The mechanics of slithering locomotion

Abstract

In this experimental and theoretical study, we investigate the slithering of snakes on flat surfaces. Previous studies of slithering have rested on the assumption that snakes slither by pushing laterally against rocks and branches. In this study, we develop a theoretical model for slithering locomotion by observing snake motion kinematics and experimentally measuring the friction coefficients of snakeskin. Our predictions of body speed show good agreement with observations, demonstrating that snake propulsion on flat ground, and possibly in general, relies critically on the frictional anisotropy of their scales. We have also highlighted the importance of weight distribution in lateral undulation, previously difficult to visualize and hence assumed uniform. The ability to redistribute weight, clearly of importance when appendages are airborne in limbed locomotion, has a much broader generality, as shown by its role in improving limbless locomotion.

Fig. 1.

Frictional anisotropy of snakeskin. (A and B) One of the milk snakes used in our experiments (A) and its ventral scutes (B), whose orientation allows them to interlock with ground asperities. (Scale bars, 1 cm.) (C) Schematic diagram for our theoretical model, where X̄ denotes the snake's center of mass, θ̄ its mean orientation, and ŝ and n̂ the tangent and normal vectors to the body, taken toward the head. (D) The experimental apparatus, an inclined plane, used to measure the static friction coefficient μ of unconscious snakes. (E) The relation between the static friction coefficient μ and angle θ̄ with respect to the direction of motion, for straight unconscious snakes. Filled symbols indicate measurements on cloth; open symbols, on smooth fiberboard; solid curve derived from theory (Eq. 2) by using μ_f = 0.11, μ_t = 0.19, and μ_b = 0.14. Error bars indicate the standard deviation of measurement.

Fig. 2.

Dynamics of snake locomotion. (A–C) Position (X̄, Ȳ) and orientation θ̄ of the snakes on a horizontal surface. Open circles show experimental results; solid lines show the theoretical results from a lifted-snake model, dashed lines for a uniform-weight model. Error bars show the standard deviation of the measurement. (Insets) (a′ and a″) show photographic sequences of snakes moving on smooth and rough surfaces respectively. (D) Snakes' forward speeds Ū on an plane inclined at angle φ. Smooth curves represent theoretical predictions of steady-state speeds using μ_f given in the figure and frictional anisotropies of μ_t = 1.8 μ_f, μ_b = 1.3 μ_f. Three regimes of motion exist: for φ < 0°, the snake successfully slithers downhill; for 0° < φ < 7°, the snake successfully slithers uphill; for φ > 7°, the snake slides backwards when slithering uphill.

Fig. 3.

Dynamic load distribution of the snake during lateral undulation. (A) A snake undulating on a mirrored surface, lifting the curves of its body. Although this technique was used to facilitate visualization rather than to study locomotion directly, a similar behavior is observed on rougher surfaces, on which the snake progresses easily. (Scale bar, 1 cm.) (B and C) Visualization of the calculated propulsive forces on a model snake with uniform (B) and nonuniform (C) weight distribution. Arrows indicate the direction and magnitude of the propulsive frictional force applied by the snake to the ground. Red lines indicate sections of the body with a normal force <1; the red dot indicates the center of mass. Inflection points of body shape, shown in black, show where the load is greatest. Note that in these simulations, although the weight distribution is nonuniform, the snake's body remains in contact with the ground everywhere along its body.