Squirrels, Cats, NASA - Connecting the Dots

The genesis of this blog was this Youtube video by Mark Rober:
https://www.youtube.com/watch?v=hFZFjoX2cGg

The video shows squirrels brilliantly conquering a diabolically difficult obstacle course to get at a delicious treat. If you’re not one of those who’ve seen it (22.5 million in the first week, late in May) don’t miss it. Around the 16 minute mark he (Mark) demonstrates the launch platform in slow motion. It turns out that squirrels are amazing at figuring out where and how they’ll land when flying through the air. 

Just like cats! And Mark mentions cats’ ability to land on their feet when dropped upside down. He also discusses briefly the physics behind this ability. Angular momentum (or Moment of Inertia) plays a part. Cats and squirrels control their rate of spinning by extending or pulling in their legs. Figure skaters do this as well. Pulling your arms in makes you spin faster; extending your arms slows your spin. Of course, figure skaters have to keep at least one foot on the ice. Here’s an illustration of that from my book Faster, Higher, Smarter.

 

Squirrels and cats flying through the air have four appendages to use to control their angular momentum. 

 

But that’s not the whole story. Figuring out how cats can turn over in a split second to get their feet under them took scientists nearly three hundred years. 

First up was Antoine Parent, a French mathematician best known for a three volume treatise on Analytical Geometry in 1700. He explained (incorrectly) that the upside down cat (A below) hollows its back, moving its centre of gravity above its axis (B); this makes it unstable, causing the cat to rotate to the feet down position (C). The explanation doesn’t work because there’s nothing supporting either end of the cat, so there’s nothing to make it rotate. 

 

Many other scientists studied the cat problem. Probably the most famous was James Clerk Maxwell, who formulated the laws of electro-magnetism, unifying electricity, magnetism and light. Maxwell developed a reputation while at Cambridge in the 1830s for throwing cats out of windows. (He denied this, saying that he only dropped cats onto a table or bed, from a height of inches). No-one came up with any good explanations. Many suggested that the cats “cheated” by pushing off against the hands that were dropping them. The difficulty for scientists in solving the problem was that cats right themselves faster than the human eye can follow. 

A breakthrough came in 1894. Etienne-Jules Marey, a French scientist, made brilliant use of the new technology of chronophotography. He took a series of pictures at 12 frames/second, of a cat turning over in the air. Marey was inspired by the work of Edward Muybridge, who famously took a series of pictures of horses in motion, settling an age-old debate about whether all four hooves are ever off the ground. (They are).

The images start at the right and move to the left.

But even this wasn’t quite enough to solve the problem. It showed clearly enough that the cat wasn’t pushing off against the hands dropping it. Marey gave an almost correct explanation of the cat changing its angular momentum first by pulling in its front paws and extending its back legs to give it more intertia at the back, and allowing it to turn its front half more; and reversing the procudure to allow the back half to 'catch up'. But this still doesn't explain how the cat starts out with no angular momentum but can still rotate. There were also suggestions that the cat achieved that by rotating its tail. The tail rotation theory, though, didn’t explain how tailless Manx cats can also fall feet down. 

The solution had to wait for NASA-funded scientists Kane and Scher. In 1969 they published "A dynamical explanation of the falling cat phenomenon". The key to their model is the exceptional flexibility of the cat's spine. The cat bends to approximate two cylinders (chest and lower body) at right angles to each other. The total angular momentum of each of the “cylinders” and the overall connected body remains zero as the cat twists around to place its legs below it. 

Why did NASA fund the study? Because it needed to develop strategies for astronauts floating in space to orient themselves. It worked! Thanks, kitty. 

Astronaut Bruce McCandless on First-ever Untethered Spacewalk