Re: In a vacuum, can an ant survive a fall that would kill a human?

Vaughn,

Your question certainly took me on a merry chase through the library! I 
was hoping to give you a definitive answer from a noted authority, but 
apparently no one has published crash-test results for ants (at least, no 
one I was able to find!). The short answer, from what I could work out, is 
that the ant probably would survive a fall in vacuum that could cripple or 
kill the average human. For details of my reasoning, read on!

One thing I was able to find was data from the NHTSA (U.S. National 
Highway Traffic Safety Administration) about crash test results for 
humans. Data from their Biomechanics and Trauma Division research is 
available at http://www-nrd.nhtsa.dot.gov/departments/nrd-51/BiomechanicsTrauma.html. 
The NHTSA standard for a sudden impact 
acceleration on a human that would cause severe injury or death is 75 g's 
for a "50th percentile male", 65 g's for a "50th percentile female", and 
50 g's for a "50th percentile child". These figures assume the human is 
taking the impact on the chest/stomach, the back, sides or the head. The 
average value is about 65 g's, so I used that for the fatal impact 
acceleration on a human being. Another figure the NHTSA uses is the 
duration of an "average" impact event on a human, which is 15 milliseconds 
(15/1000 of one second).

Using those figures, I used the relation 

v=at

to estimate the impact velocity given a known impact duration t and impact 
deceleration a. I substituted 65g (638 meters/second^2)for a and 15 
milliseconds for t to find how fast a person has to be going to be 
injured. The speed is actually relatively low, only about 10 meters per 
second (32 feet per second).

I was curious about how high this potentially fatal fall would be, so I 
went on a bit further. Substituting these figures into the relation

t=v/a

and using 1 g (9.8 meters/second^2) as the acceleration due to gravity on 
a falling body and 10 meters per second as the velocity v at the end of 
falling time t, I get a figure of about one second in free fall for our 
hapless human. One further relation,

X=v(0)+1/2at^2

gives the distance fallen, X, if an initial velocity, time, and falling 
acceleration are known. v(0) - 0, and a and t are known, so substituting 
gave an answer of about five meters, or slightly less than twenty feet -- 
not far at all. 

Given that, I then turned to the ant. Nearly everyone has flicked an ant 
off a table or an arm at one point or another, and the ant usually is 
unharmed by it. I used my finger as a test subject, and came up with an 
average "flick speed" at the end of my finger of about 4.8 meters per 
second (about 17 feet per second). 

I assumed that the effect of flicking the ant would be very like an 
elastic collision between two objects, and that the mass of my finger is 
significantly greater than the ant's mass. These assumptions led me to a 
relation for the effect of a large moving object on a much smaller 
stationary one in an impact:

v2=2v1

where v2 is the velocity of the small object after the collision, and v1 
is the speed of the larger object before the collision. Substituting 4.8 
meters per second for v1 gives a post-flick speed of 9.6 meters per second 
(about 34 feet per second) to that little ant.

Taking that speed, I once again looked at the original relation v=at, and 
rewrote it as

a=v/t

to find the acceleration the ant had to undergo during that impact with 
the finger to reach that velocity v of 9.6 meters per second. I used the 
same 15 milliseconds the human got for his/her impact for t, and the 
result was 639 meters/second^2, or just a shade over 65g (which was a 
surprising convergence that prompted running the problem again!).

So, while an impact deceleration of 65g can kill or cripple a human, it 
would appear that ants can take an acceleration of about the same 
magnitude and still keep trucking.

I hope this has been helpful!