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Ok, so I have this OC(original character) called Tomoniki(which means 'action figure' in my language/conlang) that is an android that is 6 inchs tall, and weighs 4 ounces. She, to my knowledge is pretty strong for her size.

She can lift up to 3 pounds and drag/pull around 8 pounds normally, but she can pull up to 10 if she goes on all fours. Since she can also climb like a lizard or frog does, and can carry up to 3 pounds 'wallcrawling'. She can also leap 2 leggedly up to 3 feet horizontally, but if she is running or squats and uses all for limbs she can leap around 6 feet horizontally. She can jump around 28 inches vertically with 2 legs, and can reach around 3 feet in a deep squat or with her arms. She can run up to around 3 1/2 feet(41 inches) a second unencumbered on 2 legs, but can go twice that if she drops down on 4 limbs.

Now what I want to know is what would these feats scale up to if she was 6 feet tall and 160 pounds.(please do not say 'but square-cube law says..., just imagine her 'robotness' defies this somehow)

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    $\begingroup$ I feel like you're asking an unnecessary question here. How fast and how strong does your character need to be for plot/game balance/whatever reasons? That's what really matters here. Magical size changes are magic, and therefore can give you whatever numbers you want. $\endgroup$ Commented Oct 8, 2021 at 8:57
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    $\begingroup$ @StarfishPrime You can say that about every single question on this site. Why bother working out rules and systems when we can write whatever works for the plot? $\endgroup$
    – KeizerHarm
    Commented Oct 8, 2021 at 9:36
  • $\begingroup$ @KeizerHarm that's not even slightly the case. This site is absolutely packed with questions of the form "I want X. How can I get it, or at least justify it?" or "I'd like to do Y. What will happen?". There's a goal, a purpose, some constraints. $\endgroup$ Commented Oct 8, 2021 at 9:39
  • $\begingroup$ @StarfishPrime Ok, and you do not count this question as a form of "I'd like to do Y. What will happen?", perhaps because the mechanism of growth is insufficiently specified? $\endgroup$
    – KeizerHarm
    Commented Oct 8, 2021 at 9:50
  • $\begingroup$ @KeizerHarm they haven't stated what they want. There's magic: a thing gets bigger! An answer was given with some implausible extrapolation: OP says "too fast!". Clearly, they want something... there's a setting, there's a goal, there's game balance, there's technological limitations, there's something that must constrain the answers. But they haven't shared it. If they'd stated their goal, they could just handwave it in, because magic, in the same way that answer answer could be handwaved in. $\endgroup$ Commented Oct 8, 2021 at 9:57

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Assuming your android is made of the same materials and has the same proportions as a human, then its strength would scale linearly with its size. So a 6 foot tall android would be able to lift 6 times as much weight and drag/pull around 24 times as much weight. However, its jumping and running abilities would not scale linearly because they are limited by the strength of its legs. The maximum force that can be generated by a muscle is proportional to its cross sectional area, so bigger muscles can generate more force. But the cross sectional area of a muscle also scales with the square of its length, so longer muscles don't generate as much force per unit length. This means that taller beings have proportionally weaker legs (all else being equal), which limits how high they can jump and how fast they can run.

A rough estimate of the scaling factor for jumping height would be the cube root of the ratio of leg lengths. So if your android's legs are twice as long, it will be able to jump 8 times as high (2^3 = 8). The scaling factor for running speed would be closer to the square root of the ratio of leg lengths because running speed is limited by how fast the legs can move through the air, which is proportional to their surface area (and thus scales with the square root of their length). So if your android's legs are twice as long, it will be able to run 4 times as fast (2^0.5 = 4).

Putting all this together, we get that a 6 foot tall android would be able to lift 6 times as much weight, drag/pull around 24 times as much weight, jump 48 times as high, and run 8 times as fast unencumbered on 2 legs (4 times as fast on 4 limbs).

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I'm going to scale the feats up based on weight rather than height because I think that would affect it more.

Base formula: 160 pounds is 640 times 4 ounces, so I'll be multiplying them by 640.

  • Lifting/wallcrawl carry/2-legged horizontal jump: 3 * 640 = 1920 pounds/feet
  • Normal drag: 8 * 640 = 5120 pounds
  • 4-legged drag: 10 * 640 = 6400 pounds
  • other horizontal jumps: 6 * 640 = 3840 feet
  • 2-legged vertical jump: 28 * 640 = 17920 inches (1493 1/3 feet)
  • other vertical jumps/2-legged run: 3 * 640 = 1920 feet (/second for run)
  • 4-legged run: 6 * 640 = 3840 feet/second
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  • $\begingroup$ Wow!!! Is there a way to rein it in a bit, especially the speed? Should I make her lighter? $\endgroup$ Commented Oct 7, 2021 at 18:31
  • $\begingroup$ Actually, making her lighter would increase it even more! (example: 20/4 = 5, 20/2 = 10) Making her heavier would work, though. $\endgroup$ Commented Oct 7, 2021 at 18:39
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    $\begingroup$ Using the same scaling technique, a virus will be able to run faster than the speed of light, and will be able to benchpress black holes. One simply cannot apply mass scaling like that. $\endgroup$
    – PcMan
    Commented Oct 7, 2021 at 19:12
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    $\begingroup$ Aerodynamic drag scales linearly with cross-sectional area, and hence proportional to the square of the character's height. It also scales proportionally to the square of velocity. Your running and jumping extrapolation cannot make sense in an atmosphere, even if the underlying reasoning were sound (as as PcMan pointed out, it ain't). $\endgroup$ Commented Oct 8, 2021 at 8:53
  • $\begingroup$ Wait so your logic is: becoming heavier means that you can jump higher? Sounds odd to me $\endgroup$
    – datacube
    Commented May 24 at 12:35
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Scaling 6 inches to 6 feet is an increase in linear dimensions of 12 times. So, use that scaling for speed- or linear dimension- based measures.

For weight/lifting/volume based measures, scaling from 4 ounces to 160 pounds body weight is an increase of 640 times, so use that.

So:

  • Lift up to 1920 pounds and drag/pull around 5120 pounds normally, but she can pull up to 6400 if she goes on all fours. Since she can also climb like a lizard or frog does, and can carry up to 1920 pounds 'wallcrawling'
  • Leap 2 leggedly up to 36 feet horizontally, but if she is running or squats and uses all for limbs she can leap around 72 feet horizontally. She can jump around 28 feet vertically with 2 legs, and can reach around 36 feet in a deep squat or with her arms.
  • Run up to around 41 feet a second unencumbered on 2 legs, but can go twice that if she drops down on 4 limbs.

By the way, this uses the square-cube law. However, I haven't taken the robot's additional mass into account fully... it's just a naive application due to 'magical robotness'.

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  • $\begingroup$ Yup, just checked. [Robotness] isn’t a tag yet. For this and the @Boringwriter answer the robot is very very broken when they attempt any of these feats. Material strength does not scale up per the square cube law. If “robotness defies material properties” somehow then Starfish was right about magical answers. This gets the alt-reality tag at least if not magic. $\endgroup$
    – Vogon Poet
    Commented Mar 8, 2022 at 3:15

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