Sea snake swimming:
wave in, thrust out

Drag on the sides of a travelling wave pushes the body forward

INTERACTIVE 3D

Speed -

Wave speed -

Efficiency -

Strouhal -

Drag to orbit · wheel to zoom · the camera follows the snake · slow motion makes the wave easier to see

Presets

Body wave

Tail-beat frequency1.5 Hz

Wavelength / body length1.0

Tail amplitude / body length0.12

Head amplitude / tail amplitude0.25

Body and water

Body length1.0 m

Body diameter2.5 cm

Drag law

Tangential drag coefficient (quadratic)0.040

Normal / tangential ratio K (linear)2.0

Live numbers

Body shape (ghost frames, amplitude envelope)

Steady speed vs wavelength

Independent checks (live)

The science

Body wave. The snake bends its body into a wave that travels from head to tail: y(x,t) = A(x) sin(kx − ωt), k = 2π/λ, wave speed V = ω/k = fλ. The amplitude grows toward the tail, A(x) = A_t [a₀ + (1−a₀)(x/L)²].

Resistive force theory. Each slice of the body feels a force from the water that depends only on its own velocity, split into a component along the body (tangential, small) and across it (normal, large): linear F_t = c_tv_t, F_n = K c_t v_n (Gray and Hancock, tiny Reynolds numbers) or quadratic F = ½ρ d C v|v| (inertial regime, what a snake actually swims in). Because normal drag exceeds tangential drag, a sideways-moving slice that is tilted pushes the animal forward. The forward thrust is T = ∫(F_t − F_n y_x) dx.

Steady swimming. The swimming speed U is the root of ⟨T⟩(U) = 0 over one period (found by bisection). For small amplitude and linear drag the result reduces to U/V = (K−1) b²/2 with b = 2πA/λ: the animal slips backward relative to its own wave, so U/V < 1.

Efficiency and cost. Mechanical power W = ⟨∫(F_tv_t + F_nv_n) ds⟩; efficiency here is η = U D_straight(U)/W, the power needed to tow a straight body at U divided by the power spent. Cost of transport divides W by muscle efficiency (assumed 25 %), mass and speed. Strouhal number St = 2 A_t f/U; fast swimmers cluster around 0.2 to 0.4.

Simplifications: the body is treated as a slender thread in a plane with arc length approximated by the projected length (amplitudes above ~0.15 L stretch it slightly); no pressure recoil, no body inertia in the force balance (steady mean thrust only; the time-domain check adds mass); drag coefficients are typical round numbers, not measurements of a species; no ground or surface effect; the tail paddle area is not modelled separately (a real sea snake gets extra thrust from its flattened tail); the sea snake is generic, not a specific species. Sea snakes also surface to breathe, which this model ignores.

Independent educational model; the snake and reef are stylised illustrations.

Sea snake swimming:wave in, thrust out

Sea snake swimming:
wave in, thrust out