Small is Mighty: the Square-Cube Law

Why is the ant mightier than an elephant?

License: Creative Commons BY-NC-SA

[superzilla]

Funny thing is that the Square Cube Law was actually mentioned in the 2016 movie. when Godzilla first arrived at Japan, the senator called a meeting to calm everyone down. "The creature cannot come up onto land without crushing itself under its own weight" but then Godzilla gave a middle finger to science and came up onto land anyway. Lol

[TheRaNetwork]

so if you have a bunch of ants working together to make one big ant-elephant, would the ant-elephant be stronger than the elephant?

[carultch]

An elephant is 100 times larger than a mouse per linear size, and weighs times as much.  Lighter than equal densities/equal proportions would predict, but it is still the right order of magnitude.

A mouse's femur is 1.1 cm long, with a diameter of 0.7 mm.
An elephant's femur is 1 meter long.

If direct compression pressure were the governing failure mode, we'd expect an elephant's femur to have a diameter of 50 cm.  A square-cube law, exactly as this video would predict.  This is an extremely impractical femur, to be so thick that its thickness is half its length.

If buckling were the governing failure mode, we'd expect an elephant's femur to have a diameter of 18 cm.  This seems much more reasonable, but it still is seems rather thick for a bone proportion.

The actual femur of an elephant is 8.6 cm in diameter.  The ratio of diameter to length is only slightly larger for the elephant (0.086) than for a mouse (0.063).  Not nearly enough to justify either scaling argument.

Something else is going on here.  Anyone know what it could be?

[rachdarastrix]

this is why I don't make dragons larger then 48 feet and then give them wings so massive they can be tucked away with 3 folds to not get in their way when walking.

[NevolmonGaming]

"average human can only lift half his own weight" looks like somebody has never been to the gym.

[menacevang]

Damn Galileo be making everyone look like a slacker

[JokingJoker]

Is funny how people forget that AIR has weight and MAKES PRESSURE. Gravity IS NOT A FORCE!

[vnnyboy]

strength--directly proportional-- to cross section area of the legs??? doesn't an opposing force like the muscles or the MATERIAL used to support the structure matter?? i mean.. one can balance an insane amount of weight on 4 diamonds standing as pillars but covering a small surface area

[_baller]

This is like how something is faster the smaller it is....but this is about strength

[AbdallahEzzatKoji]

the square cube law should work all the time right.

but it confuses me when we deal with fractions.

lets say we have a cube, its volume is L^3, and its cross section is L^2.

So if we start with L=0.1("unit"), then its cross section is 0.01 (unit squared), and the volume is 0.001 (unit cubed).

When the dimension doubles to become 0.2 (unit), the cross section grows four times which is 0.04(unit squared), and the volume grows eight times faster which is 0.008 (unit cubed).



I knew what what seemed wrong, I mistook that the values before 1 (unit) is greater for lower powers. However, still the higher powers always have a higher rate of increasing (which is the idea), and the values pass the breaking point at 1 (unit).

It creates an illusion jumping between different units of measure. take a 2 cm, the cross section is 4 cm^2, and the volume is 8 cm^3, it is not right to compare different types of quantities e.g. a volume and a cross section. still numerically 8 is greater than 4, "the volume is greater than the cross section". If we take the same cube and measure it in meters, its length is 0.02 m, cross section 0.0004 m^2, and the volume m^3. numerically is smaller that 0.0004, "the volume is smaller than the cross section".

Anyways it is one of the times when you know the answer to your question right after you speak out you question.

[alongeasy]

Its only my humble opinion.

All of this is only HALF TRUE. Gravity play a MAJOR ROLE. Unless u ENLARGE an ANT, maybe ANT also cant SUPPORT more weight because of GRAVITY.

Also CUBE LAW sometimes doesnt apply to ALL. There is sometimes LARGER object with LARGER volume but with SMALLER MASS. I mean THE CUBE is LIGHT. Compare to SMALLER CUBE.

[sirasoi]

Amazing 👌 very interesting video 👌keep sharing 👍

[AwesomeWikidStudios]

Came here because Zero Punctuation mentioned this in his RE2 review and I'm dumb and didn't know what it was

[Akanio_Vatheros]

So, a really big dinosaur can sustain it's own weight as it is, but to scale it up to an even bigger size, it would have to be a mecha dinosaur to support it's own weight, otherwise, it's fleshy body will collapse, is that right? Kinda getting the gist, dunno why my brain is having a hard time understanding the concept.

[thecarwithinternetaccess]

The voice of the lady makes my ears bleed

[doctorpanigrahi]

You ignored a crucial parameter and that's density .

[MarcoPolo-yjjj]

and the ant. Is able to pick more weight because gravity dont effect smaller objects. that's why the ant has a shell around. It's body because gravity has almost no effect on. It so. It has pure muscle beneath the shell

[DarkxV]

I have a friend in high school who is only 163 pounds and can lift almost 400 pounds.

[Acein]

Turned it off because the background drums are obnoxious.

[TheKunnche]

I don't feel so inferior as a tiny body builder anymore. Basically I'm doing just as well as or better than the big lugs hunkering around 🤭