Daffodil Biomechanics

Hit by a gusty spring breeze, the daffodil turns its back.

Story by Adam Summers ~ Illustrations by Sally J. Bensusen

Consider a field of daffodils: A carpet of gaudy yellow flowers dancing in the breeze, revealing in their movements the direction of each puff of wind. The contrast between the sunny petals and the vibrant green of the stems; the joyous waggle of each flower. This is the stuff of poetry and art.

Hidden away in the interplay between flower and stem, however, is also an elegant morsel of biomechanics that explains how this flower can act like a weather vane while others just sway back and forth. The petals of the daffodil, as well as those of many other plants in the genus Narcissus, do not point skyward (as do those of the tulip blossom, for instance) but droop to one side of the stem. This makes the flower appear to be gazing downward, giving it a charming air of contemplation. (The genus, of course, is named after the beautiful young man of Greek mythology who became so enamored of his reflection in a pool that, according to one version of the myth, he fell in and drowned.)

Not surprisingly, the reality is less romantic. Shelley Etnier, now at the University of North Carolina at Wilmington, and Steven Vogel, of Duke University, have studied the daffodil's nodding posture-which enables it to reorient in a breeze, essentially turning its back to the wind-and found that the explanation for this ability lies in the material properties and cross-sectional shape of the daffodil's stem.

Spider legs, bat wing bones, flower stems, and many other structures are subject to two different sorts of deformation: torsion (twisting along the long axis) and bending. A garden hose, for example, is not given to twisting but bends quite easily. (This can be frustrating to gardeners who use a long hose to water plants far from the faucet: pulling the hose often bends it, shutting off the flow of water and thus requiring the gardener to walk back along the hose to straighten out the kinks.) A flat plastic coffee stirrer, by contrast, resists bending but twists easily. A long, flat roadway suspended in a windy canyon above a river is not very good at resisting torsion either-as evidenced by the famous collapse of the Tacoma Narrows suspension bridge. On November 7, 1940, just one year after it was built, this bridge began twisting back and forth in the wind with such force that it broke apart and fell into the water below.

The main reason a garden hose doesn't twist much is that it has a circular cross section. Resistance to torsion is (sorry, math phobes) set by the fourth power of the distance of each bit of material in the cross section from the central axis, with all those fourth powers added together. For a given amount of material and for both hollow and solid structures, a circular cross section maximizes that number and thus gives the best resistance to twisting.

Slice across a tulip stem, and you will see that it, too, has a circular cross section. In contrast, a cross section of a daffodil stem looks more like a football, or a lemon, cut the long way. This lenticular shape is less able to resist torsion but does resist bending (flexing) quite well, as long as the force hits it on the narrow edge. (For example, a floor joist-often a two- by eight pine board-is always set with its narrow edge up, which gives it a tall and narrow cross section. If the joist were set the other way-with the wide edge up-the floor would bounce like a trampoline.)

To measure torsional stiffness in daffodil and tulip stems, Etnier and Vogel used an ingenious device that holds one end of a stem still while twisting the other end with a known force. The stiffer the stem, the fewer degrees it rotated. The scientists also measured bending stiffness by propping the ends of the stem up on a couple of blocks and then hanging a weight from the center. The stiffer the stem, the less it drooped. These two measurements gave the ratio of twistiness to bendiness. Not surprisingly, the twistiness of the daffodil was much higher (fourteen times higher, in fact) than its bendiness, explaining why these plants are far more likely to turn in the wind than to bend over. This ratio was nearly twice that of the upward-gazing tulip.

Etnier and Vogel also conducted experiments to find out why daffodils don't merely twist in the wind but do so with their blossoms facing downwind. Placing cut flowers (on intact stems) in a wind tunnel, they showed that the force on the bloom is highest when it is facing into the wind and lowest when it has rotated 180°. Flowers started to twist in response to the wind when it hit speeds of about 12 miles per hour; by 22 mph, they had completely turned their faces away from the wind. As wind speed increased, the petals consolidated themselves into a tighter and tighter bundle. Even at nearly 35 mph, the flowers remained undamaged. Above 20 mph, however, the stem began to bend over in addition to twisting, bringing the flower closer to the ground, where wind speed is lower.

I would like to think that these observations might have a positive influence on the design of useful objects-umbrellas, for instance. Most of us know from soggy personal experience that umbrellas, like daffodils, have a tendency to reorient themselves according to wind direction and, subsequently, to assume a shape far less suited to keeping us dry. Perhaps there are enough differences between umbrellas and daffodils to stop me from rushing out to line up investors for the "antidaffobrella" (for one thing, umbrellas don't swivel along the length of their "stems"), but I wish someone would do something about this problem. The only other step I can envision, drawing on the daffodil's example, is to crawl on my belly during a rainstorm, hoping to keep my umbrella out of the worst of the wind.

Adam Summers is an assistant professor of ecology and evolutionary biology at the University of California, Irvine (asummers@uci.edu).

Twister!