Clock 15:55Sun 0°Airborne 0 / 0Landed 0Alignment Φ 0Power 0 W/birdRaptor awayFPS 0

Drag to orbit, wheel or pinch to zoom. Dark birds are drawn about 5x life size. Blue streaks are the recent paths of 90 tracked birds. Orange glow marks birds alarmed by the raptor: watch the turn spread outward from them.

Starling Roost at Dusk

Turning waves, raptor pressure and the energy cost of flying in a flock, from the last light until the birds drop into the reeds.

Flocking rules

Flight

Dusk and raptor

Live readouts

Power curve of one bird

Alignment and alarm

Experiment: reaction time and a turn

Two identical 600-bird flocks fly side by side (same random numbers). In one, the 80 front birds are forced to turn 70 degrees for 0.4 s. The curve shows what fraction of the flock ends up pointing more than 10 degrees differently from its control twin. It runs on your device and takes a few seconds.

Independent numerical checks

Controls

Drag / one finger: orbit; wheel / pinch: zoom. Presets change the rules and the raptor together. Sliders act at once; "Flock size" and "Reset flock" rebuild the flock.
The dusk clock runs from the afternoon to after sunset; the sky, lights and the settling time follow it. Scrub it with "Dusk clock speed".
"Raptor strike now" sends a falcon in from 140 m away. It never catches anything: it breaks off after 9 s.

The science

Topological interaction. Each bird reacts to its k nearest neighbours (k = 6-7 in the field data of the STARFLAG project), not to everything within a fixed radius. Desired direction: d = w_a â + w_c ĉ + w_s ŝ + w_r r̂ + w_f f̂ + noise (alignment, cohesion, separation, roost pull, flight from the raptor); the heading then turns toward d with a reaction time τ: Δθ = θ (1 − e^−Δt/τ), capped at ω_max Δt.

Flight power (Pennycuick, fixed-wing form). P_mech(v) = A/v + B v³ with A = 2 k (m g)² / (π ρ b²) (induced) and B = ½ ρ (S C_D)_eq (body drag + wing profile, lumped). Minimum power at v_mp = (A/3B)^1/4, best range (minimum energy per metre) at v_mr = (A/B)^1/4. Chemical power is P_mech/η with η = 0.23; fat holds 37 kJ/g. Constants: m = 75 g, b = 0.38 m, k = 1.2, (S C_D) = 2.4×10⁻⁴ m² (model values, not a measured bird).

Banked turns cost power. In a coordinated turn tan φ = v ω / g and the wing carries n = 1/cos φ times the weight, so the induced term grows by n²: P = n² A/v + B v³. A flock that turns sharply therefore burns more fat. The tracked power per bird above is averaged over birds that are airborne.

Turning waves. In real flocks a turn spreads through the flock faster than the birds fly (20-40 m/s, Attanasi et al. 2014), explained by inertial "spin" dynamics. This model has only a first-order reaction lag, so it shows the delayed, spreading response and its dependence on τ, but it does not reproduce those measured wave speeds. Simplifications: point birds, no aerodynamics between birds, no wind, constant air density 1.2 kg/m³, birds drawn 5x oversize, a few hundred to a couple of thousand birds instead of 10⁴-10⁵, the raptor is a pursuit-curve agent. Assets built with Blender; scene by Three.js.