The first thing is the horizontal vs. vertical axis. The horizontal axis is the one that most people are familiar with: the big-ass propeller on a tall tower:
A vertical axis turbine is a little different, and operates differently:
A few different designs for different theories of operation.
The Vertical Axis Wind Turbine (VAWT) has a couple of advantages: it doesn't matter what direction the wind is coming from, where the horizontal axis one has to be steered into the wind; and the VAWT runs slower and quieter and is more bird-and-bat safe.
The downside of the slower operation is that the generator design has to take into account the slow rotation, and has to either use gearsets to speed up the generator, or have a direct drive generator design that can handle slow rotational speeds.
There's a really big advantage to the VAWT: the HAWT needs to steer into the wind, and the wires to the generator can get wrapped up like a tetherball if they're directly connected. The common solution for this is a slip-ring connector, but that's then a part that can wear out and cause other problems. Another option is to vertically mount the generator and put a 90-degree geartrain in place similar to the differential in an automobile-- but this has its own set of problems including wear and power loss due to the mechanical inefficiencies. There's also a distinct advantage in the VAWT to handle turbulent flow, which is really really common in residential areas.
So I'm pressing into the VAWT design, and I want to do a direct-coupled generator for maximum efficiency.
Now generator design is something of a black art. The best models for this are neodymium permanent magnet rotors with stationary coil stators, and they can generate quite a good bundle of electricity. In a really general sense, the power is generated by moving the coil through the magnetic field; the faster the motion, the more power can be generated. There's a lot more to it than that, but them's the basics. (Technically it's an alternator, but it ain't that big a change.)
It gets a bit more complicated when you start considering that to smooth out the operation, you want the alternator/generator to have multiple phases: the most common is a three-phase design, the reasons for which are way too complex to go into here, but the basic idea is that you have three stator coils that are equally spaced, with some number of magnets rotating around them. The equal spacing of the coils makes the phases of the waveforms equally spaced, and distributes the "cogging" effect equally to keep everything in balance.
The three-coil design is nice in theory, but is really impractical: in order to generate a reasonable amount of power, the magnets have to rotate at a tremendously high speed (like 7200 RPM or higher). To counter this, most alternators have more poles-- sets in multiples of three-- and the general rule is the number of sets divide the rotational speed necessary by that number: for instance, most automotive alternators have 8 sets of stator coils (24 in total), so the optimum speed is around 7200/8, or around 900 RPM to be useful.
The catch is that the topography of the magnets has to align on the boundaries; for example, with the 8-stator set for a car alternator, you can divide the circle into 8 "pie" sectors, and each pie sector has to have the exact same layout of magnets. The reason for this is that each sector gets tied together, and the sectors have to exactly match, or the differences generate significant heat and energy losses.
The tricky part is determining the number of magnets to fit the three coils. The number of magnets can not be equal to the number of coils, or the three phases match. In order to maintain the equal phase offset, there has to be some different number of magnets and coils per sector so that if you divide the sector into thirds, in each third, a different coil is fully engaged.
SO the problem is this: how many magnets fit in the same sector space as the three coils for a three-equidistant-phase generator, and how can that be scaled to an n-phase generator where n is a prime number? (Hint: for a single-phase generator, the number of magnets equals the number of coils.)
I have a workable answer for the first part.
There is a bit of moot in this. The way in which the sector coils are connected together drives the type of power generation (whether it boosts voltage or current), and because the optimized connection topology is different based on the rotational speed (which is related to the wind velocity), I have an idea that would change configuration in real-time as necessary to optimize the efficiency of the generator in whatever wind speed was happening at the time. One way of doing this is to run the leads from each individual coil separately from the generator down the tower and rectify each coil voltage individually, then combine them as needed post-rectification; the downside is that gets to be a whole lot of wire (two per coil, figure at least 90 coils). The second way of doing it involves switching the coils in the generator housing pre-rectification, but that involves some complex zero-crossing detection switches that can handle some high current/voltage loads (the coils are inductive and have a lot of energy in them). I'll probably end up with a kind of hybrid, where sets of coils are connected, but those sets will have wires coming down the tower so there will still be multiple rectifiers and a DC combiner. That reduces the number of wires needed and eliminates the zero-crossing switches at the expense of a tiny bit of efficiency.
Someone should really hire me.