Author Topic: Extreme Heights and Weights  (Read 321 times)

blorpderg

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Extreme Heights and Weights
« on: September 05, 2017, 01:46:46 AM »
(Second attempt at posting this, might have screwed up the first time)

Howdy!  I'm making a game that involves the player (a non-anthro dragon) growing/shrinking frequently, from as small as .1 inches to several hundred feet, as well as gain/lose fat very fast.

My question: Does anyone have a solid equation I can use for levels of fatness at different sizes?  I've been trying for days to come up with something, but it always falls flat at the more extreme sizes (both large and tiny, slim and blob).

I'm primarily trying to figure out when the player should become immobile, and when they would be completely unhindered by their weight.  (Also, I would be able to use this for descriptions of the player)

pirateGuy

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Re: Extreme Heights and Weights
« Reply #1 on: September 05, 2017, 04:42:22 AM »
You have good timing, since at least one of those questions I spent a while chatting about with someone for a game recently.  For extreme heights, you can scale any shape up proportionately with the square-cube law. However much bigger something is as a percentage than it was before, it's (that many times) cubed heavier.

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

You can shuffle around the placement of the variables depending on what you want to calculate, but you can use a baseline reference of different weights at a set height to figure things out for other heights. EX

Start with 5' 6" (or 66 inches) for your baseline, and say 'normal' is, oh, 155 to 185 (just picking numbers from a BMI scale). You can plug that into the equation to see what 'normal' would be for a 20' (240 inches) tall individual with the same proportions-

Lower bound = 155 * [( 244 / 56)^3] = 155 * (4.357 ^3) = 155 * 82.719 = 12,821.449 lb
Upper bound = 185 * [(244 / 56)^3)] = 185 * (4.357 ^3) = 185 * 82.719 = 15,303.019 lb

So, using our baseline, we can scale set points to any size. A 20' tall individual with the same basic body shape as our baseline would be underweight at under 12,821 lb, overweight at greater than 15,303 lb, and normal weight at anywhere between those two markers. The weight of really big things is something that's often underestimated, but scaling up in three dimension increases volume and weight really fast!

blorpderg

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Re: Extreme Heights and Weights
« Reply #2 on: September 05, 2017, 11:33:26 AM »
You're a lifesaver!  I'll give this a shot when I get home from work today.

docarrol

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Re: Extreme Heights and Weights
« Reply #3 on: September 06, 2017, 06:08:38 PM »
Depends on how "realistic" you want your magical, growing fattening, dragon game to be, but if you're already looking at using the square-cube law, keep in mind that
  • weight & fat volume will scale with the cube of the height change
  • strength for muscles and max loading of bones both scale with the cross sectional area of the muscle/bone, which scales with the square of the height change
Which in practical terms means that fat and weight will increase much, much faster than your ability to stand up and move around when you grow, making you much less mobile at larger sizes even if your relative proportions stay the same. By the same token you'd be proportionately stronger and more mobile at smaller sizes, if you shrink.

So if your height doubled, your weight would go up 8x but your strength would only be 4x, making you half as strong (and I assume half as mobile) relative to your weight. If you shrink to half your height, your weight would be 1/8th, but your strength would be 1/4, making you twice as strong relative to your weight.

Or to put in the same terms as pirateGuy's equation:
new strength = old strength * [(new height / old height) ^ 2]

blorpderg

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Re: Extreme Heights and Weights
« Reply #4 on: September 06, 2017, 11:08:15 PM »
Funny enough that works our perfectly with the type of game I'm making (an idle game, might make a post about it in the future).

I can use the decreasing ability to hold one's own weight up as the player gets larger as a sort of soft-cap, and allow for a 'prestige' system to allow the player to shrink back down, but with more abilities and a higher capacity.

Player starts out small and weak, grows until they physically cannot grow any further.  Then the player prestiges, increasing their ability to hold their weight, and allowing further progression!

Thanks to the both of you!  I wouldn't have been able to get this in-depth without you!