As these devices first appeared around 1891 there is no rocket science involved, but just care and forward planing which hopefully these notes may help you with.
These are the basic points about Tesla coil design that use conventional spark gaps, and that I have picked up and found useful.
There is of course a great deal more than this especially if you move onto the electronic side of coiling, although personally I will leave that to the clever ones.
Whatever path you take the best course of action is to join a newsgroup where you will find people who have years of empirical experience under their belt.

The basic points to consider:

Balance: Everything centres around getting a balance. Any one particular aspect of the design is either affected by something else, or it in turn will affect something else. So before you change one thing, think about what else it will affect.

Software: Programs like those found Here and (my favourite) JavaTC help enormously.

Research: For a complete novice the web is a mine of information. But remember these things can seriously harm you, so bearing that in mind don't take one single website as your guide. Viewing various sources lets you see what advice is correct, what is wrong, and what is just plain dangerous.

Location: Consider where you going to run the coil before you build it, so you can size it accordingly. The bigger the coil (in output power and therefore in physical size) the bigger the space that is required to run it. My 8 inch diameter coil is too big to run indoors, so it has to be in the garden, not the warmest of places in the UK winter, nor in the summer sometimes either.

Transportation: Unless you can roll the coil out into the garden complete, you may have to design it to breakdown and re-assemble easily. Big coils can get surprisingly heavy when the whole thing is assembled! I can only assemble and run the coil if someone does it for me because of health issues, so in my case it had to come apart easily. But making them so they dismantle is an excellent idea for everyone.

Cost: The cost for virtually every component goes up significantly with the size of the coil that you are building. Double the size of the coil and cost might rise threefold or more! So fully plan it out with software and price everything up. I know it is boring but its worth it in the long run.

Components: The HV power source, NST, OBIT, MOT, PIG etc, and the secondary coil diameter size are totally inter-dependant to one another.

Capacitor: The total capacitance value needed is also linked to the HV power source mentioned above. The capacitor size chosen needs to be capable of being recharged within milli seconds, so bigger capacitance values demand higher wattage supplies.
If using an NST avoid having a capacitance value that is in resonance with the transformer's inductance. NST's, unlike other power sources, can be rather fragile and will not handle a high resonant rise in voltage. (Don't confuse resonance here with resonance between the primary and secondary coils of the tesla coil itself.) If though you are using a more robust 'PIG' as your power supply, resonance can be used to your advantage however.
Resonance:The AC equivalent of 'resistance' is reactance. So if the reactance of the inductor matches the reactance of the capacitor, the two will cancel one another out. This is called resonance and with very little resistance left in the circuit, apart from the wires themselves and the internal resistance of the power supply, it will mean the voltages across the capacitor can soar. This in turn will damage the NST and eventually the capacitor itself.

NST: NST's in the UK and Europe have a maximum voltage of 10,000 volts, or 15,000 volts in the USA. As mentioned above, avoid a resonant cap value when using these.

Power: NST's and OBIT's etc can be run in parallel to double the current and thereby also doubling the power. Multiple NST's however cannot be run in series to double the voltage though. Just isolating the cases is not enough, it is more complex than that.

Secondary Diameter: A good guide for low power coils below 500 Watts would be a 2 inch to 3 inch diameter. While 500 to 1000 Watts would be 3 to 4 inches, 1000 to 1500 Watts is 5 to 6 inches, over 1500 Watts and your looking at 8, 10, 12 inches or more!

Aspect ratio: This relates to the diameter versus the height of the winding of the secondary coil. This must be within certain limits which are mainly dependant on the power available. If the height is not enough then you will get too many damaging streamer strikes down to the primary. If it is too high the coil will be inefficient.
The aspect ratio for low to medium power coils (1 kw and less) is around 5:1, otherwise 4 to 4.5:1 seems to be popular. As an example a 5 inch coil at 1200 Watts would have a winding that is 20 inches tall. As the former (on which the coil is wound) will need around 2 inches left unused at each end, the whole thing will end up ~24 inches.
These figures are open to some variation.

Secondary Turns: Generally nowadays people aim for around 1200 / 1400 turns or even up to 1600 turns for smaller power coils. In the past the 'golden' figure people aimed for was 900 to 1000 turns, and even today there is more debate over this aspect than any other topic in tesla coiling.
It's important to remember though that these are not like conventional transformers where the number of turns affects the output voltage.
However it is not only the number of turns that are important but also the diameter of the winding wire your using. This is because there is another factor you may need to consider as well, and that is the windings inductance value. Fortunately it normally works out right by itself as explained below.

Coupling Coefficient: The number of cycles needed to exchange energy between the primary and secondary depends on the physical proximity or coupling coefficient(k) between the two windings. A low coupling means not only more cycles, and consequently more losses in the spark gap, but also the tuning can become more difficult. A too high a coupling however will give the problem of racing sparks** and especially if the spark gap is a static, it will have a harder task in quenching. Getting it right is by trial and error.
Normally the bottom of the ACTUAL secondary winding (not the coil former) would be within half an inch or so of the horizontal plane of the primary.

**Racing sparks are where the secondary coil has surface sparks rushing up and down its surface.






The best component to get first is always the HV power source (NST, OBIT, MOT, PIG) so you will then know the power that you have available to plan your design with. The HV power figure is very important because it not only dictates the diameter of the coil that you can build, but it may affect the amount of capacitance used in the primary circuit.

Once you know the power you will know the diameter you're using and you can decide on a suitable aspect ratio, which in turn allows you to work out the coils height. Next having decided on the number of turns needed (see above) you grab your calculator. By trying different gauges of wire, try to find a combination that gives you all the requirements your looking for (number of turns, within the height and diameter constraints that the aspect ratio allows).
You will normally find that the inductance value of your secondary design will work out satisfactory and you need not concern yourself with it at this stage. (JAVATC estimates this value if you really need to know)

Once you know all your secondary specifications you can next decide on a size for your 'top load' or Toroid. Its minor diameter will normally be similar to the secondary diameter, while the toroid's major diameter will be a bit less than the height of the secondary winding. All this then allows you to work out the resonant frequency of the secondary.
A very good guide explaining the whole design procedure can be found at the Deep Fried Neon website. Using the site above or using free design software like JAVATC is undoubtedly the best way of seeing how one component affects another.

As already mentioned, knowing the HV power source specifications (voltages and current) allows you to choose a suitable primary capacitance value. Small coils will use 10 to 20 nano farad (nF) up to very large 10-15KW coils needing up to 150nF. A bigger cap means more energy discharged into the secondary, but you MUST have sufficient power from your transformer source to fully recharge the cap in the short (milli secs) time period available.

The next stage is to work out the number of primary turns you require. The aim is that the inductance of the primary combined with the value of the capacitor will give you a resonant frequency figure that matches the frequency of the secondary inductance combined with the capacitance value of the Toroid.
It is best to try to aim for around 12 to 14 turns to be available(allows for adjustment) on the primary and aim to have your tap at around 10 turns.

Getting the primary coil's geometry correct so you can tap it at 10 turns (or whatever) is best done using the JavaTC program. The inner diameter coil of the primary wants at least an inch clearance around the secondary coil's diameter. So a 6 inch diameter secondary coil will have a primary with its inner coil at around 8 inches diameter. Most people use 0.25 or 0.375 diameter inch copper tubing.
The spacing between each turn in the coil should be at least the diameter of the tubing used. This stops 'flashover' between turns but also allows room for a clamp onto the tube to make your 'tapping point'.


Provided you follow these guidelines for the primary sizing you should find it gives a reasonable inductance value. Too low an inductance will result in excessive current flowing in the primary circuit and consequently bigger losses occurring in the spark gap. But too high a value will give you weak looking purple sparks that lack power. I explain more about this below.

If you don't balance things correctly, and no one ever does from the start (personal experience), the coil will still run, but the performance will be below that possible from a well designed coil, and it may even damage some of your components.

The Very Basic Tesla Circuit Diagram





Although I have not shown one, you should really include an RFI filter in the incoming power line. In Tesla coil use they are protecting the incoming power, or house mains circuit, from any interference that the coil is sending back.
Normally the filters are labelled 'In' and 'Out' or 'Line' and 'Equipment' or something similar, but when using them in a Tesla situation it is generally considered that you now need to connect them in reverse. In other words the side that was designed to connect to the incoming mains feed, now needs to connect to the coil instead. This is because your protecting the mains from the Tesla interference.

However some people say this is incorrect, see here for a well respected and experienced coiler's views.
Tesla coils nowadays have very little real use in main stream science so any building and research is nearly all done by amateurs. The result is that some issues are ongoing and yet to be resolved. A good example was the size of the capacitor needed. At one time it was always considered desirable to use a value that was resonant with the HV supply. This is now recognised to be bad practice with NST's for the reason mentioned above.
The important thing to remember is try to stay within the now widely accepted, and empirically tested norm to start with.