FROM FLUTTER TO TUMBLE - INERTIAL DRAG AND FROUDE SIMILARITY IN FALLING PAPER

In an experiment on thin hat strips falling through a fluid in a verti cal cell, two fundamental motions are observed: side-to-side oscillati on (flutter) and end-over-end rotation (tumble). At high Reynolds numb er, the dimensionless similarity variable describing the dynamics is t he Froude number Fr, being the ratio of characteristic times for downw ard motion and pendular oscillations. The transition from flutter to t umble occurs at Fr-c = 0.67 +/- 0.05. We propose a phenomenological mo del including inertial drag and lift which reproduces this motion, and directly yields the Froude similarity. [S0031-9007(98)06387-X].