Tumbling cards

When a stiff rectangular card is dropped in still air with its long axis horizontal, it often settles into a regular mode of motion; while revolving around its long axis it descends along a path that is inclined to the vertical at a nearly constant angle. We show experimentally that the tumbling frequency Ω of a card of length l, width w and thickness d (l≫w≫d) scales as Ω∼d1/2w−1, consistent with a simple dimensional argument that balances the drag against gravity.