The higher frequency causing increased losses in the rectifier is about 1 millionth of your resistive losses in the alternator.
Getting that out of the way, I'm reasonably certain that what needs to be investigated is the optimum torque vs losses for a given volume of magnet. i believe i said this in 2010 on this forum.
i'm reasonably certain that the result is going to produce something on the order of fewer, larger magnets, given that the perimeter of the copper coil is what produces your copper losses, but the area of the magnet pole is what produces your voltage.
the problem being for an axial flux machine, you end up with triangles instead of squares, which makes the perimeter to area ratio rather bad. so the research done on the optimum inner diameter to outer diameter of trapezoidal iron cored axial flux machines turns out to be.. about 2/3. inner diameter 1/3rd of outer diameter, for iron cored machines where torque production was designed to be maximized. in the case of wind turbines, since we don't care if the turbine could be 16" diameter made from half inch magnets or 24" diameter made from 1/4" thick magnets, instead you want maximum torque per dollar, not most torque for a given diameter. larger diameter may be cheaper if you can use a thinner disk and thinner magnets, and more of them.
https://www.researchgate.net/publication/282465892_Design_of_an_Axial_Flux_Permanent_Magnet_Synchronous_Machine_Using_Analytical_Method_and_Evolutionary_Optimization
some interesting information in the above paper.
might be interesting to build one according to one of those optimizations.
150mm outer radius, 80mm inner radius, 6 coils 10 poles. magnets 5mm thick.
a reasonably close fit for the magnets is to make trapezodal shapes from 3 magnets:
3inch by 1 inch magnets 1/4" thick
2" by 1" magnets
1.5 by .5" magnets.
as the machine grows larger at some point it is cost effective to jump to 1/2" magnets.
see the attached image for what it looks like.
imo the magnets fill the trapezoidal space (which you only want 80% filled) pretty well.
maybe change the 1.5 by .5" wide magnet for 1.5 x 3/4" and make the coils more round instead of trapezoid.
again the biggest issue is actual cost of the magnets by volume. in theory its proportional to volume but in real life you have to calculate volume discounts on the magnets. might even be cheaper to build a whole lot of machines from individual 1x1 blocks instead of 3x1 and 2x1 blocks, which may not even be available in 1/4" thickness.
I agree.
Early on I asked when does one suppose the 4:3 ratio breaks down and what you said is exactly what I meant.
I read a study last night and I wanted to save it so anyone here could read it. It was beyond me in engineering talk with all the math it showed, but the jest of it was they tested several different pole/coil combos for a dual axial pma. In the end they determined that a 24/18 was optimal. The only part I did not like and that they did not have was more coils. They stopped at 18 coils. I think they did try something like a 26?? mag 18 coil, but they were also testing the 4:3 ratio as well in this study. They also did not do small number of coils like a 12-9.
I hate it when I do that, because I can get to reading and look up and it has been 2 hours and 20 different articles ago and so if I try to go back and find it again, it is almost impossible. I am getting better at saving some of that stuff, but I do not do it very often. Mainly because not much just plain blows my hair back anymore. Much of what you read, when you are really getting deep into a subject is just the same thing over and over in slightly different words.
As for cost of said builds, I really do not care at this stage. I mean I am poor and so it did not matter what I was going to build and put up, and then buy a controller for, then buy some monitoring and testing equipment for, and then by some fun stuff to modify it all with and then buy some batteries, it was going to take me some time to come up with and or gather all the stuff anyway. I mean if I had $50,000 laying around, I would probably throw my hat in the ring with designing a fuel cell and not be trying to design a wind turbine.
I also tend to side on the side that says that if I can build something that is running after I am gone, I left my mark. I have built a ton of stuff and some of it was a constant pain in my arse and just plain did not work as well as I had hoped. I have drawn out (rough draw, waiting on some drafting tools and paper to make a final) what I want to build. IDK why and I can not explain it exactly, but when I ponder it, it just makes sense. Last night, I was again (after reading that study) wondering if I should just go with an 24-18. As I pondered it something (I can not recall what now) came up and once again I decided the correct course of action, given my mag size and my wire size told me that a 32-24 was going to be the way to go.
OH and in that study they were also examining the angle you reference. They to say that triangles would be optimal. Now in no way quote me on this and remember I just woke up, but I think that if you add more poles and more coils, for starters you end up with a larger diameter rotor and stator, but because of that the angle between mag side and coil leg becomes much more conducive to what we are trying to accomplish. Which I had already kind of figured out because I fist drew up my project on a 14in rotor and it will not fit. It will, but the mags are going to be right to the edge of the disc. Which as I have said, we need to give the pole stuck to the plate something to do like align some iron so we can get the pole facing our coil gap something else to do.. But by drawing it out (a 32-24) I realized that my mag angle is only 11.25 degrees from the center of the disc. and my coils are only 15 degrees. If I went with a 24-18 they would be 15 degrees on the mags and 20 on the coils. (22.5 on mags and 30 on coils for a 16-12 set up) Now I have no idea how much that 1.25 difference in angle relation between mag and coil is going to make, from a 32-24 to a 24-18, but it is going to make a difference in efficiency. To much math for me to figure out. As you said though, there is a point where cost and complexity just are not going to be worth it. Again to much math for me to figure out and kind of subjective to boot. Right now, working with the mags I have, the wire I have and figuring out the dimensions, weight, wing/prop size, desired rpm, location (available wind and direction changes, what is available on the market for controls, and so on, I am comfortable with this project I am working on.
BTW I apologize fro many of my posts, and how they sound, I often times get on the computer after waking up and having my first cup of coffee and I have always been one to take awhile to fully wake up. Believe me as much as I do not make sense to the world in the morning, the world does not make sense to me in return.
Oh and as to your first sentence, frequency is dependent on rpm. Yes it is also dependent on poles (but only as it pertains to rpm), but you can have 80 poles and have the same frequency as one with 16 poles, you would just need to spin it slower. I get that some question then the stall of a higher pole machine, which I have some ideas about also, but in the end as always it boils down to catching the correct amount of wind, for the most part. Like I said I have some ideas on this subject as well.
50th edit. lol
I also understand that if we make our coils with centers shaped more in a triangle shape, this to changes the angle of mag edge to coil leg. But when we do this, we all know you can only go so far or you will end up with cancellation between the two legs as the end of the coil towards the center of the rotor are going to be such that the coil center is narrower then the mag. So yes I have considered this factor as well. In the end the closer the angle of both the mag and the coil leg, the better. Like I said a 16-12 design will have a 22.5 and 30 degree mag and coil, which is 7.5 degrees difference. A 24-18 will have a 15 degree and 20 degree, which is 5 degrees difference. More triangle shaped, as we have said is going to cause more cancellation. Everyone thinks that the point of having your coil tapered is to make it fit in a smaller diameter circle and accept a little cancellation loss, but that is only half of it, because as a rectangular magnet spins in a circle, you are going to want the edge of it to align with the coil leg windings as close as it can. So the more taper we add to our coils, it not only cancels from one side of the leg to the other, it further puts more degrees of angle from magnet edge to coil windings. Thus not cutting through the flux lines in an efficient and less than optimal manner.
Again ideally we would be using triangular shaped magnets. But we are constrained there, and if we were not, we would be using them.