propulsion system

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Work backwards from the stretched length with the gun fully cocked and ready to shoot. When bands stretch their volume does not change, they just get longer and thinner. Once you have decided on how much stretch you want to use work out the stretched length and diameters to extend the full length of the cocked gun in terms of the run of the bands. The uncocked or relaxed band lengths can then be calculated as you know the relaxed diameter of the bands. If you want some pre-stretch then you calculate that in the same way as pre-stretching means the bands before cocking occupy the band run lengths on the gun before being cocked, but if detached from one anchoring end would occupy a shorter length on the gun. Use too much pre-stretch and you risk shortening the life of the bands and may at the fully cocked position make them yield which may snap or permanently lengthen them thus losing power from the bands and effectively weakening them.

You need to take a length of the desired rubber size (or sizes), say 50 cm, and stretch it out progressively measuring the force after allowing the rubber to relax each time (which it will do on a cocked band gun). Say at double the length (1 meter), triple the length (1.5 meter) and quadruple the length, in other words 2 meters, if the rubber will take that amount of stretch. Measure both rubber diameter as well as the force with a measurement gauge and use stacked weights to apply the force using a pulley and hook on one end to dangle the weights. Armed with this data it is a simple job to work out the length of the non-stretched bands to be used on the gun before cocking. This is the scientific method and is exact rather than the pseudo-science you may have read elsewhere. If you do not comprehend these directions through language difficulties then find someone who does.