Cookies on this website
We use cookies to ensure that we give you the best experience on our website. If you click 'Continue' we'll assume that you are happy to receive all cookies and you won't see this message again. Click on 'Find out more' to see our Cookie statement.

In a series of videos launching The Mathematical Observer, a new YouTube channel showcasing the research performed in the Oxford Mathematics Observatory, Oxford Mathematician Michael Gomez (in collaboration with Derek Moulton and Dominic Vella) investigates the science behind the jumping popper toy.

A jumping popper toy

 

Snap-through buckling is a type of instability in which an elastic object rapidly jumps from one state to another. Such instabilities are familiar from everyday life: you have probably been soaked by an umbrella flipping upwards in high winds, while snap-through is harnessed to generate fast motions in applications ranging from soft robotics to artificial heart valves. In biology, snap-through has long been exploited to convert energy stored slowly into explosive movements: both the leaf of the Venus flytrap and the beak of the hummingbird snap-through to catch prey unawares.

Despite the ubiquity of snap-through in nature and engineering, how fast snap-through occurs (i.e. its dynamics) is generally not well understood, with many instances reported of delay phenomena in which snap-through occurs extremely slowly. A striking example is a children’s ‘jumping popper’ toy, which resembles a rubber spherical cap that can be turned inside-out. The inside-out shape remains stable while the cap is held at its edges, but leaving the popper on a surface causes it to snap back to its natural shape and leap upwards. The snap back is not immediate: a time delay is observed during which the popper moves very slowly before rapidly accelerating.

The delay can be several tens of seconds in duration — much slower than the millisecond or so that would be expected for an elastic instability. Playing around further reveals other unusual features: holding the popper toy for longer before placing it down generally causes a slower snap-back, and the amount of delay is highly unpredictable, varying greatly with each attempt.

See more videos: Episode two: how fast the popper toy snaps, and how its unpredictable nature can arise purely from the mathematical structure of the snap-through transition.

Find out more about the Mathematical Institute at Oxford.

Similar stories

Seven MPLS researchers elected to the Royal Society

In all, eight scientists from the University of Oxford have joined the Royal Society as Fellows. All but one are from departments in MPLS Division.

Sale of donkey skins linked to trade in illegal wildlife products

Newly published research from WildCRU in the Department of Zoology, in collaboration with the Saïd Business School, raises important concerns about whether the trade in donkey skins is being used as a cover for smuggling elephant tusks, pangolin scales and other illegal wildlife products.

MPLS researchers make the Forbes Europe '30 under 30' list

This annual list is intended to illustrate the power that young entrepreneurs and leaders have to transform business and society.

Wytham Woods’ Great Tit study celebrates 75 years and reveals how spring has advanced a calendar month in that time

On 27 April 1947, the first Great Tit egg of the year was counted in the University of Oxford's 'living laboratory' at Wytham Woods. It was to be the start of a deep and on-going relationship between the bird population and generations of researchers.

Three MPLS researchers secure multi-million pound European grants

Four ‘excellent research leaders’ at Oxford, three of them from MPLS Division, have today been awarded major European Research Council (ERC) Advanced Grants to fund boundary-pushing research projects in Biology, Linguistics, Mathematics and Physics.

Sapphire fibre developed by Oxford engineering researchers could enable cleaner energy and air travel

As part of an EPSRC-funded cross-sector collaboration involving Rolls-Royce, researchers in the Department of Engineering Science have developed a sapphire fibre sensor that can tolerate extreme temperatures and has the potential to enable significant efficiency and emissions reduction improvements in aerospace and power generation.