# Square-cube law

1. Jul 18, 2015

### Tiiba

I don't know whether this is physics or biology. I think that depends on the answer as much as the question.

1) Hollywood says a big hulking giant would be a huge threat.
2) Critics laugh and say that a big hulking giant wouldn't even be able to walk.
3) Horses are fast, mice are slow, and ants are just pitiful. Sure, ants are pretty macho in proportion to their mass, but they can't run that fast.

So why? Is there a point where this trend is reversed? Elephants are pretty fast, too.

2. Jul 18, 2015

### DiracPool

3. Jul 18, 2015

### Tiiba

Why does the square-cube law not make small animals faster than large animals?

4. Jul 18, 2015

### Bandersnatch

You're confusing two things here: speed and structural strength.

Of course you can make bigger strides when you're larger. But being larger also means you need increasingly stronger limbs, that can support your weight and survive the stresses of walking.

Since the material making up supporting structures (bones, chitin) cannot be made physically stronger, the only way to support more weight is to have larger cross-section bones.

The square-cube law means that it's not enough to double the thickness (cross-sectional area) of a limb to support a 3-dimensionally larger object, like a human-proportioned giant. You can see this at work in the examples of animals you've provided: limbs of an ant, mouse, horse and elephant grow increasingly thicker w/r to the body as you go up in size.

At some point, the size of the limbs (as compared to the body) needed to support the weight of the animal becomes prohibitively large.

5. Jul 18, 2015

### Tiiba

You know, I think I have it.

Maximum speed depends on drag cross-section, while power available, which depends on metabolism, goes up with mass. Is this correct?

Dividing 8x power by 4x drag force gives 2x speed.

I did a calculation some time ago that predicted things the other way around. I think I totally forgot about metabolism.

6. Jul 18, 2015

### Bystander

Think it through carefully --- you've got waste heat/energy to dissipate --- you've skipped a few details that might contribute to understanding the functional relationships you're tossing around so casually.

7. Jul 18, 2015

### Almeisan

What makes something fast is a lot more complex than the square cube law, which says exactly what it says and nothing more (though it has implication).

The average (relative)speed of a N2 molecule is 475 m/s. That's fast, and those molecules are small. The largest known living organism are fungi that stretch large distances (kilometers). They do not move at all.
Then, there's large animals that move pretty fast and tiny organisms that move with the current only. What about spiders that use silk to travel with air currents. Apparently they can reach an altitude of 5 kilometers. I wonder how they do on a list of fastest animals. What is their terminal velocity. Apparently this is unknown and depends on how much silk they use. Apparently every animal as small or smaller than a mouse survives terminal velocity impact on 'softer' surfaces,

Maybe it makes more sense to express speed relative to body size.

Last edited: Jul 18, 2015