An Alternate PM Alternator Design

[finnsawyer]

This led to the simple design shown below:





All coils are wound the same way.  The coils move clockwise as shown over the magnets.  Coil one is over a north pole with maximum flux through it.  Coil two is just about to move over a south pole.  Coil three is nowhere near a magnet.  As the coils move the flux through coil one will decrease causing a negative pulse.  Coil two will also experience a negative pulse as it moves over the south pole.  The voltages across the three coils are shown below.  Note that I've ignored the ramp up and ramp down of the voltages.





The fourth curve shows the voltage waveform when the three coils are connected in series.  It is a single phase series of pulses.   The total resistance will be the sum of the resistances of the coils.  This can then be connected to a full wave bridge rectifier.  However, it is not likely anyone would build this alternator except for demonstration purposes.  Let's step it up to the next level.





We now have six coils spaced every 60 degrees and four magnets spaced every 90 degrees.  So, the coil to magnet ratio is always going to be 3:2 for this type of alternator.  Note the peculiar geometry.  The magnets are wedge shaped with an angle of MA degrees.  Coil two ends at 90 - MA/2 degrees.  So, coil one ends at 30 - MA/2 degrees, since it's 60 degrees behind coil two.  Coil one starts at a negative angle.  We define an angle WA for the angle subtended by the width of the wire.  Then we can write that coil one begins at  -(WA + MA/2).  So, the total width of coil one is then 30 + WA.  The inside dimension of the coils are then given by 30 - WA.  This is the maximum size magnet that can be used given WA.  In reality you would pick the size of the magnet, the width of the wire or number of turns and then size the rotor to fit the angular requirement.  

As mentioned, the three phases would be connected in series to get the output.  If we connect the a and b windings of each phase together first we can do some electronic alchemy.  Say phase two is in the middle.  We can bring out a wire from between a and b of phase two and make it common (ground or G).  This is similar to a center tapped transformer winding.  What does this get us?  We now need only two diodes and we cut the resistance in half.  We do not cut the voltage in half.  The waveforms are shown below.





The peak voltage is now three quarters of what it was before.  It occurs for only one third the time, however.  Still this would probably not a problem, since at cut-in the power in the wind is low anyway.  In fact, as the wind speed increases the peak value of the wavform will increase untill the lower pulses cause conduction.  If we assume we are charging a battery with no change in voltage, the current and hence power into the battery will be limited by the alternator resistance.  The plot below shows a general power curve.  A hypothetical wind power curve is also shown.

Breaks in the power curve always occur near 1.5 and 3 times the battery voltage.  This means that the alternator can follow the wind's power curve somewhat better than a normal alternator design.  Of course, the whole thing is also dependent on the blade assembly's ability to track the wind.

One final thing.  Just as you can rectify to a positive voltage, you can also rectify to a negative voltage.  This means you can also connect a battery to G in a negative fashion.  This allows you to get 12 volts out by using two six volt batteries or 24 volts by using two 12 volt batteries.  The alternator ground floats  on a battery voltage relative to system ground.

[willib]

a quote form Carl Sagan's book " Cosmos "

"There were also Heron of Alexandria, inventor of gear trains and steam engines and the author of Automata, the first book on robots; Apollonius of Perga, the mathematician who demonstrated the forms of the conic sections; Archimedes, the greatest mechanical genius until Leonardo da Vinci; and the astronomer and geographer Ptolemy, who compiled much of what is the pseudoscience of astrology: his Earth-centered universe held sway for 1,500 years, a reminder that intellectual capacity is no guarantee against being dead wrong."

[drdongle]

So in a nut shell..... what would be the advangage to this system?

[Chagrin]

Wouldn't this cog pretty hard?

[finnsawyer]

Cogging only occurs if the coils have iron cores.  There is no need per se to have iron cores.  Even if they had iron cores, one third of the coils will not be over magnets at any one time.  Furthermore one set of coils will be moving off of a magnet as another set moves onto a magnet.  So, one set is pulled in the direction of motion as the other is pulled opposite.  The effects should cancel out.  This may, in fact be a low cogging design.  I hadn't thought of that.  Thanks for the comment.

[finnsawyer]

Possibly low cogging (see the other comment).  There is no limit on the size of the coils.  For instance, a one inch diameter magnet could have a three inch diameter coil around it with a one inch diameter center hole.  Just scale the rotor accordingly.  Because of the upward opening power curve for the center tapped version, which more closely follows the wind power curve, it may be possible to have better low speed performance as well as reasonable higher speed performance.  See Flux's recent comments in that regard.  By using two six volt batteries with the center tapped version instead of one twelve volt battery, one can cut the cut-in speed almost in half.  And of course, you're using fewer magnets, though likely with more copper, which might reduce the overall cost.  I guess this really isn't a 'nutshell' explanation, but then considering the complex issues involved, there probably isn't one.

[finnsawyer]

O.K., I guess you're trying to say that I,m "dead wrong".  Well, instead of pushing out pointless verbiage why don't you come right out and say why it's wrong.  Let's start with Faraday's Law.  I don't mind being told that I'm barking up the wrong tree, but I like people to have the intellectual honesty of saying why.

By the way, it's my understanding that Heron of Alexandria was dead right.  The only problem was that he never thought of connecting his "steam engine" to a gear train.  Of course, that would have messed up an economy based on slave labor, but it sure would have helped in pumping out the mines.  That was the first use of the steam engine, by the way.

[vawtman]

Finsawyer you should just build it and see what happens since you have the plan.Theres always something better out there somewhere.Dont know till you try.

[finnsawyer]

You're right, of course, but current circumstances don't permit me to do so.  That said, I've seen some postings lately where people are looking for alternate generating possibilities.  This might fit the bill for some of them.  I put this out as a diary so people could see the possibility.  What's the point of sitting on this for a year?  And besides, isn't this a community effort, to advance the use of wind power?  I have no doubt the concept will work and if someone wants to try it they are welcome to do so.  In any case it will take many attempts to feel out the size and other requirements to make an alternator that performs at either six or twelve volts at a reasonable rpm.  So, I would hope anyone making one of these would provide their results even if they seem to be a failure.  I realize people would not want to sacrifice their expensive magnets to something that's untried, so I suggest using circular magnets mounted on a disk with a threaded rod mounted to it.  This way the magnets could be used with different size rotors and coils until a usable design is found.  Anyway, I bet some people have four magnets lying around just waiting for a good use.  

[kitno455]

i dont get it. you have just increased the resistance of each coil significantly by making it longer, but you did not increase the portion of the coil that actually gets hit by flux. and, if you space everything out so that it acts like single phase, it will just vibrate like single phase?

dual rotor aint broke?

allan

[finnsawyer]

First off, every coil goes from a state of no flux through it to a maximum flux less leakage just like in any design.  If you scale a particular version up by a factor of two by keeping the same number of windings, you get four times the flux with twice the speed for eight times the voltage.  You also have increased the coil volume by eight for the same number of turns or four if you keep the same length for the coils.  Since you probably do not need an eight times factor increase in voltage you have the option of decreasing the number of turns by using heavier wire (the coil size must still be doubled for this example).  So, you can lower the resistance.  This is much like any design.  Resistance does matter and is part of the design.  It should be obvious that a larger machine can provide more power, which means lower resistance.  It does help that by going to the center tap the effective resistance is cut in half.

What you see here is the first step in an engineering design, a concept.  The next step is to prove it.  It is possible that vibration issues may arise.  But they are mechanical not electrical.  Or actually electromechanical as they involve interactions between the electromagnetic forces and the  mechanical vibrational states of the physical structure.  If you go back and look at the first set of voltage curves, you will notice that the positive voltage spikes, formed from the addition of pairs of coil outputs are 120 degrees apart in time as are the negative spikes.  In other words three phase behavior is embedded in the design.  This is a hybrid between single phase and three phase and it will have its own characteristics.

Since this is my diary I'm going to do a bit of ranting here.  When scanning the net once for wind power I came across a comment concerning the lack of "anything new in wind power".  Back in the 70's when the energy crunch hit everyone was out trying different things.  That spirit seems to be gone.  Now it's become "cookie cutter" wind power design.  I doubt that in twenty years everyone will be doing what you see here.  There still are improvements to be made.  The dual rotor may not be broke, but then neither was the 36 Ford in 1936.  The car you drive today is far different.  Things change.  You can see why I put this in a diary.  I'm not speaking to those who are satisfied with the status quo, but rather those who really want to advance the cause of wind power.  Time will tell whether this design has a role to play in that.  In any case, it's out there for anyone to try.  Just call it the Mattson Alternator, if you will.

I don't want to appear to come down too hard on this site.  There is an undercurrent of innovation here, and the discussions are definitely useful.  The idea for this design came out of Jerry's "Jerry rigging" of the alternator output.  To my mind this is the real power of the Internet.

[kitno455]

sorry dude, i was not trying to get you angry or hi-jack your diary. i was just trying to point out that you made your coils have lots of extra dead wire that is never crossed by the mags, and therefore contributes only resistance to your output?

allan

[elvin1949]

Finsawyer

 This is something that i will do a lot of studying

about.Got me to thinking [rust flying everywhere]

outside the box? yes but that is good.

later

elvin

[SmoggyTurnip]

Finsayer,

I can't seem to figure out

how the coils are connected

together from your explaination

(for the second diagram).

Maybe you could do a drawing

showing how the coils are

connected? I would like to

do some calculations.

[viron]

Finsawyer, I'm a no knowledge person trying to research an optimum easy to build design before I play.  Your alternator looks intersting so I emailed a link to the discussion to my technical partner, he's head of the electrical failure analysis lab at Kennedy Space Center.  He's onboard for the project and has a few other interested people at work.  If it seems reasonably plausible to minds that should know I'll build your alternator.

For a wind mill I've settled on a Savonius design optimized by UC Long Beach.  It is a full blown lift motor with a TSR of 1.6.  The choice is because I live in a class 2 wind zone in Florida.  The design appears to have good torque and decent speed that would be advantageous to gentle coastal breezes.

http://www.energy.ca.gov/2005publications/CEC-500-2005-084/CEC-500-2005-084.PDF

Your theoretical output curve is attractive because it ramps up fairly quickly at the low end and reduced cogging is always a benefit.

I to am flying in the face of popular opinion on windmill design.  Hopefully we can be helpful partners in this crime.

Viron

[finnsawyer]

The coils are assumed all wound the same way with the voltages as shown.  Simply connect the negative side of V1a to the positive side of V1b to form V1.  Do the same for the other two phases.  Then connect the negative side of phase one to the positive side of phase two and the negative side of phase two to the positive side of phase three.  If you wish to bring out the 'center tap' that is taken off from the connection on phase two between V2a and V2b.  The important thing is that when V1a is going negative (as shown) then so is V1b.  Similarly, when V2a is going negative then so is V2b.  When phase three encounters the north pole, as it will do, then both V3a and V3b must both create a positive pulse.  At this point it's basically defining the winding of the coils such that these relationships hold.  In building this it requires checking the voltages when turning the rotor to make sure the relationships hold.  In that sense a diagram would be of no real help since I can not predict how someone will set up his coils.  Note that if it happens that V1a actually goes positive while V2b goes negative then you just exchange the plus and minus signs on V1a.  That is, you redefine the voltage V1a.  These kind of ambiguities are quite common in electronic circuits, but are really of no consequence as long as we are consistent in our definitions.  I hope this helps.  

[finnsawyer]

No offense taken.  I like the give and take.  It tends to expand the mind.  A while back we were speculating here about trading magnets for copper.  Well, this may do that.  Not necessarily a bad thing.  But still, it has to produce enough power at a reasonable cost.  The jury will be out on that for a while.  

When you speak of dead wire I presume you are referring to the wire along the top and bottom of each coil.  I guess I missed that in your comment, although I was aware of the issue.  That wire is there to complete the loop.  Every design has to put up with it.  To minimize its effect you have the magnet be as large as the inside of the coil.  Also make the magnets and coils round.  The alternator should still work in that case, but don't expect nice rectangular pulses.

[finnsawyer]

It'll be interesting to see what your guys say.  If they're really taken with it, maybe I'll patent it!  Ha!  I'm willing to bet someone has tried this design in the past.  It seems too obvious to not have been noticed.  But one never knows.  The super strong magnets are a recent phenomena.

That change in the power curve is interesting.  It's something that has not been seen before, as far as I know.  It should be possible to hit the power curve of the mill at two points instead of one.  Keep in mind that curve was hypothetical.  While the shape is correct so will any curve scaled up or down from it be correct.  The ramp up at the low end depends on the resistance of the alternator.  In general a lower resistance requires a larger alternator.  Probably larger than with the regular design.  Keep in mind that in this design the coils are not spaced tightly, so a larger rotor would be expected.  In other words go into this with your eyes open.  That said I am willing to give any help and insights that I can.

This might be a good place to suggest a plan of attack for a first case design.  Use circular magnets.  Decide on a coil diameter.  This will determine the size rotor you will need.  Pick a number of wire diameters.  Wind coils of the specified size with all the wire sizes (the number of turns will depend on the wire size).  Mount the magnets on the rotor and make stators using the different size coils.  Try the different rotor stator combinations and evaluate each one.  From this data you can predict what size magnets and coils you need to meet your design specifications.  It would also be nice if you presented your results here.  Good luck!

   

[finnsawyer]

Good!

[SmoggyTurnip]

Your curve is showing peak voltage with respect to rpm.

Since the wave form is is pulses the actual rms voltage

is less than the rms value of a sin wave with the

same peak voltage.  The output power for this design

will still go with the square of the RPM so it will

not match the wind power curve any better than the

standard design.

Any magnet passing over any air filled coil at a fixed velocity will produce an RMS voltage in that coil that is directly proportional to the velocity of the magnet,  this does not depend on the shape of the magnet or the shape of the coil or the strength of the magnet field, or resistance of the wire.  That is to say for a given magnet and coil moving the magnet twice as fast will produce an RMS voltage twice the magnitude.  

The maximum power that can be derived from that coil is V^2/(2*R).

These 2 facts taken together imply that any alternator that moves a constant

magnetic field over fixed air filled coils will  have a power curve that is proportional

to the square of RMP, regardless of the arrangement of the coils and magnets.

[kitno455]

as i understand it, having the magnet as large as the inside of the coil will not minimize the effect. the parts being passed over by the magnet are the only parts that generate voltage. in your design, thats the short sides of the coil, while the long sides just contribute resistance.

just my guess, but it looks like you can get the more power from the same mags and less wire, by going with smaller coils.

allan

[finnsawyer]

While it is true that each voltage pulse will have a value proportional to the rpm, they have different values.  One is two thirds the peak voltage, the other one third.  They will cause conduction in turn as the rpm increases.  What the battery sees is an average current that increases at different rates at different rpms, the rates being higher at higher rpms.  What you get is a 'piece wise linear curve'.  The change in power to the battery at high rpms per unit change in rpm is greater at high rpms than say near cut-in.  This curve opens up in the same way the wind speed power curve does.  You can never get a perfect match, but you may be able to match the power curve at two points.

A little elaboration on matching curves may help.  The general curve for a cubic is:  P = AxV^3 + BxV^2 + CxV + D.  In this D = 0, as no voltage no power.  With the three coefficients A,B,and C we can easily match the curve of the power into the battery at three points.  Unfortunately wind power only has the coefficient A.  This severely limits any matching.  We can try to improve the matching by modifying the wind mill's characteristic.  For instance, we can lower the efficiency of the wind mill at high wind speeds by changing the pitch of the blades.  At low wind speeds we might let the mill move toward stall but keep it from stalling.

[finnsawyer]

There are two things that make or break an alternator design.  Firstly, you need to get the proper voltage at the cut-in speed.  This depends on the number of turns (note turns, you can't make an alternator with only radial wires) and the strength of the magnetic flux.  Larger flux, fewer turns.  That applies to this design as well.  Once you have established the number of turns the second requirement is current carrying ability or resistance.  The solution to lower the resistance is to use heavier wire for the same number of turns.  You now made the coil bigger.  This requires a larger rotor.  That will give a lower cut-in rpm.  That is true for this design as well.  So, for a proper combination of magnet size, wire size, number of turns, and rotor size it should be possible to satisfy the design criteria.  The problem of course is that these things are all interrelated.  It will take while to sort them out.  The design currently used was obtained by trial and error.  I suspect the same will hold true for this one.

[SmoggyTurnip]

"While it is true that each voltage pulse will have a value proportional to the rpm, they have different values.  One is two thirds the peak voltage, the other one third.  They will cause conduction in turn as the rpm increases."

Yes, I agree they will each increase at different rates but they will

each be with the square of RPM.

Coil1 = K1*RPM^2

Coil2 = K2*RPM^2

Coil1+coil2 = (K1+K2)*RPM^2 = K*RPM^2

So in the end the power curve is with the

square of the RPM.  This means it can

be reproduced by another dual rotor machine

of standard design.

"A little elaboration on matching curves may help.  The general curve for a cubic is:  P = AxV^3 + BxV^2 + CxV + D.  In this D = 0."

Yes this is true - the power in the wind follows the cube of wind velocity, but B, V, and D are 0.

As far as the power curve of the blades go we really don't

know the formula for it - it could even be a fourth power,

it really depends on the blades, - one thing we can say is that

it is concave down everywhere.

In matching the alternator to the blades the 2 curves that have

to intersect are :

 1) the alternator power verses RPM and

 2) blade power at the shaft verses RPM.

The blade power curve is concave

down everywhere and the alternator

power curve is K*PRM^2. They

can only intersect at 2 places

- one of them being (0,0).

[finnsawyer]

A short response.  Power into the battery is proportional to current.  Current is charge per unit time.  As the rpm goes up you dump more charge per unit time into the battery after each break point.  A regular alternator doesn't do that.  By the way, when a regular alternator is charging a battery the current is equal to the alternator voltage minus the battery voltage divided by the alternator resistance.  Power into the battery is that current times the battery voltage.  It goes up linearly with rpm.  

[SmoggyTurnip]

Sorry finsawyer,  I guess I just don't understand

what you are saying.  I must be missing something

here.  I don't see where these "break points"

are. I am not saying you are wrong - I just don't

get it.

[finnsawyer]

Sometimes it's hard to tell where people are having problems.  Let's try it this way.  When the alternator hits cut-in at let's say 100 rpm, the highest voltage pulse will cause conduction.  I've called this voltage Vp, which varies linearly with rpm.  I'm going to ignore the diode voltage.  So the current that flows from the alternator for the duration of that pulse is:  Ib = (Vp - Vb)/Ra, where Vb is the battery voltage and Ra is the alternator resistance.  I'm also ignoring the battery resistance to keep this simple.  So, the power into the battery is given by VbxIb during the duration of the pulse.  The energy into the battery is given by

Eb = PtxVbxIb = PtxVbx(Vp - Vb)/Ra, where Pt is time duration in seconds of the pulse.  The energy out of the alternator then becomes Ea = PtxVpxIb = PtxVpx(Vp - Vb)/Ra during the pulse.  The percent of energy (or power) going into the battery is given by Eb/Ea = Vb/Vp.  This is the type of behavior you would expect from a regular alternator.  

When the alternator hits 150 rpm the second highest pulse becomes large enough to cause the diodes to conduct.  That speed is the first break point.  So now we have a second pulse causing conduction.  Its value is 2/3 that of Vp.  So, for that pulse we may write Ib2 = (2/3xVp - vb)/Ra.  The energy delivered by that pulse is given by Eb2 = PtxVbx(2/3xVp - Vb)/Ra.  The energy from the alternator during that pulse is Ea2 = PtxVpx(2/3xVp - Vb)Ra.  Since both pulses now contribute, we must add their contributions to get the total energy into the battery, which gives:

   Eb = PtxVbx(5/3xVp - 2Vb)/Ra.  Ea = PtxVpx(5/3 - 2Vb)/Ra.

This applies from 150 rpm to 300 rpm.

Finally, when the alternator's speed hits 300 rpm, the second break point, the third pulse will be large enough to cause the diodes to conduct.  This pulse has an amplitude of 1/3 that of Vp.  We now get a current of Ib3 = (1/3xVp - Vb)/Ra, for an energy value of Eb3 = PtxVbx(1/3xVp - Vb)/Ra.  Ea3 = PtxVpx(1/3xVp - Vb)/Ra.  The other two pulses are also contributing so we need to add this to the contributions from the others. We get: Eb = PtxVbx(2xVp - 3xVb)/Ra.  Ea = PtxVpx(2xVp - 3xVb)/Ra.  You get the average power by adding up the energy contributions from all the pulses per cycle (there are two of each) and dividing by the time in seconds per cycle.  These equations show that the rate at which the alternator puts power into the battery as a function of rpm is increased by 2/3 after the first break point and is twice as great after the second break point as its initial value.  This is the basis for the power curve that I gave.  

[SmoggyTurnip]

OK now I get it.

I'm not sure why I didn't get it before,

probably because I'm not used to thinking

about batteries - strictly heating for me

so far.

It is not easy to analyze, but interesting

to think about.

[viron]

Finsawyer,

Here's my technical partner's, Larry Ludwig's, assessment.  In general he thinks it would be good for producing power at very low wind speeds as it would reduce EMF drag.

Skimmed the discussion and drawings.  The only serious advantage to this is that low wind speeds will still produce pulses (less system EFM drag) which can be rectified so that you can always produce some voltage.  Electronically the voltge can be built to a higher level with a chopper circuit.    This might be useful in a battery based system where trickel charge (high voltage, very low current) helps to maintain the charge. If you were to look at there diagrams and draw lines to the top of each pulse you would get a sine wave which is what overlapping coils whould produce.  In an alternator, these three overlapping coil voltages are rectified to a pure dc.  The three coil set allows for less ripple smoothing to have to ocur so that less loss occurs in the rectification and smoothing circuit.

    If our desire is to always generate some voltage, even at low wind speeds: we could have our PIC keep a low drag PM pulsed alternator engaged at low RPM and a High drag, High voltage generating alternator swithched in ( and the other swithed out) at higher RPMs.  Then we could have retification circuits for each one designed around what were doing with the outputs.  The High RPM could be a direct feed to the system under use, with a small bleed to the batteries.  The low RPM system could only feed/charge the battery.  This is typically the type system I had envisioned for a home power system.  A high voltage battery set with an inverter for producing AC at high output periods and a low current, high voltage electronic circuitry for just charging the batterys during low output periods.   I could talk to Pete about an electriclly actuated clutch system or a mechanicat RPM activated clutch system the we could read electrically to determin system operation parameters/switching.

[finnsawyer]

I disagree that the only advantage is the low speed performance.  The changing power curve also would be an advantage.  Flux, in his recent postings pointed out that with the conventional alternator design one has to give up low wind speed performance to get the best out of system at moderate wind speeds.  For instance, if you size the alternator to give good matching with the turbine at 10 mph, you give up performance at 15 mph where the wind has about three times the power available.  With this design at a little over fifteen mph the alternator power curve increases by 67 percent, so you track the available power better in that region.  Catching that low wind power may actually be quite beneficial as the wind blows more of the time at lower velocities.  So capturing more of that energy while still getting reasonable performance at the higher velocities may actually yield more usable power on average.

I presented this design for the case of charging a battery where pulsed dc doesn't matter.  That is, while this will have more ripple than a three phase system, for charging a battery it doesn't matter.

I don't see any reason why this alternator couldn't be made to produce more power at higher wind speeds by introducing centrifugally operated iron cores for the coils.  At low rpms they are retracted.  At a certain point they are inserted in a controlled manner.  This would be easiest to do if the coil assembly rotated.  With the magnet assembly rotating it would be necessary to mount the centrifugal weights on the back of the rotor and transmit their effect through the shaft by the use of a rod.  The question is how something like this would compare in cost to adding a second alternator?

     

[finnsawyer]

There is a relatively simple way to determine rotor diameter assuming you know your magnet size and coil size.  Assume we want to make a 12 magnet 18 coil version.  The magnets will be spaced every 30 degrees around the rotor and the coils every 20 degrees.  Place the zero degree line at 12 0'clock on a sheet of paper or piece of cardboard.  A coil will be centered directly over a magnet on this line.  The next coil will be at 20 degrees and the next magnet at 30 degrees.  Draw radial lines at these two angles.  Place a coil or cut out of a coil centered along the 20 degree line and a magnet or cut out of it centered along the thirty degree line.  Move them radially along the lines.  When the coil just touches the magnet with both the same distance from the center you will have determined the proper size of the rotor.  If the rotor size would be too large go to a smaller coil.  Note that I assume the center hole of the coil is the same size as the magnet.  

[Lumberjack]

now that I have digested most of this:

 We now have six coils spaced every 60 degrees and four magnets spaced every 90 degrees.  So, the coil to magnet ratio is always going to be 3:2 for this type of alternator.  Note the peculiar geometry.  The magnets are wedge shaped with an angle of MA degrees.  Coil two ends at 90 - MA/2 degrees.  So, coil one ends at 30 - MA/2 degrees, since it's 60 degrees behind coil two.  Coil one starts at a negative angle.  We define an angle WA for the angle subtended by the width of the wire.  Then we can write that coil one begins at  -(WA + MA/2).  So, the total width of coil one is then 30 + WA.  The inside dimension of the coils are then given by 30 - WA.  This is the maximum size magnet that can be used given WA.  In reality you would pick the size of the magnet, the width of the wire or number of turns and then size the rotor to fit the angular requirement.  

I am not sure what you really meant to say here. Perhaps you could clarify this for us?

As mentioned, the three phases would be connected in series to get the output.  If we connect the a and b windings of each phase together first we can do some electronic alchemy.  Say phase two is in the middle.  We can bring out a wire from between a and b of phase two and make it common (ground or G).  This is similar to a center tapped transformer winding.  What does this get us?  We now need only two diodes and we cut the resistance in half.  We do not cut the voltage in half.  The waveforms are shown below.

 

If I understand you correctly you want the coils wired like this:

- D -1a-1b-2a - G -2b-3a-3b- D -

D= diode , G = ground

Problem, a single normal diode only conducts in one direction so you will only get positive or negative voltage out, the reverse voltage is blocked and the output is zero.

Ignoring the diode problem, this is just a normal multi-coil single phase generator with an odd center tap. The normal output with a full wave bridge would be 6 (4x) pulses. If the system voltage is (1x) then 4 of the pulses are wasted because they would be under system voltage. As an average, only (2x) of usable voltage is generated per pulse. In the normal non tapped the average value would be (3x) per pulse. As your system voltage rises the situation worsens. At (2x) you would only get 2 usable pulses of (1x). There has to be a clearer way to say this but I have had to much coffee.....

You stated elsewhere that you wanted a winding that could be used for 6 or 12 volts. The simple solution is to wind each coil 2 in hand. For 6 volts run them in parallel and for a 12 volt application wire them in series. If you wound 4 in hand the stator could be wired for 6,12 or 48 volts.

I have noticed you tend to use peak voltage when you really mean RMS voltage. Peak voltage is semi-constant whenever the coil reaches saturation while RMS voltage varies with the speed due to frequency and pulse width changes.

The term ground tends to imply a connection to earth or chassis and 0 volts. Neutral implies no connection to a chassis or earth and the voltage is not always zero.

             

[finnsawyer]

You need not shout. "" will do.  I've probably discussed all of this here or there.  What I usually do in comparing this with the standard three phase arrangement is to assume one inch diameter magnets and two inch diameter coils with twelve magnets (the three phase is restricted to numbers of magnets divisible by four, this design can use any even number of magnets).  The magnets alternate poles and are spaced every 30 degrees.  The 18 coils are spaced every 20 degrees.  The coils are arranged in three groups of six.  When the coils of group one are centered exactly over the magnets having north poles, the coils of group two (and three also) will just be touching magnets having south poles.  This determines the geometry as well as the size of the rotor and the stator.  I'm going to rotate the coils here instead of the magnets, as I think it's easier to see the action, although the result would be the same.  As the coils rotate (in either direction), the coils of group one are moving off of a north pole creating a negative pulse (arbitrary choice).  At the same time the next group of coils advancing in the direction of rotation (call it group B) is moving unto a negative pole, also producing a negative pulse.  The last group (C) is moving between magnets producing no voltage.  Carrying on, group B now moves off of a south pole producing a positive pulse, while group C is moving on to a north pole producing a positive pulse.  Group one, (or A if you wish) is now between magnets producing no voltage.  At this point we have produced one complete cycle of the output waveform in moving one eighteen of a revolution.  So, we get eighteen cycles per revolution.

I'm not going to discuss the center tapped version at this time.  It has different characteristics, which may be useful, but I think you should completely understand the basic design first.

The output of this alternator will be single phase, as all the coils are connected in series.  As far as winding the coils is concerned, for this exercise the total amount of copper per coil remains constant.  If you wind the coils with the same wire as used in the three phase but two in hand, you will end up with the voltage (of my design) cut in half and the resistance reduced by a factor of four (which results in 3/4 of the resistance of the three phase, for instance).  Both voltage and resistance are important.

"I have noticed you tend to use peak voltage when you really mean RMS voltage. Peak voltage is semi-constant whenever the coil reaches saturation while RMS voltage varies with the speed due to frequency and pulse width changes."

I don't mean RMS or Root Mean Square voltage.  It is not a very good measure for an alternator who's output is not a pure sine wave.  Your RMS meters will give an erroneous reading.  What you are missing is that for a given alternator the ratio of the peak voltage to the "average voltage" stays constant with RPM.  When charging a battery peak voltage not average voltage gets you there first.  I explained that in the other thread.  Coils never reach "saturation".  They can't.  They do not contain any iron.  Nor are the speeds reached by these alternators high enough for hysteresis or inductive effects to become important.  Keep in mind that the iron parts are not in saturation to begin with.

"The term ground tends to imply a connection to earth or chassis and 0 volts. Neutral implies no connection to a chassis or earth and the voltage is not always zero."

Ah, semantics, semantics.  The neutral of the 220 volt supply to my house is definitely connected to ground (Earth).  On the other hand the center tap of a transformer could be connected to the Datum Node (ever hear of that) or ground of a particular circuit, which you could connect any way you see fit.  Many tools today are not grounded.  The alternators we are discussing here are by their nature floating and can be "grounded" in any way you see fit.  Many circuits will show a circuit ground, the connection of which is optional or up to the user.  So, take the "ground" that I mention and connect it to your chassis, or the neutral of your house or the Earth, or leave it floating.  I don't care.  The sense that I was using "ground" was a common point about which the output voltage is defined.  That is, the circuit ground or datum node.