The sandfish, a type of desert lizard, can vanish into a sandy substrate in a blink of an eye. Approaches that draw on mathematics, physics and engineering provide complementary insights into how the animal achieves this feat.
Biomechanists, with help from Isaac Newton and William Froude, have developed a good understanding of the forces involved in locomotion on solid ground1. Even if an animal should slip beneath the waves and undulate into the deep there are equations and techniques, courtesy of Claude-Louis Navier, George Stokes and computational fluid dynamics, that nicely explain and predict its motion2.
However, when an animal moves through a granular material, predictability and theoretical underpinning have been as elusive as seeing a world in a grain of sand. In a paper in the Journal of the Royal Society Interface, Maladen and his colleagues3 describe how they have used a refinement of their resistive force theory to show that a sand-swimming lizard moves forward about as fast as it can. Their model will allow biologists and engineers to explore locomotion in granular solids with unprecedented ease and speed.
Sandfish (Scincus scincus), also known as skinks, are not fish but lizards. They are drab, tan-coloured creatures with short, sprawling limbs. But they have one impressive ability—when startled, a sandfish can vanish completely into a North African or Middle Eastern dune in less than a second (Fig. 1). If you dig at the spot where it vanished you will find nothing but sand, the lizard having wriggled away under the surface.
In earlier work using X-ray videography, Maladen and colleagues4 found that sandfish move not by paddling with their legs but by undulating their bodies from side-to-side to swim through the sand. The sandfish throws its body into an S-shape with an amplitude of about 20% of its length. This sinusoidal wave travels backwards along the body at about twice the speed with which the animal moves forward, amounting to a wave efficiency of about 0.5. In their new work, the researchers used this conclusion as a benchmark for further studies with simulations, mathematical models and a robotic lizard.
The behaviour of a granular material such as sand is tricky to understand because it can act as both a solid and a fluid. The many small particles can flow like water but, under the right conditions, sand can be as unyielding as the rock from which it came. This is where resistive force theory (RFT) comes in.
The theory was inspired by models of tiny aquatic organisms moving in water, where movement is constrained by the viscosity of the fluid. In granular materials, however, it turns out that frictional drag is more important than viscosity, and drag values for short segments of the submerged object are an important input of RFT. One innovation of this work3 is the use of drag values derived from simulations rather than those laboriously gathered by pulling objects through media of differing density. Using the simulation-derived drag values and kinematics measured from videos, Maladen et al.3 found that RFT predicted the wave efficiency reasonably well, although not perfectly.
An alternative to RFT is a numerical modelling technique that takes into account the interactions of spherical grains with each other and with a deforming, submerged solid shaped like a sandfish. However, simulating sand-sized particles would take weeks of computer time. Fortunately, sandfish are happy to burrow in glass beads 3 millimetres in diameter. By observing the lizards moving through the beads, and then using the larger particle size in the simulations, Maladen et al. cut computing time to 'mere' days. The agreement between the simulation and the lizards' performance was better than that derived by RFT, but the procedure was much more time-consuming.
The advantage of both the RFT and numerical modelling techniques is that parameters can be varied to explore patterns and seek optima. Initially, the most striking result was the finding that wave efficiency continues to rise as the animal's body is thrown into higher-amplitude waves. But these sharp bends mean that the sandfish covers less forward distance with each undulation. When the forward speed was plotted against the ratio of amplitude to wavelength, the peak speeds occurred at ratios ranging from 0.19 to 0.27 for the various simulations. The authors found that the data collected from actual lizard performance lie at this same peak. Thus, it seems that when fleeing from a potential predator, kinematic efficiency takes a back seat to a speedy retreat.
Designing a biomimetic robot teaches you as much about biology as it does about engineering5,6. In this case, Maladen and colleagues3 used a sand-swimming robot to determine whether the theory, and the practice as demonstrated by the lizard itself, could be translated into the realm of engineering. The robot consisted of six connected segments, powered by servos, packed in a latex sock and wrapped in a spandex swimsuit.
The researchers showed that the robot is able to swim in granular media at similar speeds to those observed in the other models and in live organisms, but at efficiencies 30% below the predicted maximum. By simulating the segmented robot in the numerical model, they determined that this discrepancy in performance was due to the robot's low number of intersegmental joints. It was not until the researchers used more than 15 segments, creating a robot capable of forming a smoother curve, that wave efficiency approached a maximum. Perhaps the reason that many sand swimmers are elongate, smooth-bodied and small-limbed, with many vertebrae, is to better fall into a curve without the sharp bends that sap energy.
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Particulate Science and Technology (2017)
Journal of Mechanics in Medicine and Biology (2014)