Re: Why do leaves flutter and tumble when they fall?

Hello Kate,

First of all, I'd encourage you to do some experiments with stability and instability of falling objects. The best system to start off with, perhaps, would be small cone-shapes made of paper; cut a bunch of circular pieces of paper, bend them into cone-shapes (cut a wedge out of each circle and tape the edges together), and see how they fall under different circumstances. Some setups will tend to fall smoothly, some will tend to tumble!

• Try putting some small weights - a paper clip or a dime - at the center of the cone. Then try putting weight around the cone's edge.
• Make cones with different opening-angles; some very sharp, like an ice-cream cone, some very flat.
• Does a given object behave differently when dropped (say) upside-down, rightside up, sideways, etc.? Or does it always "find" the same orientation? (In particular, you may find that poking a hole in the center of a cone may allow it to "recover" better from a bad start!)

Ultimately, in order for it not to flip over, there must be no net torque on the object. This means that the aerodynamic forces and the gravitational forces are centered at the same place. (If gravity was pulling hard on the left, and air pushing up on the right, the object will tilt to the left, for example). So, you can take any leaf (or paper-cone), hold it in any orientation, and ask "Where is the center of the aerodynamic forces? Where is the center of the gravitational forces?" If they're not in the same place, the leaf will not be able to stay in that orientation while falling. But there are lots of choices of orientation, usually there is at least one with no net torque. In theory, a leaf could fall smoothly, without rotating, in this position. But there's a catch.

You must think about the results of very small "accidental" rotations. In some cases, a small accidental rotation will merely result in a torque pushing the object "back to center" - returning it to its stable orientation. A falling objects tilts a tiny bit to the left, and feels a force to the right. It swings to the right, maybe overshoots, and feels a force to the left, and so on. You can see how this might result in "fluttering"! In other cases, a small accidental rotation will result in a torque away from the center - thus flipping the object over. The object tilts a tiny bit to the left, feels a force pushing it even further left, feels an even stronger force to the left, and thus around it goes.

Since the shape of a leaf is so complex - irregular surfaces, a stem, sharp edges - its aerodynamics will tend to change a lot, whenever the orientation changes a little. (You mention vortices - vortices are generated by edges, and can be the source of very rapidly-changing forces! Another word for this might be "turbulence", and a closely related word is "chaos"!) Thus, even if a stable orientation (i.e. an orientation free of torque) exists, it will be perturbed by very small forces, which cause very small rotations, which cause very large changes in the balance. It's probably very hard to predict exactly how a leaf will fall, it is a good bet that it will not fall smoothly.

Shall I try to sum this up in one sentence? "The orientation of a falling leaf probably has no good stable equilibrium", and I'll point you towards another MadSci answer that explains stable equilibria in a very different context.

Hope this helps,

-Ben

PS. Another useful thing to think about is the parachute! Modern parachutes are designed specifically to avoid any sort of oscillation or fluttering. I'd bet that scientists have spent more time studying parachutes than leaves ...