I believe it simply scales by doubles and halves.
So for example:
Item weighs 200
Diminutive: 25
Tiny: 50
Small: 100
Medium: 200
Large: 400
Huge: 800
Gargantuan: 1600
Colossal: 3200
However... Where did you get the value for tiny to be 0.1?
From memory, I also believe it doubles and halves.
However, it begs the question, if equipment weight only goes up and down by a factor of 2, why does enlarge person increase weight by a factor of 8 (doubled height, width, and length)? Shouldn't it be the same for living and non-living material?
At the very least, a set of large platemail SHOULD be 4 times heavier than medium platemail. You could keep the same thickness (height) of steel, but the length and width both double for each plate.
My boyfriend and I were also confused by the table on page 153 of the Core Rulebook, and for the same reason...the multipliers seemed strange, especially in relation to the carrying capacity multipliers for different size creatures (page 170). We realized that the weights for Tiny, Diminutive, and Fine are all the same because the average Strength for both Diminutive and Fine creatures is 1, while the average Strength for Tiny creatures is 2 (Bestiary page 296). In essence, Diminutive and Fine creatures have such low Strength that they are basically not on the same scale as creatures of Tiny size or higher. This becomes a very complicated issue, because carrying capacity, Strength bonuses (or penalties) for size, and the raw weight of the creature all factor in. If a colossal humanoid creature gets +32 Strength compared to a medium creature, and a x16 carrying capacity, but is not actually exactly 16 times the size of the medium creature...how much should its sword weigh? We concluded that the x12 weight factor for a colossal humanoid creature must be based on a rough estimate of its size, an assumption that it is roughly 12 times bigger than an average human. That was our attempt at understanding all of this, anyway.
As Jason Rice pointed out, however, that colossal humanoid would weigh far more than 12 times an average human, so how come its sword only weighs 12 times a human-sized sword? After all, an average Fin Whale, which is about 67ft. long and thus a colossal creature, weighs 132,000 pounds--66 tons, according to the Smithsonian Institute Animal Visual Guide. This isn't an answer so much as a rumination on the problem. It would probably help if there were any bipedal creatures on Earth larger than humans.
OK, so my boyfriend and I have been doing some math, and here's what we came up with. A longsword (random choice) weighs 4lbs. in Pathfinder, and an average human with 10 Strength has a maximum carrying capacity of 100lbs. Thus, a longsword takes up 1/25th of an average human's carrying capacity. Because large creatures get a Strength bonus in addition to a carrying capacity bonus, you have to determine each size category's average maximum carrying capacity in order to get a ratio. An average large humanoid has a maximum carrying capacity of 600lbs., an average huge humanoid has a maximum carrying capacity of 3,680lbs., an average gargantuan humanoid has a maximum carrying capacity of 22,400lbs., and an average colossal humanoid has a maximum carrying capacity of 133,120lbs. (All of these carrying capacities were determined by the size Strength bonuses in the Bestiary pg. 296 and carrying capacity rules in the Core Rulebook pg. 170-171). In order to maintain ratios, and have a longsword weigh 1/25th of their total carrying capacity, a large longsword would have to weigh 24lbs., a huge longsword would have to weigh 147.2lbs., a gargantuan longsword would have to weigh 896lbs., and a colossal longsword would have to weigh 5324.8lbs. These numbers assume that the longsword is bigger in every dimension and has the same basic measurement ratios as a normal longsword. These numbers also provide us with ratios to use for all items for these sizes. By this reasoning, large creatures need to have their stuff weigh 6 times more than normal, huge creatures need to have things weigh 36.8 times more, gargantuan creatures need to have things weigh 224 times more, and colossal creatures need to have things weigh 1,331.2 times more.
In short, here are some new multipliers for page 153 (round as you see fit):
Large x6
Huge x36.8
Gargantuan x224
Colossal x1331.2
The same principle can be applied to small, tiny, diminutive, or fine creatures, and you end up with the following:
Small x.5
Tiny x.1
Diminutive x.025
Fine x.0125
Feel free to check my math! It's certainly possible I've made a mistake. But if I haven't, then here are some much more satisfying (I hope) multipliers. =)
Someone posted a link to this thread and described this method as using proper "physics" to determine weapon weight for different size categories. The goal was to determine the weight of a morningstar used by a cloud giant.
I gave a somewhat streamlined response that made two assumptions:
1. The cloud giant's arms are short and stubby - the same length as a human's. Longer arms would have resulted in even greater forces, and I wanted to keep it simple.
2. The wooden shaft of said morningstar is quite solid, but weightless.
So here we go:
So you go from 6lbs in the hands of a medium creature (approx 6') to a huge mace in the hands of a cloud giant (18') being 1344 lbs?
The thread you referenced was using D&D rules, which as shown here http://www.dandwiki.com/wiki/SRD:Morningstar describe the step from medium to large as 2x. Your assertion then is that from large to huge, we increase mass by 100x. Mind you those rules put the mace as over 2x what they historically actually weighed.
So let's start with the D&D version of the medium sized morningstar at 6 lbs. Since steel weighs 0.283 lbs/cu. inch, that gives us 21.2 cubic inches of steel, which gives us a solid cube 2.76 inches on all sides. Morningstars weren't typically just a simple cube though; by shaping it into a ball with spikes, you'd typically end up with something at least double those dimensions.
So let's apply that to a 1344 lbs morningstar:
1344 lbs = 4749 (rounded down) cubic inches of steel which gives us a perfect cube 16.8 inches on each side. Craft that into a morningstar shape and you're talking a steel ball 3' across.Compare each to the height of the creature wielding them to get a ratio of comparison:
6" by a 72" creature = the human is 12 times the height the head of his morningstar.
3' by a 18' creature = the cloud giant is only 6 times the height of the head of his weapon.--------------------------------------------------------------------
First point: the system you are using to make these conversions is not accurate. It involves a lot of assumptions, has little grasp of what these figures actually look like, and is not following "physics" very well.
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So let's move on to the force calculations for swinging something like that.
Let's compare the swing of a morningstar to the swing of a bat. Statistically, professional athletes are said to hit with the tip of their bat for 8000 lbs of force. So if we ignore the fact that a cloud giant has longer arms, and thus a faster swing...
f=ma
f1=8000lbs, m1=6lbs, a1=8000/6 = 1333Now we redo that with a 1344lbs weapon and we get 1791552 lbs of force from a cloud giant with arms the length of Babe Ruth. Longer arms would mean...gah, nevermind.
You can go to this site here to compare it to a car crash: http://hyperphysics.phy-astr.gsu.edu/hbase/carcr.html
In order to get the kind of force you're talking about behind such a swing, you would have to compare it to a car, weighing 3200 lbs, crashing into a person who is standing still while the car is traveling at...calculating...130 mph. I don't care what armor you're wearing or what level you are, that's insta-kill with nothing left for your loved ones to bury.
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Second point: Your hypothetical giant, if we were to shrink his arms down to the length of a human's, is still swinging harder than a 3200lbs car moving at 130 mph.
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Now let's move on to the scaling of strength. Many people have heard the interesting fact that ants can carry 50 times its body weight. How can a creature with no lungs and no heart manage such an amazing feat of strength?!
Answer: it has nothing to do with their biology, but the physics of size. As mass increases, the amount of force need to move it increases. But this increase is not a straight increase. As the mass increases, the amount of force needed to move it increase exponentially. Same pattern goes for trying to move an object faster and faster, which is why it takes infinite energy to hit light speed.
Here's a link to a graph portraying this: http://www.madsci.org/posts/archives/may99/927263695.Gb.1.jpg
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Third point: because of mass scaling, a creature 3x as large as a human moving an object 3 times as big as the object the human is trying to move would need to use 9 times the force. The leap of 100x you're talking about would mean 10,000x the force to swing it. With stubby human arms. More if you want to swing it in the arc of an 18' tall giant's reach.
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Conclusion: we need to find a different system that what that link you gave proposed for determining weapon size and weight for different size categories, cause that aint "physiscs".
PS. These sizes could be brought into much more manageable ranges by dramatically slowing down the acceleration and end speeds of their attack swings.
PPS. Anyone curious about the thread that directed me here, here it is: http://paizo.com/forums/dmtz5890?A-Plea-Physics-IS-Compatible-with-High-Fan tasy#26
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I am going to make my own numbers for this based on the idea that each size catagory is twice the height(takes 4 times the floor space and 8 times the volume) of the previous size catagory. since halflings are half as tall as humans. if anyone wants to help out that would be cool.
To maintain proportions if the ht is 2x then so is the w and d.
a 2' cube is made twice as long(two cubes) and twice as deep(four cubes) and twice as tall(eight cubes)
this makes things rather odd for halflings though, packs hold 1/8 as much and an average halfling should weigh 21.25 lbs if same build but half as high as a 170 lbs human.
After reading this thread, I can't stop imagining full plate for a fine creature... Lets armor those ants!
Not until i get snake barding.