Here are my thoughts how to design elements for Papa Bear, which is a 29 inch diameter L and L kiln with 2 sections. There are 3 elements in each of the sections and 2 elements in the floor, so there are 8 elements in all. Since we want to have 60 amps, which will give us 14,400 watts, we divide the kiln into 3 different sections of 20 amps each. Each of these sections will be wired in parallel to each other.
But within each section the elements will be wired in series. So the top section will have 3 elements wired in series, the bottom section will have 3 elements wired in series, and the bottom of the kiln will have 2 elements wired in series. That makes 8 elements in all.
Let's look at the top section. We have 240 volts, we want 20 amps, so we need 12 ohms. (240/20 = 12) Since we have 3 elements in series each element needs to be 4 ohms.
Now there are a lot of ways to get an element of 4 ohms depending on the diameter and type of wire, but I have decided that I am going to use either 11 gauge or 12 gauge Kanthal A1 wire. 11 gauge is thicker (.091 inches) than 12 gauge (.081 inches) and I would rather use 11 gauge than 12 gauge because it will last longer. 11 gauge wire also has less resistance than 12 gauge wire --- .106 ohms/foot as opposed to .134 ohms/foot. It's easier for the electrons to travel through a thick wire.
However I have been told that 11 gauge wire is very difficult to work with because of the strength needed to wind the element, and also to install the wound element in the kiln. I don't have experience with this, but I do like the idea of using 11 gauge.
Let's calculate the length of the wire needed for 4 ohms. 11 gauge is 4/.106 = 37.74 feet of wire and 12 gauge is 4/.134 = 29.85 feet of wire.
Now we have to wind these wires on a mandrel and there are a couple of things we want to keep in mind, these courtesy of Kanthal. http://www.kanthal.com/C12570A7004E2D46/062CC3B124D69A8EC1256988002A3D76/D1D355F37C940491C12572B9003FD970/$file/1-A-5B-3%20UK%20resistance%20alloys.pdf?OpenElement
First of all we want the diameter of the element itself to be between 5 and 6 times the diameter of the element wire. This is so the heat can get out of the back of the element, and also so the element does not fall over when it is hot -- if the diameter is too big, the element won't be able to stand up when it is soft.
Secondly, we would like to be able to stretch that element so that we have close to 1.25 element diameters between each pair of adjacent coils. We want to be able to take a piece of wire that the element is made of, insert it in the coils, and be able to wiggle it around a little. This is so the heat from the back of the element can make it out. Kanthal defines the "pitch" of the element to be the distance between the top of one coil and the top of the next coil and they specify that the pitch should be between 2 and 3. Our pitch above was 2.25. We don't want the elements to be stretched too much so we want to keep the pitch below 3 for an ideal element.
When Papa Bear arrived the elements were of probably 17 or 18 gauge (They measure .040 inches) and the pitch was approaching zero. Just an unstretched element laying in the holders. I was only able to get a few cone 10 firings from them and now they will not even go to bisque.
Next -- the winding of the elements.