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

Quantum Technologies for Fundamental Physics: exciting science awaits

Funding Physics Research

Oxford’s Department of Physics is playing a key role in three of the seven quantum projects supported by UK Research and Innovation (UKRI).

UK population movement falls 59%, compared to -89% in March - COVID-19 Monitor

COVID-19 Engineering Maths Research

The latest data from Oxford’s COVID-19 Impact Monitor shows the January lockdown has, so far, had one third less national impact on movement than the March shutdown. The figures demonstrate that some regions are still moving at more than 50% of pre-pandemic levels, despite the tough restrictions and calls for people to remain at home.

COVID-19 transmission chains in the UK accurately traced using genomic epidemiology

COVID-19 Research Zoology

A team of scientists, led by researchers from the Universities of Oxford and Edinburgh, has analysed the first wave of the COVID-19 outbreak in the UK and produced the most fine-scaled and comprehensive genomic analysis of transmission of any epidemic to date.

Light-carrying chips advance machine learning

Materials science Research

A team of international scientists has demonstrated an initial prototype of a photonic processor using tiny rays of light confined inside silicon chips that can process information much more rapidly than electronic chips and also in parallel - something traditional chips are incapable of doing.

Spotting elephants from space: a satellite revolution

Engineering Research Zoology

Using the highest resolution satellite imagery currently available, researchers at the University of Oxford Wildlife Conservation Research Unit and Machine Learning Research Group have detected elephants from space with comparable accuracy to human detection capabilities.

How is my town doing? A local view of COVID-19 reproduction rates

COVID-19 Research Statistics

Led by Professor Yee Whye Teh, a team from the Computational Statistics and Machine Learning research group at the Department of Statistics has built a model that monitors the daily spread of the virus locally.

Similar stories

Quantum Technologies for Fundamental Physics: exciting science awaits

Funding Physics Research

Oxford’s Department of Physics is playing a key role in three of the seven quantum projects supported by UK Research and Innovation (UKRI).

UK population movement falls 59%, compared to -89% in March - COVID-19 Monitor

COVID-19 Engineering Maths Research

The latest data from Oxford’s COVID-19 Impact Monitor shows the January lockdown has, so far, had one third less national impact on movement than the March shutdown. The figures demonstrate that some regions are still moving at more than 50% of pre-pandemic levels, despite the tough restrictions and calls for people to remain at home.

COVID-19 transmission chains in the UK accurately traced using genomic epidemiology

COVID-19 Research Zoology

A team of scientists, led by researchers from the Universities of Oxford and Edinburgh, has analysed the first wave of the COVID-19 outbreak in the UK and produced the most fine-scaled and comprehensive genomic analysis of transmission of any epidemic to date.

Light-carrying chips advance machine learning

Materials science Research

A team of international scientists has demonstrated an initial prototype of a photonic processor using tiny rays of light confined inside silicon chips that can process information much more rapidly than electronic chips and also in parallel - something traditional chips are incapable of doing.

Spotting elephants from space: a satellite revolution

Engineering Research Zoology

Using the highest resolution satellite imagery currently available, researchers at the University of Oxford Wildlife Conservation Research Unit and Machine Learning Research Group have detected elephants from space with comparable accuracy to human detection capabilities.

How is my town doing? A local view of COVID-19 reproduction rates

COVID-19 Research Statistics

Led by Professor Yee Whye Teh, a team from the Computational Statistics and Machine Learning research group at the Department of Statistics has built a model that monitors the daily spread of the virus locally.