MY SIMULATOR

Falcon Wind Tunnel

Lift, induced drag and the vortex wake of a bird wing.

INTERACTIVE 3D

L 0 NW 0 NL/D 0CL 0Re 0FPS 0

LIFT0 N

DRAG0 N

STROUHAL-

SLOW-MO⏱1x

Falcon in the Wind Tunnel: Lift, Induced Drag & Vortex Wake

A model falcon hangs in a glass wind tunnel. Change the air speed, the angle of attack, the wing span and the wing beat, and watch the air curl round the wing, the lift and drag change, and the tip vortices form behind it.

Model bird, illustrative values. Mass, wing area and drag constants are model values, not measurements of a real animal. The animal is only shown for science education.

Scenario

Air, wing and wing beat

Flight report

Lift coefficient against angle of attack

Power needed in level flight

One wing beat: lift and net streamwise force

Missions

Independent numerical checks

Also run outside the browser: node src/check.js (minimum-drag speed by golden-section search, Glauert lifting-line series, blade element sum against the closed form, circulation integral, induced-drag identity).

Model values and simplifications: parabolic drag polar with C_D0 = 0.03 [assumption], span efficiency e = 0.95, a thin-airfoil section slope of 2π corrected for finite aspect ratio, a soft stall above 15°, a single horseshoe vortex of the elliptic-loading strength for the picture of the wake, and a quasi-steady blade-element model of the beat (no leading-edge vortex, no dynamic stall, no feather flexing). Mass 0.8 kg, area 0.11 m² and span 1.05 m are illustrative [check against a source].

Controls

Drag / one finger: orbit; wheel / pinch: zoom; Hero / Top / Wake / Wing buttons (keys 1-4) move the camera; Space pauses.
Sliders: air speed U, angle of attack, wing spread (folding the wings), wing-beat rate and amplitude, and the bird's mass.
Scenario buttons load ready-made cases. The slow-motion slider slows the air and the wing beat so you can follow them.
Blue streaks are the air; gold arrows are the lift along the span; blue arrows are the downwash left in the wake.

The science

Lift. L = ½ ρ U² S C_L. For a thin airfoil C_L = 2π(α − α₀); on a finite wing the slope falls to a = a₀ / (1 + a₀/(π e AR)). Above the stall angle the flow separates and C_L drops while drag climbs.

Circulation and the wake. The lift needs circulation round the wing, L = ρ U Γ₀ (πb/4) for elliptic loading. The circulation cannot end at the wing tips, so it trails away as two tip vortices; they push the air between them downward at w = Γ₀/(2b). The streaks you see are advected by the Biot-Savart field of one horseshoe vortex.

Induced drag. Tilting the lift backwards by the downwash angle w/U costs D_i = L w / U = L²/(½ ρ U² π b²) for an elliptic wing; the polar is C_D = C_D0 + C_L²/(π e AR). A longer, narrower wing has less induced drag.

Best speeds. In level flight L = W, so slow flight needs a large C_L and a lot of induced drag, fast flight needs a lot of parasite drag. Drag is smallest at V_md = √(2W/ρS) (k/C_D0)^1/4 and the power at V_mp = V_md/3^1/4, with k = 1/(π e AR).

Wing beat. Each strip of the wing moves up and down, so the air meets it from a slightly different angle: on the downstroke the angle of attack grows and the force tilts forward (thrust), on the upstroke it shrinks. The Strouhal number St = f · 2A_tip / U compares wing-tip speed with flight speed; cruising birds and fish cluster near 0.2-0.4 [check against a source].

Not modelled: leading-edge vortices, dynamic stall, feather flexing and gaps, body and tail lift, ground effect, turbulence in the tunnel, tunnel wall interference (the tunnel is drawn bigger than the model assumes), vortex roll-up and decay.