Presets
Parameters
Live readouts
Model check
The science
Why a V saves energy
A lifting wing sheds a pair of counter-rotating tip vortices. Between them the air moves down (the induced downwash that costs the bird induced drag); outside them it moves up. A follower whose wing sits in that upwash gets a forward-tilted lift vector and needs less power. Induced drag from lifting-line theory is Di = L² / (½ ρ U² π b²) for elliptic loading, with downwash w = Γ0/(2b) and Γ0 = 4L/(π ρ U b).
Each bird's wake is modelled as a vortex pair a distance b0 = πb/4 apart with a Rankine core; the saving of a follower is the lift-weighted upwash over its wingspan divided by its own downwash, summed over every bird ahead and faded by an exponential decay length. The classic far-field upwash Γ h /(π (y² - h²)) is used as a numerical check.
What this view adds
The saving of a single follower as a function of its lateral offset (the sweet spot just outboard of the vortex), the mean saving versus flock size, and the per-bird numbers shown on every bird in the formation.
Simplifications
Steady far-wake vortices, no roll-up or flapping unsteadiness, no wing phase tuning (real birds time their flaps to the wake), identical birds, only the induced share of power can be saved. Flock-level numbers are indicative; published formation estimates (Lissaman and Shollenberger, 1970, and later work) are sensitive to exactly these choices.