A 20 kg beaver works a woodland stream at golden hour. Chewing speed (incisor power over wood hardness) decides how fast a tree falls; bark feeds the animal under a Kleiber energy budget; logs are dragged to the dam; the dam raises the pond; the pond spills over a notch as a waterfall. Give orders, or let the beaver decide.
Educational model, not wildlife-management or dam-safety advice. One lumped pond, one working beaver plus a family that helps in the background. Constants marked [assumption] are typical orders of magnitude, not measurements. The stream depth below the dam is drawn for looks.
The science
Chewing. Wood is removed at q = Pmech(1 − 0.4F) / us cm³/s (Pmech = mechanical power of the jaws, F = fatigue, us = specific cutting energy of the wood, J/cm³: soft aspen ~10–15, oak ~35 [assumption]). Felling cuts an hourglass notch of volume V ≈ 0.26 D³ and cutting a stem through 0.14 D³ [assumption], so time grows with D³: a 12 cm aspen takes ~14 min, a 24 cm one ~2 h at the defaults.
Energy budget. Basal metabolism follows Kleiber: BMR = 70 M0.75 kcal/day (662 kcal/day = 32 W for 20 kg). Work costs BMR + Pmech/η with muscle efficiency η = 0.2; cold water adds 3 % per °C below 15 °C [assumption]. Bark gives ~0.55 kcal per gram fresh (digestible) [assumption] and can be eaten at ~150 g/h, so foraging pays off only if felling is quick — harder wood can starve the model beaver.
Hauling. Dragging a piece of mass m needs force μ m g (μ = 0.6 on land, 0.12 afloat); speed is capped by 0.55 m/s and by the available power (35 W), work μ m g d, metabolic cost work/η. Pieces are at most 75 % of body mass.
Dam. A trapezoid section (crest 0.6 m, faces 1:1.5) of length 14 m holds wood volume Vd = φ Ld H(0.6 + 1.5H), solid fraction φ = 0.3 [assumption]; each log adds m/ρw and the crest H follows. Wood rots slowly and is eroded if the water tops the whole crest.
Pond and waterfall. Storage V(L) and area A(L) come from the baked terrain heights (sorted-cell sums, exact for the mesh). dV/dt = Qin − Qseep − Qweir − eA. Seepage through the sticks is Dupuit-Darcy, Q = K(1 − s)Ld(h² − hT²)/2T; spill over the 3 m notch (0.3 m below the crest) is a broad-crested weir, Q = Cw B e3/2, Cw = 1.6. Raising the dam therefore raises the equilibrium pond level; the page's check solves that level independently by bisection.
Honest limits. No predators, no ice mechanics (winter only changes food and metabolism), one lumped pond, helpers modelled as a fixed wood income and food demand, trees regrow in the grove after 6 h, animals drawn slightly large.