Mark Megahan
If you happen to have at least one cat for a feline friend, (don’t dare call them a pet or they give you an attitude, they think you are their pet.) you know half the acrobatic things they do are impossible. They have such highly developed instincts for survival that they can cope with falls from extremely high places. That doesn’t mean they can walk away from all of them. Physics explains there’s actually a formula for how likely it is for a particular feline to be harmed by a particular drop. FR = ½ x ρ x A x cW x v2.
The falling cat problem
Physicists have been puzzling over the “falling cat problem” for centuries. There are actually two of them which are closely related. The first aspect the experts were scratching their heads over is the way cats always land on their feet. The experts came up with an answer which turned out to be wrong. That made them go back and find a better answer.
Once they had that figured out, they went on to figure out why one survived a fall from the window of a 32nd-floor apartment onto hard asphalt. There are many reports of high falling cats who walked away from the cat-astrophe, while many others get seriously injured and killed from much shorter falls. Now we know why.
The cat who holds the free-fall skydive record decided to jump out the open window of a 32nd-floor apartment in New York City. There isn’t much that’s soft to land on around there. It was rushed to the vet with “a collapsed lung and broken teeth” which required a two day stay in the animal hospital.
It returned home and never did that again. That’s precisely the reason “that other similar situations have given rise to the adage that cats have nine lives.” Just because they can do it doesn’t mean physicists can explain it.
Back in the 1800’s, experts were “stumped by photographs of cats spinning on their own axis while falling and then landing on their feet.” Just like the flight of the bumblebee, that trick was considered an infraction of the laws of physics.
The standard experiment involved “a person holding a cat by its legs so that its back is facing the ground. Then the animal is released.” The result is the same pretty much every time. “At first, the feline floats upside down in the air with its back facing the ground. But in the next shots, something happens that seems to defy the laws of physics: the cat turns and lands on its paws.”
Conservation of angular momentum
Things don’t just start spinning all on their own. Except cats. That’s supposed to break the law on “conservation of angular momentum.” At first, the experts “assumed that they obtain the momentum necessary for this movement by pushing off from the surface from which they fall.” A cat doesn’t need a push.
James Clerk Maxwell, the guy who figured out magnetism, was stumped. “He conducted several experiments in which he dropped cats from various heights (including from open windows) and onto beds and tables.”
In 1969, the first “falling cat problem” was solved. After they dropped enough cats, physicists figured it out. “If you look closely, you can see that a cat’s upper and lower body rotate in opposite directions. Thus, conservation of angular momentum is preserved. If the animal rotates like a pepper mill in two different directions, the change in angular momentum is zero.” That ball of fluff rubbing against your ankle is a born acrobatic “acrocat.” Exactly like figure skaters, “by placing their front paws close to their body, they reduce their moment of inertia.“
That means “their upper body rotates quickly around its own axis. With their hind legs, the animals then employ the opposite effect. They stretch their legs to create as large a moment of inertia as possible. As a result, the upper body rotates through a large angle, while the legs rotate less in the opposite direction.”
Once that was straightened out, they started working on why vets reported that “while the severity of the damage increased up to a height of about seven stories, it seemed to decrease thereafter. In other words, a fall from the 11th floor could end more gently for a cat than one from the sixth floor.” That got another physics ticket for breaking the law of gravity. The higher the fall the harder the impact, except for cats. Friction in the air slows the fall. The “air resistance depends on the cross-sectional area A, the drag coefficient cW, the air density ρ and the velocity v of the falling object: FR = ½ x ρ x A x cW x v2.” At the top, the velocity is zero. The faster the fall, the more friction, based on the surface area of the critter.
Generalizing it all out, “when a cat falls from a low height, it is weightless for a short time. Instinctively, therefore, it will extend its legs underneath it to land on all fours. At high fall heights, however, this strategy is not useful: aligned legs can lead to serious injury because the animal’s weight is distributed awkwardly. This difference may explain why the survival rate decreases with increasing height—at least up to the seventh floor. But at greater fall heights, the frictional force becomes noticeable during the fall.” That helps the cat relax. Kind of like what happens with alcohol in a car wreck. They might need to use the jaws of life to pry you out from under the passenger side dash but you’ll live to face the DUI hearing.
