

Physics itself does not care about units. Units are only for our measly human convenience. Also, adherence to any form of religion, even the "metric" one, is highly unscientific! You are the true heretic, heretic!

5. ## Re: The physics and physiology of slings and slingers

Originally Posted by Neyak
I learned the hard way that in the British and American society reference to such units gives many readers a more intuitive grasp of "how big" something is.
but what about literally (almost) the rest of the world :'( ? i have no intuitive idea what a pound is. 0.4563478348573645873645873456 kg?...

also, you used metres. don't americans find feet or yards more intuitive?

6. ## Re: The physics and physiology of slings and slingers

I think Americans would find "feet" more intuitive, while British people might consider the "yard" natural ... I'm of (non-British European) origin and was under the impression that in the metric world the "pound" is just colloquial for half a kilogram (close enough to the Imperial unit for our rough estimates to not worry about that difference), but maybe that's not universally true. In any case, notice my original post used metric units for the most part, in particular, the final tension in the sling was in Newtons and only subsequently translated into a 'pound weight' to help some of the Imperial-unit folks around here. ... It's not the point!

What does add to my original point however is that the usual way to hold the sling is to wrap one end around your wrist and hold the other between your fingers (the latter is the one you let go, obviously). This means they must also have had a really strong grip in order to not have the second end slip through between their fingers. Unless they had some other technique. The more I'm looking into this, the more I am tempted to do some experimentation. Better find a big field with no one around because chances are my accuracy is not that of the Rhodians... Does anyone know of any reports on experimental archaeology of the sort?

7. ## Re: The physics and physiology of slings and slingers

Neyak, I find your question to be it very interesting: what was the real effective range of the slings? You can see on Youtube how to shoot, and that it may really do harm - but they show shooting at perhaps (just my eye) 20-40 meters, while I don't know if it's possible to be effective at, say, 70 meters. And 400 meters?

8. ## Re: The physics and physiology of slings and slingers

It makes no sense to say that "physics doesn't care about units" when you convert your said unit in Newtons without knowing if you use a pound or half a kilogram...

Now all you have to do is measure the mass of one of those projectiles, or use an average compulsing all the data... But if you suppose half a kilogram because that's what our grandparents used (it is true that the MKS system is also new for continental europeans, especially for common usage) but you don't really know the true mass, well your calculations will be screwed up.

Other than that, it is good to see that brain is used to try to counter common knowledge, because common knowledge is the first responsible for missunderstandings.

9. ## Re: The physics and physiology of slings and slingers

Originally Posted by Floren d'Asteneuz
It makes no sense to say that "physics doesn't care about units" when you convert your said unit in Newtons without knowing if you use a pound or half a kilogram...
What I mean by that is that you can work with whatever units you want, you'll get an answer that has the same physical meaning, just expressed differently. You could work in furlongs/fortnight for your speed and you still get the right answer, just expressed in different units. You just have to be consistent and convert correctly. I did most definitely not mean that you can just replace pounds by kg with the same numerical values. Goodness.

The whole calculation was a rough estimate, hence the difference between 453 g and 500 g leads to a roughly 10% error that I'm not worried about (is it 1000 N? Or 1100 N? -- doesn't matter. But it's not 200 and not 50,000). And we do have estimates for the true mass based on finds, including lead weights specifically designed for slings.

The source for the 400 m is http://chrisharrison.net/index.php/Research/Sling -- which I found following the reference from the Wikipedia page on the sling. In the article, the author states that some slingers might have achieved as much as 700 m (presumable without any accuracy), which just seems almost unbelievable to me. The recorded Guiness World Record, recorded in modern history, is 437 m, according to the same article (citing another reference), but in ancient days there were a lot more people spending a lot more time getting good at it, so chances are some would have achieved greater distances back then. In any case, that shots of several hundred meters were common is pretty widely accepted, I think. However, slingers were reported to have different slings for different distances, so they'd probably had some heavy-duty one for the long one -- maybe those had a different release mechanism, so you didn't have to hold a cord of 1000-N tension between your fingers? That's just me speculating, though. Any pointers would be great.

10. ## Re: The physics and physiology of slings and slingers

Thanks for the link Neyak! It was a very interesting read, and I was anxiously looking for a semi-productive way to avoid actually working!

It seems that the biggest aspect of the equation that is hard to grasp or recreate is the proficiency element. If it really was common for slingers from certain notable regions to be trained from childhood (a fair assumption, given that it was a dual use skill that would allow one to acquire food) then there is simply a huge amount of data that we can't rightly get at, unless you happen to know someone who trains their kids in antique weapons proficiency from a young age.

Regarding distance, I don't find the estimates from antiquity that outrageous, given that a contemporary man fired 437 meters, and he said he thinks he could have fired even further using a better sling and lead shots. If the sling reached its pinnacle of design in Hellenic times, and people then were also using some of the best designed shots ever (conical cast lead), then that would make a big difference already from what modern slingers can accomplish, and the higher proficiency easily makes up the rest of the difference.

A further interesting question that would be worth running by a medical professional (if you happen to know one) is how sling use as depicted from antiquity would affect a human's body. I mean, even if someone only rarely participates in combat or uses the sling for hunting, the proficiency required for such tasks would still necessitate regular practice. I would wonder if such practice would be highly damaging to the slinger's wrist, elbow, or shoulder, similar to the way professional American football quarterbacks or baseball pitchers often have shoulders that are just wrecked.

11. ## Re: The physics and physiology of slings and slingers

Ok...

- When you hunt, your goal is not to throw a rock at an animal at 400m distance. To try to advance closer to make sure that you hit precisely and with enough impact.
Because let's remember that while the projectile has a constant mass, it has a negative acceleration and will end rolling on the ground if the distance is too long. You won't kill or hurt anything with that.

- When you are at war, your goal is not to eyeball a guy, it is to hurl a rain of rocks (or lead or whatever) in a specific zone. You are looking for the zone effect, not the precision.
(Let's remember that the musket had the same purpose : to aim "in the direction of" the target (the big huge line in front of you). If you wanted more pricise shots, rifles were your choices.
Rifles radically changed our way of thinking war and shooting and often it is our perception of shooting that is seen in our interpretation of ancient weapons)

Because of those two things, I think it is improbable that anyone would use a sling to throw an object at 400m efficiently ("efficiency" being defined by the two assertions above)

If you can throw a projectile at 400m, it will not be efficient, either for hunting nor for war.
If you want to aim at a specific target, it is important to be close enough.
If you want to be less precise, you can allow yourself more latitude, but you still need enough velocity at the end to make damage.

So I think the assertion "we can throw a one pound rock at 400m" is not correct to begin with.

But what I think is irrelevant :

The two equations we have here should be related to :

- Deceleration of the projectile in the air (may be done by calculation OR with empiric data)
- what is the velocity of the projectile at the time it leaves the sling.

Your work gives us a lot of insight regarding the second point.

12. ## Re: The physics and physiology of slings and slingers

I don't see the point your are getting at Floren. Yes, when hunting you need to get close and be able to aim well. This just implies that you don't hunt with a sling from 400 m. When you are part of a military unit engaged in battle you are aiming for an opposing unit, and not individual men. This just implies that aim is not as important at range for military purposes. I don't think anyone has been saying that slingers would from 400 m or further be bulls-eyeing guys on the noggin. These are separate questions about accuracy and range, but both suppose a certain advanced ability with the weapon, both to get extreme precision at short range and moderate precision at long range.

We can drop all the hunting talk if that helps you, but there is no reason why a half kilogram stone fired from 400 m would be ineffective in war. For starters, from a (very rough) sketch of the flight path of a stone fired 400 m with a departure angle of 45°, it seems the its peak altitude would be about 200 m (ask Neyak though; he's clearly better with the math). Now, regardless of the velocity the stone has when it hits that apex, that means it will be falling roughly 200 m before it hits someone. I am no surgeon, but I would assume that regardless of where it hits you, a stone simply dropped from that height would do serious damage, even with you wearing some sort of protection. Given that there is almost no drag coefficient for a cylindrical stone flying point first through the air, the only appreciable deceleration would be from gravity on the way up, but that will be matched by gravity on the way down. The long and the short is that it will be going quite fast! As for the velocity of the stone when it leaves the sling, that is precisely what Neyak calculated to begin with, determining certain minimum velocities that would be necessary for achieving certain distances.
Originally Posted by Neyak
Suppose you want to shoot a 1-pound weight 400 meters. And say you do it at a 45-degree angle, which (ignoring air resistance) would give you the greatest range at a given launch speed. Your launch speed would have to be about 63 m/s -- let's say 70 if you take into account air resistance
Moreover, from the article Neyak posted it says that "An experienced slinger could throw projectiles at speeds over 90m/s, while the longbow could fire arrows upwards of 60m/s", adding that shot from a sling would also have a higher impact velocity because the vanes of an arrow slow it considerably in flight while a stone does not. If you haven't read that article, I'd recommend; it's quite good!

I guess my confusion is that you seem to simply be saying all of the references are lying, given that they often give distances of around 400 m (but also going far above that) and some of those references are from people who have no reason to play up the slingers' abilities. Is that you point, that 400 m is simply impossible, and the historians/scholars are trying to pull a fast one?

13. ## Re: The physics and physiology of slings and slingers

Simple : Because in the fisrt post of this thread, the friction of air is ignored.

So the trajectory of your projectile will consider the same velocity at the throw and at the impact, which is not correct.
No, for warfare, if you, as a target, are posted at a place where the rock will be too slow, you will not receive a lot of impact, especially with a shield.
If the throw initial speed is 70m/s, the speed when the object reach the targed will be reduced a lot.
I don't say anything else. What I mean is that to understand more about slings, we need to focus on air friction and object speed at impact, not on accuracy or object speed at launch.

Except gravity (on the Y axis, the projectile will move upward, facing gravity, then downward, in the same direction of gravity) there is nothing that will accelerate the projectile. It has an initial velocity and a negative acceleration due to air friction.

14. ## Re: The physics and physiology of slings and slingers

Again, I would suggest that you read the article Neyak posted above. The author, who appears to be a proper scholar in the domain, cites slings as having a roughly 30% higher departure velocity than longbows, and as having a much lower drag coefficient due to the arrow's vanes. An arrow has a smaller point of impact, granted, but that is the only advantage they have over slung stones or casted lead shot. Thus, if bows can be lethal, then why not slings?

I get your points entirely, but they directly contradict what historians say about slings and what modern scholars say as well. I am just trying to understand what your thoughts are: slings can't kill, they can't kill at range, they aren't/weren't effective weapons of war?

15. ## Re: The physics and physiology of slings and slingers

There's something wrong with some details (only?) in this article. Eg. this doesn't look much plausible "half a kilogram or more in mass were sometimes used in slings" as in another book I read that rhodian projectiles were 20-30 gram. Well, it's 20-time difference and I find it difficult to imagine throwing such heavy stuff with a sling. Or maybe he means that special slings mentioned by Vegetius, on a long (a few meters) shaft - but they were used for different purposes.
I'll keep reading and I'll post if I find something odd.

16. ## Re: The physics and physiology of slings and slingers

It is most certainly true that air drag will slow imply that the projectile hits the ground at a slower rate than what it had when leaving the sling. However:

1. The air resistance of a dense object (such as one made of lead), with a reasonable aerodynamic shape (such as those found), is fairly small compared to what is needed. So yes, your projectile is not going to arrive with the same 70 m/s with which you released it, but it might well still go at something like 50 or 60 m/s, which is still bad enough if you're at the wrong end of the trajectory. I'm obviously assuming throughout we're talking about roughly even ground -- if you shoot down a hill your projectile might well arrive faster than its initial speed. Yes, it has negative acceleration due to air resistance, but not enough to be harmless by the time it arrives -- Without doing the math (which is a pain because you can't really do it analytically, i.e. with pencil and paper and without a computer), you can still come to that conclusion -- because otherwise the same would happen to modern artillery shells and early modern canon balls and any other long-range siege apparatus in history. I suspect there are simulations for that sort of thing (taking air resistance into account) online, I will look.

2. The projectiles will not arrive rolling on the ground, or slow enough for someone to catch it, but they will dig themselves into the ground. Air resistance will actually mean that they hit the ground at a steeper angle than their launch angle (it would be the same in the air-drag-free case. I remember watching some youtube video of a guy experimenting with slings and he was complaining how he kept losing projectiles because they got stuck (and he had much lower velocities and weights than what we're talking about).

Very light (20-30 g) projectiles would likely have much lower ranges -- because air resistance is roughly proportional to forward-facing area of the projectile (that is, as "length squared") while mass is proportional to volume ("length cubed") -- so if you double the linear dimension of your projectile, keeping all else equal, your air resistance quadruples but the mass is eight times what it was, so overall the effect of the air resistance (in terms of the projectile's deceleration) is halved -- it's why it's easier to throw a fist-sized rock a significant distance than a small pebble, even though is easier to lift.

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