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This morning I saw an ant and suddenly a question came to my mind: how do ants actually carry items much heavier than themselves?

What's the difference (in physics) between us and them?

Danny Beckett
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Paul
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  • This is a question for Biology, not Physics. A good question, though. – HDE 226868 Dec 16 '14 at 02:33
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    But i mentioned ,in physics... I dont want to know about biological details..i want to know about the physics. – Paul Dec 16 '14 at 02:36
  • But the answer presumably has to do with how ants are built, not the physical forces at work. – HDE 226868 Dec 16 '14 at 02:37
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    Michal basically got it right. The cool thing about this is, that Galileo's last book "Discourses and Mathematical Demonstrations Relating to Two New Sciences" ("Discorsi e dimostrazioni matematiche, intorno à due nuove scienze"), published in 1638 already contained a very good treatment on the idea of mechanical scaling laws. – CuriousOne Dec 16 '14 at 03:13
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    This question appears to be off-topic because it is about entomology and not physics. – Kyle Kanos Dec 16 '14 at 03:22
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    This is absolutely a physics question. The only biology you need to know is "ants are small". After that, it's all physics. Keep this open. – Floris Dec 16 '14 at 03:29
  • @HDE226868 How ants are built matters because it determines what relevant physical forces are at work. – Joel Dec 16 '14 at 05:57
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    https://en.wikipedia.org/wiki/Square-cube_law#Biomechanics – Tim S. Dec 16 '14 at 14:49
  • @Tim S. - Make your comment an answer. The square-cube law is what makes this physics. This law rears its head in a number of places, not just ants vs. humans. – David Hammen Dec 17 '14 at 08:39
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    similar to, "why don't toy cars smash into pieces when pushed off a high table?" – Jodrell Dec 17 '14 at 11:50
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    Possible duplicates: http://physics.stackexchange.com/q/10793/2451 and links therein. – Qmechanic Dec 17 '14 at 15:47
  • I would hazard a educated guess that the answer to your question can only correctly be answered in a evolutionary sense. They are strong because they need to be strong. If human survival had depended on them carrying ten times their mass, then evolution likely would of shaped them so that they could, probably without drastically changing the physics of the situation. There is only tiny differences between us and other great apes, but last I heard the best research into it still had chimps with approximately twice the strength to weight ratio. – Jonathon Dec 18 '14 at 17:25

3 Answers3

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Strength is proportional to a surface area divided by volume, but since volume is directly proportional with mass and I can't get an accurate density (I am guessing approximately both for mass and size.), I will use mass instead.

According to Wolfram Alpha, the average mass of the human body is 70 kilograms. The surface area of a person weighing 70 kg with a height of 170 cm is 1.818 square meters. This gives us a weight/surface area ratio of about $38.5 \frac{kg}{m^2}$.

So now, how much does an ant weigh?

This article provides a variety of different numbers, varying from 1 mg to 60 mg. Since the biggest ants will be soldiers, I assume that the approximation will be slightly smaller than 30 mg. Say 25 mg or 0.000025 kilograms.

Now comes the interesting part. Not Wolfram, not even uncle Google knows the surface area of an ant.

This Britannica page says that ants range from 2 mm to 25 mm. Let's eliminate the soldiers since they are huge. (A big worker would be as long as 8 mm.) That gives an approximation of 5 mm.

I gave the animation industry a shot and tried to measure the surface area of this free ant model. The length of the ant is now 0.005 - let's call it a meter.

dimensions of the ant

This gives us a surface area of about $4.87\cdot 10^{-5}$, or $0.0000487$ square meters. So an ant that weighs 0.000025 kg with a length of 5 millimetres has a surface area of about $0.0000487 m^2$. This gives a weight/surface area rate of about $0.5335 \frac{kg}{m^2}$.

So, the uniform strength of an ant is about thirteen times more than a human's.

How much can a human carry while walking a long distance, maybe even climbing? Maximum 20 kilograms for most people. That is slightly more than a quarter of our weight (about 0.28).

How much can an ant carry? About 1 gram - the weight of a leaf, or 40x the weight of an average ant.

4 divided by .28 = 14. So ants are about 14 times stronger than we are. (Carrying capacity according to body mass.)

Jon
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altac bori
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    The militaries of the world will assure you that any physically able person, including female soldiers, can [be made to] carry much more than 20kg for long distances, including climbing, crawling, etc. – Peteris Dec 16 '14 at 05:04
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    We presume that the person weighs 70 kg. 1/3 of it makes 20,3 kg.. For mountain climbing, this weight seems quite average to me. – altac bori Dec 16 '14 at 05:20
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    Sure, for mountain climbing it's perfectly reasonable, and your point works perfectly with a conservative 20kg estimate; it's just that 'what weight can a human carry over rough terrain' for an average conscript/recruit after basic training often is 50-55% of body weight, so 20kg is not nearly a maximum. – Peteris Dec 16 '14 at 05:45
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    @Peteris http://www.washingtonpost.com/wp-dyn/content/article/2009/01/31/AR2009013101717_2.html Trained American Marines in Afghanistan are getting injured by loads of >50% body weight, and the recommended weight by the Navy is 50 pounds (~22kg) which is well in line with the author's numbers. – March Ho Dec 16 '14 at 08:38
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    @MarchHo exactly, that same article lists that typical loads tend to be 100 pounds or much more than that, so that's certainly a much better reflection of "how much can a human carry while walking a long distance" and "maximum x kilograms" than the loads that are 'recommended'. – Peteris Dec 16 '14 at 09:29
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    I wouldn't consider loads that cause consistent injuries in some of the most well trained and strong individuals of the human species to be representative of "how much can a human carry while walking a long distance" – March Ho Dec 16 '14 at 09:31
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    He's ignoring ant soldiers, so he should ignore human soldiers too. – RemcoGerlich Dec 16 '14 at 11:03
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    Four times 25mg is 100mg = 0.1g, not 1g. – user253751 Dec 17 '14 at 07:55
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    Posting comment on behalf of @ali : You state "Strength is proportional with the surface area divided by mass". I believe that is a typo and should read "Strength is proportional with the cross sectional surface area divided by mass". Cross sectional direction being the direction of force which in an ants leg would be leg radius squared * pi. This only applies if he is talking about compressive stress which I am assuming. Wikipedia has much more details: http://en.wikipedia.org/wiki/Strength_of_materials . Section 5 of this website explains it: http://www.av8n.com/physics/scaling.htm – Floris Dec 17 '14 at 14:04
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    Unrelated: That is one damn fine ant model. – Pharap Dec 17 '14 at 19:30
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    Strength is derived from cross sectional area, not surface area. Although the two will scale in the same way it is important to be accurate. – Floris Dec 17 '14 at 22:41
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    Can you provide a reference for your "strength proportional to surface area divided by mass"? That would imply a $strength\propto \frac{1}{r}$ relationship when buckling strength in fact goes as $\frac{1}{r^2}$ - see details in my answer. Can you tell us where your $1/r$ relationship comes from? – Floris Dec 18 '14 at 02:24
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    I think @Floris is right. I can't see how surface area would come into it at all. Pretty sure it is the cross-sectional area of the muscles, which can pull around 2-3 kgf/cm^2. – Timmmm Dec 18 '14 at 11:01
  • "Strength is proportional to surface area divided by mass. According to Wolfram Alpha" in what way? All objects have surface area and mass, and most often it is not relevant to the strength of the material or how much strength it can exert on an external object. – Jonathon Dec 18 '14 at 17:20
  • As a freshman of electronics, i try to be as simple as possible. Since ants have six legs which totally differ from a human's, the result is effected. Finding the radius of one of the legs' of a family is a different matter. But since the question is "How can they carry?" It all boils down to "not be crushed under it" so i thought an ant like a prism. The result is not exact but even how much a human being can carry varies wildly. And Jonathan Wisnoski, they are different sentences. – altac bori Dec 19 '14 at 02:14
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I think the answer has less to do with their construction and more to do with their smaller size

For more information lookup Scaling Laws.

Basicly the mass of a object scales as it's size cubed so a ant 10 times the size will be 1000 times heavier. But the strength of an organism depends on the cross sectional area of muscle (I've heard this somewhere, not sure about the details), and hence scales as the size squared. So an ant 10 times the size will only be 100 times stronger.

Putting those two facts together the strength to weight ratio of an organism varies inversely with it's size. Hence smaller organisms even with the same construction will be able to lift more in relation to its mass.

Note: When I say size I'm referring to the linear size of a body as measured with eg a ruler

Michal
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    Assuming the same muscle material it is pretty obvious that strength is proportional to the cross-sectional area of the muscle. Just imaging putting to muscles next to each other (in parallel). You've clearly doubled both the strength and the cross-sectional area. Good answer btw. – Timmmm Dec 18 '14 at 11:03
  • @Timmmm: Just imagine putting muscles next to each other (in parallel). You've clearly doubled the strength, cross-sectional area, mass, and volume. So it's pretty obvious that strength is proportional to, uh, . . . one of those. (As it happens, it is in fact true that strength is proportional to the cross-sectional area. But you should be wary of confirmation bias, of deciding that things are "obvious" because you already know them. The history of science is full of people continuing to accept falsehoods that seemed "obvious" to those who "knew" them.) – ruakh Dec 22 '14 at 07:25
  • @ruakh It's obvious that stength is a function of cross-sectional area. I was just using the doubling thing to show that the function is linear. In this case it really is obvious. I'm pretty sure sailers from centuries ago knew if you put two ropes together they could carry twice the load because they're twice as thick (in terms of cross sectional area). – Timmmm Dec 22 '14 at 10:15
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Strength / weight is a funny thing. The stress on a long thin rod (like an ant's leg) is limited by the Buckling strength which is given (for rod that can freely rotate at each end) by

$$F = \frac{\pi^2EI}{L^2}$$

where $I$ is the second moment of area which scales with $r^4$ - so

$$F \propto \frac{r^4}{L^2}$$

So when you make an object 2x smaller, the mass is 8x smaller but the strength is only 4x smaller. This means that smaller objects are stronger for their weight.

AFTERTHOUGHTS

Ants have an exoskeleton meaning that their legs derive most of their strength from the outermost part of their body (think "skin as tough as bone"). This makes the "second moment of area" of the support structure much larger than you would expect - see that $r^4$ term above... This is one reason why the skinny legs of the ant are quite so strong - all their strength is on the outside.

Having established that the (exo)skeleton of the ant has greater structural strength, weight for weight, than that of larger species, we still need to address the question of muscle strength. Here we need to look at the surface-to-volume ratio. Doing work with a muscle requires oxygen - which is obtained by exchange of oxygen with the atmosphere. Now if we assume that the volume of muscle scales with the volume of the animal, and thus with $r^3$, and the surface area of the lungs, or spiracles in the case of ants (tubes from the skin to the muscles) scales as $r^2$, then you can see that the "lung to muscle ratio" (LMR) is

$$LMR \propto \frac{1}{r}$$

so the smaller you are, the less likely you are to run out of breath. Even if the lung is a fractal surface with a fractional dimensionality greater than 2, it will be less than 3 and the LMR is still larger for smaller animals. Diffusion of oxygen - same story, because it has much less far to go.

In short- by dint of their size, the structure of an ant is more resistant to buckling; and their metabolism (ability to burn oxygen) is better which means their muscles can work harder.

Clever little things, really.

Floris
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