How Sandfish Lizards Swim Through Sand: The Strange Biomechanics of Granular Locomotion

The sandfish lizard (Scincus scincus) was named in the medieval period for the apparent contradiction that the schoolroom version of biology made it: a scaly four-legged terrestrial animal that swims. The Bedouin populations of North Africa and Arabia have known about the behavior for thousands of years; medieval Arab pharmacology used powdered sandfish as a treatment for various ailments; the species appears in the writings of Avicenna. The actual mechanism of how a terrestrial lizard propagates through loose sand at high speed was not understood until 2009, when Daniel Goldman's biomechanics group at Georgia Tech used X-ray imaging to capture the lizard's body kinematics in the previously-opaque medium.

What the medium is

Sand is not a fluid in the technical sense. Fluids flow continuously under any applied stress; sand has a yield stress below which grains stay in place and above which the material flows. The behavior is properly called granular: a collection of solid particles whose collective response to stress depends on the packing density, the grain shape, the grain size distribution, and the rate at which stress is applied.

The 30-35 degree angle of repose that all dry sand displays (the angle at which a pile of sand will remain stable rather than slumping) is the macroscopic expression of the yield stress. Below the angle, friction between grains keeps the pile in place; at or above the angle, the topmost layer slides until the angle is restored.

The dynamics under disturbance are more complex. Slow stresses below the yield stress produce no movement. Stresses above the yield stress produce localized failure and grain rearrangement. Rapid stresses can produce momentary fluid-like flow followed by re-jamming as the grains settle into new contact networks. The sandfish's locomotion happens in this fluid-like regime: the lizard moves fast enough to keep the sand around its body in a continuously-failing state, but slow enough that the inertia of the displaced sand does not dominate.

The 2009 X-ray result

Goldman's lab worked at Georgia Tech with a small medical X-ray system, a transparent acrylic box filled with controlled-size glass beads (used as a sand substitute with reproducible grain properties), and sandfish lizards purchased through the herpetological pet trade. The X-ray imaging let them see the lizard's body inside the granular medium and track its kinematics frame by frame.

The result, published in Science in 2009, was unexpected. The lizard does not use its legs to push against the sand. The legs are held flat against the body, useless for granular locomotion. The propulsion comes from undulatory body waves: the lizard bends its body in a series of S-shapes that propagate from head to tail, similar to the body wave pattern of a swimming fish or a slithering snake. The undulation rate is around 1-2 Hz, and the wave produces a forward velocity of around 25 cm/s, comparable to the lizard's surface running speed.

The geometry of the wave is precisely controlled. The lizard maintains a body angle of about 22 degrees relative to its direction of motion, and the wavelength is about half the body length. The waveform is sinusoidal rather than the more triangular waves that some snake species use. The lizard's head is wedge-shaped to push sand upward as it advances, creating a temporary cavity that the body slides into.

The granular physics

The interesting question is why a fish-like body wave works in a granular medium where it would not work in, say, water (or rather: it works in water but produces different forces). The answer comes from resistive-force theory: the body of the lizard experiences forces from the granular medium that are anisotropic and have a specific dependence on body angle.

The lab measured these forces directly by dragging instrumented rods through sand at controlled angles and speeds. The result is that the force perpendicular to the rod is about three times the force parallel to it, at modest speeds. This 3:1 anisotropy is what makes the undulatory locomotion work: the body segments that are moving perpendicular to their length (the parts of the S-wave) generate more thrust than the parts moving parallel to their length lose to drag. The net effect is forward propulsion.

The 22-degree body angle that the lizard maintains is, according to the lab's modeling, the angle that maximizes the propulsive efficiency for the local granular properties. The lizard appears to actively select this angle: it does not just produce a body wave and let the granular physics sort it out, it controls the wave geometry to operate at the efficient point. The control mechanism is presumably hardwired in the motor system; the lizards do not require training to swim through sand and seem to do it from hatching.

The drag-vs-locomotion regime

The lizard's body wave is geometrically similar to the wave a swimming snake or eel uses, but the forces involved are quite different. In water, the swimming is dominated by inertial forces (the fluid has to be accelerated out of the way), and the body geometry that maximizes thrust is one that produces large transverse acceleration of the surrounding fluid. In sand, the swimming is dominated by frictional forces (each grain has to be pushed against the static friction of its neighbors), and the body geometry that maximizes thrust is one that exploits the perpendicular-vs-parallel force anisotropy.

The transition between regimes is gradual. In wet sand (where the grain interactions have a substantial hydrodynamic component) or in fluidized sand (where the grains have been agitated enough to behave like a fluid), the dynamics shift toward the inertial regime, and the optimal body wave geometry shifts accordingly. The sandfish operates in the dry-granular regime where the friction-dominated dynamics are correct.

The other granular swimmers

The sandfish is the best-studied case but not the only one. Several other lizard species swim through loose sand using variants of the same mechanism: Sphenops sepsoides, Chalcides ocellatus, several scincid lizards in the Australian deserts. The shovel-nosed snake Chionactis occipitalis of the American Southwest uses similar body-wave locomotion in sand. The sand boa Eryx species use a more saltatory mechanism. The diversity of solutions suggests that granular locomotion is a niche that biology has explored several times independently when the ecological conditions favor it (loose substrate, predator escape, thermal regulation).

The marine analogs (sand lances, dragonfish, certain eels) inhabit a different but related regime: they swim into wet sand and propagate through it using mechanisms that combine granular and fluid-like physics. The transition between these regimes was the subject of subsequent work by Goldman's group and others.

The robotics interest

The result motivated a substantial wave of robotics research. Robots that have to operate in granular media (Mars rovers, agricultural soil sensors, mine-clearance equipment) inherit the same physics problem that the sandfish solves. The standard wheeled-robot approach works on packed surfaces but fails in loose sand because the wheels just spin and dig. The body-wave alternative, demonstrated in several lab robots since 2010, is substantially more reliable for granular surfaces.

The applied work has not yet produced a commercial granular-locomotion robot; the body-wave robots are still in the lab. The barriers are partly engineering (designing actuators that can produce smooth body waves at the relevant frequencies in a compact form factor) and partly economic (wheeled and legged robots are good enough for most practical applications, and the niche where granular locomotion is strictly necessary is small).

The remaining puzzles

The basic mechanism is well-understood, but the details of how the lizard controls the body wave are still not fully characterized. The sensory feedback that lets the lizard maintain the 22-degree body angle in the absence of visual cues (it is, after all, underground) presumably involves proprioception in the body musculature and possibly some form of touch sensing through the scales, but the specifics have not been pinned down. The lizard's respiratory mechanism while submerged (it surfaces every few seconds to breathe) involves nasal valves and modified scales that probably also help keep sand out of the eyes and ears, but the integration with the locomotion is not fully characterized.

The longer-term evolutionary question is whether the body-wave locomotion is a derived feature in the sandfish lineage or whether it represents the ancestral state for a clade that has subsequently lost the capability in lineages that returned to surface locomotion. The phylogenetic comparative work is still ongoing.

Three observations

First: medieval Arab natural philosophers correctly identified the basic behavior of the sandfish in literature that survived for centuries, but the underlying mechanism had to wait for X-ray imaging and granular physics modeling that did not exist before the 21st century. The pattern of long-known biological behaviors revealing surprising mechanisms when modern instruments arrive is consistent: bee navigation, bird magnetoreception, plant cell-to-cell communication, fungal mycelial networks, salamander limb regeneration are all cases where the basic phenomenon was known for decades or centuries before the mechanism became accessible.

Second: the granular physics that the sandfish exploits is a recently-developed area of physics, mostly post-1985, with substantial parts still under active investigation. The biological example predated the physics by 30 million years (the lineage diverged from other scincids in the late Oligocene), which is the recurring pattern: biology is doing physics and engineering for hundreds of millions of years before human science catalogues what biology has been doing.

Third: locomotion adapted to a specific substrate is often poorly served by locomotion designed for a different substrate. The sandfish does not run on the surface using legs and then dive into the sand and use the same legs in a less efficient way; it has a completely different mechanism (legless body waves) for the granular regime. The recurring pattern in biology is that specialized environments produce specialized mechanisms that look unfamiliar from the perspective of less-specialized organisms. The implications for engineering are that copying biological mechanisms is often substrate-specific in non-obvious ways.

The deeper observation is that the inventory of substrates in which animals move is much broader than the schoolroom version of biology suggests. Air, water, and solid ground are the obvious cases. Granular media, biofilms, mud, fluidized substrates, tree canopy, ice, and snow each support animals adapted to that specific substrate, and each substrate has physics that differs from the others in ways that the locomotion adapts to. The sandfish is one example; the seal swimming through pack ice, the woodpecker climbing tree bark, the basilisk lizard running on water, the spider walking on water surfaces, and the gecko climbing glass are others. Each is the product of millions of years of selection pressure operating on the specific physics of the relevant substrate, and each represents engineering knowledge that the human catalogue is still in the early stages of recovering.