For a bit of a Savage Species-esque racial HD thing I'm doing, I'm trying to calculate the height and weight of a storm giant at each racial HD (1 through 19).
Due to campaign specifics, the starting height was 6', appearing as a lanky but well build young girl (equivalent to a 14 year old human girl). The starting weight was 190 pounds, to represent the extra muscle mass from a +4 starting strength.
The final height will be 20'2", using a formula of "every HD, gain height in inches equal to that new HD". So at HD 2, gain 2 inches, 3 at 3, 4 at 4, etc, etc.
But the final weight, according to the Bestiary, should be around 12,000 pounds, technically a little less, since this giant is both female and 10 inches shorter than the listed 21' average height.
I've spent a rather ridiculous amount of time on the internet trying to solve this, looking at height to weight charts, BMI indexes and formulas, and so on. I've stopped short of the tedious and not very accurate last resort of plugging data into a line graph until it "looks about right". The only bit of helpful info I can give is that according to one BMI calculator, a 21' human weighing 12,000 pounds is horrifically obese, with a BMI of 180, relative to the 25 BMI of our giant's starting 6' height and 190 weight. But said height to weight charts are horrifically bad at accounting for muscle density, and storm giants are described as being incredibly well build and proportioned.
So, can anybody help me with this mathematical nightmare? A formula, or even just a set of numbers so that I can say "at this HD you weigh this much"?
What you need to factor in is that for every double in height, a humanoid (or really any creature) increases its mass by a factor of 8. At ~24' tall, a giant will have a mass 64 times that of a 6' tall human of equivalent build.
All you need to do is plug that into your formula for height increase. I don't know that it's worth all the effort you're putting in - you'll have to start addressing where the hell this character is finding all that extra mass, for instance - but you can pretty much do it like this:
Current weight = original "build" weight * (current height / original height) ^ 3
Your post was helpful, but I'm afraid that I might not be following it well.
When you say origional build weight, do you mean the 190?
So Current Weight = (190*(74/72))^ 3? That gets me something like 7 million pounds, so I know I'm doing it wrong somehow.
A 21' tall human that weighed what it "should" weigh to not be obese would actually not live that long. Their bones and organs can't function properly (pushing blood through that much vein, holding up that much muscle mass, etc).
So a "normal" 21' tall human would that also had a higher strength (more muscle mass, likely), would specifically need a much more dense bone structure and likely much more powerful organs to push the air and fluids around in such a large body.
This is why you'd get a weight that is "much higher than it should be".
7 million pounds is definately off though.
Going from Medium to Large increases your weight by a factor of 8. Going from Large to Huge is another factor of 8 (so 64 over the Medium).
A 200 lb human at Medium should be 12,800 lbs at Huge to "function properly".
Find out how many inches are in each size frame (how many before you are considered Large, and then how many more until you are considered Huge), average it out to a nice round number, and then break down the multiplier so that it increases weight from 190 to 12,000 over the appropriate range of inches.
I'll clarify:
Current weight = original "build" weight * (current height / original height) ^ 3
Translates, with your numbers, to:
Current weight = 190 lbs * (current height/6')^3
Order of operations means you do the parenthetical work first, then cube that result, then multiply it by 190 lbs. For instance, try when she's 12 feet tall:
190 lbs * (12'/6')^3 = 190 * (2)^3 = 190 * 8 = 1520 lbs
and when she's 21 feet tall:
190 lbs * (21/6)^3 = 190 * (3.5)^3 = 190 * 42.875 = 8146 lbs
The +50% weight added in the giant description accounts for the issue Kaisoku brought up - to support that kind of weight, a giant's bone and muscle structure would have to be significantly more dense than "normal" for a human. We can add that to the formula as a linear modifier, to get a result like:
Current weight = (190 lbs * (current height/6')^3) * (.8 + .2 (current height/6'))
Which will result in a final 21' weight of 12219 lbs.
For my part, I gotta say 190 lbs sounds pretty beefy for a teenage girl, even one thats 6-foot tall. Formula can be adjusted for any weight, so adjust as you see fit.
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I can see a "person" that is 21' tall weighing that much. irst of all consider just how TALL that really is!
An 18-wheeler is 13'6" tall. Find one and stand next to the trailer and look up. It's pretty darn tall. An "average" two-story building is about 20 feet. Find one and stand next to it and look up. Pretty freaking tall. Then imagine just how BIG a person would really be compared to the giant. An average human might be, what, knee high to the giant!
An elephant is about 10-13 feet at the shoulder. That means the giant is too tall to even ride an elephant as a mount! It would be like a human riding a Great Dane (yes everyone says they are as big as horses but really, an adult human cannot ride one-sorry). I mean really that is really really really BIG! Giraffes get to be about 18 feet tall, and would STILL be shorter than the giant!
All I have to say is, I am glad there are no REAL giants!