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[GoblinCookie]

Basically speaking the whole size concept in the game has me completely stumped; a human is 70,000 units in size and a human is 6 foot tall on average.  However 70,000 is *not* how tall the human is, it is the total size of the creature in ALL dimensions measured as if they were in 1D.  Say I wanted to make a 12 foot humanoid, I would not simply set the creature to be 140,000, because the creature gets bigger in 3 dimensions rather than 1 dimension.  Not being a mathematician (unlike Toady One) I am quite confused as to how big the 12 foot humanoid would actually be. 

The way that size works at the moment is as if the creature were made of sand and every size unit is a single grain of sand.  If you made a taller humanoid simply making it 140,000 then what you are actually doing is stretching the existing humanoid proportionately thinner, since as the creature gets taller in one dimension it gets thinner in proportion, so the resulting creature is 2/3rds thinner (?) in relation to it's height than it was at the beginning  .

In order to increase the creature to 12 feet without stretching it, you would have to times the creatures size by 6 (?) in order to double it's height; while to make creature 3 feet you would divide it by 6.  So a 12 feet humanoid is 420,000 size units big instead of being 140,000, assuming that it's proportions are exactly the same.  In reality however, we have every fantasy giant's least favourite piece of mathematics, the Square Cube Law.  If we simply scale the human up in proportion as we have done above, then the resulting giant will simply collapse under it's own weight and come to a sticky end; fantasy game rule book illustrators take note  . 

The square cube law comes for the annoying fact that as a creature gets bigger, the surface area of the creature only increases in 2D, hence the square but the total weight of the creature goes up in 3D.  Basically summarised, the height of the creature is ignored when deciding how much weight the creature is able to carry, but the height of the creature adds to the weight; only the width and depth of the creature contribute to it's weight carrying ability; so being a fairytale giant is quite a problem.  To get around this, our fairytale giant has to increase both of it's other dimensions by the same amount as it's increase in height; basically resulting in a creature that 'looks vaguely humanoid' rather than a 12 foot human, but what do our giants care as long as they can actually walk?

Assuming that the creature is capable of supporting it's own weight in normal gravity on the surface then the other two dimensions each would carry half of the weight of the creature on top of their own weight (?).  This means that we need to increase these two dimensions by twice the proportion of the increase in height in order, this would mean that we would have to take the final result of the proportionate increase and then X it by 4 (?).  So the formula would be as follows. 

6ft Human Size 70,000
X6 (scaled increase)
12ft Human Size 420,000
X4 (square cub law increase)
12ft Fantasy Giant 1,680,000

The same principle applies if we want to make a 24ft fantasy supergiant.

12ft Fantasy Giant 1,680,000
X6 (scaled increase)
24ft Fantasy Giant 10,080,000
X4 (square cub law increase)
24ft Fantasy Supergiant 40,320,000

[Nahere]

Not *6. It's 2*2*2=8 (or 2^3) for each dimension to double. For the other stuff, one way of handling it is to use stronger materials when constructing larger creatures, or to mess with their BODY_APPEARANCE_MODIFIER:BROADNESS and LENGTH in order to make them more stout without being taller.

[AceSV]

I prefer to keep in mind that there is no such thing as dimension in DF, only mass.  So a 140,000cm³ creature would be twice the weight of an average human.  A creature cannot have twice the height of a human because there is no such thing as height. 

So when you start talking about the upper limits of the Square Cube Law, you're talking about the dinosaurs.  A lot of the largest dinosaurs are frankly impossible or impractical.  For example, Tyrannosaurs walk around on two legs with no arms.  If a Tyrannosaur falls down, it has no way to break its fall.  With all supposedly 8000kg of Rex crashing down on its hip, ankle, rib cage, head or spine, that animal is probably never going to stand up again.  And Tyrannosaurs almost definitely got knocked down in the course of doing business because they hunted enormous animals like Triceratops, Ankylosaurs and Hadrosaurs, and morphologically seem to be equipped to fight with rival Tyrannosaurs as well.  To compare, a really big elephant is around 5444kg. 

So a lot of scientists theorize that the giant dinosaurs had some sort of additional adaptation for being enormous that we can't figure out from just the bones.  It's possible that dinosaurs were a lot less dense than mammals and reptiles, since many birds are.  I've also read that in the few cases where muscle has been preserved in dinosaur fossils, they were much more muscular than was expected, which suggests some kind of unique body structure. 

I think there were a few giant proto-humans.  The only name I can remember is gigantopithecus which is 10ft tall.  Also, there are actual human beings that get up to 12 feet tall, and they tend to not follow the normal human body plan exactly. 



Yeah, I'm rambling.  Point is, Square Cube Law defying super giants actually existed and probably had special modifications that would render a perfect scaling up of weight and volume irrelevant. 

[Max™]

Uh, actual humans? Robert Wadlow was 8'11" and the closest otherwise was like 8'7" I think. Nobody has gotten within a few feet of 12' tall.

Gigantopithecus was as close to humans as we are to a gorilla or orangutan, and 10' is pretty far beyond the upper end of serious size estimates. 8' standing upright or ~6' knuckle-walking was more plausible assuming the molars scale up appropriately.

[GoblinCookie]

Not *6. It's 2*2*2=8 (or 2^3) for each dimension to double. For the other stuff, one way of handling it is to use stronger materials when constructing larger creatures, or to mess with their BODY_APPEARANCE_MODIFIER:BROADNESS and LENGTH in order to make them more stout without being taller.

Yes, of course it is 2*2*2 that makes it easier to calculate the size of something as well.  All I have to do is decide how much each dimension increases by as the creature gets larger.  2/2/2 if we want to make the creature get smaller as well.  The only question here is what order to do I do things in if I want to reduce a creature in one dimension while increasing it in another, does it matter?

The body modifiers do not work because they are modifiers based upon the average of that particular creature.  With maximum broadness and length we are still only talking about the tallest or broadest possible human within the field, so we are still limited by the square-cube-law limitations built into the human form.  The human form can only support a creature up to the size of 8ft something, when you go above that you stop being able to walk unaided. 

Hence the tragic story of Robert Wadlow, the world's tallest ever man who died at 22.  Up until he reached the size of 8ft something he was able to walk about and do things without artificial help.  It was only when he reached that size that he started to need artificial aids in order to stand and it is these aids (not his size directly) that led to his untimely demise. 

The human form then is inherently limited to 8ft.  Fairytale giants in the sense that they are normally illustrated are only possible up to that height, beyond that and you have to think about adopting a different humanoid body structure and the bigger your giant the less human it will look; something rarely understood by illustrators because they do not generally have much grasp of maths/physics.   

I prefer to keep in mind that there is no such thing as dimension in DF, only mass.  So a 140,000cm³ creature would be twice the weight of an average human.  A creature cannot have twice the height of a human because there is no such thing as height. 

Indeed, but the size clearly reflects all the dimensions that the creature is supposed to have.  That is why giant creatures (megabeasts and the like) have such immense size, because the size is the amount of stuff the creature is made of, or as you put it it's mass which increases in all dimensions not one. 

So when you start talking about the upper limits of the Square Cube Law, you're talking about the dinosaurs.  A lot of the largest dinosaurs are frankly impossible or impractical.  For example, Tyrannosaurs walk around on two legs with no arms.  If a Tyrannosaur falls down, it has no way to break its fall.  With all supposedly 8000kg of Rex crashing down on its hip, ankle, rib cage, head or spine, that animal is probably never going to stand up again.  And Tyrannosaurs almost definitely got knocked down in the course of doing business because they hunted enormous animals like Triceratops, Ankylosaurs and Hadrosaurs, and morphologically seem to be equipped to fight with rival Tyrannosaurs as well.  To compare, a really big elephant is around 5444kg. 

So a lot of scientists theorize that the giant dinosaurs had some sort of additional adaptation for being enormous that we can't figure out from just the bones.  It's possible that dinosaurs were a lot less dense than mammals and reptiles, since many birds are.  I've also read that in the few cases where muscle has been preserved in dinosaur fossils, they were much more muscular than was expected, which suggests some kind of unique body structure. 

I think there were a few giant proto-humans.  The only name I can remember is gigantopithecus which is 10ft tall.  Also, there are actual human beings that get up to 12 feet tall, and they tend to not follow the normal human body plan exactly. 

Yeah, I'm rambling.  Point is, Square Cube Law defying super giants actually existed and probably had special modifications that would render a perfect scaling up of weight and volume irrelevant. 

There are no upper limits to the square cube law in general.  There are only the upper limits of the creature's basic body form and proportions combined with the material strength of what the creature is made of.  This means that there is no problem with T-Rex because T-Rex while humanoid does not follow the human body plan, the upper limits to the square-cube law for that creature are therefore far higher than for a human.

The key thing to understand is the reason that there *is* a square cube law is because the weight of the creature increases in a cube while the area that holds up that weight only increases in a square.  Think of it in the following manner, the other two dimensions hold up the third height dimension; but since a T-Rex's is so long it can plausibly hold up the weight of the T-Rex's height.  The key element here is surplus carrying capacity, basically the weight that the material of the other two dimensions that those dimensions can carry on top of the weight of those dimensions themselves. 

To make a 12 foot giant then, I must increase the length and width of the humanoid creature by double the amount of the increase in height.  That would conclude that the formula would be 2*4*4, the latter two are the supporting dimensions while the first is the height of the creature.  The reason why it is *4 is that the present creature's supporting dimensions must produce twice as much carrying capacity as they weigh, the carrying capacity of each supporting dimension must be 50% of the total amount the supporting dimensions weight in order for the creature not to collapse under it's own weight.

Creatures supporting dimensions however typically carry surplus carrying capacity.  The human form has a surplus carrying capacity of 2ft, hence the human form is limited to 8ft.  What limits the potential carrying capacity of the creature is that it increase the cubic volume (what DF Size is in RL) of the creature, which determines the amount that the creature must eat or the amount of materials needed to make the creature.  Evolution (or design) tends to reduce the creature down to the carrying capacity needed to support it's height (with a bit extra) because it increases resource/energy efficiently. 

[cochramd]

To make a 12 foot giant then, I must increase the length and width of the humanoid creature by double the amount of the increase in height.  That would conclude that the formula would be 2*4*4, the latter two are the supporting dimensions while the first is the height of the creature.  The reason why it is *4 is that the present creature's supporting dimensions must produce twice as much carrying capacity as they weigh, the carrying capacity of each supporting dimension must be 50% of the total amount the supporting dimensions weight in order for the creature not to collapse under it's own weight.

You're oversimplifying things. If I double the height and quadruple the length and width of every piece of a creature, I'm getting 32 times the load and only 16 times the cross-sectional area. Not all body parts provide structural support, however, and instead increase in size based on the need of other biological functions. The key to getting bigger and remaining (relatively) structurally sound is to have the cross-section of your load bearing parts increase at the same rate as your total load; you can't just multiply the dimensions of the body as a whole, you need to consider the load-bearing and non-load-bearing parts separately.

[Max™]

Incidentally, I am curious why nobody mentioned it being volume.

[miauw62]

I don't get the point of this thread. DF doesn't simulate materials supporting other materials, length or broadness do not matter at all.

A larger creature will weigh more and be tougher because of thicker material layers, and that's pretty much it afaik.

[GoblinCookie]

You're oversimplifying things. If I double the height and quadruple the length and width of every piece of a creature, I'm getting 32 times the load and only 16 times the cross-sectional area. Not all body parts provide structural support, however, and instead increase in size based on the need of other biological functions. The key to getting bigger and remaining (relatively) structurally sound is to have the cross-section of your load bearing parts increase at the same rate as your total load; you can't just multiply the dimensions of the body as a whole, you need to consider the load-bearing and non-load-bearing parts separately.

I am not oversimplifying, merely simplifying because otherwise I will not have a formula simple enough to easily work with. 

Remember that the Square-Cube-Law applies to every creature in existance, it does not suddenly kick in once you reach a certain size.  The rule is that the surplus carrying capacity of the other two dimensions (the square) supports the weight of the height of the creature, so it is like two men holding up a third man standing on their shoulders.  The dimensions surplus carrying capacity is the total capacity of all the tissues in a given dimension to support more weight than the tissues themselves weigh, all creatures (regardless of size) must have a surplus carrying capacity in their supporting dimensions equal to 50% of the weight of the supported dimension.  Any less than that and the creature will collapse under it's own weight, regardless of how small it is. 

Yes, some types of tissue (like fat) does not produce surplus carrying capacity while other types of tissue (like bone) produces a huge amount of surplus carrying capacity.  This is the simplication, by increasing the amount of the latter type of tissue while increasing the former type the creature can reduce the amount of square-cube scaling it needs to undergo.  However we shall assume that the creature carrying capacity is already optimised at it's original size so that it cannot reduce it's non-surplus carrying capacity tissues any more without other negative consequences.  Less fat might help the giant hold up it's own weight but it needs to have more fat to cushion it's internal organs should it fall over for instance.  We do not have to consider the load bearing and non-load bearing parts seperately, because these can be bundled together as one dimension as what matters is the ability of the dimension as a whole to support the third dimension. 

The formula then for making a 12ft giant is therefore 2*4*4, is this mathematically correct?

I don't get the point of this thread. DF doesn't simulate materials supporting other materials, length or broadness do not matter at all.

A larger creature will weigh more and be tougher because of thicker material layers, and that's pretty much it afaik.

It also makes them stronger as well as making them easier to hit and probably a whole load of other stuff we probably do not know about.

The point of this thread is to give us a mathematical means to figure out, given the lack of dimensions defined in the raws just how big DF creatures actually are.  It is also of modding use if we want to add creatures of a particular size into the game.

Apparantly a 12ft giant is size 2,240,000.

[cochramd]

We do not have to consider the load bearing and non-load bearing parts seperately, because these can be bundled together as one dimension as what matters is the ability of the dimension as a whole to support the third dimension. 

The formula then for making a 12ft giant is therefore 2*4*4, is this mathematically correct?

No, no, you're still oversimplifying. If you have a steel flagpole, doubling its height will always double the stress from its own weight on it, even if you increase its thickness at the same time; the decrease of gravity with altitude notwithstanding, a tower of any certain material would always collapse on itself after reaching a certain height regardless of how thick you make it. Likewise, doubling the height of a creature will always double the stress on its load bearing parts, no matter how much thicker you make them.

The trick to all this is since creatures aren't made of only structural parts, and that increasing thickness increases what load can be supported beyond their own weight; in your 2x4x4 proposal, the non-structural parts would be causing twice the stress as in a normal creature, but if non-structural parts only increased by 2x2√2x2√2 while the structural parts still increased by 2x4x4, then they would be producing the same stress as in a normal creature. There could be another amount the non-structural could increase that would cause the total stress to be the same, but the fact that you need several non-structural parts to live severely complicates things.

You want a simple answer to "how much does a 12 foot man weigh?" Well, the largest polar bear ever caught was 11' 1" on his back legs and weighed 1002 kilograms, so 1002 Urists x (12/11)^3 = 1301 Urists should be about right. Not sure what that is for size, but you have access to wikipedia and dwarfortress wiki, so I'm sure you can figure it out using the average size of polar bears.

[miauw62]

You will always end up with arbitrary numbers in your calculations. How much extra width is needed to support more height? You can't get a meaningful number for this. It depends on material, structure, species, it might even be a function of the height. And the square cubed law, when applied to real life, is more of a general principle, like Godwin's or Moore's law.
You will never be able to extract a meaningful height out of body size, basically.

[GoblinCookie]

No, no, you're still oversimplifying. If you have a steel flagpole, doubling its height will always double the stress from its own weight on it, even if you increase its thickness at the same time; the decrease of gravity with altitude notwithstanding, a tower of any certain material would always collapse on itself after reaching a certain height regardless of how thick you make it. Likewise, doubling the height of a creature will always double the stress on its load bearing parts, no matter how much thicker you make them.

Remember that there are both thickness and length at work here, two supporting dimensions and not one.  There is no limit to how high your tower can get, the only thing is that it eventually ceases to be a tower and becomes a rectangle with the supporting dimensions bigger than it's height. 

The trick to all this is since creatures aren't made of only structural parts, and that increasing thickness increases what load can be supported beyond their own weight; in your 2x4x4 proposal, the non-structural parts would be causing twice the stress as in a normal creature, but if non-structural parts only increased by 2x2√2x2√2 while the structural parts still increased by 2x4x4, then they would be producing the same stress as in a normal creature. There could be another amount the non-structural could increase that would cause the total stress to be the same, but the fact that you need several non-structural parts to live severely complicates things.

We simply do not have to make a distinction between the two.  The reason is that we already know that the supporting parts in the two supporting dimensions are able to support at least 50% of the weight of the third dimension on top of their own weight and the weight of any non-structural parts in their own dimension. 

The problem here is that the supporting parts of the creature do not support their own weight in the third-dimension, so the whole weight of the bone has to be supported along with everything else in the third dimension *by* the bone in the other two dimensions, therefore whole weight of the third dimension can be bundled without distinction just as the other dimensions supporting capacity can be bundled.  The bones have to get four-times as thick *and* long for every doubling of the creature's height but you cannot increase the bones size in a dimension without making the other tissues bigger as well; if you have bigger bones in a dimension, then you have to have bigger muscles in that dimension as well (and so on). 

While elephants do have disproportionately thicker bones than mice, mice are not virtually boneless blobs and elephants are not virtual skeletons.  Instead the non-structural parts have increased disproportionately as well, which implies that your idea that only the structural parts have to increase disproportionately to the other parts in a dimension is not correct. 

You want a simple answer to "how much does a 12 foot man weigh?" Well, the largest polar bear ever caught was 11' 1" on his back legs and weighed 1002 kilograms, so 1002 Urists x (12/11)^3 = 1301 Urists should be about right. Not sure what that is for size, but you have access to wikipedia and dwarfortress wiki, so I'm sure you can figure it out using the average size of polar bears.

I am not interested in how much the polar bear weighs, the game automatically figures that out when you define the size+materials of the creature.  I want to know just how big the creatures are, so that if I want to add in a 12ft giant say I will know what to enter in the size category.

You will always end up with arbitrary numbers in your calculations. How much extra width is needed to support more height? You can't get a meaningful number for this. It depends on material, structure, species, it might even be a function of the height. And the square cubed law, when applied to real life, is more of a general principle, like Godwin's or Moore's law.
You will never be able to extract a meaningful height out of body size, basically.

The Square Cube Law is an unbreakable universal law, rather like gravity; everything follows it exactly.

Yes, the numbers do depend somewhat on the creatures dimensions.  Quadrupeds have an easier time with the square-cube law than humanoids because they tend to be longer than they are high.  None of that fundamentally matters, a dragon is fundamentally a scaled up crocodile, we know that the dragon is 30ft long because we know how big the crocodile would be if it were 30 foot long and it happens to match up with the dragon.

[cochramd]

Remember that there are both thickness and length at work here, two supporting dimensions and not one.  There is no limit to how high your tower can get, the only thing is that it eventually ceases to be a tower and becomes a rectangle with the supporting dimensions bigger than it's height. 

Oooooooooooh boy.

I see know that there is a fundamental lacking in you knowledge that prevents you from understanding what you are talking about. Allow me to educate you: if I have a block on some surface and press down on it, that is going to induce a STRESS in the block. If this stress is too high, it will deform as determined by its material properties. The MAGNITUDE of this STRESS is EQUAL to the APPLIED FORCE, in units of your choice, DIVIDED by the CROSS SECTIONAL AREA of the block, in units appropriate with regards to the force. This means that since CROSS-SECTIONAL AREA INCREASES WITH THICKNESS, it is also true that for all other things being constant, STRESS FROM AN APPLIED FORCE DECREASES WHEN THICKNESS INCREASES. However, CROSS-SECTIONAL AREA is INDEPENDENT OF HEIGHT, so INCREASING HEIGHT DOES NOT DECREASE STRESS FROM AN APPLIED FORCE.

TL;DR: No, height is not a supporting dimension.

[GoblinCookie]

Oooooooooooh boy.

I see know that there is a fundamental lacking in you knowledge that prevents you from understanding what you are talking about. Allow me to educate you: if I have a block on some surface and press down on it, that is going to induce a STRESS in the block. If this stress is too high, it will deform as determined by its material properties. The MAGNITUDE of this STRESS is EQUAL to the APPLIED FORCE, in units of your choice, DIVIDED by the CROSS SECTIONAL AREA of the block, in units appropriate with regards to the force. This means that since CROSS-SECTIONAL AREA INCREASES WITH THICKNESS, it is also true that for all other things being constant, STRESS FROM AN APPLIED FORCE DECREASES WHEN THICKNESS INCREASES. However, CROSS-SECTIONAL AREA is INDEPENDENT OF HEIGHT, so INCREASING HEIGHT DOES NOT DECREASE STRESS FROM AN APPLIED FORCE.

TL;DR: No, height is not a supporting dimension.

That is exactly what I have been saying.

[cochramd]

That is exactly what I have been saying.

No, because then you wouldn't have said this:

There is no limit to how high your tower can get, the only thing is that it eventually ceases to be a tower and becomes a rectangle with the supporting dimensions bigger than it's height.

Any increase to the size of the object will increase the force applied to it by gravity. Increasing the thickness will cause the ratio between mass (and the associated force) and cross-sectional area (and therefore, the strain as well) to remain constant, while increasing the height will increase it. You build a tower high enough, and eventually the stress will become too high and the whole thing will collapse. There is not a lot to misunderstand here.