Bio-aerial Locomotion 2011

Geckos exhibit an unusual phenomenon that inspires exciting possibilities in human engineering. While frogs, lizards, and most other organisms that have self-orienting responses while falling use aerodynamics, geckos use principle of conservation of  angular momentum.

Professor Robert Full’s lab at UC Berkeley has studied this behavior extensively. In the video from their study, notice how the gecko spins it tail clockwise in the vertical plane to induce counterclockwise horizontal yaw.

One of the chief issues with high altitude research rocket flights (from 30km altitude to 200km altitude) is recovery of the rocket and payload after the flight. Deployable parachutes often fail to deploy, or if they do cause the rocket to drift out of range of tracking equipment. They are also volume and mass inefficient, both of which must be minimized for high performance flights. The solution would presumptively be to innovative utilize hardware that is already on board the rocket for recovery.

The long, skinny anatomical arrangement (high length/diameter ratio) of many geckos and lizards parallels that of a sounding rocket. The only thing that needs to add is a tail for aerodynamic control- and we can provide that by extending a part of the rocket out the back.

The booster component of the rocket is made up of the airframe and the rocket motor inside the airframe.  Once the fuel inside is used up, the spent motor is simply an empty aluminum casing. Luckily, the spent motor hardware should have about the right length/mass proportions when extended such that the forward closure of the casing is flush with the aft end of the rocket. We will henceforth consider the rocket airframe to be the “body” and the spent motor casing to be the “tail.”

The rocket ascends traditionally, with center of gravity ahead of center of pressure to create stability (1). This is the same reason why arrows fly straight—because the heavy tip keeps the center of gravity (CG) forward of the center of aerodynamic force, i.e. the center of pressure (CP). CP can be imagined as where a cardboard cutout of the arrow’s shadow would balance, since there’s more surface area near the fins, the CP is closer to them than the nose.

At apogee, the motor casing is ejected out the back of the rocket and then locked in place by a circular bearing that can rotate in just one direction (2). This changes the CG/CP relationship such that they are close to the same distance from the nose tip. This means that the rocket will not favor a nose-first or tail-first re-entry, but rather a neutral horizontal profile.

As the rocket descends through the atmosphere, air pressure induces rotational movement on the motor casing “tail” via the unidirectional bearing to spin in a clockwise direction (3). Because of the conservation of angular momentum, the rocket airframe will flat spin counterclockwise as it descends (4). As the rocket descends, more air will push on the motor casing “tail,” causing it to spin faster, and causing the airframe to flat spin faster, increasing drag, distributing heat effectively, and slowing the descent rate as a function of altitude. The accidental recovery of the University of Cincinnati’s Pathfinder project via flat spin proves that the flat-spin recovery technique is sound. In this case, the rocket wasn’t damaged from its impact in the ocean because enough energy was dissipated in the spin. It is the author’s hope that the concept can be refined by the BU Rocket Team and other organizations in the near future.

Sources:

• Active tails enhance aerobial aerobatics in geckos, A Jusufi, D I Goldman, S Revzen R J Full, Proc. Nat. Acad. Sciences, Vol. 1805, pp. 4215-4219 (2008)
• Righting and turning in mid-air using appendage inertia: reptile tails, analytical models and bio-inspired robots, A Jusufi, D T Kawano, T Libby, R J Full, Bioinsp. Biomim., Vol. 5, 045001, 12pp. (2010)