sn-pyramids.jpg

Bin Liu

Heavy bass. This subwoofer plays a constant beat that pumps the air up and down inside the wind tunnel. The diffusers allow air to flow without turbulence so that the paper pyramid floats inside.

The Unusual Physics of Floating Pyramids

By: 
Kate McAlpine
2012-02-07 14:55
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Think that floating pyramids are more metaphysics than physics? Think again. Results just in from an experiment that levitated open-bottomed paper pyramids on gusts of air reveal a curious phenomenon: When it comes to drifting through the air, top-heavy designs are more stable than bottom-heavy ones. The finding may lead to robots that fly not like insects or birds but like jellyfish.

Physicist Jun Zhang and his colleagues at New York University wanted to better understand how flying bugs control the orientations of their bodies. Do they have to work at it, or are they naturally stable? Robotics isn't yet to the point at which machines with flapping wings are easy to make, so Zhang's team chose to simulate the effect of flapping wings by creating stationary fliers floating on moving air. They used a subwoofer to oscillate the air inside a cylinder, "acting like a wind tunnel with air moving up and down," Zhang explains. At 10 to 50 beats per second, the tempo corresponds to wing-flapping at hummingbird speed.

The researchers placed hollow paper pyramids inside the cylinder. The objects were about 1 to 5 centimeters high and were made of tissue paper or letter paper on carbon fiber supports, like tiny homemade kites. Physicist Bin Liu led the experiments, attaching a beadlike weight to a post running down the center of the pyramid and changing the height of the bead to give the object a different center of mass. Common sense says that the pyramid should be most stable when the bead is at the bottom of the post, like ballast in the hold of a ship. But when the team released the pyramids over the subwoofer, the opposite was true: the bottom-heavy pyramids were likely to flip over and fall, whereas the top-heavy ones remained upright and continued to hover (see first video), the group reports in an upcoming issue of Physical Review Letters.

Airborne. A pyramid with a low-hanging weight can’t right itself; it remains tilted and falls. A top-heavy pyramid quickly straightens out and continues to hover.
Credit: Leif Ristroph

The team suspected that the effect was due to swirls of air that develop along the pyramid's sides. To see the swirls in action, Zhang's group examined a two-dimensional version of the pyramid experiment in water. They placed upside-down V shapes into a pan of water and rocked it to create currents. As the water ran past the V, it created tiny whirlpools at the ends of the V's two legs (see second video). These swirls pushed away from the upside-down V, moving downward, which exerted an upward force on the V-the same mechanism that creates lift in the pyramids.

Fluid movement. Tiny whirlpools appear as shadows at the ends of the V, generated by the water flowing up and down. If the V is level, the swirls go downward, exerting an upward push on the V, but if the V is tilted, the swirls go in different directions, and their combined push could straighten the V out.
Credit: Bin Liu

If the V was tilted, however, the swirls went in different directions: Those on the higher leg shoved it sideways, while the lower leg got a weaker upward push. This would straighten the upside-down V. Team member Leif Ristroph showed that the same sorts of swirls roll off the sides of the pyramids: They push the pyramid upright as long as the center of mass is above the tilted-up side, much in the same way that you can balance a vertical stick on the end of your finger by moving the bottom of the stick in the direction of the tilt, Zhang says. For bottom-heavy pyramids, this same mechanism causes them to flip over-it's like moving the top of the stick in the direction of the tilt, encouraging it to fall.

Robotics engineer Hod Lipson of Cornell University suggests that he may have already seen the stability mechanism at work in flapping, flying robots made in his own lab. "[This result] opens up new, unexplored design opportunities," he says.

In particular, Zhang's team suggests that flapping pyramid or cone robots could combine stability and maneuverability. They would quickly right themselves if they leaned further than 30° in any direction, but within 30°, they should move freely. Although the robots wouldn't be like any insect known to entomologists, the flapping cones would have living analogs in the sea. Computational scientist Petros Koumoutsakos of the Swiss Federal Institute of Technology in Zurich, whose team made a computer model of a swimming jellyfish in 2009, says that jellyfish create swirls of water similar to the swirls of air that balance the pyramids.

"The team proposes a very unique and interesting approach," says Hao Liu, a biomechanical engineer at Chiba University in Japan. He awaits experiments to show that flapping pyramids and cones can stay aloft.

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