The Physics Of Falling Leaves


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Downward spiral

The leaves fall early this autumn, in wind. - Ezra Pound, The River Merchant's Wife
Neuron movement, cell division, and spreading fires. What do these disparate phenomena have in common? Each has been examined in the lab of the Weizmann Institute's Prof. Elisha Moses, who studies the physical properties of natural systems. But ask Moses about his work in the Physics of Complex Systems Department and he'll downplay the immediate benefits of his research. 'I grew up with the idea that a good scientific experiment is elegant, simple, and useless,' he says. 'I usually stay away from the applied side.'
One project, however, has definitely taken a practical turn. The story began in 1995, when then master's student Hagai Eisenberg walked into the lab and dropped a sheet of paper. The page fluttered serenely to the floor. 'This is what I want to study,' he told Moses, and began research into how non-spherical objects behave as they fall in a liquid or gas. The problem had been a challenge in fluid mechanics for over 150 years - ever since 19th-century physicists James Maxwell and Lord Kelvin attempted in vain to offer equations that accurately predict the path of such falling objects. Eisenberg and Moses, along with visiting scientist Dr. Andrew Belmonte, now at Penn State University, built a thin glass tank - so thin that it could represent a two-dimensional system - and filled it with liquid. They then dropped a series of thin strips, metal or plastic, into the tank.
By making precise observations with the help of computer-enhanced imaging and flow-visualization techniques, the scientists developed a theoretical model that could accurately predict the course a strip would follow as it fell to the bottom of the tank. This two-dimensional model can be extended to the phenomenon of falling leaves or other objects in three-dimensional systems.
The scientists found two general types of motion: 'flutter,' in which the falling strips move back and forth from side to side, and 'tumble,' in which the strips rotate end over end. Their calculations also suggested an inherent logic. The type of motion, they discovered, is determined by a numerical constant known as the Froude number. Originally defined to describe the behavior of sailing vessels, this constant is also used to predict the maximum speed at which two- or four-legged animals can walk or trot before they must begin to run or gallop. In the case of falling strips or leaves, the Froude number defines the relationship between the size of an object and its weight: a long strip will flutter while a shorter strip tumbles.
Papers were published, Eisenberg moved on to Ph.D. work, and the new mathematical model found its way outside the lab. 'The behavior of falling objects is endlessly harder to predict in the real world's three dimensions,' says Moses, a lesson he learned in a Manhattan movie theater, trying to drop a quarter into a cup on the bottom of a fish tank to win free tickets. 'Even though I knew the algorithm, I probably lost four or five bucks before my wife dragged me away,' says Moses. 'But our model is pretty good - I was close every time.'
The team found that their model could be used to explore not only how a leaf falls to the ground but also the way a ship goes down at sea as did the Israeli submarine Dakar, which disappeared in 1969. When news of the Dakar's discovery off the coast of Crete made headlines, Moses and Eisenberg realized that their understanding of falling objects could help naval researchers who were trying to understand exactly what happened during the ship's last moments. After three decades of mystery, their mathematical model together with three-dimensional experiments carried out in collaboration with the Israeli Navy, helped to quantify the motion of the original ship, providing new insights into the Dakar tragedy.
'It's rewarding to see how basic research probing the fundamental principles of how nature behaves, can suddenly prove to be of unique importance,' says Moses.
Prof. Moses' research is supported by the Levine Institute of Applied Science and Minerva Stiftung Gesellschaft fuer die Forschung m.b.H.