A glacier flows into a fjord and its front is stretched, so crevasses open from the surface. When a crevasse reaches sea level a block calves off, and a floating block either stays upright or rolls over depending on its shape. Orange bar = freeboard, dark wedges = crevasses, turquoise = meltwater, black and blue dots = centre of mass and centre of buoyancy. Constants are typical teaching values, not a forecast for any real glacier.
Fills the crevasse with 0 to 30 m of water and measures when the first block breaks off, against the closed-form prediction.
Press the button.
Simulates the roll of blocks with width-to-height ratios from 0.3 to 1.5 and finds where they stop rolling over.
Press the button.
The science
Why a glacier front cracks. Near a calving front the ice is stretched along the flow at a strain rate ε̇ (here flow speed / stretching length). Glen's flow law ε̇ = A τn with n = 3 gives the tensile stress that opens crevasses, Rxx = 2 (ε̇ / A)1/n. The rate factor A depends strongly on ice temperature (typical table values from 2.4×10-24 Pa-3 s-1 at 0 °C to 2.1×10-25 at -15 °C; spot-check before any serious use).
Crevasse depth (Nye zero-stress, Benn et al. 2007). Ice pressure grows with depth as ρi g z, so the net tension vanishes at ddry = Rxx / (ρi g). Water of depth w in the crevasse pushes outward and adds (ρw/ρi) w, so d = Rxx/(ρi g) + (ρw/ρi) w. The check above finds the same depth by bisection on the tip stress.
Calving criterion. The front calves when the deepest surface crevasse reaches sea level: d ≥ ha, where ha is the freeboard. A grounded front (H > Hf = (ρw/ρi) dw) has ha = H - dw. A floating front has ha = H (1 - ρi/ρw), about 11 % of its thickness. The two formulas agree exactly at flotation.
Front thickness over time. H = H0 - α (advance - retreat) - thin·t: the front advances at the flow speed onto thinner ice (surface slope α), the climate thins it, and each calving of length Lc moves the front back to thicker ice. For a grounded front the freeboard therefore falls at thin + α u and, once cycling, calvings come every α Lc / (thin + α u) days: a closed form tested against the time-stepped model.
Floating block stability. A rectangular block of width W and height H floats with draft d = (ρi/ρw) H. The metacentric height is GM = d/2 + W2/(12 d) - H/2; it is positive (upright is stable) only when W/H > √(6 (ρi/ρw)(1 - ρi/ρw)) ≈ 0.76 (the classical rectangle result used in iceberg-rollover studies, e.g. Burton et al. 2012). The 3D model does not use this formula for the motion: it clips the block polygon against the waterline, finds the heave that conserves displaced area, and takes the torque from the centroid of the submerged area, so the threshold is reproduced rather than assumed.
What is simplified. The glacier is a flowline slice extruded sideways, with a constant surface slope, constant strain rate and one idealised crevasse family (five wedges, depths scaled for clarity). Calving is a single deterministic trigger; real fronts also calve from undercutting by submarine melt, tidal flexure, damage history and melange back-stress, none modelled. Block length Lc is an input, not predicted. The berg is a 2D rectangle rolling about its centre of mass with an illustrative added-mass factor of 1 and a damping ratio of 0.1; in water shallower than its draft only the part that fits is kept ("thickness limited by the fjord depth"), as a grounded block cannot float. Waves are a visual pulse, not a hydrodynamic solution. Drift and melt of the berg are visual only. The time-lapse is paused while a berg rolls so the roll runs in physics time (multiplier selectable). The research boat is for scale only (about 14 m). Not a prediction tool for any real glacier.
Boat, mountain backdrop and ice/rock textures built and baked in Blender; scene and physics in Three.js. Educational model.