A weird physics puzzle of a cat falling from a height

© WGBH

Leviathan Press:

Several years ago, I heard a photographer friend tell me about a legendary story about a cat he raised who fell from a high-rise building (about 10 floors) and was only slightly injured. I thought it was incredible at the time: even though I have seen countless cats land swiftly after accidentally falling from cat climbing frames or tables, I am still shocked by the high survival rate of cats after falling from high altitudes. Another cat-raising friend told me that his cat accidentally fell from the 5th floor, and when he found it, the corner of its mouth was bleeding, but after a thorough examination by the veterinarian, it was found that there were no signs of fractures or organ damage.

Although I have imagined countless times that the cat spread its wings like a flying squirrel when it fell... but the reality tells us that even without a protective cloak, the cat can still survive (with a high probability).

warn:

Don't throw a cat without any protection

To satisfy your unnecessary curiosity

When the famous physiologist Étienne-Jules Marey presented a series of photographs at a meeting of the French Academy of Sciences in October 1894, his colleagues were in uproar. In a series of subsequent reports, one attendee declared that Marey had merely presented a scientific paradox that violated the basic laws of how objects move.

**The controversy was caused by a cat. ** Specifically, a cat fell from the sky and twisted in mid-air before finally landing. The falling and landing itself were not the problem, but the process of the cat twisting in the air.

Etienne-Jules Marey provided a photograph of a falling cat that was published in Nature in 1894.

For years, scientists have believed that cats must jump off a fixed surface to land. This assumption stems from a physics concept called conservation of angular momentum, which states that an object that does not rotate will not move without an external force. Without a push, the cat has no leverage to turn right. But Marey's series of photos show a cat twisting after it begins to fall, with nothing around it.

In the decades that followed, scientists offered many explanations, many of which were vague. “Even today, you still find people arguing about the reasons why cats fall to the ground,” said Greg Gbur, a physicist at the University of North Carolina at Charlotte.

© Oxford University Press

Experts agree that cats probably don't violate the laws of physics, but have evolved to exploit the slightest nuances -- even when the environment seems unsurvivable, said Gerber, author of Falling Felines and Fundamental Physics.

Gerber told me that the puzzled physicists at the French Academy of Sciences had oversimplified the cat's angular momentum. Angular momentum can be conserved in a spinning object (a cat) as long as half of its body rotates in one direction and the other half rotates in the other direction, which sounds a bit like a pepper grinder. The two sides of the body then act as a fulcrum for each other, giving each other an equal and opposite push, which is the rotational force. This phenomenon happens in cats.

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“Cats have a very flexible skeleton,” says Barbro Filliquist, a veterinarian at the University of California, Davis. Cats bend their spines so much that they almost split their bodies in two , like “a knee joint in your back,” says David Hu, a mechanical engineer at the Georgia Institute of Technology.

© Wikipedia

When a cat is suspended upside down, the half of its body closest to its head usually turns first. To do this, it must turn faster than the rest of the body— a cat might tuck its front paws in toward its belly while keeping its back paws out to accomplish the maneuver (similar to how a figure skater pulls his arms during a quick turn).

The cat then relaxes its front legs while tucking its back legs toward its belly . This time, the side closest to the rear rotates faster, pulling the rest of the body into a right-side-up position. At the same time, the tail may act as a propeller to speed up the rotation. This isn’t necessary, Gerber told me: Manx cats (a type of cat that has almost no tail) can also land smoothly.

Manx cat. © The Spruce Pets

Cats can turn incredibly quickly, says Hanno Essén, a physicist at the KTH Royal Institute of Technology in Sweden, who has modeled a cat’s righting reflex.[1] A cat can reposition itself within a few feet in a fraction of a second. This process helped Essén’s playful kitten, Mooshe, land safely after falling from a window some 40 to 50 feet (12 to 15 meters) above the ground.

**While this may not seem aerodynamic, they still face considerable risks when falling from heights, which is exacerbated by the fact that buildings are getting taller and taller in the city.[2] **Carly Fox, a senior veterinarian at Schwarzman Animal Medical Center (AMC) in New York, said that nearly a quarter of the pets admitted there in the past seven years were traumatic falls. In the worst cases, so-called high-rise syndrome can cause cats to suffer nosebleeds, broken mouths, collapsed lungs, broken legs, and even ruptured organs.[3]

In a way, the higher the drop point, the worse the cats generally fare. Some studies, including the AMC study,[4] show that if the drop point is six or seven stories high, the injury rate may not change or may even decrease as the height increases. Scientifically, this is really strange , says Rhett Allai, a physicist at Southeastern Louisiana University.

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Reid has written about this phenomenon for Wired magazine. “It’s not that ‘higher is better.’” Some of the data may be biased, and it’s hard to tell if the cats are exaggerating when the owner takes them to the vet, while other studies have come to the exact opposite conclusion.[5]

The data were not only patchy but also contradictory.[6] “We had no idea what was going on,” says Michael Kato, an emergency and critical care veterinarian in California.

If this pattern is consistent with the laws of physics, it could explain the amazing leaps that some cats display from great heights. Gerber once saw a cat fall from a tree 100 feet (30 meters) high, yet the height seemed to be of no concern to it. Fox recently treated a cat who survived a 19-story fall. A cat named Sabrina once fell from a height of 32 stories and survived, which was nothing short of a miracle. Another cat, Jommi, was said to have fallen from a 26-story building, smashed through the roof of a tent, and was later found licking his fur near the point of fall, unharmed.[7]

"I've seen cats fall from seven, eight, nine, even 10 floors with lacerations and broken legs, and they can recover from that with treatment," said Christine Rutter, an emergency and critical care physician at Texas A&M University.

Studies have shown that the survival rate for high-rise syndrome in cats has consistently exceeded 90% [2] , “which is crazy to me in the emergency room and ICU where I work,” says Sophia Amirsultan, an emergency and critical care physician at North Carolina State University.

© techcrunch

The secret may involve another physics loophole. In the first few dozen feet of a fall, a cat's body accelerates, and the force of its impact on the ground increases. For a cat falling from about two to five stories, this is a tough call. But at just over five stories, an 11-pound cat hits the ground at a terminal velocity of 60 miles per hour. And no matter how high you fall from there, the thump won't get any louder. It's crazy: There doesn't seem to be a limit to how high a cat can fall and survive, Alan told me.

**Reaching terminal velocity may make a cat feel weightless, Rutter told me, and may even cause it to “stop panicking” and let its legs loose. **A cat’s body can more evenly distribute the impact of the inevitable fall. This could explain why Kato and his colleagues found that cats who fell seven stories or more tended to suffer injuries to their torsos and jaws, rather than to their limbs.

Rabbits also seem to have a pretty good righting reflex. Scientists have found that some geckos can also land safely by waving their thick tails.[8] But perhaps only house cats can do it perfectly: they have an amazing sense of balance, can find their balance instantly when they need to flip, and have extremely fast reactions, a flexible back, and super-flexible limbs to execute this maneuver perfectly.[9] Mairin Balisi, a paleontologist at the Raymond Alf Museum of Paleontology in California, told me.

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Emir Sultan told me that cats evolved to be quick-witted and arboreal, with a somewhat fluid[10], slightly shock-absorbing[11] physique. Several veterinarians told me that dogs tend not to fall as well as cats. Barish said that even some of the larger cats don’t always land safely. She added that if they always landed safely, The Lion King probably wouldn’t have been made. (Scar instigated little Simba to roar near a herd of wildebeests. The wildebeests, stimulated by the lion’s roar, were frightened and ran down the mountain. A large number of wildebeests rushed towards Simba. Fortunately, Mufasa arrived in time to save Simba, but he himself was not spared. Mufasa could have been saved, but he was pushed off the cliff by Scar’s conspiracy and was eventually trampled to death by the wildebeests.)

I asked Gerber if humans could learn to mimic a cat's gyroscopic turns. He told me that we can already do it. The best divers and gymnasts probably turn their bodies like cats; NASA also wants astronauts to learn how to fly in zero-gravity space from cats.

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But cats always “do better,” Gerber told me, even though they might not enjoy space travel.

Perhaps no one understood this better than Marey, who published a paper in Nature a month after the conference that drew attention to the fact that his subjects, cats, had their “expressions of offended dignity” immortalized on film.

References:

[1]iopscience.iop.org/article/10.1088/1361-6404/aaac06

[2]onlinelibrary.wiley.com/doi/epdf/10.1111/vec.13206

[3]www.vettimes.co.uk/app/uploads/wp-post-to-pdf-enhanced-cache/1/high-rise-syndrome-in-cats.pdf

[4]pubmed.ncbi.nlm.nih.gov/3692980/

[5]pubmed.ncbi.nlm.nih.gov/15363762/

[6]www.ijvm.org.il/sites/default/files/feline_high_rise_syndrome_in_israel.pdf

[7]www.lifewithcats.tv/cat-is-unharmed-after-26-story-fall-from-high-rise-building/

[8]www.pnas.org/doi/10.1073/pnas.0711944105

[9]link.springer.com/article/10.1007/s42235-020-0048-x

[10]www.drgoulu.com/wp-content/uploads/2017/09/Rheology-of-cats.pdf

[11]www.hindawi.com/journals/abb/2019/3815612/

By Katherine J. Wu

Translated by Zhao Hang

Proofreading/Rabbit's Light Footsteps

Original article/www.theatlantic.com/science/archive/2022/09/falling-dropped-cat-reflex-physics/671424/

This article is based on the Creative Commons License (BY-NC) and is published by Zhao Hang on Leviathan

The article only reflects the author's views and does not necessarily represent the position of Leviathan