your best guess

[Astro]

Dual axial.  14in x 1/4 thick a36 steel plates. 24 pole. 24 coil. 14 awg wire. 8 winds wide x 8 winds deep (should be about 1/2in wide and half inch thick on the legs) coils (so somewhere between 50 and 64 winds depending on how it goes). Mags are n52 1 x 1/2 x 1/2. coil center is .39 x 1 x .5

According to the numbers that should be the size coil at .068 diameter 14 awg. Actually 1.584, but from watching others vids on winding about that many winds, their coils look much larger. Could just be the camera??? Then again they were using 2x1 mags.
 So what is your guess on how this little thing performs?

[hiker]

If the coils appear larger They may have wound two in hand or three,using a lighter gauge wire,,

[Astro]

If the coils appear larger They may have wound two in hand or three,using a lighter gauge wire,,

 Yeah money got a little tight around here and I decided to build a smaller version then I wanted to.When I set out to do this, I had the "no smaller then #12" for the coils, as the smallest I wanted to have the coils. I did not want to mess with anything smaller amperage wise. But then I looked at the bright side, and figured if I build for a larger one in the build out of all this, the next mill will seem cheap compared to the overall cost of everything.

[kitestrings]

Sorry, I may have missed something... is it a 24-pole, or 12 pairs of magnets, 12 pole?  The most common configuration with 3-phase is a 4:3 ratio, so if it where 12-pole you'd have 9 coils; if it were 24-pole you'd have 18 coils.  There are of course other configurations, but I'm just trying to follow.

In any configuration, you might consider winding a single test coil and spinning it up to make sure you have the right number of turns for the voltage you're aiming for.  ~ks

[Astro]

Sorry, I may have missed something... is it a 24-pole, or 12 pairs of magnets, 12 pole?  The most common configuration with 3-phase is a 4:3 ratio, so if it where 12-pole you'd have 9 coils; if it were 24-pole you'd have 18 coils.  There are of course other configurations, but I'm just trying to follow.

In any configuration, you might consider winding a single test coil and spinning it up to make sure you have the right number of turns for the voltage you're aiming for.  ~ks

 I was thinking 8 coils per phase for 24 coils and 24 magnets per disc. Sorry I did not word it correctly.
But you are right it comes out to 18 coils , 24 mags if I want a 4:3 ratio. I was thinking about that first and figured I would just make it easy on myself and go 24 - 24.

[Astro]

Never mind. New plan.

[MagnetJuice]

OK, new plan. I can't wait to hear it! 

In answer to your original question,

"So what is your guess on how this little thing performs?"

I calculated the output of that alternator as follows:

2 magnet rotors with 24 of those small magnets each and 18 coils will give you 24 volts DC at 150 RPM.

If you double the RPM to 300, you will get 50 volts DC.

Regardless of the speed that you turn it, the power available from those 48 magnets is limited to about 600 watts. I don’t know if you have a particular reason to use 14 Ga. wire. A 17 Ga. wire would be adequate to handle the current of that alternator.

I you would use larger magnets with the same size or smaller steel plate; you could get 1200 watts or more.
The cost of 2 x 1 x .5 Neos is still reasonable in the US. Less than $10 each.

Furthermore, if you use the larger magnets, you only need 24 instead of 48.

I could be wrong but I think that you want to build a small alternator for the VAWT that you have in mind to build. Right? 

Ed

[Astro]

OK, new plan. I can't wait to hear it! 

In answer to your original question,

"So what is your guess on how this little thing performs?"

I calculated the output of that alternator as follows:

2 magnet rotors with 24 of those small magnets each and 18 coils will give you 24 volts DC at 150 RPM.

If you double the RPM to 300, you will get 50 volts DC.

Regardless of the speed that you turn it, the power available from those 48 magnets is limited to about 600 watts. I don’t know if you have a particular reason to use 14 Ga. wire. A 17 Ga. wire would be adequate to handle the current of that alternator.

I you would use larger magnets with the same size or smaller steel plate; you could get 1200 watts or more.
The cost of 2 x 1 x .5 Neos is still reasonable in the US. Less than $10 each.

Furthermore, if you use the larger magnets, you only need 24 instead of 48.

I could be wrong but I think that you want to build a small alternator for the VAWT that you have in mind to build. Right? 

Ed

 Well, thanks. I just pulled the #14 from thin air if you want the truth. I wanted to build a big one, but the cost is to much right now. Plus I plan to try a few things on it and figured a scaled down version might be a good idea first. But I really wanted to build one with #12 or two in hand. I wanted to put out 20 amps or so minimum (that is why the #14). I have the smaller mags already. Since getting them I have changed the plan a couple times. LOL. I was shooting for the upper 100's in wattage and hoping for around 750-900. However if those mags are going to top out at 600 watts, I do not have a problem winding out of smaller wire and saving the #14 for a for a different mill.   If you are telling me that those size mags will max out at 600 watts, there is no sense wasting the larger wire.
All that said, I can live with my first build putting out 600 watts. Not quite at the level I was hoping for, but physics cares more about the real world then it does hope. I can also live with winding with a little smaller wire. (a few more turns will bump my voltage a little and that is very ok with me). So I was in the same ballpark of where I wanted to be and your help is helping me a tremendous amount in refining and trying to get as much out of this build as I can.
I appreciate it.
So now, one more dumb question. I understand the sine waves and the 4:3 relationship, however when I drew out a 24-18 set up today, you come out with 20 degree coil centers and 15 degree mag centers. This to me looks like a lot of cancellation is going to happen. I mean a lot! Am I missing something? I looked at it for awhile today and did not see a way to change polarity or how the series of coils would be wired to not have all that cancellation. So my thought is why do it then? Why not run a 18-18 set up then? Does the frequency difference between 18 and 24 make up for the cancellation, thus making 24 more efficient?
Which is going to bring up other questions. Such as, when does that break down. I mean if a 12-9 set up is good, wouldn't a 24 18 set up be better then? If the frequency is making up for the difference of the cancellation? Why do so many build 12-12 set ups if 12-9 is better? Due to size limitations and such?

Thanks.
 

[MagnetJuice]

I think that some images could help you to visualize the interaction between magnets and coils and the wiring of the stator.



I think that when it comes to designing an axial flux alternator, one of the rules that most builders follow is to pack as much copper and magnetic flux in the smallest size disc that can deliver your desired power.

If you want 1000 watts and you can get it with a 12 inch magnet rotor, it makes no sense to build a magnet rotor 16 inches in diameter.

Like we said before, don’t be afraid to ask questions.

(I forgot to add in the previous post that I used 60 turns per coil for the calculations)

Ed

[Astro]

That is how I had it drawn. You re right, I drew it to help me see it better. Looking at your pic the first thing this morning I am now seeing that it will be a positive and a neg over each leg of the same coil. Which makes more sense. My drawing was just center lines all the same color and was much harder to visualize.
As for keeping it as small as possible, I get that. But why if you are going to build a 12 mag, why not go 9 coils? Because the coils would simply be to large to fit on a brake disc? To hard to wind out of large wire or to many in hand?
I understand people copying what they have seen on youtube, but there are some smart people here and I am wondering why they would go with a 12-12 over a 12-9, or a 16-12, if the 4:3 ratio is better. I have only ran some numbers on my current parameters and so I have no idea and am asking.
 I was hoping this little one I am building would be a little smaller but it is what it is. I had originally thought about 12 coils, but thought the voltage would be to low with 60 turns of 14. I could fudge a little and make the coils a little thicker then what the mags are, but I did not think that would be enough anyway, so I decided on 18 coils. Now that you are saying 600 watts on a good day is it's max with these mags, I could drop down to a 16 awg and 100 winds and still be very close to the same dimensions as I had with the #14 at 60 turns. But, even then I do not think I can squeeze enough in to drop it down to 12 coils. It would be very close. I could then get away with a 10in plate.
That make sense? Sorry I am on my first cup of coffee. Basically why do people choose a 12-12 non 4:3 set up? Wouldn't the same 12 coils work better with 16 mags or if you only had 12 mags, go 9 coils?

 
 

[Adriaan Kragten]

In my public report KD 341, I give in chapter 9 two ways how it can be explained that a voltage in generated in a coil. The second way of explanation is most usable for axial flux generators with no iron in the coils. The upper picture of figure 5 out of KD 341 gives the optimum 1-layer winding for a generator with eight poles. The lower picture gives a slightly modified winding for which more copper is possible. Figure 6 gives another slightly modified winding which might be easier to manufacture.

The basic principle is that the angle in between the heart of the left leg of a coil and the heart of the right leg of a coil is taken the same as the angle in between the heart of an armature north and the heart of an armature south pole. For an 8-pole generator, this angle is 45°. For a 1-layer winding you have six coils. If this condition is fulfilled, a north pole is just opposite to the left leg of coil U1 when the south pole is just opposite to the right leg of coil U1. This means that the voltage generated in the left leg is just in phase to the voltage generated in the right leg and this means that the maximum possible voltage is generated in one turn of a coil. If you make a 3-phase winding, you see in the upper picture of figure 5 that the angle in between the right leg of coil U1 and the left leg of coil V1 is 15°, so 1/3 of the armature pole angle.

If you use another pole number for the armature, the ratio in between the given angles of armature and stator must be kept the same. So for a 24-pole armature you have 18 coils. The angle in between the poles is 360 / 24 = 15°. So the angle in between the left leg and the right leg of a coil must be 15° too. The angle in between the right leg of a coil and the left leg of its neighbour becomes 5°.

The winding given in figure 5 and 6 of KD 341 is a so called 1-layer winding. For such a winding, all coils are lying in one plane and there are no crossing coil heads. This is easy for the winding of an axial flux PM-generator when all coils are cast in epoxy or polyester. However, only half of the possible places for coils is used. In the upper picture of figure 5 it can be seen that within each coil there are two position available for other wires of a second layer of six coils with two more coils for each phase. But the coil heads of this second layer will cross the coil heads of the first layer and the the total winding will therefore become thicker. But it is possible to flatten the coil heads at the crossing points. So for a 2-layers winding the double amount of copper can be used and this results in the double voltage for the same number of turns per coil. It also results in almost doubling of the maximum power. If you make a generator yourself, a 2-layers winding is mostly too complicated but commercial companies with enough manufacturing skills use this method to increase the torque density of the generator.

What I have told up to now is valid for a 3-phase winding. For a 1-phase winding, the optimum number of coils is half the number of armature poles but one has to fulfill the same condition that if a north pole is opposite to the left leg of a coil, the south pole is opposite to the right leg of a coil. For an 8-pole armature this means that the angle is 45° in between the two legs of a coil but that it is also 45° in between the right leg of a coil and the left leg of its neighbour. This means that there is only place for four coils.

[Astro]

In my public report KD 341, I give in chapter 9 two ways how it can be explained that a voltage in generated in a coil. The second way of explanation is most usable for axial flux generators with no iron in the coils. The upper picture of figure 5 out of KD 341 gives the optimum 1-layer winding for a generator with eight poles. The lower picture gives a slightly modified winding for which more copper is possible. Figure 6 gives another slightly modified winding which might be easier to manufacture.

The basic principle is that the angle in between the heart of the left leg of a coil and the heart of the right leg of a coil is taken the same as the angle in between the heart of an armature north and the heart of an armature south pole. For an 8-pole generator, this angle is 45°. For a 1-layer winding you have six coils. If this condition is fulfilled, a north pole is just opposite to the left leg of coil U1 when the south pole is just opposite to the right leg of coil U1. This means that the voltage generated in the left leg is just in phase to the voltage generated in the right leg and this means that the maximum possible voltage is generated in one turn of a coil. If you make a 3-phase winding, you see in the upper picture of figure 5 that the angle in between the right leg of coil U1 and the left leg of coil V1 is 15°, so 1/3 of the armature pole angle.

If you use another pole number for the armature, the ratio in between the given angles of armature and stator must be kept the same. So for a 24-pole armature you have 18 coils. The angle in between the poles is 360 / 24 = 15°. So the angle in between the left leg and the right leg of a coil must be 15° too. The angle in between the right leg of a coil and the left leg of its neighbour becomes 5°.

The winding given in figure 5 and 6 of KD 341 is a so called 1-layer winding. For such a winding, all coils are lying in one plane and there are no crossing coil heads. This is easy for the winding of an axial flux PM-generator when all coils are cast in epoxy or polyester. However, only half of the possible places for coils is used. In the upper picture of figure 5 it can be seen that within each coil there are two position available for other wires of a second layer of six coils with two more coils for each phase. But the coil heads of this second layer will cross the coil heads of the first layer and the the total winding will therefore become thicker. But it is possible to flatten the coil heads at the crossing points. So for a 2-layers winding the double amount of copper can be used and this results in the double voltage for the same number of turns per coil. It also results in almost doubling of the maximum power. If you make a generator yourself, a 2-layers winding is mostly too complicated but commercial companies with enough manufacturing skills use this method to increase the torque density of the generator.

What I have told up to now is valid for a 3-phase winding. For a 1-phase winding, the optimum number of coils is half the number of armature poles but one has to fulfill the same condition that if a north pole is opposite to the left leg of a coil, the south pole is opposite to the right leg of a coil. For an 8-pole armature this means that the angle is 45° in between the two legs of a coil but that it is also 45° in between the right leg of a coil and the left leg of its neighbour. This means that there is only place for four coils.

 To me this is pretty clear and the way I look at it is, if someone asks why a 4:3 is better, you simply need to show them a picture of the sine waves and say everything above this line is positive voltage. The more waves above the line the better (frequency). Also if for no other reason then it should help smooth out the 3 waves from peak to peak.
 That is as simple of explanation as I can think of.
 I also really appreciate MagnetJuice giving me some numbers to work with. I do not know all the formulas and have about been mathed out the way it is. Some days I think I have lost my dam mind taking on this project. Then I think, you know what, I will never be this young again and if history is any indicator, grid electricity will never be this cheap again, and that is enough to snap me out of it and continue to push forward. But him helping me has really refined what I am trying to do. I had a guess, a ball park guess and that was it and I was not feeling all that confident that I had an ideal configuration for my end goals. I am feeling much better about it now. Little bummed about the 600 watt max from the mags I have, but also like I said, I never figured it would touch 1,000 watts (about 800 was my guess/goal). Plus it is my experimental rig. One I can try a few ideas on and hopefully not break the bank every time I want to try something. HOWEVER being my experimental rig does not mean it should not work well. Everything has it's job to do, even the cats catch mice and so a mill that does not work well, is not acceptable.

[Adriaan Kragten]

To me this is pretty clear and the way I look at it is, if someone asks why a 4:3 is better, you simply need to show them a picture of the sine waves and say everything above this line is positive voltage. The more waves above the line the better (frequency). Also if for no other reason then it should help smooth out the 3 waves from peak to peak.
 

The ratio 4 : 3 in between the number of armature poles and the number of coils is required to get a 3-phase current. The voltage fluctuation of each of the phases of a 3-phase current is given in figure 3 of report KD 340. The DC voltage which you finally get after rectification is not determined by how much of the voltage curves are above the zero line but by the voltage difference in between the two phases which have the highest and the lowest voltage at a certain moment. So the negative voltage of a certain phase is of equal importance as the positive voltage. This is explained in chapter 3.2.1 of report KD 340 for star rectification. The voltage fluctuation of the rectified voltage is given in figure 9 of KD 340.

[Astro]

 I am talking about frequency and you are talking about amplitude. And yes since we are working with opposite poles and 3 phase, the sine wave is going to be both above and below zero. MagnetJuice had already posted that 600 watts was the most I was ever going to see out of the field lines of the mags I have and posted about. That helped me vastly, as I do not know how to figure that out and am not able to just visualize or know from experience such a thing.
 So I can not change the amplitude much because the magnets being used are established.. Well besides gap space and coil thickness. But since I am building a vawt, which already is slower on the rpm and thus frequency side then what a hawt would be, I would be further hampering a good outcome if I tried to build a 12 mag 12 coil pma for a hawt (like almost every video on youtube is about) compared to building one with a 4:3 ratio.
 To me the vawt and hawt are two totally different animals. A vawt is right off the bat hampered by frequency due to it's limited rpm. Where as a hawt is not hampered nearly as much by rpm (frequency). So in building the two, different things must be a priority. Does a 12-9 give much advantage over a 12-12 set up? IDK but even if the frequency difference is tiny going with a 12-9 set up, a vawt project needs to look for every little advantage it can.
 In the end, I think of a hawt as a 200 amp alternator on a high draw vehicle like a big diesel truck and a vawt like a 100 amp alternator on a smaller car. A hawt might make 3000 wattts in a x amount of time and then not have the wind to produce much for a day or two and a vawt might take twice as long to make the same watts, but hopefully should just sit there and almost always be chugging away.
 So the priorities for each are different when thinking about the design of each.

[Adriaan Kragten]

I am talking about frequency and you are talking about amplitude. And yes since we are working with opposite poles and 3 phase, the sine wave is going to be both above and below zero. MagnetJuice had already posted that 600 watts was the most I was ever going to see out of the field lines of the mags I have and posted about. That helped me vastly, as I do not know how to figure that out and am not able to just visualize or know from experience such a thing.
 So I can not change the amplitude much because the magnets being used are established.. Well besides gap space and coil thickness. But since I am building a vawt, which already is slower on the rpm and thus frequency side then what a hawt would be, I would be further hampering a good outcome if I tried to build a 12 mag 12 coil pma for a hawt (like almost every video on youtube is about) compared to building one with a 4:3 ratio.
 To me the vawt and hawt are two totally different animals. A vawt is right off the bat hampered by frequency due to it's limited rpm. Where as a hawt is not hampered nearly as much by rpm (frequency). So in building the two, different things must be a priority. Does a 12-9 give much advantage over a 12-12 set up? IDK but even if the frequency difference is tiny going with a 12-9 set up, a vawt project needs to look for every little advantage it can.
 In the end, I think of a hawt as a 200 amp alternator on a high draw vehicle like a big diesel truck and a vawt like a 100 amp alternator on a smaller car. A hawt might make 3000 wattts in a x amount of time and then not have the wind to produce much for a day or two and a vawt might take twice as long to make the same watts, but hopefully should just sit there and almost always be chugging away.
 So the priorities for each are different when thinking about the design of each.

I am talking about the (open) voltage. Both open voltage and frequency increase linear with the rotational speed. The loaded voltage depends on the load. A PM-generator doesn't have a maximum electrical power but it has a certain maximum torque. A PM-generator only has a certain maximum power for a certain rotational speed and a certain ratio in between the open voltage and the loaded voltage. The higher the rotational speed for a certain ratio, the higher the maximum power. Extensive measurements for different loads and different rotational speeds are given in my report KD 78 for a PM-generator made from an asynchronous motor.

As I have explained earlier the ratio 4 : 3 in between the armature poles and the number of coils is required for a 3-phase current and a 1 layer winding. For a 1-phase current of an axial flux generator with no iron in the coils you need a ratio 2 : 1 and not 1 : 1. So for a 12-pole armature and a 1-phase winding you need six coils. The angle in between the left leg and the right leg of a coil must be the same as the armature pole angle.

So for a 3-phase, 1-layer winding you have a factor 1.5 more coils than for a 1-phase, 1-layer winding and the amount of power which you can get out of a 3-phase winding at a certain rotational speed is therefore also about a factor 1.5 larger than for a 1-phase, 1-layer winding. The real ratio is somewhat smaller than 1.5 because one phase of a 3-phase winding is used only during 2/3 of the time. About 7 % of the power isn't generated during the 1/3 of the time when it isn't used. So the real factor is about 0.93 * 1.5 = 1.4.

Only for PM-generators with iron in the coils it is useful to take a ratio 1 : 1 because the magnetic flux is concentrated through the iron. However is this is done, such a generator will have a very strong peak in the clogging torque. To solve this problem one sometimes uses a ratio 10 : 9 (like for 3-phase hover board motors) but this makes that the voltages generated in different coils of the same phase are not exactly in phase to each other and it requires a totally different way of how the coils have to be connected to each other.

[Astro]

Maybe I am just to redneck and or not educated enough so that communication is a problem. I have many many times had problems expressing myself in my life, so maybe it is that. But I am going to sum up this thread as fast and as simple as I can.
I want to build a 24 coil machine. I ran numbers until I was tired of running numbers. I figured I was in the ballpark, but there were some details left to figure out.
I was wanting to cut corners and just go with a 24-24 set up, just like a 12-12 set up, except double, because I already have the mags for that. However Kitestrings pointed out in his questioning that a 24 coil rig would be better suited being built with the 4:3 ratio. Then MagnetJuice pointed out that the flux created from the size magnets I am using would not produce more then 600 watts and that I might want to think about #16 wire instead of #14.
 Now I ask, does everyone know why a coal fired steam turbine has less poles then a nuclear fired steam turbine? And a nuclear turbine has less poles then a hydro?
If you do, then you understand my thinking on a vawt build.
 My magnets are bought (well mostly now that I am going to go to 32 instead of 24). So that part of the build is what it is. I can not make them produce more then physically possible. My amplitude is going to be whatever it is and all I can do is try to keep my gap as small as possible.
So through those two guys and already knowing why a coal fired has less poles then a nuclear fired turbine we arrive at...........
Same set up as I first posted about, but instead of 24 mags, it will now be a 4:3 and have 32.
A 32-24.
This should allow me to use the #14 which I already have also.
Basically the plan is still the plan, but instead of trying to cut corners and get away with 24 mags, I am going to have to buy a few more. Because in the end I can only do so much to get the frequency up, and since a vawt is rpm limited, I only see one other option.......
Plan:
1 x 1/2 x 1/2 n52's
dual axial
32 pole 24 coil
coils wound 8 wide and 8 thick out of #14
steel plates 1/4 in min and maybe 5/16. ( I thought I ran the numbers and it would fit on a 14in plate, I will verify at some point before I get to that point)
(I am using #14 because the current draw will hopefully be more constant and not up and down so much,(see my post above about it hopefully just chugging along) so even if the wire is slightly over sized, it should help it from heating up). (I think it should put me about where I want to be voltage wise also, so it fits and it puts me in the right voltage area I want to be)
I want to thank Kitestrings for pointing out that cutting corners is not going to give me the results that I wanted. I want to thank Magnet juice for doing some math and telling me that the mags are only capable of producing so many watts and giving me a reasonable expectation. And Thanks Adriaan for taking an interest in the project and always trying to make sure everyone is as informed as they can be.
 This is why I said in another post, that it takes everyone. That no question or idea is dumb, it is just another opportunity to look at things a different way and that is always a good idea! I even went back and thought about a 24-18 set up from the conversations in this thread ( then I woud not have to buy more mags). Thought maybe I could shrink it down a bit. But I came up with the same results or lack there of as I did when I originally thought of going with 18 coils and it just does not put me where I feel as though I am getting everything out of the gen as I could. So I went back to the 24 coils. If I had gone with smaller or thinner mags, then yes I would shrink it down. But I would do so knowing that instead of shooting for 700-800 watts ( magnet juice says 600 on a 24-18 build) that I would be looking at less watts with smaller mags. My original goal was a 750 watt vawt.
 Now if anyone wants to run the numbers, do so now or forever hold your peace, because I did not run them all the way through, but only far enough to know I was close. This design should make for a nice genny for a vawt.
 What do you all think?

[Adriaan Kragten]

Why do you want a high frequency for a low rotational speed? I have designed several PM-generators with a high pole number but those generators were designed to be coupled directly to the asynchronous motor of a centrifugal pump and those motors are designed for a grid frequency of 50 Hz. So for this purpose, you need a high pole number for a direct drive generator if you want a frequency of 50 Hz at a moderate wind speed.

If you use the generated power to charge a battery, you can have a good matching and an acceptable efficiency even for a 4-pole PM-generator. If you use the windmill for grid connection, the 3-phase AC-current is rectified and the inverter can make the correct voltage and the correct frequency independent of the incoming frequency. What is important is that you get a good matching in between the windmill rotor and the generator and matching isn't different for a HAWT or for a VAWT. The only problem with a VAWT is that the Cq-lambda curve has a negative part for low values of lambda and so the generator has to be used as a motor to pass this part of the Cq-lambda curve for which Cq is negative (see lowest curve of figure 4 out of my my report KD 601 for an estimated Cq-lambda curve for a H-Darrieus rotor).

So for correct matching around the optimum tip speed ratio, your generator must have a maximum torque level which is that high that it can load the windmill rotor strong enough even at very high wind speeds. For a radial flux generator, the maximum torque level is proportional to the armature volume if the flux density in the air gap is that strong that the stator iron is close to saturation. For an axial flux generator, the maximum torque level is given by formula 6 out of report KD 341. In this formula, you can see that the maximum torque for a certain flux density Br is proportional to the product of the total magnet area and the radius r in between the heart of the magnets and the shaft axis. The total magnet area is the area of each magnet multiplied by the number of magnets. The magnet quality and the magnet thickness determine the flux density Br which you get in an air gap of a certain thickness. So you can realize a certain maximum torque level for a few large magnets of for many small magnets. The frequency will be higher as you have more magnets but it is the total magnet area and not the frequency which determines the maximum torque level.

[Astro]

Why do you want a high frequency for a low rotational speed? I have designed several PM-generators with a high pole number but those generators were designed to be coupled directly to the asynchronous motor of a centrifugal pump and those motors are designed for a grid frequency of 50 Hz. So for this purpose, you need a high pole number for a direct drive generator if you want a frequency of 50 Hz at a moderate wind speed.

If you use the generated power to charge a battery, you can have a good matching and an acceptable efficiency even for a 4-pole PM-generator. If you use the windmill for grid connection, the 3-phase AC-current is rectified and the inverter can make the correct voltage and the correct frequency independent of the incoming frequency. What is important is that you get a good matching in between the windmill rotor and the generator and matching isn't different for a HAWT or for a VAWT. The only problem with a VAWT is that the Cq-lambda curve has a negative part for low values of lambda and so the generator has to be used as a motor to pass this part of the Cq-lambda curve for which Cq is negative (see lowest curve of figure 4 out of my my report KD 601 for an estimated Cq-lambda curve for a H-Darrieus rotor).

So for correct matching around the optimum tip speed ratio, your generator must have a maximum torque level which is that high that it can load the windmill rotor strong enough even at very high wind speeds. For a radial flux generator, the maximum torque level is proportional to the armature volume if the flux density in the air gap is that strong that the stator iron is close to saturation. For an axial flux generator, the maximum torque level is given by formula 6 out of report KD 341. In this formula, you can see that the maximum torque for a certain flux density Br is proportional to the product of the total magnet area and the radius r in between the heart of the magnets and the shaft axis. The total magnet area is the area of each magnet multiplied by the number of magnets. The magnet quality and the magnet thickness determine the flux density Br which you get in an air gap of a certain thickness. So you can realize a certain maximum torque level for a few large magnets of for many small magnets. The frequency will be higher as you have more magnets but it is the total magnet area and not the frequency which determines the maximum torque level.

 I will ask again, why does a coal fired turbine have less poles then a nuclear one? Why does a nuclear one have less poles then a hydro?
Answer, because a coal fire spins at a higher rpm then a nuclear and a nuclear spins at a higher rpm then a hydro,
 That is what I was trying to explain to you, that when you were thinking amplitude I was thinking frequency.
So while a hawt might have no issues spinning at 300 rpm, a vawt might only spin at 150 rpm. In the end the frequency is going to be about the same, because one is designed to spin at a lower rpm. Remeber, it is all about sine waves above (and thus below) zero.
This is why a conventional hawt build of a genny is not going to work very well on a slower spinning vawt. Why I said that the two are totally different animals and the priorities of each are different.
You already have lower rpm with a vawt and so you have to make up for it with more poles.
 I could build a 400 pole 300 coil genny and have it spin at 1 rpm (IDK just making numbers up to make a point) and still make 60hz. From there as we have discussed, amplitude is a matter of flux inductance (mag size) and space (gap space). With voltage being determined by how many winds within our coils.
 In the end we are building something that works off of wind. Now all I can do is let God control the wind and I will do what I can do to make something work with what he is giving. I am not going to try and control the wind, that is futile. But I can do my best to make something that compliments  it and works with it.

 As for what I did not address in your post....... stay tuned, I have some ideas. Right now I am just trying to get everything together and sorted to build what I figure to be an efficient generator. What to do with it after that is the fun part. (for me anyway)

[Adriaan Kragten]

Why do you want a high frequency for a low rotational speed? I have designed several PM-generators with a high pole number but those generators were designed to be coupled directly to the asynchronous motor of a centrifugal pump and those motors are designed for a grid frequency of 50 Hz. So for this purpose, you need a high pole number for a direct drive generator if you want a frequency of 50 Hz at a moderate wind speed.

If you use the generated power to charge a battery, you can have a good matching and an acceptable efficiency even for a 4-pole PM-generator. If you use the windmill for grid connection, the 3-phase AC-current is rectified and the inverter can make the correct voltage and the correct frequency independent of the incoming frequency. What is important is that you get a good matching in between the windmill rotor and the generator and matching isn't different for a HAWT or for a VAWT. The only problem with a VAWT is that the Cq-lambda curve has a negative part for low values of lambda and so the generator has to be used as a motor to pass this part of the Cq-lambda curve for which Cq is negative (see lowest curve of figure 4 out of my my report KD 601 for an estimated Cq-lambda curve for a H-Darrieus rotor).

So for correct matching around the optimum tip speed ratio, your generator must have a maximum torque level which is that high that it can load the windmill rotor strong enough even at very high wind speeds. For a radial flux generator, the maximum torque level is proportional to the armature volume if the flux density in the air gap is that strong that the stator iron is close to saturation. For an axial flux generator, the maximum torque level is given by formula 6 out of report KD 341. In this formula, you can see that the maximum torque for a certain flux density Br is proportional to the product of the total magnet area and the radius r in between the heart of the magnets and the shaft axis. The total magnet area is the area of each magnet multiplied by the number of magnets. The magnet quality and the magnet thickness determine the flux density Br which you get in an air gap of a certain thickness. So you can realize a certain maximum torque level for a few large magnets of for many small magnets. The frequency will be higher as you have more magnets but it is the total magnet area and not the frequency which determines the maximum torque level.

 I will ask again, why does a coal fired turbine have less poles then a nuclear one? Why does a nuclear one have less poles then a hydro?
Answer, because a coal fire spins at a higher rpm then a nuclear and a nuclear spins at a higher rpm then a hydro,
 

The generators of these power plans are directly connected to the grid. As the grid must have a certain fixed frequency, the generator must have a certain pole number for a certain rotational speed. The lower the rotational speed, the more poles you need for a certain frequency. But the generator of modern wind turbines is not connected directly to the grid and therefore the frequency isn't important. Only the first Danish wind turbines were directly grid connected because one used an asynchronous motor as asynchronous generator. The gear ratio of the gear box and the pole number of the generator was chosen such that the frequency is 50 Hz at a wind speed of about 7 m/s when the rotor is running at the design tip speed ratio. This system had as main disadvantage that at low wind speeds the rotor is running too fast and that at high wind speeds it is running too slow resulting in a rather low average Cp. So this system is no longer used for big modern wind turbines. However, I have described the functioning of this system for the VIRYA-6.5 windmill in public report KD 578 for two different gear ratios.

If a small wind turbine is used for battery charging, the 3-phase alternating current is rectified and so the frequency isn't important. If a modern big wind turbine is used for grid connection, the 3-phase alternating current is also rectified so the frequency is also not important. A 3-phase inverter is used to transform the DC-current into a 3-phase alternating current of the correct voltage and frequency.

So still it isn't clear to me why you focus that much on the frequency for your wind turbine. It might be that you think of direct grid connection. But direct grid connection was never done with a PM-generator and only with an asynchronous generator. Direct grid connection with a PM-generator makes that the generator runs at a fixed rotational speed and you will get extreme high torque peaks if the generator is connected to the grid. Even if the frequency is exactly correct during coupling, the generated voltages can be just out of phase with the grid voltages and this will give a very high peak torque during coupling.

[Astro]

Why do you want a high frequency for a low rotational speed? I have designed several PM-generators with a high pole number but those generators were designed to be coupled directly to the asynchronous motor of a centrifugal pump and those motors are designed for a grid frequency of 50 Hz. So for this purpose, you need a high pole number for a direct drive generator if you want a frequency of 50 Hz at a moderate wind speed.

If you use the generated power to charge a battery, you can have a good matching and an acceptable efficiency even for a 4-pole PM-generator. If you use the windmill for grid connection, the 3-phase AC-current is rectified and the inverter can make the correct voltage and the correct frequency independent of the incoming frequency. What is important is that you get a good matching in between the windmill rotor and the generator and matching isn't different for a HAWT or for a VAWT. The only problem with a VAWT is that the Cq-lambda curve has a negative part for low values of lambda and so the generator has to be used as a motor to pass this part of the Cq-lambda curve for which Cq is negative (see lowest curve of figure 4 out of my my report KD 601 for an estimated Cq-lambda curve for a H-Darrieus rotor).

So for correct matching around the optimum tip speed ratio, your generator must have a maximum torque level which is that high that it can load the windmill rotor strong enough even at very high wind speeds. For a radial flux generator, the maximum torque level is proportional to the armature volume if the flux density in the air gap is that strong that the stator iron is close to saturation. For an axial flux generator, the maximum torque level is given by formula 6 out of report KD 341. In this formula, you can see that the maximum torque for a certain flux density Br is proportional to the product of the total magnet area and the radius r in between the heart of the magnets and the shaft axis. The total magnet area is the area of each magnet multiplied by the number of magnets. The magnet quality and the magnet thickness determine the flux density Br which you get in an air gap of a certain thickness. So you can realize a certain maximum torque level for a few large magnets of for many small magnets. The frequency will be higher as you have more magnets but it is the total magnet area and not the frequency which determines the maximum torque level.

 I will ask again, why does a coal fired turbine have less poles then a nuclear one? Why does a nuclear one have less poles then a hydro?
Answer, because a coal fire spins at a higher rpm then a nuclear and a nuclear spins at a higher rpm then a hydro,
 

The generators of these power plans are directly connected to the grid. As the grid must have a certain fixed frequency, the generator must have a certain pole number for a certain rotational speed. But the generator of modern wind turbines is not connected directly to the grid and therefore the frequency isn't important. Only the first Danish wind turbines were directly grid connected because one used an asynchronous motor as asynchronous generator. The gear ratio of the gear box and the pole number of the generator was chosen such that the frequency is 50 Hz at a wind speed of about 7 m/s when the rotor is running at the design tip speed ratio. This system had as main disadvantage that at low wind speeds the rotor is running too fast and that at high wind speeds it is running too slow resulting in a rather low average Cp. So this system is no longer used for big modern wind turbines. However, I have described the functioning of this system for the VIRYA-6.5 windmill in public report KD 578 for two different gear ratios.

If a small wind turbine is used for battery charging, the 3-phase alternating current is rectified and so the frequency isn't important. If a modern big wind turbine is used for grid connection, the 3-phase alternating current is also rectified so the frequency is also not important. A 3-phase inverter is used to transform the DC-current into a 3-phase alternating current of the correct voltage and frequency.

So still it isn't clear to me why you focus that much on the frequency for your wind turbine. It might be that you think of direct grid connection. But direct grid connection was never done with a PM-generator and only with an asynchronous generator. Direct grid connection with a PM-generator makes that the generator runs at a fixed rotational speed and you will get extreme high torque peaks if the generator is connected to the grid. Even if the frequency is exactly correct during coupling, the generated voltages can be just out of phase with the grid voltages and this will give a very high peak torque during coupling.

 One last time. I am correct, trust me.
A hydro unit can have the water gates (pressure) turned up or down to control the rpm and so can steam pressure be adjusted. THE REASON A HYDRO UNIT HAS MORE POLES THEN A COAL FIRED STEAM UNIT IS BECAUSE IT SPINS SLOWER. The water has less energy to spin the unit then the steam. Coal fired steam is at a higher pressure then what nuclear is and so nuclear spins a little slower then coal and thus has more poles. You can adjust the steam pressure and water flow to regulate speed, but you can not make the water pressure of a river equal to the steam pressure. THAT IS WHY HYDRO UNITS HAVE MORE POLES THEN STEAM DRIVEN UNITS.
 Now if you really want something to ponder. My old air compressor and many ones built around the same time have motors WITH MORE POLES THAT SPIN SLOWER, and they last forever. However I know several people that have had newer air compressors that are not very old and the motors are burnt. I see them on the for sale sites all the time. I suspect that is because in the design, the pushed the winding wire size to it's max. obviously if they burnt, but also almost all new motors used on air compressors these days are HIGHER RPM AND LOWER POLE NUMBER MOTORS.
The solution? When you buy a new compressor, change out a pulley right away to lower the rpms and thus the amps. Do what everyone else is doing and buy one and when it burns up, put a slightly bigger motor on it. IDK about elsewhere in the world but the larger home use air compressors here in the USA are junk. Yet my 50 year old one is chugging away. Same with my water piston pump from the 40's?? It was what was used when this house first got indoor plumbing. It was still here and had long not been hooked up or ran, so I took a look at it and it works fine now and did not take much at all. Quality. A word becoming obsolete in a throw away world.

[Astro]

 You see now?
So if our amplitude is only controllable by magnetic inductance (size of the magnet and it's flux). And through space (distance from said flux). Then our only other option to get more sine wave above and thus below zero (and that is the goal here) is in frequency. How do we change frequency? Rpm's or more poles.
I am not saying to make a genny that runs at 300 hz. I am saying that if you are going to build a slower rpm turbine like a vawt your frequency is going to be lower then what the same genny would be on a hawt. The exact same genny would still make the exact same amplitude, but from peak to peak (frequency) would be further apart and thus less sine waves above and below zero.
 The whole reason steam turbines are the standard is because of size. More poles mean larger generator. Larger means more cost and we all know that profit is the name of the game in big corporations. Not to mention maintenance on larger equipment means..... larger equipment and so on. In the wind world as someone said the name of the game is to pack as much into as small of unit as you can. Because for one thing it has to be way up in the air on a pole or tower and lots of weight high up creates it's own set of problems.
 I can not explain it any better than this. Well maybe I could find an analogy for someone who does not understand electricity at all.

[bigrockcandymountain]

I think the question is why do you want a high frequency?  If you are charging batteries, they will charge just fine with a 10 or 20hz frequency rectified to dc.  The frequency just doesn't matter that much if you are rectifying.  My frequency at cut in is 8hz. 

The voltage, which is what i assume you mean by amplitude, is controllable with number of wire turns in the coils, as well as flux density and rpm.  So if you wind with 20awg and do 120 turns you'll get twice the voltage of 16awg at 60 turns.

Here is how i usually see people build a generator. 

Build you magnet rotors with whatever magnets you can afford.

Put a test coil in and spin it up to get a voltage reading.  From this, decide how many turns you need to hit your charging voltage at your desired cut in rpm.

Calculate how big a wire or how many in hand to get the highest amperage rating out of your coils and still fit them in the rotor gap.

Build your coils and then spin up the complete generator to get an exact performance rating. 

Build blades to suit and get it in the air. 

I built a motor conversion, not an axial, so I'm not the expert. 

[Astro]

I think the question is why do you want a high frequency?  If you are charging batteries, they will charge just fine with a 10 or 20hz frequency rectified to dc.  The frequency just doesn't matter that much if you are rectifying.  My frequency at cut in is 8hz. 

The voltage, which is what i assume you mean by amplitude, is controllable with number of wire turns in the coils, as well as flux density and rpm.  So if you wind with 20awg and do 120 turns you'll get twice the voltage of 16awg at 60 turns.

Here is how i usually see people build a generator. 

Build you magnet rotors with whatever magnets you can afford.

Put a test coil in and spin it up to get a voltage reading.  From this, decide how many turns you need to hit your charging voltage at your desired cut in rpm.

Calculate how big a wire or how many in hand to get the highest amperage rating out of your coils and still fit them in the rotor gap.

Build your coils and then spin up the complete generator to get an exact performance rating. 

Build blades to suit and get it in the air. 

I built a motor conversion, not an axial, so I'm not the expert.

 So when you built a motor conversion or when you use a motor without converting it or opening it up and just try spinning it to make power, what do you look for, a high rpm motor or a low rpm motor? Why? Now does a low speed or a high speed motor have more poles? Say you have two motors both are 24v and draw 8 amps, but one is 3000 rpm and one is 500, which one do you choose, the one with less poles and high rpm or the one with more poles and lower rpm?
 The whole thing is to get as much ripple or sine wave above and below zero as you can within a certain amount of time. To get those electrons moving and flowing. Two ways to look at the value of waves above and below zero, one is the amplitude or size of the wave, and the other is more waves in a given time or frequency.
Another way to think about it is,  do you put a wave driven generator out in the ocean and make lots of power when a tidal wave with high amplitude comes along or do you make a little power with the frequency of each passing small wave. Think of those waves of water as moving electrons.
I am trying to build a genny that just chugs along steady. never to high, never to low. Even keel.
 I do not think a vawt is a very good commercial producer, as the size would be prohibitive and if not the size, then you would need to double the amount of them. I think that is why research on them was abandoned, because research money comes from people out to make money and either way you slice it in shear size or more machines needed a vawt simply can not compete price wise with a hawt on a commercial scale. But I am not building a commercial sized machine. I do think it is very suitable for a home use. It is functional yard art.
 
 

[Adriaan Kragten]

All what you tell about the difference in pole numbers for big power plants might be true but it is completely irrelevant for a wind turbine generator if the generated 3-phase AC current is rectified. Only 2-pole generators should be prevented because this results in a complicated winding with many coils around each other if you use the housing of an asynchronous motor. But it is possible to design good PM-generators with pole numbers in between 4 and 36 or even higher. I have good experiences and proven measurements for several 4-pole PM-generators made from asynchronous motors using the standard 230/400 V winding for 24 V or 48 V battery charging. I have also designed several 8-pole axial flux generators with relatively big magnets. But if you have only small magnets available and if you want an axial flux generator with a high torque level, you need a large total magnet area and this results in a high pole number.

A disadvantage of a high frequency is that the current and so the torque is limited because of the reactance of the winding. The reactance is an AC resistance which increases by the frequency. So the maximum power the generator can supply is limited at high frequencies. This can be an advantage, like for a bicycle dynamo it prevents that the lamps are blown if you cycle fast. But generally it is a disadvantage because you want the highest possible torque and power at a certain rotational speed.

There is another aspect which supports a low pole number and I will show this in an example.
Assume that we compare an 8-pole axial flux generator using circular magnets with a diameter of 40 mm and a thickness of 10 mm and a 16-pole axial flux generator using circular magnets with a diameter of 20 mm and a thickness of 10 mm. Both magnets are of the same quality and the air gap is also the same. So the flux density in the air gap is the same. For both generators, the pitch diameter of the magnets is chosen 150 mm which means that the distance in between the sides of the magnets is about half the magnet diameter. The diameter at the outside of the 16-pole magnets is 170 mm and at the outside of the 8-pole generator is 190 mm, so only 20 mm larger. However, the total magnet area of the 8-pole generator is two times larger than for the 16-pole generator and so the maximum torque level is also two times larger. But the maximum outside diameter of the 8-pole generator is only 20 mm larger than that of the 16-pole generator. So this demonstrates that you can better use a few big magnets than many small ones.

[Astro]

All what you tell about the difference in pole numbers for big power plants might be true but it is completely irrelevant for a wind turbine generator if the generated 3-phase AC current is rectified. Only 2-pole generators should be prevented because this results in a complicated winding with many coils around each other if you use the housing of an asynchronous motor.

A disadvantage of a high frequency is that the current and so the torque is limited because of the reactance of the winding. The reactance is an AC resistance which increases by the frequency. So the maximum power the generator can supply is limited at high frequencies. This can be an advantage, like for a bicycle dynamo it prevents that the lamps are blown if you cycle fast. But generally it is a disadvantage because you want the highest possible torque and power at a certain rotational speed.

 First paragraph. AND single phase has less sine waves above and below zero. It is not that it is to complicated, it is that it is not efficient.
 Second paragraph. This is true. I am not talking high frequency. My vawt is going to spin at a slower rpm then most hawts. So the frequency is not going to be what I would call high frequency. Since it is spinning slower it will have the same or slightly more hz then a hawt. Again I am not talking about building a 300 hz machine.

 Lastly the principals of physics of why big power plants turbines are different from high pressure steam to low pressure water (in comparison to the high pressure steam), is very relevant. If not then you are not thinking about it enough. Wind is very much a low pressure medium to try and produce power from.
Again I am not building a high frequency machine, I am trying to find a happy medium that allows it to perform with consistency. Why? Because I have watched those big commercial turbines sit there and turn in 15 mph winds and I have watched them spin at the same speed in 30 mph winds. So to me, makings idk lets just make up a number and say 10 amps almost constantly is going to be better and pay off better then making 20 amps one day and none the next.
 In sports talk, I am not interested in striking out 3 times and then every 4th time hitting a home run. I am interested in hitting a double every time up to bat.
Interesting thing about youtube videos on wind turbines. You ever notice people only want to make videos and show what they are making in watts when the wind is blowing pretty strong? They only want to show what it does on a good day? What about the other 200 plus days a year? What about during the 12 hrs at night when often times the wind is less then during the day? So to me the name of the game is not can I make 2000 watts in 30 mph winds. The name of the game is can I produce 6-800 watts on all those other days and countless hours when the wind is 12 mph or 15, or 10 or 17 or 20 or from the west or from the east or if it switches directions a couple times in a day (and it does do that here).
 Look at a car. You get in and stay the same speed and your mpg goes up, it is running along very efficient compared to if you get in and hit the gas, hit the breaks, hit the gas, hit the breaks. AND I hate to be the bearer of bad news but that same thing in electrical is very hard on electrical items. No different then having voltage spikes taking out your fridg or stove control board. Just because the items we use such as charge controllers, bridge rectifiers and such can handle something or are rated to handle something does not mean they like it or perform with good efficiency when you are essentially hitting the gas, then slamming on the breaks. IDK a lot about electronics but I do know that.
 Do you know what happens in a rectifier when you go from 60v to 20v to 50v to 80v to 10v in a short amount of time??? HEAT. Lots of heat. It does not like that. Especially when you go from a higher voltage to a lower voltage in a short amount of time. Well heat is not a good thing in these discussions. Because usually heat means less then efficient.
 

[Astro]

I have to admit you guys crack me up. I am sitting here thinking, "sure, bring up and talk to them about making a 24-18 turbine and nobody bats an eye, but bring up a 32-24 turbine and they lose their minds".
Sorry I have a strange sense of humor and find some of the weirdest things make me chuckle.

[joestue]

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.

[Astro]

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.

[Astro]

All that said in the first post, I said a coil center of .5 x 1 x .39. It is actually .369. Which I must have known because after checking the wheel I had built it is .371. Which is as close as I could get with a hand drill and a rather bent drill bit that matched the size pins I used.
But for the sake of exact, I mis spoke in the first post and it should be .369 to give the proper angle. That would put about 1 wind  per layer of thickness under cancellation with 14 awg wire at .067 diameter.
 So yeah, I will have to double check a bunch of math. When I draw it all up it will help.

[Astro]

 Having a couple tonight and talking with the wife about life. Then I found this.
https://youtu.be/GN0cMqrHEq0