Puffin Cliff Colony (2D map)

Presets

Cost of flapping flight

Mechanical power in forward flight has three parts (Pennycuick): induced Pind = 2k(mg)2/(πρb2v) (falls with speed), parasite Ppar = ½ρSbCDv3 (rises with speed) and a constant profile term. Dividing by muscle efficiency η = 0.23 gives metabolic power. The U-shaped curve has a minimum-power speed vmp = (A/3B)1/4 and a faster maximum-range speed vmr where the tangent from the origin touches the curve.

Central-place foraging

A parent flies out, fishes, and returns with a bill-load of sandeels. The load builds up with diminishing returns, n(t) = nmax(1 − e−t/τ), while each extra fish adds weight (3 g) and so raises induced power on the way home. Flying out against the wind and back with it takes d/(v−w) + d/(v+w), always longer than in still air. Delivery rate n Efish / T is maximised by a finite load (Orians and Pearson), which grows with distance.

Chick growth

Daily intake times assimilation (0.75) pays for maintenance 150(M/0.25)0.75 kJ/day and the remainder builds tissue at 5 kJ per gram, so the mass plateaus where maintenance equals 0.75 × intake (capped at an adult-like 0.39 kg). A parent can also only afford a fixed energy budget for trips (the cap switches between time-limited and energy-limited).

Honest simplifications

All coefficients are round plausible values for a 400 g auk, not measurements of a particular colony; the route is a straight line with uniform wind, fish energy is a fixed 14 kJ per sandeel, and chick growth is a one-compartment energy budget with no weather, predation or provisioning by the second parent beyond the "parents feeding" factor. The model shows why distance and wind matter, not what any real colony will do.

Compare Near colony with Far patch: the best load grows and the chick plateau falls. Use Gale to see how a headwind on the way out stretches the round trip. In Tired parent the daily cap switches from time to parent energy, which lowers chick mass.