why is it impossible for animals to grow to certain sizes without collapsing under their own weight? If you just scale everything up 1:1, why can’t they just function normally at increased sizes?

In: Biology

Structures and biochemistry don’t scale linearly like that. Just because things get bigger doesn’t mean the material they are made of is any stronger.

Imagine a cube with each edge of length 1.

The sides have an area of 1 x 1 = 1.

The volume is 1 x 1 x 1 = 1.

Now scale it up “1:1” so all the edges are now length 2.

The sides have an area of 2 x 2 = 4.

The volume is 2 x 2 x 2 = 8.

So despite you scaling all the lengths equally “1:1” by 2.

Area went up 4 times, and volume went up 8 times.

Things like strength of bones are how wide they are, so they vary by area.

Stuff like weight depends on how much stuff there is, so they go up by volume.

And as you can see, area goes up a lot slower than volume does.

This is called the square-cube law, because the sides are squares which go up a lot slower than the volume.

Bone strength is just one factor.

Stuff like heat loss is skin area (goes up with the total area of the sides), heat generation is how much organism there is ( goes up with volume)

And many other factors like oxygen flow, etc.

There are many things that simply do not scale well. One common theme is when a scale goes up many attributes increase exponentially to different exponents. Volume is related to a distance cubed. Surface area is only squared. That is a problem when an animal’s oxygen requirements depend on its volume, but the amount it’s able to take in depend on the surface area of its lungs. Other critical attributes will increase by even higher exponents, and others lower.

Then there are things that just don’t work at other scales. Capillary action doesn’t work above a certain size, and vacuum pumps cannot pump water above 34 feet.

I highly recommend JBS Haldanes 1926 essay “[On Being the Right Size](http://www.phys.ufl.edu/courses/phy3221/spring10/HaldaneRightSize.pdf)

Think about blowing a bubble. Think about how easy it is to blow a small bubble versus a large bubble. Now think about how difficult it is to blow a very, very large bubble, and have it exist for any length of time. It’s a delicate operation, is it not? Much harder than blowing a tiny bubble, and many times more difficult than keeping foam, which is made up of many, many tiny bubbles, stable.

Got all that in your head? Cool. Now imagine that the bubble is made of skin, filled with meat, and is the size of a building.

So, that’s why.

When measurements double (x2), then area goes up by a factor of 4, (2×2 ), and volume goes up by a factor of 8 (2x2x2)

cube 1x1x1

SA = 1+1+1+1+1+1=6 square units or 1×6

Vol = 1x1x1=1 cubed units

Cube 2x2x2

SA = 2×2=4, so 4×6=24 square units

Vol = 2x2x2=8 cubed units

So doubling the length will produce 8 times the volume (not double), a twice tall person will be 12ft, but weigh 1600lbs, and bones can’t support it.

I think this is pretty obvious without asking. Obviously the larger something is, the heavier it is. Forget about bones, if you scale an eye 1000 times don’t you think it will sag out of shape from it’s own weight?

Capillary action, the force that pushes water up a straw above the regular water level. This and gravity dictates how tall trees can grow by limiting how much water and nutrients they can get from the ground. Similarly, the taller an animal is, the harder its heart has to work to push blood against gravity to the brain

Animals need to be adapted for their size. Larger animals need very complex mechanisms for getting oxygen to their tissues in comparison to insects for example. Also as size increases, surface area:volume ratio decreases, so less heat is lost. Animals will therefore evolve an optimal size for temperature regulation in their environment.