Just registered for this burning question. My roommate told me that mice can survive falls of almost any length due to thier low terminal velocity stemming from light weight. I’m skeptical, and I couldn’t find an authorative source on the internet either way. So does anyone know, or can they point me in the right direction?
I doubt any kind of factual answer, but it would not be a surprise if the claim is true.
Air resistance, drag, is proportional to frontal area which depends upon dimension squared.
Weight if proportional to dimension cubed.
Suppose we have a 72" tall person who weighs 200 lb. Estimate how much a 60" person would weight.
Take 200*(60/72)[sup]3[/sup] and the answer is 115 lb. So it looks like taking the cube of the length of a person and the length of a mouse gives us a ballpark figure for the weight of a mouse.
This means that a 4" long mouse would weigh 200*(4/72)[1]3[/sup] or about 0.035 lb. (16 grams) which is in the range of weights in various internet sites.
So the weight reduction factor for a 4" mouse as compared to a 72" tall person person is about 5800
The drag reduction factor is (72/4)[sup]2[/sup] or about 324.
If the terminal velocity for a person is 120 mph, then for a mouse it should be roughly 6.7 mph or 9.8 ft/sec.
This Wikipedia article is the source for the 120 mph human terminal velocity. Several people have survived long free falls.
sup ↩︎
I found this:
from here.
So, converting from miles per hour to meters per second, I get (100 m/h)*(0.44704 (k/s)/(m/h)) = 45 m/s as the terminal velocity for an average human, rounded up a bit just for easier math’s sake.
Now, is this is 25 times that of a mouse, then the mouse would fall at 1.8 m/s. Given an average mass of 20g (from here., we can establish that when it lands, it will have a momentum equal to (0.02 kg)(1.8 m/s) = 0.036 kgm/s.
So an average human (mass of, say, 70 kg,) OTOH, will have a momentum of (70 kg)(45 m/s) = 3150 kgm/s. That’s five orders of magnitude different.
Of course, that’s just momentum, not force, but if I knew off-hand the average duration that an impact from falling at terminal velocity lasted (obviously dependant on what you landed on as well,) then I could give you the actual force (equal to the change in momentum over time divided by the change in time. The change in momentum would be from the numbers I gave above to zero, since we’re assuming whatever the mouse or person lands on will stop them.)
Let’s just say the landing takes a tenth of a second. That would mean the mouse is subjected to 0.36 N, and the human 31.5 kN. Just to give you some perspective, the femur (the largest and one of the strongest bones in the human body,) has an ultimate strength of 193 mega-Pascals (a Pascal ¶ is equivalent to 1 N/m[sup]2[/sup].) The average cross-sectional area of a femur is about 0.0005 m[sup]2[/sup]. So, 31.5 kN/0.00005m[sup]2[/sup] = 630 MPa, over three times the ultimate stress of the femur.
Now, I had a hard time finding any info on the ultimate stress of mouse bones, but it’s not that big a strech to say it’s comparable to humans (now before you say, ‘but our bones are bigger, they should be stronger,’ let me remind you that stress is normalized to area, so size has nothing to do with it, it’s strictly material properties that determine it.) I’m guessing a mouse bone (I’m not saying femur cause I don’t know if the officialy have femurs,) has maybe a 0.5mm radius, so that gives an area of 7.86x10[sup]-7[/sup] m[sup]2[/sup]. Very tiny area. So the force the mouse endures (0.36 N) divided by its area (7.86x10[sup]-7[/sup] m[sup]2[/sup]) equals 0.45 MPa. So even if the mouse bone’s ultimate stress is 1/10th that of a human’s, the stress it would endure from a fall that brings it to it’s terminal velocity is nowhere near enough to break a bone.
Of course, bone breakage is by no means a measure of the deadliness of a fall, seeing as soft tissues will get bruised and damaged at much lower stresses, but I’m just trying to give some kind of normalizng parameter that we can compare a mouse and human to.
My value for the mouse terminal velocity is 9.7 ft./sec. bouv’s adjusted for our difference in terminal velocity is 7 ft/sec. So that’s close enough to constitute agreement in this kind of estimation. That velocity is reached in a fall of about 1.5 ft.
No one claims that this sort of estimation gives an an accurate answer. The purpose is to see whether or not the claim is reasonable. It looks eminently reasonable that a mouse can survive a fall from any height, assuming that the start isn’t so high up that the mouse dies from lack of oxygen, or freezes to death.
I’ve heard of cats surviving falls out of skyscrapers. What I remember (probably wrong) is
that if they reach their terminal velocity first they have a better chance of surviving (and I’d
imagine grass might be a bit better than the sidewalk).
I suspect the origin of this story in the (somewhat) popular imagination is
But a mouse might also be aerodynamically better off, thus a direct comparison to humans doesn’t quite cut it. If they curl up into a ball, that is one thing. But if they splay their legs out, then their loose skin could create drag, which would lesson the impact as well.
-Tcat
Probably, like a human, the question is whether it dies from a heart attack on the way down.
I have to admit that I know the answer is “no”, from personal experience. In college, someone who caught a mouse in his room dropped it from the roof of our 4 story building onto the concrete sidewalk, and it was most certainly dead after impact. Don’t feel too much sympathy for the mouse - our fraternity had a rodent problem at the time, and that mouse was going to be killed one way or another.
I raised mice when I was in High school. They can survive a fall that- in terms of how far the fall in in comparison to their “hieght”- is simply amazing. And, if they got lucky, a much further fall. OTOH, I had one jump out of my hands and fall about 15’ and it died- bleeding from the ears.
So “can mice survive extremely long falls?” Yes. Will they always survive? No.
Thanks for the replies guys! Looks like there is at least some truth to this. muldoonthief, maybe the surface it landed on had a major impact (heh) in that case.
I’m also willing to bet how the mouse lands affects its odds of survival, like a cat. If it lands on its feet, then a large portion of the force can be taken by the bones, which are the strongest things in our bodies. If it fell more on its side or back, then more soft tissue will be damaged.
It’s also worth pointing out that the equations I used to describe the theoretical maximum force and stress are just that, theoretical. The real world doesn’t always obey these equations. Going by those, no one could ever survive a fall from terminal velocity, but I’m sure there have been people who have, jsut as their are mice who do die from it.
Long falls, yes. The long winters might do them in.
No doubt. In fact, thinking back, it was actually a granite walkway it landed on.
Unfortunately, I also know that a rat can’t survive being frozen with a carbon dioxide fire extinguisher then being fungoed off the roof with an aluminum baseball bat. I really wish I had missed that one.
Also in the realm of the anecdotal, I once chased a rat over the side of my garage, where it took about a nine-foot fall onto concrete. It had enough life left in it to scuttle away, though whether it died subsequently from internal injuries, I have no way of knowing. This was a medium-sized rat, maybe six inches long, less the tail.
I knew a guy in college who threw his pet mouse off of a 15 story dorm building and it survived, apparently uninjured. I think the key difference between this and muldoonthief’s anecdote is that in this case the mouse landed on grass.