I wrote a calculator that to me was easier to use. I did this for two reasons, calculating many options on paper was annoying, and I understand things better if I can write a program out of it.
You can enter the tank volume if you don't have measurements (I.E. 250 gallons), but you can't calculate the firebox opening from this. You have to actually enter the length and diameter of the tank. It asks you for the thickness of the tank walls to calculate the inner diameter, used in calculating the firebox volume.
For most calculations, I use the original post by DaveOmak (Edited by DaveOmak - 11/17/14 at 10:35pm). I didn't like having to guess at the height of the firebox opening, though. I spent hours trying to figure out how to calculate the height given the area and the radius, but I failed. Maybe I can't do it, or I just didn't try hard enough, math wasn't my absolute strongest course ever.
Regardless, I cheated, and since computers are pretty fast, I brute forced the thing. I start from a theoretical opening height of 0.001, and in increments of 0.001, I calculate the area of the theoretical opening. We already know the ideal opening size in square inches from DaveOmak's calculations, so I keep incrementing until I go over the ideal. Then, I compare the corresponding area that was a little shy of the ideal opening area, and the area that was just slightly bigger than the ideal opening area. Whichever one is closer, I use that opening height.
Perhaps I should just pick the height that just barely puts it over the ideal?
I used the following formula in calculating the area based on the radius and theoretical opening height:
Math.Pow(radius, 2) * Math.Acos((radius - segmentHeight) / radius) - (radius - segmentHeight) * Math.Sqrt((2 * radius * segmentHeight) - Math.Pow(segmentHeight, 2)). It seems to match up with the calculator given in the thread.
You can see the results below I get for my propane tank:
If you click the button to copy to clipboard, I get this:
The tool currently runs on Windows, with the only requirement having .NET 4.5.1 (
http://www.microsoft.com/en-us/download/details.aspx?id=40773)
If there is any interest, I can post the program. Perhaps I'll put it on github or codeproject as well.
Things I intend to do in the not too distant future:
- Allow for one to use two exhaust stacks, and calculate the height required based on inner diameter
- Calculate the diameter of the firebox inlet areas, assuming you put two circular inlets, one at the top, one at the bottom.
- Allow for square firebox inlets
- Allow for square cooking chamber exhaust stacks.
Hope it helps.
Mark