This is a guide on how to build a medium sized Tesla coil. I built this one from parts I had laying around, all I had to buy was magnet wire, in all I spent less than $30! For those building their first coil, I would not suggest using this a standalone source of instructions. This is my first coil, and I used a multitude of sources to make it. Also, I did the boring math part behind it. At first I tried to skip some of the math, and just "wig it" but that didn't work. For the math part I would suggest deepfriedneon.com, but I found a much simpler site : http://www.classictesla.com/java/calculat.html#WireFreq . Once you know what materials and dimensions you will use, go to this site to get the whole resonance thing synced up as closely as possible. Read this entire guide, and maybe the comments section, before doing anything. Also read some other guides and maybe the Wikipedia article on Tesla Coils before deciding whether or not to embark on a shockingly frustrating, but rewarding journey. I built this for a high school science project, and although I finished at the last minute, it didn't take more than maybe 20-30 hours of work. I entered a few contests with this so you should vote for me if you enjoy this instructable.
I also must say that by using any information in this guide you assume all risks involved with the components, operation, and construction of Tesla Coils or any part of the circuitry described. I do not take any responsibility for injury or damage resulting from the use of this information. Tesla Coils CAN KILL YOU! Whether it be the streamers, 15kV NST output, or the simple (and most dangerous) 120V wall outlet input. All the currents involved with this project are dangerous! I would recommend working with someone experienced with high voltage if you are not. Also, this device is a major FIRE hazard. Use it only outdoors. To sum it all up, this project is risky, be careful.
Step 1: My Understanding of the Inner Workings of a Spark Gap Tesla Coil
From what makes sense to me, the Tesla coil is a magnetic resonator, otherwise just a really powerful transformer. Wall outlet current is converted to 15000 V by the NST, which then charges capacitors, which (once fully charged) allow electricity to temporarily "jump" the spark gap, which allows current to temporarily flow through the primary coil, generating a magnetic field, which the secondary picks up, and converts it back to a current (of higher voltage), which then flows into the ground and into the air (What a sentence!). This process happens 120 times per second or something like that. The Tesla Coil not only steps up voltage but also frequency, which makes the pretty streamers of death that obviously fascinate you (that's why you are here). Due to this high frequency, your nerves would not feel pain from the streamers conducting into your body, but they still cause damage! Basically, your insides would cook and you wouldn't feel a thing, but that is not going to happen because you are not to touch the streamers! Don't do it! Oh yeah, the diagram is from Wikipedia, thanks to another instructable to pointing out to me which one to use. Use the bottom diagram. The top one didn't even work when I tried it, and the bottom one makes more sense.
For the High Voltage transformer, I used a 15kV NST.
For the spark gap, I used two bolts in opposite sides of PVC pipe at a set distance.
For the HV capacitor, I used salt water "Leyden jar" capacitors made of Snapple bottles.
For the Primary, I used .25" diameter copper tube.
For the secondary, I used 24AWG magnet wire wrapped around 1.5" PVC.
For the Torus, I used Aluminum Dryer Duct that I cut open and wrapped around two aluminum pie pans.