Run
Orchard
Camera
Camera presets are on the stage; drag to orbit, wheel to zoom.
Layers
Quality
Numerical checks
The science
Terminal velocity
With the leaf held broadside, weight balances quadratic drag: M g = ½ ρ c CN v² with M = σ c per unit span, so vt = √(2 σ g / (ρ CN)). It does not depend on the chord.
Free leaf
A quasi-steady plate polar: CD=CDmin+(CN-CDmin) sin²α, CL=CL0 sin 2α, force ½ρ c U² C, acting at a centre of pressure s = c·cp·(1-sin α) ahead of the centre, plus rotational damping ½ρc⁴ Cr ω|ω|. Lift and a moving centre of pressure make the tilt oscillate (flutter) or run away (tumble).
Equations of motion
(M+Ma) a = Faero + M g, I θ″ = τ, added mass Ma = ρπc²/4, I = M c²/12 + ρπc⁴/128; the hero leaf and the reference use RK4 at 1 ms, the orchard leaves at 4 ms.
Honest simplifications
Each leaf moves in a vertical plane (orchard leaves get a random azimuth), so there is no true 3D spiralling; per unit span, isotropic added mass without Kirchhoff coupling, no vortex shedding memory, rigid flat leaf, still air unless wind is set. The orchard leaves are drawn larger than life (size slider) so they can be seen from afar; their physics always uses the real chord. Reynolds number is a few thousand, so results are qualitative.