Bungee jump model with increased stretch-prediction accuracy

Abstract

This bungee jumping model improves the stretch prediction accuracy of prior models by including the effects of: rubber viscoelasticity, stiffness nonlinearities, jumper air drag, and jumper horizontal push-off. Bungee (bungy) cords are made from rubber, a viscoelastic material whose stiffness is a function of the number of cycles (cycle effect), the time interval since the last cycle (interval effect), strain rate, and temperature. Stiffness was measured, on an MTS machine, over 100 cycles at four intervals (1, 5, 60, 1440 min), three strain rates (0.17, 1.5, 5.0 s⁻¹) and constant temperature (20.5°C). At a constant cycle interval and strain rate, rubber stiffness decreased 9.8% from the 10th to the 100th cycle. This decrease was linear with the logarithm of the cycle number. Stiffness recovered 6.5% after 24 hours of non-use. Neglecting viscoelastic effects causes significant stretch-prediction errors of -11.0% (cycle effect), -3.2% (interval effect), and +1.6% (strain rate). Less significantly, neglecting jumper air drag, jumper push-off, and stress-strain nonlinearities cause prediction errors of +1.9%, +0.7%, and +0.2%, respectively. These errors are based on a typical cord, of unstretched length 7.5 m, that elongates 250%. For accurate stretch prediction, with typical sized bungee cords, viscoelastic effects are both more important and easier to implement than air drag and stress-strain non-linearity.