# Small Animal Terminal Velocity

I recently saw a cat fall probably 100 feet like in this video Cat Falls. It seemed as if the cat reached terminal velocity by the time it hit. Does this mean that cats (and other small animals) could fall any distance without much harm because of there low terminal velocity? Is there a point when (in increasing animal size) that larger animals have lower terminal velocity (so little harm to animal)?

Disclaimer: I will not test out these claims, nor do I hope you do.

• I recommend reading On Being The Right Size by J. B. S. Haldane. He says that while a mouse can walk away from thousand yard fall, "A rat is killed, a man is broken, a horse splashes." – bdsl Oct 20 '15 at 23:51

I know a lot of people say that the terminal velocity of a cat is 100 kph, but I don't know if that is verified or just a calculated estimation someone came up with. I have experimented quite a lot with falling objects, including small animals and bugs. I have documented the falling speeds of many small creatures, and the probabilities of dangerous injury/death. In my experimentation, no animals have been injured.

I have verified that most bugs/insects have safe terminal speeds of less than 20 kph. Some have terminal speeds less than $4 \ \rm km/h$. In my observations, most bugs/insects can fall unlimited distance without injury (I have seen many bugs fall $50\ \rm m$ safely, although they usually reach terminal velocity after falling only a few meters), but this is only true for the majority. Some bugs do receive injuries from free fall, and a tiny minority of bugs can die from free fall.

I could generalize that weight and body shape are the main factors that determine the speed and danger of terminal velocity. In my experience, creatures with less than $1\ \rm cm^3$ of body volume can reliably achieve safe terminal velocities. Creatures with larger body volumes than $1\ \rm cm^3$ may be injured, particularly if they have round bodies or short legs. Small Grasshoppers are not injured by free fall, but large Grasshoppers can sustain leg injuries.. Though I have never seen a Grasshopper die from free fall.

My experiments involved many hundred small creatures, and the only casualties were large round ticks, which are the fastest falling bugs I have ever observed (my measurements read in the zone of $40 \ \rm km/h$). Mice and small lizards fall just as slow as most bugs, and are also pretty much immune to falling injuries.

I am not proud of the fact, that years ago, during my experiments, I launched a cat (with a giant sling) into the sky with a parachute... And the parachute worked great: the cat fell $75\ \rm m$ and landed safely. But I repeated the test and the parachute failed... The cat fell $75\ \rm m$ without the help of the parachute, and it survived the landing pretty unscathed. It seemed to have got stunned by the landing, because it just lay there (to my horror, it looked dead!), but after a few seconds it stood up and ran along. Upon inspection, it got a bloody nose, but no bone or organ damage... It lived several years longer.

I don't recommend anyone experiment with the free fall of live animals larger than a mouse, though I think a cat has a pretty good survival chance (better than 80%) for terminal velocity landings. It definitely makes you feel sick to your stomach to see a cat hit the ground at terminal velocity, mainly because it makes an awful thudding sound. From a scientific point of view, I am inclined to agree they fall slow enough to survive unlimited fall distances. I hope my experience in this subject is useful to someone, or at least ease your curiosity :)

• This is among the most fascinating and also darkly hilarious answers I've ever read on any S.E., but I'm loath to give you an up vote because it might encourage you! But thank you for your insight. – Benjohn Apr 25 '17 at 16:04

Mathematically, terminal velocity—without considering buoyancy effects—is given by

$V_t= \sqrt{\frac{2mg}{\rho A C_d }}$

where

$V_t$ is terminal velocity, $m$ is the mass of the falling object, $g$ is the acceleration due to gravity, $C_d$ is the drag coefficient, $\rho$ is the density of the fluid through which the object is falling, and $A$ is the projected area of the object.

So an object with greater mass can have less terminal velocity if the area projected is greater assuming all other parameters are constant.

In addition to the righting reflex cats have a number of other features that will reduce damage from a fall. Their small size, light bone structure, and thick fur decrease their terminal velocity. Furthermore, once righted they may also spread out their body to increase drag and slow the fall to some extent. A falling cat's terminal velocity is 100 km/h (60 mph) whereas that of a falling man in a "free fall position" is 210 km/h (130 mph). At terminal velocity they also relax as they fall, which protects them to some extent on impact. However, it has been argued that, after having reached terminal velocity, cats would orient their limbs horizontally such that their body hits the ground first.

• Animals have roughly similar shapes. Assume a spherical cat for simplicity more than realism. Then $m \propto r^3$. $A \propto r^2$. So $V_t \propto \sqrt{r}$. A mouse would not be harmed. A cat would likely be injured or killed. – mmesser314 Apr 22 '14 at 4:51
• That cat "righting reflex" is interesting to watch when the cat is inside an airplane that is executing a parabolic trajectory. See youtube.com/watch?v=O9XtK6R1QAk – David White Sep 15 '18 at 23:49