Why cats?
In addition to the obvious – cats are the rulers of the internet – there is a lot of interesting science about how cats fall and survive! A cat has a very good sense of balance. Cats are free from vertigo even at high altitudes. In the case of a fall from a height of two to three meters, they can reflexively turn into the prone position from almost any position and land on the floor with their paws stretched downwards. To do this, the cat bends its entire body in the middle and then rotates the front and rear parts around the two now independent longitudinal axes. The process is similar to the rotation of a universal joint. Contrary to previous assumptions, the rotation of the tail plays only a minor role because its mass is far too small to give the rest of the body sufficient angular momentum. When falling from very high (but not medium) heights, this position, the extremely spread paws and the inflating loose fur at the transition from the legs to the belly act as a parachute and can significantly reduce the speed of impact and thus the risk of injury.
The cat righting reflex is a cat’s innate ability to orient itself as it falls in order to land on its feet. After determining down from up visually or with their vestibular apparatus (in the inner ear), cats manage to twist themselves to face downward without ever changing their net angular momentum. They are able to accomplish this with these key steps:
1.) Bend in the middle so that the front half of their body rotates about a different axis from the rear half.
2.) Tuck their front legs in to reduce the moment of inertia of the front half of their body and extend their rear legs to increase the moment of inertia of the rear half of their body so that they can rotate their front further (as much as 90°) while the rear half rotates in the opposite direction less (as little as 10°).
3.) Extend their front legs and tuck their rear legs so that they can rotate their rear half further while their front half rotates in the opposite directionless.
[text partly from Wikipedia] | animation by Eyytee – own work, CC BY-SA 3.0, >>
Depending on the cat’s flexibility and initial angular momentum, if any, the cat may need to perform steps two and three repeatedly in order to complete a full 180° rotation.
So there’s a good chance, our Falling Cat will survive its epic fall.
Want to get even more details?
The falling cat problem is a problem that consists of explaining the underlying physics behind the observation of the cat righting reflex: that is, how a free-falling body (cat) can change its orientation such that it is able to right itself as it falls to land on its feet, irrespective of its initial orientation, and without violating the law of conservation of angular momentum. Although amusing and trivial to pose, the solution of the problem is not as straightforward as its statement would suggest. The apparent contradiction with the law of conservation of angular momentum is resolved because the cat is not a rigid body, but instead is permitted to change its shape during the fall owing to the cat’s flexible backbone and non-functional collar-bone. The behavior of the cat is thus typical of the mechanics of deformable bodies.
The dynamics of the falling cat have been explained using the Udwadia–Kalaba equation. The Udwadia–Kalaba equation was developed in 1992 and describes the motion of a constrained mechanical system that is subjected to equality constraints. If you really want to dig into the details, check this out: Udwadia–Kalaba Equation for Constrained Mechanical Systems
Also: check out Kyle Hills blog post “How do cats survive falls from great heights?“
