# How can an an ant lift 50 times its own weight and pull 30 times its weight?

According to many sites like this one, an ant can apparently lift 50 times its own weight and pull 30 times its weight. Is it true?

Can it be proved using physics? Though most sites agree that an ant can lift many times its own weight, not all agree with exactly how many times its weight. The explanations provided if any are usually vague and do not use specific numbers. Can a specific numerical value be calculated?

Secondly, how is it possible for the ant to pull 30 times its weight? I find it unbelievable. Can anyone explain this?

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Migrate to skeptics.SE? –  Manishearth Mar 14 '12 at 10:50
+1 for nice username.. :P –  Vineet Menon Mar 14 '12 at 10:53
This could also be migrated to bio.SE.. @GreenNoob: did you know that humans can pull and sometimes lift things heavier than themselves? Your weight has no bearing on what you can lift. Its the strength of your muscles. –  Manishearth Mar 14 '12 at 11:06
Specific numbers will only be calculable for a specific species+gender of ant. –  Manishearth Mar 14 '12 at 11:08
@GreenNoob NONONONONONO!!! Wait for a mod to come and migrate it... WOuld you like it here or on Skeptics or on Bio? Skeptics you'll get referenced claims. –  Manishearth Mar 14 '12 at 11:47

This is an example of "scaling laws". Have a look at http://hep.ucsb.edu/courses/ph6b_99/0111299sci-scaling.html - for once Wikipedia doesn't have a good article on the subject.

The strength of a muscle is roughly proportional to the area of a cross section through the muscle, so strength is roughly proportional to size squared. That's why I'm a lot stronger than an ant. However the weight of e.g. a boulder is dependant on the volume, so it's proportional to size cubed. So as you increase size, the weight of the boulder increases faster than my strength does. Or to put this another way, as you decrease size your strength decreases more slowly than the weight does. That's why small creatures can lift boulders that are large in proportion to their size.

Whether an ant can really lift 50 times it's weight I don't know, but it can certainly lift many more times it's own weight than I can. The same sort of argument applies to all small creatures. For example it's why a flea can jump much higher relative to it's body size than I can, but I can still jump higher than an elephant!

Do have a look at the link because it goes into a lot more detail than I can here.

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This guy wants us to believe that he can jump higher than an elephant! </joke> –  John Gietzen Mar 21 '12 at 0:02
Thanks a lot for your answering & also for the interesting link.But my question is but how can you say that strength is related to Area of cross section of the muscle? A Google search did not give me a satisfactory definition of 'Strength' & its relation to the muscle's cross sectional area is not mentioned anywhere. Can you clarify? –  Green Noob Mar 22 '12 at 16:04
This is the relevant section from your link: But in the rest of the universe, the scaling is actually much slower. Body mass increases along three dimensions, but the strength of legs and arms, which is proportional to their cross-sectional area, increases along just two dimensions. If a man is a million times more massive than an ant, he will be only 1,000,000 to the two-thirds power stronger: about 10,000 times, allowing him to lift objects weighing up to a hundred pounds, not thousands. –  Green Noob Mar 22 '12 at 16:05
It's mentioned in several Wikipedia articles e.g. en.wikipedia.org/wiki/Muscle#Gross_anatomy and a Google for "strength muscle cross-sectional area" will find you lots of references. Bear in mind this is a simplification since there are different types of muscle, and in any case an ant's muscle is probably not directly comparable to human muscle. However the argument I gave applies even if the strength:area correlation is only approximate. –  John Rennie Mar 22 '12 at 17:04

Strength

Strength goes like area. Intuitively, the cross sectional area of a muscle counts the number of muscle fibers (actually, myofibrils). Thus, $S\propto A \propto L^2$. But mass goes like volume, $M\propto V\propto L^3$. Therefore strength is proportional to the $2/3$ power of mass, $$S\propto M^{2/3}.$$ This equation expresses the fact that an increase in mass does not give a proportionate increase in strength. For example, adding $25\%$ to your mass will increase your strength by about $16\%$, assuming your body composition and neuromuscular skills don't change appreciably.

Relative strength

In addition, we find that relative strength, strength per unit mass, goes like $M^{-1/3}$, $$\frac{S}{M} \propto M^{-1/3}.$$ Thus, after adding $25\%$ to your mass and getting $16\%$ stronger, you are actually $7\%$ weaker in terms of relative strength.

These facts are known, at least intuitively, to all athletes. In strength sports, formulas such as these are used to compare athletes across weight classes. For example the Wilks coefficient is used to normalize'' weight lifted. (In fact the Wilks coefficient is roughly $(50/M)^{2/3}$, where $M$ is the lifter's mass in kilograms.)

The ant

From the above we can also see that relative strength is inversely proportional to $L$, $$\frac{S}{M} \propto L^{-1}.$$ Thus, a man a hundredth the size of a normal man would be one hundred times more strong in terms of relative strength. In other words, if a man can lift his bodyweight, the same man a hundredth the height could lift one hundred times his bodyweight. (What if a normal man were to grow one hundred times in height? He would be one hundredth as strong in terms of bodyweight, and would be crushed under his own weight.)

It is thus not surprising that an ant can lift many times its bodyweight. Precisely how much is more a question of biology than physics, since we are comparing not only organisms of different size, but totally different morphology.

Certainly an ant can pull, in relative terms, much more than a human. In fact, ants have hooks on their feet. Think of our tiny man who can lift one hundred times his bodyweight dragging himself across a rough surface with climbing gear. It would not be surprising if he could pull on the order of one hundred times his bodyweight.

Figures

You will find below a plot of strength vs mass and relative strength vs mass, in natural units.

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Thanks. Your answer made sense but how can you say that strength is related to Area of cross section of the muscle? A Google search did not give me a satisfactory definition of 'Strength' & its relation to the muscle's cross sectional area is not mentioned anywhere. Can you clarify? –  Green Noob Mar 22 '12 at 16:00
@GreenNoob: You're welcome. Strength is proportional to area since area basically counts the "cables" in the cells that apply muscular force. A $2\times 2$ box has $4$ "cables." A $4\times 4$ box has $16$ "cables." Think also about strength of materials. Does the strength of a stick depend on volume? It makes no sense. It says if we make a stick longer it will be harder to break! The strength of the stick will go like the area of the cross section of the stick since area counts the fibers of the stick. –  user26872 Mar 22 '12 at 16:57
@GreenNoob: Suppose you are trying to pull a stick apart lengthwise. Each fiber of a stick will break at roughly the same tension. The force you must apply is the sum of the tensions needed to break each individual fiber. Thus, you need only count the number of fibers. Since the fibers have the same area this is equivalent to measuring the cross sectional area. Thus, the force needed to break the stick is proportional to area, $$F = \sum F_i = F_i N = F_i \frac{A}{A_i} \propto A.$$ –  user26872 Mar 22 '12 at 21:21