Downstroke
- PitchLeading edge firstfront edge raised
- MovingForward →downstroke
- PushUp ↑ +1.00force proxy
The edge meeting the air first is raised, so air is turned downward and the wing is pushed up.
Changes only the wing's pitch. The wingtip path never changes.
View & settings
0% never turns over, 100% is bird-like. In between, the wing stands more upright on the return stroke.
- phase φ
- 0°
- half-stroke
- down
- x heave
- +0.000
- y stroke
- +0.000
- pitch θ
- 45°
- attack α
- +45°
- lift proxy
- +1.000
- drag proxy
- 0.000
- area down / return / net
- +1.55 / +1.55 / +3.10
Keys: Space play/pause · ←→ step · F flip · C compare · Esc back to full view · R reset
Same spot in the beat, same speed. Only the tilt differs, so the push differs.
Solid: your setting. Dashed: full flip (amber) and no flip (coral).
Simplified teaching model: one rigid, flat wing slice. Arrows show a normalized force proxy, not newtons; airflow is schematic. Real wings flex and get extra force from effects left out here. What the model leaves out
Why the flip matters
- Air pushes on a tilted wing roughly at right angles to its surface. What counts is the tilt relative to the way the wing is moving: the edge that meets the air first should be the raised one.
- Downstroke: the wing sweeps forward, leading edge first and raised. The push leans up.
- Return, no flip: same tilt, but moving backward the trailing edge meets the air first, and it is the low end. The push leans down.
- Return, flipped: the wing turns over so its leading edge leads backward, raised again. The push leans up.
Try it: press Freeze & compare. The wing is held at one moment of the return stroke (phase 5π/4: x = +1.000, y = −0.707) while only its pitch changes, and the force proxy swings between −0.50 and +0.50.
The model, honestly
- Force proxy:
(stroke speed)² × sin 2αfor one rigid flat-plate slice at 65% span, normalized so the mid-downstroke peak reads 1. Not newtons, not a measured lift coefficient, not CFD. - The wingtip path is fixed: x = sin 2φ (heave), y = sin φ (stroke). The flip changes only pitch and force.
- Left out: feather flex, camber effects, wake capture, the leading-edge vortex, added mass, rotational forces and real 3D flow. Drawn air is schematic.
- Symmetric by construction: with a full flip both modeled half-strokes give equal area. That is a property of the proxy, not a measured split, and positive force in both modeled half-strokes does not prove how a real hummingbird hovers.
- Drawing choices: the wing's underside is drawn paler so the two surfaces are easy to tell apart; the side-view loop exaggerates heave and prints the factor.
What experiments found
In hovering rufous hummingbirds, particle image velocimetry around the wing put mean downstroke circulation at about 2.1 times the upstroke (5 birds, Warrick, Tobalske & Powers 2009). An earlier wake study by the same group estimated roughly 75% of weight support from the downstroke and 25% from the upstroke.
These are study-specific measurements of circulation and weight support, not a universal split, and they are different quantities from this page's teaching proxy.
Sources & notes
- Warrick DR, Tobalske BW, Powers DR (2009). Lift production in the hovering hummingbird. Proc. R. Soc. B 276:3747–3752. Near-wing PIV in rufous hummingbirds; mean downstroke circulation about 2.1× upstroke (n = 5).
- Tobalske BW et al. (2007). Three-dimensional kinematics of hummingbird flight. J. Exp. Biol. 210:2368–2382. 3D wing and body kinematics of rufous hummingbirds (N = 5) from hover to 12 m/s; wingtip paths change with speed.
- Warrick DR, Tobalske BW, Powers DR (2005). Aerodynamics of the hovering hummingbird. Nature 435:1094–1097. Wake PIV: about 75% of weight support in the downstroke and 25% in the upstroke, with inverted camber on the upstroke.
The figure-eight is an idealized Lissajous path (x = sin 2φ, y = sin φ), not a traced wingtip. In the scene the wingtip's 3D path is drawn as the current camera sees it, so from most angles it does not look like the idealized loop. The slow-motion beat lasts about 4.2 s; a real hover beat takes a few hundredths of a second. Bird, wing and flower are original illustrations drawn in code; colors are a generic hummingbird, not a specific species.