Elastic spheres can walk on water

Elastic spheres can walk on water

10 Pages · 2016 · 2.46 MB · English

Incited by public fascination and engineering application, water-skipping of rigid stones and spheres has received considerable study. While these objects can be coaxed to ricochet, elastic spheres demonstrate superior water-skipping ability, but little is known about the effect of large material 

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ARTICLE Received 23 Jun 2015|Accepted 27 Dec 2015|Published 4 Feb 2016 Elastic spheres can walk on water Jesse Belden 1, Randy C Hurd 2, Michael A Jandron 1, Allan F Bower 3& Tadd T Truscott 2 Incited by public fascination and engineering application, waterskipping of rigid stones and spheres has received considerable study While these objects can be coaxed to ricochet, elastic spheres demonstrate superior waterskipping ability, but little is known about the effect of large material compliance on water impact physics Here we show that upon water impact, very compliant spheres naturally assume a disklike geometry and dynamic orientation that are favourable for waterskipping Experiments and numerical modelling reveal that the initial spherical shape evolves as elastic waves propagate through the material We find that the skipping dynamics are governed by the wave propagation speed and by the ratio of material shear modulus to hydrodynamic pressure With these insights, we explain why softer spheres skip more easily than stiffer ones Our results advance understanding of fluidelastic body interaction during water impact, which could benefit inflatable craft modelling and, more playfully, design of elastic aquatic toys DOI: 101038/ncomms10551 OPEN 1Naval Undersea Warfare Center Division Newport, 1176 Howell Street, Newport, Rhode Island 02841, USA 2Department of Mechanical and Aerospace Engineering, Utah State University, ENGR 419J, Logan, Utah 84322, USA 3School of Engineering, Brown University, 184 Hope Street, Providence, Rhode Island 02912, USA Correspondence and requests for materials should be addressed to JB (email: [email protected]) NATURE COMMUNICATIONS| 7:10551 | DOI: 101038/ncomms10551 | wwwnaturecom/naturecommunications 1 W aterskipping has been studied for centuries with diverse motivations including: the ancient art of stone skipping 1–4 ; naval application 5–10 ; watersurface craft 11,12 ; and biological 13,14 and biomimetic 15 waterwalking While water ricochet of rigid objects has been well studied, the physics underlying the water impact of highly deformable elastic solids remains poorly understood 12,16,17 Compliant bodies such as inflatable boats 12and elastic aquatic toys 18,19 exhibit behaviour that is not readily explained within the traditional framework for rigid objects For such elastic bodies, an understanding of the coupling between the material response and hydrodynamic loading is essential in unravelling the overall dynamics An object obliquely impacting a water surface with sufficient inertia will carve a cavity on the air–water interface 20 and experience a pressuredriven hydrodynamic force dependent on object velocity, geometry and orientation 4,8,21–23 Waterskipping occurs when the upward vertical component of this force is large enough to lift the object off the water surface 8 Studies born from naval applications ranging from cannonball skipping tactics 5,8 to the dambusting Wallis bomb 10 have revealed an upper bound on the impact angleb o(angle between the freesurface and object velocity vector) below which rigid spheres will skip on water 7,8,10,21 Diskshaped stones are more amenable to skipping, particularly if one orients the stone at just the right angle 2 Further research has revealed more details regarding the oblique water impact of these and other canonical rigid body geometries 23–26 The referenced ricochet events are dominated by inertia, with negligible contributions from viscous and surface tension forces 4,20 In this regime, the physics of waterskipping also generalize to the waterwalking ability of basilisk lizards 13,14 and some birds 14,27 , and to surface craft slamming 11 In this work, we investigate the skipping of deformable elastic solid spheres on water We observe that elastic spheres can skip for impact angles nearly three times larger than predicted for rigid spheres Experiments and numerical modelling show that the spheres deform throughout impact in response to elastic waves propagating in the material In some cases these elastic waves actually interact with the air–water interface to create nested cavities We determine how the deformed geometry scales with material properties and initial impact kinematics Using an analytical model to relate deformation to the hydrodynamic lift force, we identify the mechanisms by which elastic spheres skip so readily on water Furthermore, we compute the normal and tangential restitution coefficients and find, surprisingly, that they display analogous behaviour to liquid droplets bouncing on inclined liquid films 28 Based on our findings about single impact events, we explain how elastic spheres are able to achieve multiple successive skips on water Results Elastic sphere skipping phenomena Prior research has reported an upper bound on the impact angle

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