If i was to use 80% of my strength to throw a 125 gram projectile X distance, how would that compare, powerwise, with using the same strength to sling same projectile with a sling same length as my arm (60cm)?
What formula or equation should i use?
Srff.

I think this question is too broad.
Is it a basketball, baseball, golf ball size??
Lots comes into play .
But as a general rule with correct technique I think you will throw further with a sling, or just as far with less effort.

Of course you can throw further with a sling.
How much more force is created by the extra 60cm sling length?
If i held a 125g stone and threw it underhand @80% strength.
Then a underhand sling throw @80% strength.

To properly answer this I think we need robots and some good maths.
Truthfully we don’t really know the equation because the technique is so dynamic.
Looking forward to other forum members responses

   I think such an equation would be impossible to come up with because of the variations in individual slingers' bodies, strengths, weaknesses, quirks, etc.  Using me as an example, I can't throw for crap.  So my slinging/throwing comparison would be very different from someone who has a good arm.  Mersa has the correct answer I believe.  We would need specifically designed robots to come up with an accurate equation. 

so to answer the actual question.

If you use a sling the same length as your arm, then you should - logically be able to get it twice as a far.
Realistically, because you use a completely different technique to use a sling you should be able to get it a lot further than twice as far.

I won all sorts of throwing competitions in my distant youth. Including welly throwing at the camp fete - against much taller kids.

Most british kids spend their youth kicking a ball - I always preferred to throw things.


This question gets interesting when you get a human with ridiculously long arms who is trained to throw.

I've always said if you could have got hold of randy johnson in his prime and have larry bray (himself a baseball pitcher in his youth) train him to sling - he'd have broken the world record with ease.

A skinny 7 foot tall MLB pitcher has arms longer than my arm and a decent length sling combined.
Could he throw further than i can sling ?
With a baseball - absolutely - those things are horrible to sling.
With a smaller, denser missile ? probably not. 

So yeah it does come down to the missile being thrown.
But on balance you should always be able to get it further with a sling - as long as you did both throws :-)

Its far too complex to come up with a simple equation, both distances are very dependant upon skill and specific training of muscles/actions and there are many variables with regards to ammo mass and sling design which will have non-trivial effects.

I'll say the basic facts that the energy (and therefore 'muzzle' velocity) of a projectile is a factor of the force applied and the arc over which it is applied. Longer slings create longer arcs but it's not always easy biomechanically to transfer the force. E.g. if you had a 30cm long arm and a 2m long sling you would simply not be able to utilise it very effectively. You can feel this in the tension of the cords being less. In contrast a very short sling can more easily max out the force but over a much shorter arc.

It's hard to even figure out clean rules for how slings work but when you consider that the physics is inevitably entangled with the human body you just enter another world of complexity.

There are a million factors and those are just the ones we know about. Everything from air density to the surface friction of the projectile can have an effect and even if they are tiny effects they might be adding up with other tiny effects to have a large overall effect. Broadly, slings throw further than just arms.

one approach is to throw for max range with sling and without sling and divide to find a ratio.  that will give you an empirical formula.

for me I think it is
sling velocity = 2 x pitching velocity
sling range = ~3.3 x long toss

(sling length 75-90cm)

and the range for a shot at 45° in vaccum is D= (velocity ^2)/g
https://en.wikipedia.org/wiki/Range_of_a_projectile

an average human today seems to throw 20-30m/s by hand
for an average human you would get 40m-90m long toss in vacuum
with sling (2x) 40-60m/s which give a range of 163m - 366m in vacuum
and 132m-297m with the 3.3x formula

as you can see this cant get more specific or accurate because there are too many factors in internal ballistics and external ballistics as others said above.

Sarosh wrote on Jun 30^th, 2020 at 4:35pm:

and the range for a shot at 45° in vaccum is D= (velocity ^2)/g https://en.wikipedia.org/wiki/Range_of_a_projectile an average human today seems to throw 20-30m/s by hand for an average human you would get 40m-90m long toss in vacuum with sling (2x) 40-60m/s which give a range of 163m - 366m in vacuum and 132m-297m with the 3.3x formula as you can see this cant get more specific or accurate because there are too many factors in internal ballistics and external ballistics as others said above.

I was literally just about to post all this. Nevermind I’m dumb.

Thanks folks for interesting answers.
I would say my max arm throw would now days be about 25m. With same weight ammo and my 60cm sling I could easily throw x3 that distance.
Some cricketers have amazing underarm throwing ability.

slingingrocksforfun wrote on Jul 1^st, 2020 at 4:37pm:

I would say my max arm throw would now days be about 25m. With same weight ammo and my 60cm sling I could easily throw x3 that distance.

it could be that you have trained much more with the sling than with the arm that you get more than 3x long toss.

P.S. : I think my bests are 70m with hand 235m with sling hence the 3.3x

Quote:

Some cricketers have amazing underarm throwing ability.

Except that underarm bowling is not allowed in the modern game of cricket.
Overarm bowling only.

You're probably thinking of softball pitchers and some women softball pitchers can produce amazing speed throws with purely underarm throws.

And despite how she speaks at the start - this video is NOT speeded up !
https://www.youtube.com/watch?v=si63WqBM1No

Holy moly batman, that girl can THROW !

she is slinging underhand, her arm is the sling.

Crazy fast. Reminds me of my sisters's boyfriend who's a former rugby player and built like a block of concrete. He's out ranged my slinging just throwing by hand before. It's, in fairness, not all that hard to out range me (I'm really not all that great at getting distance), but it is truly a sight to behold seeing him just launch stones across lakes like it's nothing. Makes all those feats of strength in the Viking sagas just that tad bit more believable.

CA,
I know about underarm softball pitching.
But I was thinking about the West Indies and Aussie fielders returning ball to bowler or aiming at stumps for run outs.
Srff

Sarosh - her arm movement and release is similar to my underarm slinging technique.

Sigh. Here we go again. :)
The sling is not a mystical weapon imbued with ancient power that cannot be described by mortal maths. It’s a piece of string.  That string acts as a transmission system that converts the high-strength but slow speed of an arm into a faster motion of a rock... as CA said, it basically acts like an extension of the arm, but he is also grossly oversimplifying it. An arm-length sling does not double the speed, because the sling lags behind the hand at some angle that brings it closer to the center of rotation. The effective length of the arm extension is less than the length of the sling. If you assume that the arm moves in a circular motion, the sling increases the speed proportional to the effective added length.... if the arm moves at the same speed with or without a sling.

Now... on to the  original question: power. The sling does not create power. It transfers power from the body. If you transfer 80% “arm” power into a 120g rock with your arm, and 80% power with a sling, then the power of the rock is EXACTLY THE SAME!  Certain athletes have simply learned how to transfer power more efficiently without an extension.  I know most people don’t drive stick-shift anymore, but it’s a lot like driving a car at 60mph in second gear vs third gear... either way you’re driving 60 mph. It’s just a lot easier to do in a higher gear.

NooneOfConsequence wrote on Jul 3^rd, 2020 at 8:30am:

Sigh. Here we go again. :) The sling is not a mystical weapon imbued with ancient power that cannot be described by mortal maths. It’s a piece of string.  That string acts as a transmission system that converts the high-strength but slow speed of an arm into a faster motion of a rock... as CA said, it basically acts like an extension of the arm, but he is also grossly oversimplifying it. An arm-length sling does not double the speed, because the sling lags behind the hand at some angle that brings it closer to the center of rotation. The effective length of the arm extension is less than the length of the sling. If you assume that the arm moves in a circular motion, the sling increases the speed proportional to the effective added length.... if the arm moves at the same speed with or without a sling. Now... on to the  original question: power. The sling does not create power. It transfers power from the body. If you transfer 80% “arm” power into a 120g rock with your arm, and 80% power with a sling, then the power of the rock is EXACTLY THE SAME!  Certain athletes have simply learned how to transfer power more efficiently without an extension.  I know most people don’t drive stick-shift anymore, but it’s a lot like driving a car at 60mph in second gear vs third gear... either way you’re driving 60 mph. It’s just a lot easier to do in a higher gear.

So if I read you right NOOC you, surprisingly I might add, are of the opinion that the sling is a mystical weapon imbued with ancient power that cannot be described by mortal maths?

I think that’s a new and bold direction to go considering especially you are an engineer who lets face it can be a stubborn lot. I do have to praise you for your forward thinking and opemindedness.

Along those same lines I tend to burn sage and center my chakras with an Amethyst crystal before heavy slinging sessions so as to harness my chi for maximum zen during my session.

Morphy wrote on Jul 3^rd, 2020 at 8:44am:

So if I read you right NOOC you, surprisingly I might add, are of the opinion that the sling is a mystical weapon imbued with ancient power that cannot be described by mortal maths? I think that’s a new and bold direction to go considering especially you are an engineer who lets face it can be a stubborn lot. I do have to praise you for your forward thinking and opemindedness. Along those same lines I tend to burn sage and center my chakras with an Amethyst crystal before heavy slinging sessions so as to harness my chi for maximum zen during my session.

;D That’s right Morphy... keep trolling my posts and I’m going to chakra your subpar face!   LOL!

NooneOfConsequence wrote on Jul 3^rd, 2020 at 9:20am:

Morphy wrote on Jul 3rd, 2020 at 8:44am: So if I read you right NOOC you, surprisingly I might add, are of the opinion that the sling is a mystical weapon imbued with ancient power that cannot be described by mortal maths? I think that’s a new and bold direction to go considering especially you are an engineer who lets face it can be a stubborn lot. I do have to praise you for your forward thinking and opemindedness. Along those same lines I tend to burn sage and center my chakras with an Amethyst crystal before heavy slinging sessions so as to harness my chi for maximum zen during my session. ;D That’s right Morphy... keep trolling my posts and I’m going to chakra your subpar face!   LOL!

It’s all out of love.  ;)

I like the gear analogy, makes perfect sense.

I alway think of the sling as a sort of fly wheel. It can store energy and then release it all.