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 Omega of a card of length \(l\), width \(w\) and thickness \(d (l≫w≫d)(l≫w≫d)\) scales as Omega ~ d^1/2w^-1, consistent with a simple dimensional argument that balances the drag against gravity.