  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.
