Physical modeling of real-world slingshots for accurate speed predictions

Abstract: We discuss the physics and modeling of latex-rubber slingshots. The goal is to get accurate speed predictions inspite of the significant real world difficulties of force drift, force hysteresis, rubber ageing, and the very non- linear, non-ideal, force vs. pull distance curves of slingshot rubber bands. Slingshots are known to shoot faster under some circumstances when the bands are tapered rather than having constant width and stiffness. We give both qualitative understanding and numerical predictions of this effect. We consider two models. The first is based on conservation of energy and is easier to implement, but cannot determine the speeds along the rubber bands without making assumptions. The second, treats the bands as a series of mass points subject to being pulled by immediately adjacent mass points according to how much the rubber has been stretched on the two adjacent sides. This is a classic many-body F=ma problem but convergence requires using a particular numerical technique. It gives accurate predictions (average error +2%, standard deviation 3%). The basis for these models involves measurements of pull-force vs. pull-distance. We will show how such measurements can be scaled for increased width or length, so that minimal calibration measurements are needed to support the models. With a good physical model of a slingshot one is easily able to test a wide range of parameters to determine how to get the fastest shots for a given pull force and draw length. We include examples of such calculations for popular slingshot rubber bands and tubes.