Pick a scenario; every slider below stays editable.
Flat part: basal metabolism (thermoneutral zone). Left of the knee the owl burns more just to stay warm. Gold = your plumage, blue = 60 mm, red = 20 mm. White dot = today's air temperature; dashed line = lower critical temperature.
Holling type II: the catch saturates because every lemming costs handling time. Dashed horizontal line = lemmings per day needed to cover expenditure; where the curves cross is the break-even density.
The science
Heat loss. Body heat flows out through the plumage and then into the air: G = A / (teff/k + 1/h) in W/K, with surface area A = 0.16 (m/2 kg)2/3 m², plumage conductivity k = 0.035 W/(m K) (trapped air), thickness t (wind ruffles it: teff = t / (1 + 0.06 v)), and an outside coefficient h = 6.5 + 7.2 v0.6 + 4 ε σ T3 (forced convection plus radiation to the cold sky). Heat loss is G (Tb - Ta) with Tb = 40 C.
Metabolism. The basal rate is BMR = 3.79 m0.72 W (Aschoff and Pohl type allometry, m in kg). Below the lower critical temperature Tlc = Tb - BMR/G the owl must burn G (Tb - Ta). Hunting flight costs about 8 × BMR; heat from flight replaces thermoregulation, so the model takes the larger of the two. Only 25 % of the hunting time is spent flying (the rest is perch hunting).
Hunting. Lemmings sit under snow. The swept-area rate is a = 2 r v pcap q0 exp(-dsnow/25 cm) m²/s with detection half-width r = 20 m, search speed v = 6 m/s, capture probability 0.4 and the share of lemmings that are exposed or audible q0 = 0.004 (tuned so that moderate densities give a few lemmings per day). With density N and handling time h = 300 s the catch rate is R = aN / (1 + aNh) per second of hunting (Holling type II). Each lemming (55 g, 6 kJ/g fresh weight, 74 % assimilated) gives about 244 kJ.
Reserve. Fat is 12 % of body mass at 37.6 MJ/kg; days left = fat energy / daily deficit. The simulator draws catches as a random Poisson process (seeded), so the gold curve wanders around the green expectation.
Honest simplifications. Constants are typical or tuned values for a 2 kg owl, not measurements of one bird; no moult, no body-temperature drop, no mating or nesting costs; lemming numbers are static within a run (real populations cycle over 3 to 4 years); wind and snow effects are empirical-looking illustrations. Use it to see how plumage, wind and prey density trade off, not to predict a real owl.