I just thought I would try to end this thread by not going mathematical, but by speaking about the parameters that you need to be able to keep in mind when you are designing elements for a kiln. Anyone who is interested in how we did Papa Bear just let me know and I will do a separate post on that.
At any rate this will just be a review and crystallization of what we have done so far.
The most important variable is what is called watt loading, or the amount of watts per square inch that the elements have to generate to fire the kiln. Larger diameter wire allows for lower watt loading figures, but you have to be able to fit the wire into the kiln, and larger diameter wire also has less resistance per linear foot -- it's easier for the electrons to pass through a larger wire. So as you make the diameter of the wire larger, you need more of it to achieve the resistance that you need, and it may be so much wire that it won't be able to fit. We found that 12 gauge wire worked well for us, and that Kanthal A1 was the alloy that is the most economical and useful at the same time. Kanthal also makes an APM element but the raw wire cost is almost 5 times as much. It is special wire and I feel like it is not worth the extra cost as long as you have low watt loading. I think the watt loading for Papa Bear is around 12 watts per square inch. If we had decided to use 15 or 16 gauge wire, the APMs might have been a good choice, as they can go to a higher temperature.
We also have to take into consideration the diameter of the element. The diameter should be, according to Kanthal, about 5 to 6 times the diameter of the wire. Once we wind the element so that all the wire is touching we need to be able to pull the element to just over twice its wound length. The distance from the top of one wire to the top of the next wire is called the pitch and we want it to be just over 2 times the diameter of the wire. So we should be able to put a piece of element wire of the same size in between the stretched coils and move it back and forth a little.
We need to know how large our kiln is and how many kilowatts it will take to fire it. The Robert Fournier book has this information.
And we must keep in mind what happens when elements and banks of elements are wired in series and parallel.
Here is Galen Olmstead changing the element holders so that Papa Bear can accept the larger elements. We had to grind the element holders on the lap wheel so that we will be able to easily install the elements. Galen is beginning graduate school at UF this fall and he makes some wonderful sculptural objects.