Macrostat

[RowdyMike]

Hey guys,

I'm working on a story where the basic premise is that alien soldiers come to Earth and take on humans as part of their society. I want them to be somewhere around 15-25% taller than humans (and stronger and more muscular of course). I've been using Macrostat to try and come up with the numbers, but I'm having trouble believing the results.

A couple examples:

Let's take a typical soldier, maybe 5' 10", 180. Make him 1.15 times taller and he comes out 6' 8.5", and 275. Push it up to 1.2 times taller and you get 7', 310.

However, what if we upsize Andrew Sheridan for example. He starts off 6'4", 265 and goes to 7'5", 403 and 7' 7", 458.

So I know that Sheridan is on the big end of humanity, but I am really struggling with believing the numbers. Has anyone used Macrostat before? Do we think these numbers make sense if you were to take Andrew Sheridan's frame and make him 7.5 feet tall?

Not to mention, what's it going to be like having a 450 lb alien having sex with a 150 lb human??

Or am I just trying too hard?

[BuffBoy]

I use macrostat all the time, I definitely had trouble believing some of the numbers, but then again.. I'm 6"2, If I were to double my height I would over 12 feet tall! So 1.2 times taller then 6"2 actually kind of works out with that huge amount in height gain. Its crazy to think about I know. I usually just punch in the starting weight and height, and then raise up the height to what I desire the guy to be, then look at how much weight he gained, then add additional muscle ontop of that

[nypup2train]

I assume you're asking if we believe the weight numbers. (The height numbers, you can easily check for yourself.)

5'10" = 5.8333333'

? 1.15 = 6.70833333' (.70833333 ? 12 = 8.5") = 6.8?"
? 1.2 = 7'

So the height math checks out.

Do I buy the weight math? I absolutely do!

We don't really think about how much pure additional mass goes into a body that's even a little taller, but it's a lot. (If you want to get some idea of it, think about this: someone 5' tall is only 15% shorter than your 5'10" person... but how much less than an average-size adult, does a kid who's only 5' tall weigh?)

I had a friend, a nicely-built guy, who was 6'4" tall. He worked out & had some good muscle on him, but it was primarily toned, firm weight, definitely not beefy mass. Still, he weighed two hundred forty pounds, which is more than the competition weight of some of the shorter mass monsters you see on the pro stage!

As you increase muscle mass proportionally, when you're talking about really beefy taller guys, the weights get insane really quickly. I have no doubt someone built like Branch Warren would be well over 400#, if they were anything over 6' tall. (Assuming that was even possible, which it probably isn't. at least not yet.)

[howardbeatman]

Remember the "cube-square law": if you double any object's size, you increase its volume, i.e., mass, by three times. Since bone and muscle are quite dense, the effect on weight is even greater.

Note: most people do not understand the mathematical concepts of "square" and "cube" so I substituted the concepts of "doubling" and "tripling" which are readily understandable.

[RowdyMike]

Well howardbeatman, if I use your formula, I get the same number... So I guess I'm going to have to find a way to have a 450 lb muscular rugby playing alien fuck a 150 lb human without crushing him to death.

[mike86]

I'm a mechanical engineering grad student and this is actually really simple (and I can't resist explaining).

Here's the scoop: You've got measurements of different dimensions, linear which is 1D (feet and meters), area which is 2D (feet or meters squared), and volumetric, 3D (feet or meters cubed).

If you want to make a person 1.2 times taller, that's a linear dimension. To scale their mass, which is a function of volume, you need to take the linear dimension and cube it, so 1.2^3 = 1.72. So the matching person 1.2 times taller would weigh 1.72 times as much.

I read a comparison somewhere about scaling different animals' strengths and if I remember correctly it said that muscle strength is a function of muscle cross section area. So you can do this same thing with squares and square roots for comparison. For example, someone who's scaled to be twice as tall would be roughly four times as strong and weigh eight times as much.

You can see there's a run-away effect that as a thing gets bigger it gets heavier faster than it gets stronger. This is why elephants, dinosaurs, and ants compare to each other the way they do.

Your characters who are 20% taller would be 44% stronger (but at 72% heavier, much clunkier than a human with everything else held the same). But of course, this would be taking a human and simply blowing him up so these estimates would be the minimum guesses. The bones would probably be thicker and the body would probably have considerably more muscle. There would be other effects too. Metabolism scales by mass which scales by volume while skin area scales like area, so this person will eat at least 72% more and make 72% more heat to be cooled by 44% more skin so he'll heat up faster from the same activity or naturally have a higher body temp (if it's a different species) to compensate.

[RowdyMike]

Originally Posted by mike86

Your characters who are 20% taller would be 44% stronger (but at 72% heavier, much clunkier than a human with everything else held the same). But of course, this would be taking a human and simply blowing him up so these estimates would be the minimum guesses. The bones would probably be thicker and the body would probably have considerably more muscle. There would be other effects too. Metabolism scales by mass which scales by volume while skin area scales like area, so this person will eat at least 72% more and make 72% more heat to be cooled by 44% more skin so he'll heat up faster from the same activity or naturally have a higher body temp (if it's a different species) to compensate.

Mike, that's fantastic, man. Thanks!

[lurker5]

Someone on CoiledFist made a version that also has a viewer to compare different heights

http://www.giantjesse.com/index.php

[Aielyn]

I just thought I'd point out that this Macro-stat thing doesn't get weight right, really... at least, not if one considers physiology rather than simple scaling.

Yes, if you simply scale the entire body up by some fraction in all directions, you would expect their weight to increase by the cube of the proportional increase.

But in reality, the human body doesn't quite work that way. I'm sure everyone has heard of the BMI, or Body Mass Index. In order to calculate it, one takes the weight of the person (in kg) and divide by their height (in m) squared. For a person of a given bodytype and physiological makeup, the BMI should remain roughly constant (if they increase their "fatness" or their "muscularity", it would change).

What this means is that the weight of a person should vary with the square of the height, rather than the cube of it, in order to be realistic. This is, of course, prior to any change in muscle or fat factors.

This is why the example in the original post of Andrew Sheridan sounds so absurd. Sure, if you make him grow by 17% in each dimension as a simple magnification, then his weight would increase by about 61%. But in reality, if he were to grow by that much in a more "real" manner, his weight would increase by a somewhat more modest 37%, equating to 363 lb or 165 kg.

Allow me to demonstrate a little more efficiently using a real person of significant height - Conan Stevens, who just over 7 feet tall, which is just under 11% taller than Andrew Sheridan. The square of the height ratio is 1.2289, which gives an expected weight of 265*1.2289 = 326 lb. Conan Stevens is 315 lb.

[RowdyMike]

Originally Posted by Aielyn

But in reality, the human body doesn't quite work that way. I'm sure everyone has heard of the BMI, or Body Mass Index. In order to calculate it, one takes the weight of the person (in kg) and divide by their height (in m) squared. For a person of a given bodytype and physiological makeup, the BMI should remain roughly constant (if they increase their "fatness" or their "muscularity", it would change).

That makes things make a little more sense. I was trying to use BMI but I was forgetting the square so it was all just linear, not curved. So let's see if I do this right. Assuming we bump everyone up by 15%:

Sheridan would be 7'3" and 352 lbs (210cm/160kg)
Shane Williams would be 6'5" and 224 lbs (200cm/102kg)
Derek Poundstone (who has a BMI of 45.3?!) would be 7" even and 450 lbs (213cm/205kg)

And my example of a "typical soldier" would be 6'8" and 239 lbs (204cm/108kg) with a BMI of 25.9. That's listed as "overweight" but just on the BMI scale, which seems about right if we consider that BMI doesn't take into account fat vs muscle and therefore in shape guys can often show up as overweight on BMI scales.

These numbers seem a bit better to me, though I might bump up the BMI by a factor as well. For example, if I upscale the height still by 15% and bump up the BMI by 5%, I get 370, 235, 474 and 250 respectively.

So that then leaves the subjective question - is this massive enough for some interesting plausible storylines? I know a lot of guys on here would be into MASS MASS MASS, but I'm trying to create something a bit realistic but that makes every human male feel a bit inferior and all but Poundstone completely unable to fight off the alien.

Thoughts?

[wolfotehmoon]

a

Originally Posted by RowdyMike

That makes things make a little more sense. I was trying to use BMI but I was forgetting the square so it was all just linear, not curved. So let's see if I do this right. Assuming we bump everyone up by 15%:

Sheridan would be 7'3" and 352 lbs (210cm/160kg)
Shane Williams would be 6'5" and 224 lbs (200cm/102kg)
Derek Poundstone (who has a BMI of 45.3?!) would be 7" even and 450 lbs (213cm/205kg)

And my example of a "typical soldier" would be 6'8" and 239 lbs (204cm/108kg) with a BMI of 25.9. That's listed as "overweight" but just on the BMI scale, which seems about right if we consider that BMI doesn't take into account fat vs muscle and therefore in shape guys can often show up as overweight on BMI scales.

These numbers seem a bit better to me, though I might bump up the BMI by a factor as well. For example, if I upscale the height still by 15% and bump up the BMI by 5%, I get 370, 235, 474 and 250 respectively.

So that then leaves the subjective question - is this massive enough for some interesting plausible storylines? I know a lot of guys on here would be into MASS MASS MASS, but I'm trying to create something a bit realistic but that makes every human male feel a bit inferior and all but Poundstone completely unable to fight off the alien.

Thoughts?

No, just going by your examples, that can't be correct. 6'8" and 239lbs is very thin in real life. Look here:

http://www.cockeyed.com/photos/bodie...htweight.shtml

You can see just how much height changes your perception of a person's size at a given weight. Especially keeping in mind that, in this scenario, body proportions wouldn't change much as the height scaled, you're coming up with weights that are way too small to be accurate for a human being of those heights. When human beings in real life get taller, they tend to lengthen without getting much wider. Keeping proportions constant, you'd get more comparative thickness and a MUCH bigger head; all of these considerations mean that this BMI method is greatly underestimating the weights you're trying to get. I'd suggest sticking with Macrostat's results.

[Aielyn]

Originally Posted by wolfotehmoon

a
No, just going by your examples, that can't be correct. 6'8" and 239lbs is very thin in real life. Look here:

http://www.cockeyed.com/photos/bodie...htweight.shtml

You can see just how much height changes your perception of a person's size at a given weight. Especially keeping in mind that, in this scenario, body proportions wouldn't change much as the height scaled, you're coming up with weights that are way too small to be accurate for a human being of those heights. When human beings in real life get taller, they tend to lengthen without getting much wider. Keeping proportions constant, you'd get more comparative thickness and a MUCH bigger head; all of these considerations mean that this BMI method is greatly underestimating the weights you're trying to get. I'd suggest sticking with Macrostat's results.

The issue isn't so much with the BMI-estimate, as it is with the initial number.

His "typical soldier" is 5'10" and 180 lb. That's rather slender by this forum's standard. I'm about six feet tall (184 cm) and around 160 lb, and my parents complain that I've gotten too skinny (although really, I've just lost some of the excess far - I've increased my muscle mass). As a taller person will inevitably look thinner for comparable body makeup, it makes sense that they'd look, visually, somewhat thinner when scaled up.

Many people think of this as a "typical soldier" in terms of physical build. In reality, many soldiers look more like this.

You point out what 6'8" and 239 lb looks like using that site. Here's the 5'10" and 180 lb part. Notice that, again, looking pretty thin.

[wolfotehmoon]

Originally Posted by Aielyn

The issue isn't so much with the BMI-estimate, as it is with the initial number.

His "typical soldier" is 5'10" and 180 lb. That's rather slender by this forum's standard. I'm about six feet tall (184 cm) and around 160 lb, and my parents complain that I've gotten too skinny (although really, I've just lost some of the excess far - I've increased my muscle mass). As a taller person will inevitably look thinner for comparable body makeup, it makes sense that they'd look, visually, somewhat thinner when scaled up.

Many people think of this as a "typical soldier" in terms of physical build. In reality, many soldiers look more like this.

You point out what 6'8" and 239 lb looks like using that site. Here's the 5'10" and 180 lb part. Notice that, again, looking pretty thin.

I still stand by my initial assessment. A 5'10" 180lb soldier is only arguably thin; depending on body composition, that's actually a pretty good-sized person. I will also reiterate that scaling is very different from just making a guy taller. Human beings don't generally "scale" as they go up in height; certain parts of the body don't get much bigger in comparison to others. If they WERE to, you'd expect there to be even more weight added.

I dunno, I don't even see why this is much of an argument. Aren't higher weights more intimidating and impressive anyway? It's an easy explanation that weight increases as a cubic function of height, if someone doesn't think it's believable; much easier (as is obvious here) than explaining why the 8-foot-tall behemoth over there only weighs 300 pounds.

[RowdyMike]

I guess it might help if I explain what I'm trying to do. I want to make sure that the characters in the alien society have comparable variation as we do, where some guys are (relatively) average height or size, and others are bigger and even more impressive. It's just that average height or size is noticeably bigger than ours - so much so that the smallest of the alien society is at a minimum bigger than 2 standard deviations away from the mean of humans.

That's why I was trying to use examples of natural variation within the human population and put them into some sort of formula which would calculate out the size of the alien in a comparable way. I know I could take the easy way out and say well they're aliens so they're going to be 400 lbs. But that then gives me a bit of concern as I do want the character I'm trying to define being reasonably athletic - 400 lbs strikes me as too much mass on a 7' frame for the person to be considered athletic.

I think the answer is somewhere in the middle. People are not geometric shapes, so the cube-square law isn't right because you're not cube-squaring each individual body part. I guess one could divide the body up into 6 or 8 shapes and scale each of those shapes individually using cube-square, then add it up in the end. Would require having a lot more data on an individual exemplar than I have access too.

In the end, I think it needs to be a combination of scaling based on BMI AND cube-square law together which might make the numbers feel "right" for the story.

[RowdyMike]

By the way, just found these stats from the CDC.

Average American male at age 19 is 80 kg, 177 cm, and a BMI of 25.6. - Not too far off my "typical" soldier of 5'10" (178 cm) and 180 (82 kg).

The 90th percentile male at the same age is 186cm 107kg, and a BMI of 36.4. The 95th percentile for the tallest segment (20-29) is 190 cm tall.

So let's assume this 90th percentile 19-year old is a bodybuilder (not a valid assumption among overweight Americans, but hey) and he's 6'1, 236. Using Aeilyn's method on my "typical" soldier, the "average" alien using a 5'10/180 exemplar against him would be 6'8 239. Don't think my 19 year old would be all that intimidated, but again, he's way above average for a human. Using cube-square, he'd be 6'8 275. My gut is telling me 6'8 250-260 (although without the bad hair).

Again, this is why I think it's somewhere in the middle. Need an average alien to have a bit more mass to be a bit more of a challenge for an above-average human to deal with. Of course, I can also shift the "average" alien to an exemplar off the 80th percentile 19yo male to put some distance in between the aliens and the human outliers.

[RowdyMike]

Ok, I have to admit I'm totally wrong - and any of the BMI calcs are wrong.

I found something called the Willoughby Athletic Weight - which is a calculation of what an ideal lean athlete would weigh (based on observed data). Put Sheridan's height in and his ideal lean athlete weight would be about 235, but he's 14% bigger at 265.

Obviously if everyone is 15% taller, including him, he'll still be 14% bigger than an ideal lean athlete of his height - because props are always going to be bigger.

So he becomes 7'4" inches tall. Ideal weight at that height would be 356. 14% above that is 406.

If I use mike86's formula, guess what, his weight is 406 - and he has a much simpler way of getting there. Same with macrostat. The numbers are the same to 6 decimal places, so they've got to be mathematically different routes to the same number.

In all, it's helped me understand the scale of tall really huge guys. And it's given me a new way to understand my own fitness!

[nypup2train]

*nod* Yeah, cool.

I approach this stuff more from gut-instinct impressions than strict formulas. (By which I really mean, I leverage my lifelong tendency -- curse, really -- to soak up observational data, and extrapolate from the wide range of reference points I already have.) Anyway, THOSE numbers feel much more "right" to me, given what you've explained about how you're using them.