The Break DC for 1 inch hemp rope is 23. I don't see anything regarding ropes of other diameters though. I figured that maybe the Break DC for items would increase by a set amount per inch of thickness, but while some items seem to go up by +2 per inch others vary. Doors gain +3 for the first half inch of additional thickness and +7 for the next half inch (perhaps because they're assumed to have some additional iron bands or something?)
I'm thinking of adding +2 for the extra inch of thickness and another +2 for being a "masterwork" rope since masterwork manacles gain a +2. The purpose here is to use the rope as a whale line for darting whales with harpoons. I guess similar questions could come up for other items and materials though. Should it be assumed that +1 unit of thickness equals +2 Break DC? This isn't a critical game balance issue but could come up in campaigns where the DM wants to include some "Kool Aid Man" or "Schlitz Malt Liquor Bull" moments.
Hmm....2" rope isn't twice the strength of 1" rope, it's four times the strength. Given that +8 Str is a tripling of carrying capacity, it seems that a +4 dC would match a tripling of object strength. Call it dc 28, then.
I wasn't able to check back on this until now. It turns out that I misread the bit on whaling lines and the rope used was 2 inches in circumference, not diameter. That obviously wouldn't have a high enough burst DC to give a whale any chance to fail at breaking it, but as Lincoln Hills points out, you're not trying to tie the whale to a post or anything, so maybe the leverage isn't there to make breaking the rope an issue.
Perhaps I'll just give the whale a Reflex save with a DC of 10+damage dealt to avoid getting "stuck" by the harpoon when hit and DC 20+damage dealt to get it out afterwards. I guess a nat 20 would always get the harpoon out and a nat 1 would mean it is stuck in the whale at least semi-permanently.
These probably aren't great rules to simulate whaling, but I figure that getting the PCs in boats throwing harpoons will be more fun than having them just hit the whale with spells and greatswords. An allied Sorcerer is willing to Bestow Weapon Proficiency with harpoons on them, so we'll see how it goes.
Yeah, I'd read about the use of manila, which is one reason I was going to give the rope +2 for being "masterwork". I ended up trashing the idea of the rope breaking and went with Reflex saves instead.
It turned out that nobody managed to hit the whale with a thrown harpoon anyhow. In fact, once the whale bit somebody for about 80 damage all of the PCs but one flew up to about 60-70 feet in the air to get away from it. The remaining PC's whale boat got capsized by a "smashing breach", but he did manage to stick the whale with a harpoon in melee. Next session he might end up doing some water skiing.
The players were laughing and shouting "Dicky Moe!" a lot, so I think they're enjoying the themed encounter even though I might have made the whale's offense a little too powerful. Maybe I'll give the party a little extra treasure to cover any Raise Dead expenses which might come up. Perhaps I'll also buy a Fudgie the Whale cake to celebrate their victory.