Sorry, but David did not kill Goliath with a sling stone, he stunned him and then chopped off his head with a sword and that killed him.
Saul 17 50 to 51
50 There was no sword in the hand of David.
51 Then David ran and stood over the Philistine and took his sword and drew it out of its sheath and killed him and cut off his head with it.
Also, a sling imparts far more force to a projectile due to the length of the strings (fulcrum) and the speed generated (velocity).
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Will they kill small game, rabbits, squirrels and birds, certainly but because of those animal's physiology not the merits of the slingshot...You can get nearly the same results with a throwing stick like the Indians used...Slingshots kill by blunt force at only extremely close range, beyond basically spitting distance, they will only stun and you then have to finish off the animal by slitting its throat or breaking its neck or both...Why is that? Simple basic physics, ballistics and aerodynamics!
A round ball has the wind breaking dynamics slightly greater then a brick as any blackpowder shooter will attest to and why 125 yds. is usually considered maximum killing range--it starts off slow and gets slower with distance and what kills is penetration which can only be achieved with mass plus velocity...Decrease or increase one then the other has to be changed as well to achieve the same results...Penetration does not have to be through the skin--blunt force trauma as an example, but it has to be of sufficient force to shatter the cranium causing either lacerations to the brain and death or sufficient force to render them unconscious.
Why the marble drifts to the right is due to it being off centred in the pouch before firing unlike a baseball that uses force on its seams to impart curve.
The best projectile is a steel ball bearing and if you can get them free from a garage all the better but you can buy them new fairly cheaply and used from a scrap metal yard even cheaper...Second to that is a lead roundball of no less then .50 or .54 and .69 to .75 is even better...Why? Mass.
I use a slingshot when hunting to shoot rocks into the scrub brush to chase out deer from the cover and I've also used it to get grouse, partridge and rabbits while in a blind and opportunity presents them but you are only equipped with a HP rifle and of course you don't want to shoot to scare all the deer away, so you use your slingshot.
To augment a "short term" survival pack they are excellent, beyond that they are a lark, a toy, and should never be considered as an effective, efficient and reliable killer of anything beyond small game at close range...Also, you can not survive on a diet of small game for long term scenarios--you will die of protein starvation...Yes, you bloody well will! Read up on it and also called Rabbit Starvation.