Press the button: GM from numerical hydrostatics, the bisection capsize threshold and the Archimedes balance are compared with closed-form values.

A free-floating iceberg of width W and height H (a 2D cross-section per metre of terminus) obeys Archimedes: it sinks until the displaced water weighs as much as the ice, so the submerged fraction is f = rho_ice / rho_water (917 / 1025 = 0.895 in sea water, so the draft is d = f H).

Whether it stays upright depends on the metacentric height GM = KB + BM - KG = d/2 + W^2/(12 d) - H/2 (B = centre of buoyancy, G = centre of mass). If GM > 0 a small tilt creates a righting couple; if GM < 0 the upright position is unstable. Setting GM = 0 gives the capsize criterion W/H = sqrt(6 f (1 - f)) (about 0.75 in sea water): tall, narrow bergs calving off a glacier terminus roll over. The plot shows the exact righting lever GZ(phi) computed by clipping the tilted rectangle at the waterline and finding its centroid; the berg settles at the angles where GZ crosses zero with a falling slope.

Roll dynamics use I phi'' = m g B_x with I = 1.5 (W^2 + H^2) m / 12 (a factor 1.5 for added mass) plus light damping; heave adjusts instantly. This is a rigid, 2D, quasi-static model: no ice fracture, no wave radiation, no melting, no neighbouring bergs. Same physics as the 3D page.