Many spells and effects in Pathfinder measure things in terms of volume (more often than not, in cubic footage).
For example:
Earlier today my 11th-level wizard attempted to cast make whole on a damaged sailing vessel in order to make it seaworthy again.
However, I am limited to a 110 cubic foot object, due to the spell's caster level limitations.
I asked my GM how much cubic footage a sailing vessel takes up and he said, simply, "well, it's about 90x20x10 feet, so do the math."
90 x 20 x 10 = 18,000 cubic feet
Upon further introspection, however, I realized that his "formula" is highly imprecise, as much of that "space" is open air and not part of the ship itself (the ship is not solid, it has plenty of interior rooms and such).
To get a more precise measurement of a sailing vessel I pictured how much cubic footage the vessel might take up if one were to, say, grind it up into dust.
To determine this, I asked my GM how much this particular sailing vessel weighed. He said "about 1 ton" since it is made of lighter wood that readily floats.
So I did a quick internet search and determined that wood, on average, weighs 30-40 pounds per cubic foot.
So...
2,000 lb. / 30 lb. (for light wood) = ~ 67
So, the sailing vessel, more precisely, has a volume of ~67 cubic feet.
A 7th-level caster can repair a sailing vessel of the weight and size that my GM described.
I'm terrible at math and almost as bad at logic problems, which is why I am posting here. Have I made any mistakes in my math or my reasoning?
Is there a more efficient means of determining an an awkwardly-shaped object's volume?
I could suggest you(or your DM if it's a huge issue for you guys) take a look at stormwrack, which broke sailing vessels down into a number of 'hull sections' which would be damaged and/or repaired seperately. Spell effects like make whole would be applied this way also, and helped translate the mechanics you are struggling with into a workable method.
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Earlier today my 11th-level wizard attempted to cast make whole on a damaged sailing vessel in order to make it seaworthy again.
However, I am limited to a 110 cubic foot object, due to the spell's caster level limitations.
I asked my GM how much cubic footage a sailing vessel takes up and he said, simply, "well, it's about 90x20x10 feet, so do the math."
Upon further introspection, however, I realized that his "formula" is highly imprecise, as much of that "space" is open air and not part of the ship itself (the ship is not solid, it has plenty of interior rooms and such).
To get a more precise measurement of a sailing vessel I pictured how much cubic footage the vessel might take up if one were to, say, grind it up into dust.
To determine this, I asked my GM how much this particular sailing vessel weighed. He said "1 ton" since it is made of lighter wood that readily floats.
So I did a quick internet search and determined that wood, on average, weighs 30-40 pounds per cubic foot.
So...
2,000 lb. / 30 lb. (for light wood) = ~ 67
So, the sailin vessel, more accurately, has a volume of 67 cubic feet.
A 7th-level caster can repair a sailing vessel of the weight and size that my GM described.
I'm terrible at math and almost as bad at logic problems, which is why I am posting here. Have I made any mistakes in my math or my reasoning?
Is there a more efficient means of determining an an awkwardly-shaped object's volume?
Your method of using the total mass/density to get the volume of the constructed materials is fine.
Using the smaller number to get the maximum volume is conservative and is a good plan.
Your GM's estimate of a ton for the sized vessel sounds horrid to me, but whatever level of realism works for you.
I see no reason to go with the volume of the materials rather than the total volume of the object, but that's between you and your GM. His initial 'do the math' getting to 18,000 cubic feet sounds correct to me.
If the two of you chose to go with the volume of just the materials, then the ratio of 67 cubic feet to make an 18,000 cubic foot object should be ringing all sorts of bells that something was off; in this case, the estimate of the total weight of the boat at 1 ton.
If you interpret the spell as affecting a total volume regardless of the shape, then you get situations like repairing a rope that could stretch for miles. I would probably rule that you couldn't fix things beyond your range, so fixing an entire boat that size would take at least two spells.
Of course a boat 90x20x10 feet is a pretty small boat, and even so would probably weigh a lot more than that, but this all sounds pretty nitpicky. If the boat had a hole in it or had some broken timbers, I would more than likely consider this a perfect situation for that spell. If it had been burned and blasted to bits... probably not.
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Well per wikipedia the USA-17 has a displacement of 17 short tons, and it is about 90 feet long. It is also light for its size, being made from carbon fiber and resin.
So I'd have to say a 90 foot ship made of wood would weigh closer to 20 tons. 15 if it was more of a flat bottomed river ship.
Just a thought. I've no idea how accurate that might be.
Well per wikipedia the USA-17 has a displacement of 17 short tons, and it is about 90 feet long. It is also light for its size, being made from carbon fiber and resin.
So I'd have to say a 90 foot ship made of wood would weigh closer to 20 tons. 15 if it was more of a flat bottomed river ship.
Just a thought. I've no idea how accurate that might be.
One of my fellow players tells me that wood is much lighter than a lot of the modern materials we use today (which are used for their durability and flexibility rather than their light weight).
Wood may be lighter by volume than carbon fiber materials, but the whole point of using the carbon fiber and other modern materials is that they are much stronger by weight, and so a ship built from carbon fiber is lighter than a ship of equal strength built from wood. This is why they use carbon fiber to make sailplanes instead of oak.
Viking longships were constructed in a way that made them lighter than most ships of their time. The longship Gokstad measured about 75 feet long and fifteen feet wide. I can't find the height, but it was probably in the range of 15 feet or so. It weighed 15 tons and was made primarily of oak and yew. Since weight tends to increase as the square of the length then a 90 foot ship of similar construction would weigh a bit more than 20 tons.
According to Yahoo, Oak weighs about 50 pounds per cubic foot (lots of variation depending on the type of oak, but that's a fair average). So a 20 ton ship would be about 800 cubic feet of wood.
According to Yahoo, Oak weighs about 50 pounds per cubic foot (lots of variation depending on the type of oak, but that's a fair average). So a 20 ton ship would be about 800 cubic feet of wood.
...well. Darn. And that's a light ship?
That would take an 80th-level spellcaster!
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According to Yahoo, Oak weighs about 50 pounds per cubic foot (lots of variation depending on the type of oak, but that's a fair average). So a 20 ton ship would be about 800 cubic feet of wood....well. Darn. And that's a light ship?
That would take an 80th-level spellcaster!
Or a much lower level caster working with someone skilled in shipbuilding and repair to know what needs to be repaired.
Unfortunately, most volume measuring spells like this have to be nerfed in this way. We all, i'm sure, have some images of wizards casting a spell and watching as a gaping hole in the earth opens up, and a tunnel is built for them. The only way to avoid using this to just bypass entire dungeons is to cut down volumes. So, unfortunately It does take away our ability as PC's to handle things with very large masses.
Or a much lower level caster working with someone skilled in shipbuilding and repair to know what needs to be repaired.According to Yahoo, Oak weighs about 50 pounds per cubic foot (lots of variation depending on the type of oak, but that's a fair average). So a 20 ton ship would be about 800 cubic feet of wood....well. Darn. And that's a light ship?
That would take an 80th-level spellcaster!
Well, my wizard in particular has fabricate, make whole, AND ranks in craft (ship). :P
Or a much lower level caster working with someone skilled in shipbuilding and repair to know what needs to be repaired.According to Yahoo, Oak weighs about 50 pounds per cubic foot (lots of variation depending on the type of oak, but that's a fair average). So a 20 ton ship would be about 800 cubic feet of wood....well. Darn. And that's a light ship?
That would take an 80th-level spellcaster!
Depending on the damage to the ship, I still think this spell by an 11th level spellcaster should do a good job of making a typical ship usable again. Unless the thing was broken into bits, the damage would most likely be to a few key timbers and maybe a hole in the hull (a la the "Minnow"), and that should be fixable by this spell.
As I said in my first post, I'd probably never get this picky in the game.