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The Mechanics of Slithering Locomotion Depend on the Surroundings Author(S): Daniel I Wiggling Through the World: The mechanics of slithering locomotion depend on the surroundings Author(s): Daniel I. Goldman and David L. Hu Source: American Scientist , July-August 2010, Vol. 98, No. 4 (July-August 2010), pp. 314-323 Published by: Sigma Xi, The Scientific Research Honor Society Stable URL: https://www.jstor.org/stable/27859538 JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at https://about.jstor.org/terms is collaborating with JSTOR to digitize, preserve and extend access to American Scientist This content downloaded from 132.174.250.220 on Thu, 14 Jan 2021 18:00:08 UTC All use subject to https://about.jstor.org/terms Wiggling Through the World The mechanics of slithering locomotion depend on the surroundings Daniel I. Goldman and David L. Hu ards, for example, are known to forsake and opposite reaction forces from the an Movement al of animals.is critical Eels swim, for hawks the surviv their limbs entirely and wiggle their imal's environment. If the animal moves soar,' moles tunnel and squirrels leap bodies to move through dense grasses its body in particular ways, the sum of all to perform vital tasks such as foraging, or sandy environments. For other crea the reaction forces on the animal's body mating and escaping pr?dation. These tures, such as the thousands of species can propel the animal's center of mass feats of locomotion involve the coordi of snakes, slugs and worms (and a few forward. To simplify our model, we will nation of complex biophysical process lizards), legs were so superfluous that assume that our animals undulate in a es that span scales from the tiny (ion they have been completely limbless plane. Thus we can decompose the force channels in nerve fibers that depolar for millions of years. Their long, flex acting on the segment into two pieces, ize to send and receive information) to ible bodies enable them* to enter tight one tangential and the other perpendicu the intermediate (muscles and tendons crevices and to traverse long distances lar to the segment's surface. These are coupling to skeletal elements to gener through complex and often tortuous called the axial and normal forces, respec ate motion of body parts) to the large substrates such as the tops of trees, un tively (see Figure 2). For an undulating (interaction of body parts such as feet derneath the soil or inside the digestive animal to move, the summation of the and hands with their surroundings to tracts of other organisms. forward components of the normal forc effectively generate traction). A goal of Our recent laboratory work and es on the animal must exceed the back locomotion science is to uncover gen models of terrestrial limbless locomo ward components of the axial forces. To eral principles of movement through tion have elucidated the mechanisms determine if that is the case, we first must the development of models across that make undulatory locomotion effec calculate the reaction forces from the sizes. This challenge requires the col tive in two distinct environments: above animal's environment. Although math laboration of biologists, physicists, math ground where snakes slither (Hu) and ematically this approach seems straight ematicians and engineers. Such animal within flowing substrates such as sand forward, it requires input of models of locomotion studies are also inspiring the where sandfish lizards "swim" (Gold the environment, and this is where the design of vehicles with mobility equal to man). We hope to give a glimpse of new modeling challenge begins. or greater than that of animals. how such animals can move at speeds In fluid environments, such as those Many animals move effectively with of several body-lengths per second by typically encountered by swimming out the use of limbs. Some legged liz describing the movement of snakes and spermatozoa, nematodes or sea snakes, sandfish in turn,' and drawing attention we can use what are called the Navier to the specific adaptations these animals Stokes equations to account for force pro Daniel I. Goldman is an assistant professor in the use to enhance their performance in par duced by flows. These equations, named School of Physics at the Georgia Institute of Tech ticular habitats. Although the motion of after physicists Claude-Louis Navier and nology. He received his PhD. in physics from the these snakes and sandfish may appear George Gabriel Stokes, apply Newton's University of Texas at Austin in the Center for Non similar, these animals propel themselves second law to fluid motion, and account linear Dynamics, studying fluidization of granular media. He followed with postdoctoral training at the using substrate interactions that are dis for pressure and viscosity, in order to University of California at Berkeley in the Depart tinct to their respective environments, as describe fluid movement. However, we have determined with mathematical ment of Integrative Biology, studying biomechan these partial differential equations are ics of climbing and running cockroaches. He has and physical modeling. often impossible to solve analytically, been awarded a Burroughs Wellcome Fund Career so there are many approximate models Award at the Scientific Interface and a Sigma Xi Making the Model (such as Stokes' Law for viscously dom Young Faculty Award. David L. Hu is an assistant The common features of our approaches inated disturbances) that can be used to professor of mechanical engineering and biology at to mathematical modeling are derived rapidly calculate forces experienced by the Georgia Institute of Technology. He earned his from applying what's called the resistive swimmers and fliers. doctorate in mathematics from the Massachusetts force technique, developed to model the In contrast, environmental models for Institute of Technology, then served as an NSF terrestrial locomotion can be more com postdoctoral fellow and an instructor at the Applied locomotion of small organisms in fluids. Math Lab of New York University. Address for Consider a small rod-shaped "slice" of plex. Although dry friction can describe Goldman: School of Physics, 837 State Street NW, an undulating reptile. Muscular forces interactions with spme surfaces, we lack Georgia Institute of Technology, Atlanta, G A 30332 acting on the segment, combined with validated equations for many materials 0430. E-mail: [email protected] the inertia of the body, generate equal such as mud and sand. For surfaces that 314 American Scientist, Volume 98 This content downloaded from 132.174.250.220 on Thu, 14 Jan 2021 18:00:08 UTC All use subject to https://about.jstor.org/terms Figure 1. Although their undulations look similar, these reptiles' movements are governed by different mechanics. A corn snake (Elaphe gut tata) slithers across photoelastic gelatin, which transmits light where the snake applies the greatest force. Rather than pressing itself uniformly along the ground, the snake lifts sections of its body while slithering to increase speed and efficiency. A high-speed x-ray image (inset) of a 10 centimeter-long sandfish lizard (Scincus scincus) reveals that to "swim" within sand, the animal does not use its limbs but propels itself using only body undulation. (Images courtesy of the authors and Sarah Steinmetz, Mateo Garcia and Lionel London.) can be approximated by Coulomb (or stop moving forward, the animal simply mamba, sprint nearly as fast as a human dry) friction, resistance force is indepen stops slithering. This is unlike a large can run (5 meters per second). dent of speed, proportional to the ap snake swimming in water?if it stops Working in 2009 with Michael Shelley plied normal force and opposite to the di undulating, it coasts for a distance re of New York University, one of us (Hu) rection of motion. The response of a dry, lated to its initial speed. focused on the locomotion of juvenile granular material such as sand can be milk and corn snakes because of their like a solid or a fluid, depending on ap Above-ground Mechanics ability to slither in terrestrial habitats plied stresses and the compaction of the Snakes, and some snakelike lizards with such as prairies and rocky slopes. Like material. Moreover, the compaction can out legs, are a highly successful class of all snakes, they are capable of several change after a disturbance and thus drag terrestrial limbless creatures. They have gaits, or sequences of placements of their resistance in granular media depends on evolved to span three orders of magni limbless body on the ground. We investi the history of how it was perturbed. tude in length, from the centimeter-scale gated the most common of their limbless Despite these differences, slithering threadsnakes to 10-meter-long anacon gaits, slithering. This gait is also known locomotion appears to work well in wa das. All possess the same basic body de to biologists as lateral undulation, and its ter, on flat land and, as shown by one sign: a flexible tube of flesh covered in utility to locomotion in snakes has been of our recent discoveries, even through hardened scales. This form provides them previously described on the basis of so granular material. Undulatory locomo with tremendous versatility: They can called push points: Snakes slither by driv tion in dry environments, both above slither vertically up tree trunks, transition ing their flanks laterally against neigh and below ground, has an important fea from slithering on land to swimming in boring rocks and branches found along ture that makes the mathematics more water without changing gait, travel on the ground.
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