Leatherback Dive Physiology (2D): Oxygen Stores, Buoyancy, Pressure and the Aerobic Dive Limit

Presets

Timeline

Position in the dive cycle

Live readouts

Graphs

Depth against time for the whole cycle (dive, then surface recovery)

Oxygen stores against time: lung gas, blood and muscle

Net buoyancy against depth (lung gas compressed by Boyle's law)

Metabolic power and mechanical swimming power

Oxygen used per dive against descent pitch (sweep with your other settings)

Numerical checks

running...

How to use

The turtle replays one full cycle: descent, time at depth, ascent, then a surface interval while the stores refill. Move any slider and the cycle is recomputed at once. The timeline slider scrubs through the cycle, the speed slider time-lapses it. Things to try:

Buoyancy cost. Raise lung inflation from 80 % to 100 % and watch the "buoyancy work" readout and the oxygen curve: the first 100 m of every dive is a fight against the air in the lungs.
Pitch. The last graph shows oxygen used per dive against descent pitch. A very shallow pitch lengthens the path (more drag), a very steep pitch makes the animal fight buoyancy hard; look for the minimum.
The diving reflex. Select "No diving reflex, fast": the aerobic limit drops from about 40 min to under 20 min.
Record-style dive. At 1200 m the lungs are long collapsed; some lung oxygen stays stranded and the verdict can flip to "exceeded".
Cold water. Lower the surface temperature: Q10 slows the metabolism and the limit lengthens.

The science

What this lab shows. How a leatherback turtle (Dermochelys coriacea), the deepest-diving reptile, spends a limited oxygen budget on a dive. Four ingredients are coupled: hydrostatic pressure, the lung gas that is squeezed by it (which sets buoyancy), the drag of swimming through water, and the oxygen stores that pay for the metabolism.

1. Pressure. Seawater is slightly compressible, so density grows with pressure, ρ = ρ₀ exp(β(p - p₀)), and dp/dz = ρ g. Solving gives a closed form:

p(z) = p₀ - ln(1 - β ρ₀ g z) / β, ρ₀ = 1025 kg/m³, β = 4.4×10^-10 Pa^-1

At 1280 m (the deepest recorded leatherback dive) this is about 13.0 MPa, roughly 128 atmospheres. The page checks the formula by integrating the ODE with Runge-Kutta.

2. Lung gas and buoyancy. The air in the lungs obeys Boyle's law, p V = constant, down to the depth where the alveoli collapse (a few tens of metres; the exact value is uncertain, so it is a slider). Below it the lung holds only the airway volume. The body displaces tissue plus gas:

V_gas(z) = V₀ p₀ / p(z) (z < z_c), F_B = g [ ρ_w(z) (M/ρ_T + V_gas) - M ]

With the default tissue density of 1.030 g/cm³ and 80 % inflated lungs the turtle is about 230 N buoyant at the surface (it must swim down), becomes neutral near 120 m, and is about neutral after the lungs collapse. Where F_B is negative the turtle can glide. The work spent against buoyancy on the way down appears in the readout ("buoyancy work").

3. Drag and thrust. Along the path at pitch θ: m_eff dv/dt = T - ½ρ C_D A v² — F_B sinθ (descending; the sign of the last term flips on the way up). The controller holds the cruise speed with the least thrust ≥ 0, so with enough negative weight the turtle simply glides and speeds up to its terminal speed v_t = sqrt(2 |F_B| sinθ / (ρ C_D A)). A = 0.16 m² x (M/450)^2/3, C_D = 0.12 (a ridged carapace is streamlined). At depth the turtle swims at 0.5 m/s and the flippers must also supply lift |F_B| at a lift-to-drag ratio of 5.

4. Oxygen budget. Stores: lung gas (21 % O2, three quarters usable) + blood + myoglobin, together about 20 to 25 ml/kg here. Metabolic power:

W = M w₀ Q₁₀^{(T_b - 28)/10} (1 - depression) + P_mech/η, O2 rate = W / 20.1 J per ml

Body temperature relaxes towards the water temperature with a time constant of about 40 min (a big animal has thermal inertia), which is why a deep dive into 4 to 10 C water slows the metabolism only gradually. The aerobic dive limit is the dive length at which the O2 stores reach zero: ADL = stores / mean O2 rate. The lung O2 can only be used above the collapse depth; at greater depth the remaining lung O2 is stranded until the turtle climbs again, so the real limit can be shorter than the simple ratio. At the surface uptake is a multiple of the resting rate, which sets the recovery time.

Checks in the page. (1) RK4 integral of the pressure ODE vs the closed form; (2) incompressible vs compressible pressure at 1280 m differ by the expected 0.3 %; (3) the neutral-buoyancy depth found by bisection equals a fixed-point Boyle solution; (4) integrating the equation of motion reproduces the terminal glide speed; (5) the oxygen drawdown equals the integral of the metabolic rate; (6) p V stays constant above the collapse depth.

Simplifications. One body compartment; fixed C_D; depression, collapse depth, Q10 and efficiency are plausible values, not measurements of a particular animal. Leatherbacks also use gliding, heat exchange, bradycardia and tolerate some anaerobic metabolism; none of the numbers here are a forecast for a real turtle. The record depth (about 1280 m) and the longest dives (about an hour and a half) come from different animals and tags. Educational model only.