The chameleon's tongue is said to unravel at the sort of speed that would see a car go from 0-60 mph in one hundredth of a second – and it can extend up to 2.5 body lengths when catching insects.
A team from Oxford's Mathematical Institute (working in collaboration with Tufts University in the US) derived a system of differential equations to capture the mechanics of the energy build-up and 'extreme acceleration' of the reptile's tongue.
The research is published in the journal Proceedings of the Royal Society A.
Derek Moulton, Associate Professor of Mathematical Biology at Oxford and one of the authors of the paper, said: 'If you are looking at the equations they might look complex, but at the heart of all of this is Newton's Second Law – the sort of thing that kids are learning in A-levels, which is simply that you're balancing forces with accelerations.
'In mathematical terms, what we've done is used the theory of non-linear elasticity to describe the energy in the various tongue layers and then passed that potential energy to a model of kinetic energy for the tongue dynamics.'
Special collagenous tissue within the chameleon's tongue is one of the secrets behind its effectiveness. This tissue surrounds a bone at the core of the tongue and is surrounded itself by a muscle.
Professor Moulton added: 'The muscle – the outermost layer – contracts to set the whole thing in motion. We've modelled the mechanics of the whole process; the build-up and release of energy.'
The researchers say the insights will be useful in biomimetics – copying from nature in engineering and design.