So, my current WIP is based on the idea that humans only have 5% of their height (1.7m = 8.5cm) but I'm having trouble calculating their weight, it can't be 5% because of the square-cube law but I have no idea how to calculate it.
Your mass is cubic (volume). If you shrink so that you're 95% as big in all (linear) dimensions, your mass is (.95 * .95 *.95) of what the old value was. Just (.95^3 * normalmass). About 86% of normal. Weight and mass of course scale directly together. So it's the same 86% for weight. If you used to weigh 100 pounds, and you're 5% smaller (in width, height, depth), then you'll weigh 86 pounds.
So, I might be embarrassingly wrong about this, but since insomnia is here to stay and I like learning new things (the hard way) I'll give it a go: Am I way off?
From somebody who is not much of a math or science person, I would have just assumed that if you are only 5% the size of a normal human being (but you're still considered a humanoid being... like Ant Man or Tinker Belle or something), then you would weigh 5% of what you normally would have weighed. If you're a scrawny nerd like me who weighs ~150 pounds, then you'd weigh 7.5 pounds once shrunk. I could be completely wrong, but I just assumed that it would be proportional. Maybe I'm not understanding the question.
IDK, 8.5 cm is really small, and keeping the same weight would crush their tiny body. We'll say a 5ft 100lb person is shrunk down to 5% of their original size. They would be 3 inches tall (7.62 cm). So they would weigh something 5lbs 2.267 kg), which is still fairly light, all things considered. (I hope I did the maths correctly since I am really bad at the complicated equation stuffs). Pretty weird that they would weigh so much for being so tiny. I guess they get more dense in the shrinking process?
Yes. I spent some time thinking upon this myself, but then I read about the square-cube law and it made sense somehow. I really don't know. My process of thinking went like that: I first imagined myself shrink to the size of a mouse or a lizard perhaps, it doesn't matter. If I were to be 5% of my original weight, I'd weigh 2,5 kilos. That's a lot of kilos for a being that small. I'd have to be made out of something solid and dense to weigh that much. As for the formula I tried to experiment on, I'm not even sure what length is supposed to mean for the human body so I just randomly put my height there. I don't even know if it should be measure in cms. I don't know if volume should be measured in litres either. That's why I said I might be making a fool out of myself since I don't really understand this axiom. I tried to find a more explanatory formula of this equation but couldn't (in 5 minutes).
Right, but does height affect weight? I knew a guy that was a few inches taller than me, but only weighed 115 pounds. So being basically barely muscle on bones, would make being tall and light weight possible.
I haven't spent a lot of time on these things to tell you the truth but... em... BMI. Some people might be heavier boned than others or some might... have heavier brains or something. Idk. For example I think that men that have the same height that women have, weigh more without looking fatter than women. I don't know how that works.
Well muscle is heavier than fat is, so it takes more fat to equal that of muscle by weight. I think 2 people of the same height would have approx. the same organ and skeletal weight, so I think it may be more down to matching weight with muscle and fat at that point.
The physics answer is that shrinking you would not affect your mass at all... (and, therefore, your weight) It will affect your density. You will have the same number of molecules/atoms/protons/neutrons - the same amount of matter just in a smaller space unless the shrinking process is some kind of evaporation, which would kill you ETA - or are you suggesting a new species in which humans are only a few cm tall? In which case there would be accordingly less mass, and therefore we would have the brain of a hamster
This is how I imagine it and why it makes sense. This is a pretty shitty example since z (12 cms) looks way off but I hope you get the picture. If all parameters (x,y,z) shrink in the same ratio (5% of them are left) then indeed the volume decreases faster. Instead of litres I count with kilos since we are talking about human weight, but this is a very rough estimation because humans obviously are a tad more curvy in shape.
Calculating weight is easy... just divide by cube of height reduction. So a 170 cm 60 kg person when shrunk to 5% of height would weight 0,05^3 * 60 kg = 7,5 g. Of course, as noted above, there are significant issues with species that is naturally of such height.
This is so true and so simple it almost brought me to tears. I think I rediscovered this equation by taking the ridiculously longer road:
Damn, I was not expecting this many answers. Thank you all for replying and special thanks to @Malisky and @Aldarion for finding the answer I was looking for (I think), a pity that I don't understand the logic behind it but, oh well, one can't worry about every single detail. Pretty much, yes. These "micro humans" don't lose brain functionality because "fantasy" though.
For what it's worth, I don't think brain size alone determines intelligence. If it did, then people who have less than 70-75 IQ would have smaller brains than Einsteins. And, as far as I'm aware, that's not the case. That would be some pretty big news if that was how it worked. To be honest, the scientists who are using their brains to figure out their brains are making good progress, but don't quite have all the answers yet. Anyway, if you're writing fantasy then this basically doesn't matter. If I can accept that there are "humans" who are 5% the size of a normal human, then it would be strange to get caught up on their intellect.
One of my beta readers picked up on something like this. He pointed out that tiny humans would be able to fall off buildings and survive. It might be true, but it's not fictionally true.
Oh, complicated calculations ... I'm not at all a person of math, so I don't even know whether to try to calculate or not
That makes no sense at all. Gravity is gravity -- if a normal person and a 5% micro-person both fell (or jumped) off a ten-story building, they would both accelerate at the same rate and they would both splat on the sidewalk at the same moment and with the same terminal velocity.
Depends on how tiny the human is. Air resistance depends on the surface of the body that's perpendicular to the air stream. But the weight of the body depends on the volume. Now, when you scale a thing with the diameter d up or down, the surface changes with d² and the volume with d³. That means, that the larger the body is, the more weight it has in relation to its surface. The smaller the body is, the less weight it has compared to its surface. That's why the air resistance to gravity ratio is much more in favour of survival for small bodies.
Why is this getting traction again??? I'm pretty sure that terminal velocity is calculated with mass in mind, also tiny beings are more susceptible to wind resistance which affects acceleration, and they would probably get knocked around by it, they would still die/break something from a large enough fall but the relative height required to do this would be different.
Ackchually, there is a size at which small creatures (given they have a biologically sensible density) cannot fall to death anymore, no matter how far the fall. The trick is that air resistance is not only dependent on the surface of the body, but also on the speed SQUARED. The faster you become, the even more the resistance force grows. But the gravity with which you're accelerating towards earth is constant. At some point the air resistance force completely compensates the accelerating gravity force, which is the point when you reach terminal velocity. If you're small enough, your terminal velocity is also small enough that the common biological bodies can survive it.
I don't do math if I can help it. I looked up kangaroo rats. Their bodies are 3" long. They weigh about half an ounce. If one rearranges that half ounce into human form (thinner body, fuller legs), I think it would be about right.
