Moving Stationary Objects Underwater
This is a simplification of Archimedes’ Principle applied to characters moving stationary objects underwater. I designed this for a High Seas Adventure Campaign where the party’s first mission together was to salvage some pirate treasure from a sunken ship. As I designed the map and challenges there, I realized that the two players who could breathe water at the beginning of the game did not have very high Strength scores (they were both playing caster classes). I wondered if they would be able to move some of the very heavy items I was going to put there.
Then I remembered my high school physics; Archimedes’ Principle basically states that a fluid will exert a buoyant force on any submerged object equal to the weight of the fluid displaced. In practical terms this means solid objects underwater effectively weigh less and are more easily moved than normal. The variable to be considered is the density of the submerged object.
The list below goes over common materials in Pathfinder and a multiplier for each of the materials. Use this list by taking the weight of the object in question and multiplying it by the most applicable modifier in the table. The result will be the effective underwater weight of the object. Each multiplier is based on the ratio of the density of the object (in parentheses) compared to the density of water (1). Technically seawater is 1.025, but I found the difference to be negligible for the game. The calculation can be represented as such: Let n equal the density of an object in grams per cubic centimeter. Multiplier = (n-1)/n.
I pulled the densities from Google searches. The density for stone is an average density of Granite. Adamantine is based off of diamond, as my research indicates that the myth of the metal started from the discovery of diamond veins in coal deposits (a blackened, shiny, super-hard material). Mithral is based off of silver, as the Tolkien legend of Mithril basically describes the material as similar to silver, but magically enchanted to outperform steel.
Feel free to correct my math on this; I’m a much better conceptual writer than mathematician, especially when it comes to Fluid Dynamics.
Material Multiplier
Stone(2.75) = .63
Iron(8.00) = .875
Steel(8.05) = .875
Gold(19.32) = .95
Silver(10.5) = .90
Diamond(3.51) = .72
Gems(2.50) = .60
Adamantine(3.51) = .72
Mithral(10.5) = .90
Looks good to me (I'm a physicist, I teach this stuff).
My one comment is about the special materials. For mithral, mechanically it makes an iron/steel weapon or armor weigh half as much, I'd go with a density of 4.00 instead of the density of silver. Yes it is based off of silver, but it's magical super strong super light weight silver.
Adamantine weapons/armor have the same weight as conventional ones, so I'd go with the density of iron/steel.
I like your ideas GralphidB. I looked too much at the origins of special materials instead of how Pathfinder treats them. I think I'll start using those densities. Fortunately we're early enough the game that the party hasn't dealt with special materials much, so they'll never know the densities changed!!
For anyone who cares, here's an updated list to use:
Material Multiplier
Stone(2.75) = .63
Iron(8.00) = .875
Steel(8.05) = .875
Gold(19.32) = .95
Silver(10.5) = .90
Diamond(3.51) = .72
Gems(2.50) = .60
Adamantine(8.05) = .875
Mithral(4.00) = .75
My engineer self can't help but appreciate your work. Thank you very much, sir. :)