Force to pull back rubber bands

I am designing another slip gear catapult, and I just want to know if there’s some formula for how much force/torque is required to pull a rubber band given the angle & the distances from where the catapult pivots to where the rubber bands are attached.
I’m just going to be freshman, don’t know a lot about physics, but I know very basic trigonometry.

There is an equation known as Hooke’s Law, which states the energy held within a spring is equal to the distance it is pulled back multiplied by some constant, added to some inherent load of the string. Obviously though, the rubber band will not maintain its elasticity. You could make a force - distance diagram, and see the force vs. distance in order to try to find the constant, but because of the fact that rubber bands will lose elasticity, its better to to just test amount of rubber bands.

@tmwilliamlin168 first off, I really would stay away from Skip gear this year. In my experience the amount of force required to pull back something that can launch a star is actually more than the amount of torque even high strength gears can handle, so you’re either going to end up with exploded gears or having to double up lots of gears. IMO slip hear isn’t worth it this year.

As for the formula, there are just to many variables to take into account to actually end up with an accurate result, like friction, motor efficiency, battery voltage, varying rubber band tension, etc. I would recommend mostly just guessing end checking, by starting off with a really high ratio and going down to find a sweet spot. A formula is going to either be too inaccurate or take too long to calculate, either way wasting your time.

I don’t need exact values, I just need relative values to compare things.

Rubber bands don’t quite follow Hooke’s law compared to a spring

It just says to pull the rubber bands slow and don’t hold them for too long.

Here is a sample of what 81M did for testing the different rubber brands this past year. Get a set of weights from physics class and measure the deflection of different weights to get the pull back force. Since rubber bands do not exactly adhere to Hooke’s law, you can see it is non-linear. They did this for a variety of rubber bands to find the right combination.

This will get you in the ball park.

I did mention that since the rubber bands lose elasticity over time, the so called constant would not be held constant, but the general principle holds. More than likely, if you found the constant every few matches, and used that value accordingly, you would probably get decent results.

I was under the impression that kx^2/2 was for energy within a spring, and kx was force. I realize I posted it wrong at first, but I did fix it, which makes sense, as kx^2/2 is the integral of kx.

@ShadowIQ was right the first time with kx as force. kx^2/2 is the work performed by a spring. I went back and looked at the Wired article above again, and I was way off with my understanding. It was actually saying that rubber bands do weird things when held under tension. My bad.

Is there a correlation in that data? I think maybe testing would be much easier now.