## Falling: “The tale of the gecko”

The gecko has the fastest air-righting response ever measured.

When falling, geckos are able to right themselves turning their body in mid-air, and always land safely on their feet. It is fascinating to watch the slow-motion videos of the lizard dropping from a belly-up position, then using a swing of the tail to turn around into a skydiving posture. Even more fascinating is to understand the simple physical principle that explains their maneuver: conservation of angular momentum.

The research group of Prof Robert Full at UC Berkeley has conducted exciting work explaining how the lizards use their tail for their mid-air righting prowess—the fastest righting reflex ever measured (about 1/10 of a second). Below is a short video which summarizes the findings.

The results of a first set of experiments, performed by PhD student Ardian Jusufi, were published in the Proceedings of the National Academy of Sciences¹. Among other observations, they describe the air-righting reaction in detail, as follows:

1. as soon as it falls (belly-up), the gecko spreads its legs wide
2. it then pitches its tail so that it points downward, perpendicular to its body
3. the tail now swings around the longitudinal axis of the gecko, which produces a counter-rotation of the body due to conservation of angular momentum
4. the body executes a full turn, to end right-side up, and the tail stops turning
5. the gecko keeps falling, arms extended like a skydiver

The scientists then built an analytical model of the righting mechanics. The angular momentum of a body is the product of its moment of inertia and its angular velocity:

At the start of the fall, the gecko has zero angular momentum (there are no external torques acting on it). If one considers the body segment separate from the tail, then the sum of the angular momentum of each piece must continue to be zero:

A simple geometrical model can be used: the body as a rigid elliptical slab, and the tail as a thin cone rotating perpendicular to the body. With biometric data, a realistic estimate of the moments of inertiaof body and tail are entered into the equations, and then a change in the angle of the body is obtained from a change in the angle of the tail:

This simple model correctly predicts the reorientation of the body of the gecko! Now, there is enough information to build a device that can emulate the behavior of the gecko: the RightingBot².

References

¹ “Active tails enhance arboreal acrobatics in geckos”, A Jusufi, D Goldman, S Revzen, R Full, PNAS Vol. 105, pp. 421-–4219 (2008) [pdf]

² “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, Bioinspiration & Biomimetics, Vol. 5, pp. 1–12 (2010) [doi]

posted on September 17, 2011 at 1:46 pm

Challenge question: How big of a tail would you need to be able to execute a mid-air righting manoeuvre?

posted on September 18, 2011 at 12:00 pm

The tails of geckos seem to be about 40 percent of their body length, and since there are no organs in their tail, I assume that the tail is 25-30% of the gecko’s body weight. Using these figures, I guess I would need a tail about 30 inches long and weighing 40-50 lbs.

posted on September 18, 2011 at 2:39 pm

After viewing the video about the experiment of the gecko, I assume that the speed of rotation of the tail is 3 times faster than the speed of rotation of the body itself. Using the formula, the weight of the body is 3 times more than the weight of the tail. Also, in the magnified pictures of the gecko, it seems that the length of its tail is equal to half the length of its body to tail. Based on these figures, I guess that I would need a tail of about 35 inches long (approx length from head to bottom) and weighing about 45 lbs ( one quarter of my total weight).

Morgan posted on September 18, 2011 at 6:55 pm

Soooo I did the tail assignment based of off the Flat-Tailed House Gecko (this was the species most studied in the Berkley experiment) and using cm. After doing some research (http://www.ecologyasia.com/verts/lizards/flat-tailed_gecko.htm) I found out that a Gecko can grow to be about 14 cm from snout to tail tip. If this is the case, the tail itself is usually about 6 or 7 cm. Therefore, I would say that I would need an 81.3 cm tail. I calculated this by using a ratio (I am roughly 162.6 cm tall):

Gecko – 14cm/7cm
Me-162.6cm/x

The tail is also usually about 1/4 the weight of their body (according to a gecko forum on http://www.geckosuk.com) and I would therefore need about a 38 lb tail

posted on September 18, 2011 at 7:15 pm

Is this question asking specifically about a mid-air righting maneuver that works the same way as the gecko’s? Because it doesn’t say so anywhere and if it’s talking about any mid-air righting maneuver then the tail size doesn’t matter. Our bodies are set up more similar to that of a cat’s who don’t use their tails to right their bodies in mid-air. A human can just twist their spine to right themselves in mid-air, just like a cat. However, to perform a maneuver that is like the gecko’s a human would need a tail at least as long as their body and about half the person’s weight. This is because, while the tail is thinner than the body, it would need to be almost entirely muscle in order to move it fast enough to right the person in mid-air.

posted on September 18, 2011 at 7:26 pm

Very good point, Colby. Yes, I was thinking of a mid-air righting maneuver like the gecko’s, i.e., using the inertia of the tail to produce a zero-angular momentum response in roll of the body from belly-up to belly-down.
You are right that the cat’s righting response is based on twisting of the spine, and in their case the tail is not used at all in this maneuver.
Let’s assume that we are not going to twist the spine, and we just want a big tail to swing around.

posted on September 18, 2011 at 8:41 pm

Judging by the video, as well as information that I have found, the average gecko has a tail that is about 60% of the length of the rest of its body. Therefore, I assume that I would have a tail that is approximately 43 inches long. Also, the weight of the tail of the average gecko is about 25% of their total body weight. This would make the weight of my tail about 38 pounds.

posted on September 18, 2011 at 10:35 pm

To aid my calculations I used the following sites:
http://polypedal.berkeley.edu/twiki/pub/PolyPEDAL/PolypedalPublications/Jusufi_PNAS.pdf
and
http://www.ecologyasia.com/verts/lizards/flat-tailed_gecko.htm

Using the information I collected from these sites I discovered that the Flat-Tailed House Gecko (the one in the experiments) had an SVL (snout to vent length) of 6 cm and a STL (snout to tail length) of 14 cm meaning its tail is about 8 cm. I also found that the average weight of the geckos in the experiment was 3.17 g and that it’s tail weighed .29 g on average.

I then set up two sets of ratios using my height and weight accordingly to find that I would need a tail of 100.2 cm and 13.63 pounds.

posted on September 19, 2011 at 1:03 am

Using the model given for the righting formula (Angular Velocity of tail/Angular Velocity of body= -(Moment of Inertia body/Moment of Inertia tail)) and Wolfram Mathworld, I calculated that a 9 lb., 5 ft. long tail would do the trick, which seems awfully small. First we need to make the assumption that my tail is a cylinder and that my body is a 150 lb. cylinder with a 1 ft. radius. Assuming that both my tail and body make the 180 degree turn in the same amount of time, all we need to do is calculate the Moment of Inertias. From Wolfram I got that the formula for a cylinder spinning about the symmetry axis (body) is 1/2MR^2 and the formula for a cylinder spinning about the end (tail) is 1/3MH^2. Plugging in my weight and “radius”, I got that any combination of MH^2=225 would be a functioning tail for me.

If my math is right, a reasonable sounding tail of 9 lb. and 5 ft. would work. The geckos seem to have a much higher percentage of their mass distributed to their tail than this though, so I think I messed something up.

http://mathworld.wolfram.com/MomentofInertia.html

charlies posted on September 19, 2011 at 11:55 am

Like Morgan, I also found that the average Flat-tailed House Gecko grows to about 14 cm in length. The average body length (snout to vent length) is about 6.9 cm (http://bangkokherps.wordpress.com/2011/05/06/flattailed-house-gecko/). This means that the average tail will be around 7 cm (c. 50% of the body length.) I am about 172.7 cm (5’8″) tall and weigh roughly 160 lbs. According to the following article, http://www.pnas.org/content/105/11/4215.full, the tail weighs roughly 10% of the geckos total body weight. Therefore, I would should need a tail that is 86.35 cm (c. 28. ft.) and weighs about 16 lbs.

Samuel Nichols posted on September 19, 2011 at 1:01 pm

Using the following siteshttp://bangkokherps.wordpress.com/2011/05/06/flattailed-house-gecko/
and
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2393739/
I found that on average the flat tailed house gecko, the same species from the experiment, is about 14 cm long with a 6.9 cm tail, which is about 50% of the body length, and the tail is about 10% of the total body mass. Because I am 72 inches tall and weight 185 lbs, I would need a tail about 37.5 inches long (about a yard) weighing 18.5 lbs to oull off the air right maneuver.

Ardian Jusufi posted on September 20, 2011 at 9:47 pm

Thank you for your interest in the research on aerial righting maneuvers of lizards. The dimensions will vary from species to species. In the case of the Flat-tailed House Gecko, Hemidactylus platyurus, it is true that the tail is approximately 10% of the animal’s total body mass. Moreover, the length of the tail is about equal to that of the body (SVL) in this case. If you were an astronaut floating in space trying to change the orientation of your body, one creative idea would be to do that with a robotic tail. Note that humans have comparatively larger hind legs than these geckos. How might changes in shape interfere with the righting?

Solange Coughlin posted on October 26, 2011 at 8:14 pm

From the measurements of geckos we looked at in class today, the average mass of a gecko’s body is 3 g, and the average mass of its tail is .3 g, meaning the tail is about 10% the mass of the body. From this link: http://www.ecologyasia.com/verts/lizards/flat-tailed_gecko.htm I found that the length of a gecko’s tail and body are 8 and 6 cm, respectively, meaning the tail is about 133% the length of the body. Based on these figures, my tail would have to be about 212 cm long and weigh about 13 lbs.