1. ## A weird question about scale.

I have question about scaling as a kind of thought experiment.

Let's say I have a guy, let's call him average Joe: He is 1.80m tall, weights 80kg and can lift 80kg

now I somehow scale him down to 1/2 size (and let's ignore all those pesky biological things that could go wrong)

So, now I have half-size Joe: He is 90cm tall, weights 10kg, and I'm not sure how much he could lift, or how his strength would scale.

I would argue that he could lift around 20kg, because his new muscles would have 1/4 of the diameter of average Joe's one.
They would also only be half the length, but I don't know if and how that figures in somehow.
I'm not a Biologist, but maybe someone here knows about Biology, muscle scaling or small scale humans.

2. ## Re: A weird question about scale.

Classic Square-Cube law case. https://en.wikipedia.org/wiki/Square%E2%80%93cube_law

Your reasoning is correct. This is why ants can lift many times their body weight and elephants can't. If you scaled up an ant to the size of an elephant it wouldn't be able to lift itself up. It would also explode from overheating.

3. ## Re: A weird question about scale.

I suspect this is where the Square-Cube law rears it's ugly head. In general, smaller organisms can lift a larger percentage of their mass than larger creatures. Most ants can lift ~10 times their mass. Most humans can lift maybe half their weight. Having done none of the research or math, my guess is that being scaled down to half size will result in more than one-eighth strength.

And ninja'd.

4. ## Re: A weird question about scale.

One of the fun things about the square cube law is that some things also work out to pretty much neutral. For instance: animals good at jumping all the way from a flee to a tiger can jump to roughly the same absolute height, raising their center of gravity around 2 meters or so from its regular position. As an animal scales up their weight goes up with a third power function, their strength only by the second power. But jump height is determined by leg length as well, as it determines how much distance and time you have over which the muscles can apply force. And a first power times a second power is a third power. Run speed is similar to that as well, though maybe not as cleanly demonstrable. But the speeds of animals with different sizes but similar builds tend not to be extremely far apart.

5. ## Re: A weird question about scale.

Originally Posted by Lvl 2 Expert
One of the fun things about the square cube law is that some things also work out to pretty much neutral. For instance: animals good at jumping all the way from a flee to a tiger can jump to roughly the same absolute height, raising their center of gravity around 2 meters or so from its regular position. As an animal scales up their weight goes up with a third power function, their strength only by the second power. But jump height is determined by leg length as well, as it determines how much distance and time you have over which the muscles can apply force. And a first power times a second power is a third power. Run speed is similar to that as well, though maybe not as cleanly demonstrable. But the speeds of animals with different sizes but similar builds tend not to be extremely far apart.
I've read that another one such scale-invariant thing is how much time it takes an animal to empty its bladder (at least comparing mammals, of course). I've tried figuring out why, not quite sure though.

6. ## Re: A weird question about scale.

Originally Posted by SirKazum
I've read that another one such scale-invariant thing is how much time it takes an animal to empty its bladder (at least comparing mammals, of course). I've tried figuring out why, not quite sure though.
Specifically, male dogs, humans, and elephants all take about twenty seconds to empty a full bladder.

7. ## Re: A weird question about scale.

Originally Posted by Lvl 2 Expert
animals good at jumping all the way from a flee to a tiger can jump to roughly the same absolute height,
To expand on this: one might figure that falling is like jumping in reverse, so animals of all sizes should be about equally good at breaking a fall, at least as long as they land on their feet. This is not true in an environment with air, because speeding up is done by mass, a third power function, while slowing down is done by air drag, a second power function. So larger animals land harder. But in a vacuum, would this work? If I found the height from which you need to drop a tiger to usually kill it, and I dropped a cat or a mouse from that height in a vacuum chamber (before they suffocated or got too panicked to land, I can tell this is going to be a tricky experiment to perform), whould they actually die?

Originally Posted by SirKazum
I've read that another one such scale-invariant thing is how much time it takes an animal to empty its bladder (at least comparing mammals, of course). I've tried figuring out why, not quite sure though.
I... can't really explain that one either.

Bladder volume is 3rd degree, the size of the hole is 2nd degree (although honestly larger animals could just have a relatively larger hole, there's nothing really stopping the anatomy from changing here), so assuming the relative same hole size and stuff we're missing a first degree in favor or larger animals somewhere. Maybe larger animals build more pressure? The thickness of the bladder wall is a frist degree function? It shouldn't be the extra gravity right?

8. ## Re: A weird question about scale.

Originally Posted by Lvl 2 Expert
It shouldn't be the extra gravity right?
Apparently, it more or less is gravity. More specifically, larger bladders have higher flow rates in part thanks to the extra pressure contributed by the increased weight of the urine (and in part because of the increased cross section of the urethra, of course). Source: this video

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