Flying Fox Night Flight: Wing Power, Foraging Range and Pollen Carry-Over Between Flowering Trees

A camp of grey-headed flying foxes leaves its roost at dusk to feed on eucalypt nectar. How fast should a bat fly to waste the least energy, how far can it commute, and how much pollen on its fur actually reaches a different tree? Change the bat, the wind and the trees and read the numbers.

Scenario

Preset

Time warp

Flight speed

The bat

The landscape and the night

Pollen

Live numbers

Flight power against airspeed

━ induced · ━ parasite + profile · ━ mechanical total · ━ metabolic (W)

Through the night

━ seed set (%) · ━ net energy per bat (kJ / 10) · ━ cross-pollen deposited (k grains / 10)

Experiments (simulated vs closed form)

Run an experiment. They use private copies of the model and do not touch your night.

Independent numerical checks

Also run outside the browser: node src/check.js.

Educational model with illustrative nectar, pollen and energy numbers. The 3D scene is a diorama: distances are compressed 100 times and trees and bats are drawn much larger than the distances they cover; the map in the corner shows true distances. The bats flap at the speed predicted for their size, not at simulation speed.

Controls

Drag or one finger: orbit; wheel or pinch: zoom; the view buttons switch between an overview, a chase camera that follows one bat, a flowering tree and the roost.
Pick a preset or use the sliders; the night runs from 19:00 to 05:00 and stops at dawn.

The science

Flight power. A flying animal pays three bills. The induced power is the cost of holding its weight up by pushing air down: P_ind = k (mg)² / (2 ρ S_d U) with S_d = π b²/4 the area swept by the wings, k = 1.2 a correction factor and U the airspeed. The parasite power moves the body through the air, ½ ρ S_b C_D U³, and the profile power drags the wings, ½ ρ S C_pro U³. Together P_mech = A/U + B U³, a U-shaped curve.

Best speeds. Setting the derivative to zero gives the minimum-power speed U_mp = (A / 3B)^1/4 (the speed for staying in the air longest) and the maximum-range speed U_mr = (A / B)^1/4 = 3^1/4 U_mp (the speed for the least energy per metre). With a constant basal part added to the metabolic power the best speed for range moves slightly higher; the model finds it numerically. Metabolic power is P_mech/η + BMR with η = 0.25 and a basal rate 3.5 m^0.75 W.

Wing beat. The flapping frequency follows Pennycuick's scaling f = m^3/8 g^1/2 b^-23/24 S^-1/3 ρ^-3/8: heavier bats with smaller wings flap faster. The 3D bats flap at this frequency in screen time.

Foraging. Each bat leaves the roost in turn, flies to the tree with the best ratio of standing nectar to distance, feeds for a bout (8 minutes by default, 0.25 kJ/s), and moves on until it has gathered its night's energy (default 600 kJ) before returning. Energy spent is the flight power times the flight time plus 1.3 × BMR while feeding. Trees refill nectar at a constant rate. Wind adds to or subtracts from the ground speed along each leg, so a headwind makes the same trip cost more.

Pollen. While it feeds, a bat's fur picks up pollen from the tree (up to a limit). At the end of each bout a fraction f of every load on the fur is deposited on the stigmas of that tree and a fresh load is picked up; grooming and wear remove pollen from the fur at rate λ. Pollen from the same tree counts only a quarter as much for seed set (self-incompatibility), and seed set is 1 - exp(-(R_out + 0.25 R_self) / R₅₀). For a bat shuttling between two trees the load of foreign pollen arriving at a tree has an exact steady state, x = G P / (1 - G² (1 - f)²) with G = e^{-λ(T_flight + T_bout)}, which is checked against the agent model.

Honest simplifications. Flapping flight is reduced to a steady-flight power curve (no acceleration, climbing or turning cost); the efficiency, drag coefficients, basal rate, nectar numbers, pollen quantities and seed-set constants are illustrative, not measurements; real flying foxes also eat fruit and leaves, commute tens of kilometres, forage in groups and roost in thousands; trees are identical. Check the literature before quoting any number from this page.