Don't Make Me Put My Foot Down

I was walking back to my apartment a couple of days ago, and chose to take the path surrounding Taylor Lake- with its infamous geese. It was a pretty warm day and thus there were an endless number of these loud, messy birds around, but what struck me was that half of them were sleeping standing up on one foot with their head tucked into their body in what seemed like a nearly impossible balancing act. Once I started to research how these birds can possibly maintain this stance, I found that the avian physics research community is especially interested in how the Flamingo, with its long thin legs, maintains this obscure sleeping position shown below.

                                                           

                                                        http://yourdailytree.blogspot.com/2012/02/let-sleeping-geese-stand.html  

      

http://theconversation.com/neuromechanics-of-flamingos-amazing-feats-of-  balance-78160

Its been hypothesized that birds sleep like this to conserve heat. Yet the question still remains- how do they do it!? Two major schools of thought arose on this topic- one proposing that the birds use muscular strength to stabilize themselves and switch legs to conserve energy, and another proposing that the birds are perfectly balanced by gravity without the help of muscular strength. Researchers Young-Hui Chang and Lena H. Ting from the Georgia Institute of Technology went so far to prove the later point that they positioned flamingo cadavers (from flamingos that had undergone natural deaths) in an upright position on one leg to see if the birds could balance without muscular help. And they did!

It turns out that once the leg locks into place, the flamingo’s center of mass shifts forward. Once they tuck their head in, their center of mass rests perfectly above the normal force at the point where their foot touches the ground as shown in parts a and b of the figure below from Chang and Ting’s paper. In the segment free body diagram shown in part c, M_h and M_k represent hip and knee joint movements respectively, and H_y and K_y represent hip and knee reaction forces respectively (equal to mg at that point). The authors argue that these large knee and hip joint movements are necessary to balance the bird since the horizontal femur is not advantageous for muscle contraction in that region. Lastly, the researchers show that as the ideal knee joint angle is about 95 degrees while the ideal hip angle is about 10 degrees in part d. We know from the equation l=rθ that as the hip joint angle increases, the bird will cover a greater linear distance, and thus be more likely to fall as shown in the diagram below. This bird demonstrates that since all forces usually can't be used perfectly by animals, prioritization is necessary. Here, by tucking in its leg, the bird increases its hip joint angle and thus the linear distance that could be covered by its leg due to gravity, throwing it off balance. However, it shifts its center of mass forward and ultimately winds up balancing with out additional support.