Presets
Playback
Wind
Mean speed plus gusts and turbulence.
Cloth
Changing weight or size restarts the flag.
Layers
Model checks
The science
Model
The flag is a grid of 25 x 17 point masses joined by structural, shear and bend springs (Hooke's law plus a damper along each spring). The left column is pinned to the pole. Each time step (1/600 s) sums the forces and integrates them with semi-implicit Euler:
m dv/dt = m g + Σ [ k (L - L0) + c dL/dt ] e + FaeroWind force
Each triangle of the cloth feels a pressure force proportional to the relative air velocity normal to its surface:
F = ½ ρ Cd A un |un| n un = (w - v) · nwith air density 1.2 kg/m3 and Cd = 1.2 for a flat plate. A cloth lying along the wind feels almost no force; once it bulges, the normal component grows, the flag is pushed, snaps back and flutters. The wind has a steady part, a slow gust and fast turbulence.
Honest simplifications
- No aerodynamic lift, vortex shedding or boundary layer: flutter here comes from the pressure-drag feedback plus elasticity, so frequencies are indicative only.
- No self-collision; the explicit integrator needs small steps and moderate stiffness.
- Real fabric bends and shears differently from isotropic springs.
What to try
- Try Dead calm: the flag hangs still and gravity stretches the springs a little.
- Steady flutter: read the flutter frequency; raise the wind and it rises.
- Heavy banner: heavier fabric droops and flaps slowly.
- Lower the stiffness and watch the maximum strain grow.