Calculate humanoid weight after scaling?

[Papewaio of The Org]

new weight = old weight times (new height divided by old height) cubed

new weight = old weight * (new height / old height) ^3

so

New weight = 200 * (0.9) ^ 3
New weight = 200 * 0.729
New weight = 145.8 pounds

 

[Nightfall]

Holy crap dude! I'm an artist, you trying to kill me? For me, I'd just take the percentage. Do you guys actually calculate real weights? If so, what are you going to do for equipment?

I think they just find pieces of metal and weld them onto their bodies.

 

[LightPhoenix]

Yeah, if you take a cube of 1x1x1 filled with water, and cut any one dimension to 0.5, you now have half as much water in the cube. So what's the formula? Math isn't my strong suit obviously.

There's actually two formulas that are used.

The volume for any box is height times width times depth - V = xyz. If you were going to reduce the size to 10% (which I'll call "r") along every direction, you would end up with the formula V = (x times r)(y times r)(z times r), or V= xyzrrr, or V = xyz(r^3). That r ^ 3, or, r*r*r, is where you get the 0.1%.

The other formula is a general physics/chemistry formula, D = M/V. That is to say, density is equal to the mass divided by volume. Weight is simply mass times the force of gravity pulling down on you (W = M*g), so if density is the same, then when you lower volume, you lower weight by the same amount.

So, if volume is lowered to 0.1%, weight is lowered by the same amount.

 

[Nightfall]

So should I just suggest that we try something else?

 

[LightPhoenix]

Holy crap dude! I'm an artist, you trying to kill me? For me, I'd just take the percentage. Do you guys actually calculate real weights? If so, what are you going to do for equipment?

While that's certainly a valid simplification, it ends up grossly overestimating the weight of an object when it's reduced, and likewise underestimating it when it's enlarged. If you keep track of encumberance, it's fairly important. To use the original example, the seven inch matchstick-man ends up weighing twenty pounds if you use a simple percentage, which is obviously ludicrous.

I've never been a fan of encumberance anyway though.

 

[mmu1]

new weight = old weight times (new height divided by old height) cubed

new weight = old weight * (new height / old height) ^3

so

New weight = 200 * (0.9) ^ 3
New weight = 200 * 0.729
New weight = 145.8 pounds

Right.

However, if we're not simply talking about reducing or enlarging someone by magic, but trying to design "realistic" humanoids by scaling up and down from real-world humans, then additional factors become involved.

This has to do with the fact that if you just increase linear dimensions, then bone strength (which depends mainly on the bone's cross-sectional area) doesn't keep up with the increase in weight. (the area only quadruples, while the weight is increase eightfold - the good old cube-square law)

Which means that almost without exception, bigger and heavier creatures are more stocky than just the increase in weight would indicate, and smaller ones are more slender. So if you really want to go all out, add some extra weight when scaling up, and remove a little more weight when scaling down. I'd say +/- 10% extra for every 25% you increase or decrease the height by is a decent fudge factor...

(Or you could calculate how much thicker the bones of something would need to be to be equivalently strong, but that's just bone - there's no good formula for muscle mass, and besides, bone strength doesn't quite keep up with increasing size anyway, in nature - it's one of the reasons why, for example, a cat jumping down 20 feet would most likely be ok, a human jumping down the same distance would likely be hurt but might get away with minor injury, and an elephant would completely shatter its legs)

 

[Nightfall]

Light,

Admit, you just want to live in 0 g like the rest of us gravity based mortals that grumble under the weight of stuff.

 

[JVisgaitis]

While that's certainly a valid simplification, it ends up grossly overestimating the weight of an object when it's reduced, and likewise underestimating it when it's enlarged.

True, but I'm not one for using formulas. Would I would probably do is search online for average heights and weights of people and guesstimate what it should be.

 

[LightPhoenix]

True, but I'm not one for using formulas. Would I would probably do is search online for average heights and weights of people and guesstimate what it should be.

Yeah, I can't say I'd ever use a formula for it unless it really mattered. In the original instance, I would just hand-wave it as being negligible weight. For enlargement, I'd probably just describe the effects without worrying if someone will collapse a bridge.