The Straight Dope

Go Back   Straight Dope Message Board > Main > General Questions

Reply
 
Thread Tools Display Modes
  #1  
Old 10-30-2006, 07:57 PM
CurtisM CurtisM is offline
Guest
 
Join Date: Oct 2006
Can mice survive extremely long falls?

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?
Reply With Quote
Advertisements  
  #2  
Old 10-30-2006, 08:38 PM
David Simmons David Simmons is offline
Charter Member
 
Join Date: Nov 2001
Posts: 12,684
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)3 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)^3 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)2 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.
Reply With Quote
  #3  
Old 10-30-2006, 09:09 PM
bouv bouv is offline
Guest
 
Join Date: Aug 2000
I found this:
Quote:
Thus approximating a mouse and manís body as a sphere, and assuming that we have a radius 5 times that of a mouse Ė the terminal velocity of a man (about 100 mi/hr) would be 25 times that of a mouse! This form of the equation can be solved for Poise and the experiment timed (to determine terminal velocity) so that we have a handy way to measure viscosity.
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 kg*m/s.

So an average human (mass of, say, 70 kg,) OTOH, will have a momentum of (70 kg)*(45 m/s) = 3150 kg*m/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 (Pa) is equivalent to 1 N/m2.) The average cross-sectional area of a femur is about 0.0005 m2. So, 31.5 kN/0.00005m2 = 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 7.86x10-7 m2. Very tiny area. So the force the mouse endures (0.36 N) divided by its area (7.86x10-7 m2) 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.
Reply With Quote
  #4  
Old 10-30-2006, 10:29 PM
David Simmons David Simmons is offline
Charter Member
 
Join Date: Nov 2001
Posts: 12,684
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.
Reply With Quote
  #5  
Old 10-30-2006, 11:10 PM
John DiFool John DiFool is offline
Guest
 
Join Date: Jun 2006
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).
Reply With Quote
  #6  
Old 10-30-2006, 11:19 PM
Rhubarb Rhubarb is offline
Guest
 
Join Date: Nov 2001
Quote:
Originally Posted by John DiFool
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).
Cecil's column on falling cats. No mention of mice, though.
Reply With Quote
  #7  
Old 10-31-2006, 06:09 AM
hawthorne hawthorne is offline
Guest
 
Join Date: Apr 2000
I suspect the origin of this story in the (somewhat) popular imagination is
Quote:
J. B. S. Haldane, "On Being the Right Size", 1928
Drop a mouse down a thousand-foot mineshaft and it gets up and walks away. A rat dies, a man breaks, a horse splashes.
Reply With Quote
  #8  
Old 10-31-2006, 06:55 AM
Tomcat Tomcat is offline
Guest
 
Join Date: Mar 2000
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
Reply With Quote
  #9  
Old 10-31-2006, 07:04 AM
R. P. McMurphy R. P. McMurphy is offline
Charter Member
 
Join Date: Jun 2002
Posts: 3,743
Probably, like a human, the question is whether it dies from a heart attack on the way down.
Reply With Quote
  #10  
Old 10-31-2006, 09:04 AM
muldoonthief muldoonthief is online now
Member
 
Join Date: Jul 2003
Location: North of Boston
Posts: 7,286
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.
Reply With Quote
  #11  
Old 10-31-2006, 09:28 AM
DrDeth DrDeth is online now
Charter Member
 
Join Date: Mar 2001
Location: San Jose
Posts: 22,892
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.
Reply With Quote
  #12  
Old 10-31-2006, 10:47 AM
CurtisM CurtisM is offline
Guest
 
Join Date: Oct 2006
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.
Reply With Quote
  #13  
Old 10-31-2006, 11:34 AM
bouv bouv is offline
Guest
 
Join Date: Aug 2000
Quote:
Originally Posted by CurtisM
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.
Reply With Quote
  #14  
Old 10-31-2006, 03:53 PM
BobLibDem BobLibDem is online now
Guest
 
Join Date: Jul 2003
Long falls, yes. The long winters might do them in.
Reply With Quote
  #15  
Old 11-01-2006, 10:57 AM
muldoonthief muldoonthief is online now
Member
 
Join Date: Jul 2003
Location: North of Boston
Posts: 7,286
Quote:
Originally Posted by CurtisM
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.
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.
Reply With Quote
  #16  
Old 11-01-2006, 11:21 AM
Sal Ammoniac Sal Ammoniac is offline
Member
 
Join Date: Apr 2005
Location: Beans, Cod
Posts: 4,457
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.
Reply With Quote
  #17  
Old 11-01-2006, 12:07 PM
engineer_comp_geek engineer_comp_geek is online now
Robot Mod in Beta Testing
Moderator
 
Join Date: Mar 2001
Location: Pennsylvania
Posts: 8,908
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.
Reply With Quote
Reply



Bookmarks

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is Off
HTML code is Off

Forum Jump


All times are GMT -5. The time now is 04:33 PM.


Powered by vBulletin® Version 3.8.7
Copyright ©2000 - 2014, vBulletin Solutions, Inc.

Send questions for Cecil Adams to: cecil@chicagoreader.com

Send comments about this website to: webmaster@straightdope.com

Terms of Use / Privacy Policy

Advertise on the Straight Dope!
(Your direct line to thousands of the smartest, hippest people on the planet, plus a few total dipsticks.)

Publishers - interested in subscribing to the Straight Dope?
Write to: sdsubscriptions@chicagoreader.com.

Copyright © 2013 Sun-Times Media, LLC.