Self-similar retraction of a shot rubber-band

Stretching and shooting rubber bands is a familiar experience for both children and adults, yet the initial dynamics are so quick that they are generally missed. When a cut elastic strip is stretched from its end and suddenly released, the dynamics depend on a balance of stretching and inertia. However when a rubber band is stretched, a region of high-curvature is created and it is unclear how this curvature affects the dynamics. Here, we demonstrate that during the retraction of a circular rubber band, a wavelength develops at the rear which increases in size as time progresses. Through a combination of experiments and modeling, we investigate the speed at which the back of the elastic retracts and observe a self-similar shape that depends on stretching, inertia, and bending. These retraction dynamics illuminate how a rubber band can pass by a thumb when discharged without hitting it.