Turns out that while the calculation is conceptually trivial, it does require skills from the first full year of calculus. It has a trigonometric substitution under an integral, and the end result is not pretty. It has about half a dozen terms, and an arcsin. Here is a photo of the meat of it:
Because it's not straightforward enough to do on the fly, I made a spreadsheet in 2-inch increments and will post it on my wall for when I dip the tank. Here is a screenshot:
Also, because I really am hopelessly nerdy, I wrote a matlab script. Oh dear. I really, truly am hopeless. Email me if you'd like to have it! I love it. It's such a beautiful example of the practical applications of higher math. People tend to think that higher math is only for theoretical constructs or at least only for people in the field, such as scientists and engineers. But here is an application of calculus that is completely, unarguably practical.
The best part of this nerdy story is that I confessed to a friend what I had done, and he told me he'd done the exact same thing! And we then compared our respective matlab scripts! HAHAHAHAHA!!!
7 comments:
just make sure you didn't make any errors in your script so you don't end up freezing your cheap chinese arse one of these days! (not that you aren't already freezing your cheap chinese arse in that outhouse haha)
you are my hero!
-bt
Haha! Don't worry; I verified by several other methods, and by my friends' as well! Anyway, the oil stove does a pretty lousy job of heating the house. I use mostly the wood stove! The oil stove is just for backup and when I'm either asleep or not home to tend the fire!
Math is hard...let's go shopping!!
Nice! I've just been using a stick and congratulating myself on having a lot of oil left in May.
Duuuuuuude. I would've gotten the $20 stick.
Actually I've gotta give you props for grunting out the calculations. I've done my fair share of math in my years, but it would never occur to me to sit down and work these things out. That explains why I never made it to grad school.
Way to go, Arvay!
Mdr thinks it was fun to do that, it is kind of like people climbing the peak of Himalaya, a challenge and an accomplishment, not to save money. The smartest part was that was only for the backup use, because you won't mass with the operation of the wood stove.
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