Slingshots are only good at the small scale. Human fingers are for dexterity. Mechanical fingers are too slow and fiddly; often SO slow that the heat energy stored in the rubber is lost. This leads to a spiral of failure.
The back of an envelope calculations are that we need a certain amount of potential energy.
Energy_potential (J) = mass * gravity * height.
Energy_potential (J) = 0.5 kg * 10 N/kg[1] * 10 meters.
Energy = ~50 J.
[1] 9.80665
I’m just going to assume 500 grams is enough for the total of the rope and weight.
Energy Kinetic = 0.5 * m * v^2
50 J = 0.5 * 0.5 kg * v^2
v = (50 J / (0.5 * 0.5 Kg))^(1/2)
v = 14.142 m/s
A small M8 bolt (M8 by 10 mm long) with an extra nut would be a better choice. Tie a fixed loop to match the diameter of the bolt. Make sure this knot is “rocket tight”, and the loop remains a tight match to the bolt. This tiny bit of rope is to make the supreme sacrifice, it will not be reused. Attach bolt through loop and secure using second nut. The line should be completely secured.
You want to stick with small dense projectiles, these are easier to hold and much easier to correctly release.
So “what if”
My personal view, which you are free to disagree with is 16 lbf is plenty. (I have used 23.5 Kgf or 51.8 lbf draws too, with very different goals.)
So the draw weight is a maximum of 16 lbf.
Ergonomically, a ¾ butterfly draw is the most powerful.
I’ve added a little extended fork, because why not... (OK maybe more than a little.)
I’ve set the draw distance as 132 cm, (Purely from the goal of cutting 7 blocks of a piece of flatband.)
Energy estimate: 48.4 J or 35.7 ft-lb
Speed estimate: 13.91 m/s
(These are my old assumptions…) If I use a ball of string, I need a bigger pouch. I quickly throw this out, The only slightly sneaky variable is the density of the ball of string. 500 kg/m^3 ?
Let’s re-do that draw length part, and think a little bigger!
I’ve set the draw distance as 157 cm.
(Purely from the goal of cutting 6 blocks of a piece of flatband!)
Energy estimate: 57.1 J or 42.1 ft-lb
Speed estimate: 15.1 m/s
Flatband stock:
0.7 mm thick, 150 mm wide and 2 meter long.
I choose the thickness to match the draw force I wanted. Most stock rolls are the size as above.
Bands needed:
33.33 cm long, I was aiming for 6 blocks from a 2 meter roll.
Each block can be cut to make 4 sets of bands.
Each piece of rubber tapers from ~21 mm at the fork to ~16 mm at the pouch.
By stacking individual pieces of rubber left to right, then right to left you should have neat little rectangle boxes, it’s less wear on the rotary knife and no wasted rubber.
The bands are to be tied to 28.9 cm.
Draw force: 15.72 lbf or 7.13 Kgf
Because I’m pulling a wild guess out of thin air for the weight of the string… the results are pretty meaningless. However the design of the bands is as good as I can do. With a suitable pouch (remember the pouch needs to be accelerated too!) you should get most of the performance.
If you want a peek behind the curtain:
I figure for a given draw that I can 'guess' the speed, with mathematics we can happily set the answer to whatever we like
Some simple rules, some healthy number crunching by a computer a few iterations... "edit that part out!"
So I figure14.75 m/s would be about right. By the power of strong nerdom I guess 278 grams would work. (This is the weight plus ball of string.)
Next I make it big guess of how dense this ball of string should be. (Technically a suitable 'carrier' like an M8 bolt should also be capable of taking ALL the energy without exceeding 61 m/s or 200 fps ... Accelerating things is pretty difficult, even with a very long draw.) An arborists throw bag is likely to be much much heavier than what I'm thinking. I might believe they got this part right.
So I'm left trying to guess the density of the string... which might as well be a dodgy black box. This is used to size the leather pouch. And I'm counting the weight of the leather...
So my latest answer is:
278 grams at 14.24 m/s or 46.7 fps giving 28.3 J or 20.9 ft-lb.
Q1. What about one of those dog ball throwing aids ?
Or using an Atlatl to throw a spear with line you know a bit of bushcraft.
