Maths and Weapon Sizes

[Cybern]

I don't want a math class - I already did enough of these already - but my math teachers always said that they were gonna be usefull someday...

Here's my question:

In normal situations, when you double the size of an object, you double all of its 3 dimensions, therefore its mass increase by x8 (2x2x2).

So, x2H => x8W
and x1/2H => x1/8W

The height is then equal to the cubic root of the mass.

A large weapon weights double its mass. Using real world height/mass formula, the lenght can't be doubled too.

So, how tall is a large weapon?

Lets say that a Medium Greatsword is 6' long and weights 8lb. If a Large Greatsword weights 16lb, its height is x1.26 (the cubic root of the mass, rounded), or 7'7". If the same is true for Huge Weapons, then a Huge Greatsword weights 32lb, and its height is x1.26x1.26 (x1.59), or 9'7".

Are my maths ok? They sound ok to me, but then a Huge creature wields a "relatively" smallish sword? Should the rule be that Huge Weapons are larger (ex.: x8W instead of x4W, so about double the Height of a medium version) ?

This ain't a critical issue for most games (and most people don't care), but I still want to know because of a situation that has happened some time ago in our game.

Thank you all for reading this far

 

[eryndel]

Your math's right. If you double the mass each dimension should be multiplied by the cube root of two. That does make the weapons a little short (and smaller weapons a little long. A small greatsword is 4 feet 9 inches long, Tiny is 3-10, Diminuitive is 3 feet.) It quickly get disproportionate the farther from Medium you get. Perhaps use x2/ x8/ x32/ x128 for large/huge/gargantuan/collosal. It might even out better.

Werner

 

[Umbran]

There's more than one way to skin a cat.

Assuming uniform density, in order to double the mass, you need to double the total volume. There's many ways to do that. There's no rule saying that the weapon must keep the same proportions in the size increase.

So, you can double the mass by multiplying each of the three dimensions by the cube root of two. You can also double the mass by doubling the length and leaving the other two dimensions alone. You can also double the mass by multiplying length and width by the square root of two, but keeping depth constant. There are an infinite number of variations which all yield the same result.

Somewhat simplified, what you have is:
Original weapon: W x L x D = V
New weapon: aW x bL x cD = 2V

So that a x b x c = 2. There are an infinite number of combinations of a, b, and c which will satisfy this condition.

 

[tauton_ikhnos]

If weapon proportion changes from size to size, it ceases to function like original weapon. By rules it is same weapon, however.

A greatsword which increases width by 20%, depth by 10%, length by 51.5%, will double mass. However, will work more like longsword or rapier than greatsword. Do that twice, result is more like easily-broken twig than any kind of sword.

Sword is unlikely to be exactly same in each dimension, but very likely to be pretty close. At a guess:

24% width, 24% depth, 30% length. A 40" blade (length of a tall man's leg) at Medium will thus become:
- 52" at Large (length of giant's leg minus 1/3rd)
- 68" at Huge (length of titan's thigh bone)
- 88" at Gargantuan (dagger sized)
- 115" at Colossal (length of foot; barely a dirk)

Even with +50% length each time, sword rapidly becomes worthless to original intent.

However, game not about realism. In realistic setting, weapons would change entirely as you shift up in size. Spiders don't work at human scale, and swords don't work at colossal scale - gargantuan humanoids would use weapons more like wrecking balls, giant trowel, tree club.

 

[Dogbrain]

However, game not about realism. In realistic setting, weapons would change entirely as you shift up in size. Spiders don't work at human scale, and swords don't work at colossal scale - gargantuan humanoids would use weapons more like wrecking balls, giant trowel, tree club.

Oddly enough, for some strange reason, outside of D&D, great huge smashing things are considered the "typical" weapon of gargantuan humanoids. It looks like "realism" is in better agreement with mythic sources than the game is.

 

[Newbie]

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