Day 0On ice 0 / 0Floe limit — animalsFreeboard — cmSkin — °CState —FPS 0

Drag to orbit, wheel / pinch to zoom. The floe slab is scaled to the simulated area and thickness and floats at the Archimedes freeboard; walruses glow pink when blood is sent to the skin (heat to lose) and stay brown when it is held back (cold). Animals that do not fit wait in the water.

Walrus Ice Floe: Freeboard, Blubber Heat Loss and Haul-Out Load Limit

How many walruses can one floe carry, what does resting on it cost in the cold, and how long does the ice last?

Floe and herd

Weather and sea

Walrus body and day

Time

Live readouts

Heat loss per walrus vs air temperature

Freeboard vs number of walruses

Floe thickness and carrying capacity over time

Independent numerical checks

Controls

Drag / one finger orbits, wheel / pinch zooms; the view buttons jump to the haul-out, a top view and the waterline.
Time scale = simulated days per real second; the floe melts or freezes while the clock runs. Reset floe restores the starting thickness and area.
Presets set several sliders at once; every slider can be changed afterwards.

The science

Buoyancy. Floating ice displaces its own weight plus the load: draft d = (ρ_i A h + M)/(ρ_w A), freeboard f = h − d. With no load f = h (1 − ρ_i/ρ_w) ≈ 0.107 h. The floe stays usable while f ≥ f_min, so the load limit is M_max = (ρ_w − ρ_i) A h − ρ_w A f_min. Space is a second limit: one animal needs about 4.2 m² (scaled by mass^2/3) at about 75 % packing. Real floes also tilt and break; this is a flat rigid slab.

Skin heat balance. Heat flows from the 36.5 °C core through tissue of conductance C = k_b/L_b (blubber k_b = 0.2 W/m/K) multiplied by up to 7 when blood is sent to the skin (vasodilation). Skin temperature follows C (T_c − T_s) = f_e h_a (T_s − T_sa) + f_i h_i (T_s − T_ice), with convective h_a = 6 + 3.7 v (wind v, m/s), sol-air temperature T_sa = T_a + 0.5 α I / h_a and ice contact h_i = 10 W/m²/K. Heat loss is Q = A C (T_c − T_s), body area A = 0.1 m^2/3 m². Resting metabolism is taken as 1.8 × 3.4 m^0.75 W.

Regulation. The animal chooses the conductance that makes loss equal to resting heat production if that lies between the vasoconstricted and fully dilated limits. Below the lower critical temperature it must burn more (shivering or raised metabolism); above the upper one it cannot shed heat in air and goes into the water. Huddling replaces air-exposed skin by body-to-body contact (no loss): f_n = 0.07 z with z neighbours.

Ice budget. dh/dt = (F_c − F_w − F_top)/(ρ_i L_f): conductive growth F_c = k_i(T_f − T_a)/h (Stefan; closed form h² = h₀² + 2 k_i ΔT t/(ρ_i L_f)), ocean heat F_w = 25 (T_w − T_f) W/m², surface melt from warm air and sun; the edge erodes at twice the basal melt rate. Snow cover, brine, waves and currents are ignored.

Illustrative parameters for an adult of about 1 tonne; real animals vary by sex, age and season. Walruses are protected animals and disturbance at haul-outs harms them: this page models only the physics of resting animals. Models (walrus, ice floe, polar terrain) built with Blender and rendered with Three.js.