Number 374 (Story #3), June 3, 1998 by Phillip F. Schewe and Ben Stein
TUMBLE AND FLUTTER: how paper falls to the ground is impossible to describe exactly with the laws of physics because of the mathematically intractable equations governing the fluid flow of air. To gain at least some understanding, scientists beginning in the 19th century, have modeled this problem in 2 dimensions. Now, experiments at the Weizmann Institute in Israel (Andrew Belmonte, University of Pittsburgh, 412-624-9385) have provided the first quantitative tests of these 2-D theories. In the experiment, researchers dropped thin strips of metal, plastic, and brass into a thin fluid-filled tank, which forced the strips to move in a two-dimensional plane. What determined whether the falling strips predominantly oscillated from side to side (flutter) or rotated end over end (tumble) was the Froude number, the ratio of the time it takes for the strip to fall its own length to the time it takes for the strip to move from side to side. Longer or lighter strips, which have a low Froude number (like an 8.5 x 11" page) flutter while smaller or heavier strips (e.g., a business card) tend to tumble. (Try it yourself.) The vortices set up by the falling strips may be relevant to the question of how airplanes stall, and may be exploited by insects to enable them to fly with great efficiency. (Upcoming article in Physical Review Letters.)
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