D&D Math: Making sense of creature weight in relation to size

Xeviat · November 08, 2006, 05:57:44 PM

I have recently been working on a mechanic for throwing creatures and objects, determining the distance of the throw. I resumed work on this after I saw the throwing mechanic from Mutants and Masterminds. While it is clean, it requires the use of two charts, and uses more variables than what will be on someone's character sheet.

So, I've been stairing at the carrying capacity table and the weights listed for creatures based on size for a little more than a day now, and I want an equasion for this (for weights). Here are the points (note = x is size, y is weight; x of 1 is fine, x of 2 is diminutive, x of 3 is small ... x of 9 is collosal. The weights listed are the maximum weights for a creature of that size category, assuming that the creature is as dense as a human. I've changed the numbers slightly to fit in with the progression, as the current numbers listed were approximations).

Size	Weight
1	0.125
2	1
3	8
4	64
5	512
6	4096
7	32768
8	262144
9	2097152

Heck, it can probably be done with sizes 1-5 for simplicity, since those numbers are more managable. Each time x increases by 1, y is multiplied by 8.

snakefing · November 08, 2006, 06:19:14 PM

Edit: original was mistaken.

y = 8 ^ (x-2)

Poseptune · November 08, 2006, 06:39:51 PM

Quote from: snakefingEdit: original was mistaken.

y = 8 ^ (x-2)

yep

Xeviat · November 08, 2006, 06:42:36 PM

Much thanks ... now to find my calculator so I can do decimal exponents ...

Xeviat · November 08, 2006, 06:47:24 PM

While the Left-brainers are here, here's a question:

Should the effective strength of an object be determined by it's mass/weight?

Again, I'm working on a throwing system, and trying to make reasonably set Strength DCs for objects. Creatures are simple: A creature's DC is 10+str mod+size mod. I justify this because stronger people generally weigh more than lighter people (there is a question of overweight people, but I think that will be covered best by a trait/flaw system; I will be modifying the D&D weight system for PCs to utilize strength scores). I could use an opposed Str+size mod check, but that creates much more variance (potential for defender to roll a 1 and the initiator to roll a 20, and thus the difference is huge).

Again, would determining an object's effective strength score with it's mass/weight be a reasonable aproximation?

Epic Meepo · November 08, 2006, 07:01:38 PM

EDIT: D'oh!

Xeviat · November 08, 2006, 08:23:51 PM

I don't mean for the damage the object will deal; I mean for what DC the strength check to throw it will be.

Damage dealt with a thrown object will be done just like weapons: objects will have a damage rating based on their size (size is largely determined by weight, but also by dimensions), and a thrower will apply their strength modifier (just like with weapons).

Xeviat · November 08, 2006, 08:46:22 PM

I have another one for everyone.

2	25
6	50
10	100
14	200
18	400
22	800
26	1600

Every time x increases by 4, y doubles.

I tried a couple myself, but I have no idea how you guys came up with the first (other than trial and error).

Captain Obvious · November 08, 2006, 09:29:49 PM

I'm not sure i you physical can debate what these limits are. Maybe i'm reading the thread wrong, but if a creature goes up one size x+1 then the creature is scaled up to be twice as large in all dimensions. However, since volume relies on 3 dimensions, is you make something twice as large, it's mass (and weight as well) must increase by a factor of 2x2x2 or times 8( as shown earlier). This causes a size increase of 1 to multiply the weight by 8. It's simply a fact of geometry.
Now it is entirely possible that i missed the point of this thread as i did not read every post in detail (just the first few and then skimmed the rest before replying), and if this is the case i would appreciate it if someone could set me straight.

snakefing · November 08, 2006, 10:29:12 PM

Actually, ~, you are partly right. Generically, if you scale up an object by a factor of 2 in each linear dimension, it will increase by a factor of 8.

However, this doesn't actually work for creatures, at least those with a skeleton. The reason is that if the weight scales by a factor of eight, the cross-sectional area of the bones will only increase by a factor of four. That is, the weight increases faster than the strength of the bones. Eventually the increase of weight will be so much that the bones will no longer be able to support it.

For real life creatures, the size of bones has to increase faster than the proportional increase in order to compensate this.

As for the most recent progression, the formula is:
y = 25 * 2^((x-2)/4)

Captain Obvious · November 08, 2006, 10:33:31 PM

Ho ho! Looks like we've got an expert on our staff. (heh, we're not a staff - that implies responsibility).
I will bow out to your expertise.

SA · November 08, 2006, 10:41:07 PM

Quote from: snakefingThe reason is that if the weight scales by a factor of eight, the cross-sectional area of the bones will only increase by a factor of four. That is, the weight increases faster than the strength of the bones. Eventually the increase of weight will be so much that the bones will no longer be able to support it.

For real life creatures, the size of bones has to increase faster than the proportional increase in order to compensate this.

That's something I did not know, and oddly enough, can put to good use.

Would muscular increase follow similar principles?

Xeviat · November 08, 2006, 10:58:25 PM

Currently, creature weights in the Monster Manual were described increasing by factors of 8. That second chain of numbers is what I'm going to propose as a change to the carrying capacities; the current carrying capacities are flawed.

A creature increasing from medium to large gets a +8 strength bonus (increasing it's carryinc capacity by almost 4 times), and it is now large (increasing it's carrying capaicity by 2 times). Thus, when those are together, it's carrying capacity almost increases by 8 times ... almost.

A 10 str human can carry 100 pounds (within the limits of a medium sized creature's weight); an 18 strength large human can carry 600 pounds (still within the large limits); but the next kick means the Huge creature's 26 strength can't lift a weight within it's own size category.

I'm not sure if that's right in progressions.

snakefing · November 08, 2006, 11:28:55 PM

Quote from: Machinegun PoliticsThat's something I did not know, and oddly enough, can put to good use.

Would muscular increase follow similar principles?

I am no expert on biology, being more of a physicist. But I do believe that muscular strength is a function of the number of muscle fibers, which like bone strength is proportional to the cross-section size of the muscle. (All other factors being equal.)

So the short answer is: yes, I think it would.

limetom · November 09, 2006, 01:41:06 AM

Quote from: SRDThe figures on Table: Carrying Capacity are for Medium bipedal creatures. A larger bipedal creature can carry more weight depending on its size category, as follows: Large Ãƒ'"2, Huge Ãƒ'"4, Gargantuan Ãƒ'"8, Colossal Ãƒ'"16. A smaller creature can carry less weight depending on its size category, as follows: Small Ãƒ'"Ã,Â¾, Tiny Ãƒ'"Ã,Â½, Diminutive Ãƒ'"Ã,Â¼, Fine Ãƒ'"1/8.

Quadrupeds can carry heavier loads than characters can. Instead of the multipliers given above, multiply the value corresponding to the creatureÃ¢,¬,,¢s Strength score from Table: Carrying Capacity by the appropriate modifier, as follows: Fine Ãƒ'"Ã,Â¼, Diminutive Ãƒ'"Ã,Â½, Tiny Ãƒ'"Ã,Â¾, Small Ãƒ'"1, Medium Ãƒ'"1Ã,Â½, Large Ãƒ'"3, Huge Ãƒ'"6, Gargantuan Ãƒ'"12, Colossal Ãƒ'"24.

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D&D Math: Making sense of creature weight in relation to size

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