Morphy wrote on Apr 7
th, 2021 at 9:02am:
Ya, as has been said that is the big issue with shotgun slings. You are getting the worst of both worlds.
Imagine how much slower a 10 oz stone slings than a 1 oz stone. Now apply that same speed but instead of the benefits of much heavier ammo you have all the drawbacks of a slower, larger stone with all the drawbacks of a very light projectile.
For shotgun slings I assumed velocity of launch would be consistent regardless of ammo weight division but this is one other thing that makes the scaling even worse if you compare like for like launch energy. Air resistance scales as velocity squared, so higher speed is harshly penalised by air drag.
A 200g stone going 40m/s and a 40g stone at 90m/s have roughly the same launch energy (via 1/2mv^2) however the 200g stone will retain energy over it's trajectory much better. Even if it doesn't go as far it will hit with a much greater percentage of it's launch energy compared to the 40g fast stone which will have bled a lot of energy by the time it lands.
In fact you can work through the scaling on the drag equation to calculate that at launch the 200g will experience only 5^(2/3) * 0.4444^2 =57.7% of the drag force experienced by the 40g stone, even though it is much larger in size and 5x harder to decelerate for a given force due to its increased mass. So not only does the 200g rock require 5x the force to cause the same deceleration, but it's actually experiencing LESS force because per energy you can travel at a much lower speed.
tl;dr moving something fast is harder to do than moving something large in air.