Tuesday, March 2, 2010

The supposedly herculean feats of ants

Most of us have heard that ants can carry weights hundred times of their own. Just recently, BBC News ran a story related to this ability.

Image Source: Wikimedia Commons.

In most people, this conjures up images of SUV-sized ants effortlessly lugging around buildings, reminiscent those in classic Sci-Fi film THEM!; more still, of mimicking the ants and creating super-strong materials and actuators that are vastly stronger than anything we have access to today.

This is however a pipe dream. This apparent strength is a consequence of being small, and not of some specific capability of ants. The villain is scaling laws -- the rules that describe how physical properties change with size.

Here is how it works:

The mass of an object that has characteristic length L (that is, is roughly of size L in height, width and depth) is described by m = ρL3, where ρ is the density of the object.

The weight a muscle can lift is given by Mmax = cL2, where c is some material constant that is independent of size. You can see why this is by realizing that this is very much like the strength of a string -- and making a string longer does not make it stronger, but making it thicker does.

What we are interested in is the ratio of these quantities (i.e. maximum carry weight over mass):
Mmax / m = c/(ρL)

Ignoring c and ρ as they are independent of size, a pattern emerges. If we put in a very small value of L--a very small characteristic length--this ratio becomes very large. If we put in a large L, it becomes small.

So, what does this mean? Well, the smaller the muscle, the more it can carry relative to it's own weight.

In conclusion:

An ant that is 1,000 times larger than it is weighs a billion times more, but is only a million times stronger, so it's strength to mass ratio decreases by a factor 1000.

A human that is 1,000 times smaller than it is weighs a billion times less, but is only a million times weaker, so her strength to mass ratio increases by a factor 1000.

Returning to the SUV-sized ants, such ants would not be able to support their own weight, let alone carry buildings around, and an ant-sized human would be stronger than anything it's own size.

this value is a bit larger than SUV-size, but correct in an order of magnitude ballpark sort of way.


  1. Although wouldn't an ant sized human have an enormous surface area and risk freezing to death?

  2. True enough. But humans can adapt (people do live in arctic regions and whatnot). Just have to make miniature clothes to compensate for the heat-loss.