Magnet's velocity, in Wind Generator

[wil]

I tried some searches and didn't find what I was looking for so here we go...

Simple question: Does the velociy of the magnet passing the coil make a difference?

It must, so if it does then could a person increase the diameter of the magnet path and lower the rpm to achive the same output?

e.g.

If I have a rotor running at 120 rpm, and the magnets are on a 12" diameter path and the generator is producing 12 volts.

Could I then increase the magnet's path diameter to 14.375" and slow rotor down to 100 rpm and achive the same voltage?

The velocity is the same so would the voltage be the same?

Thanks,

Wil

[RP]

This would would work to increase the voltage but now you'll have wider coils to line up with the magnet poles and thus more resistance which means lower overall POWER.  Of course you could use twice as many magnets and coils (of the same size as the smaller unit but then you're expense goes up.

If you just need a higher voltage, you'll be better off winding more turns, even if it means smaller wire.  As your coils get wider you have all that copper running sideways to connect the two "legs" of the coil that does nothing but add resistance.

It's all a tradeoff...

[wil]

Ok, what I'm really trying to understand here is what role the velocity plays in the over all scheme.

In the example, the two cases where ment to have the same number of magnets and coil gemetry (# of turns, size etc.)

The only concern is velocity.

I realize the number of turns in a coil would make a difference and I understand the nature of resistance; I don't know if resistance would play a big role in the examples since we are only talking about around 7" difference in circumference.

Thanks,

Wil

[RP]

Well with double the face (linear) velocity, you'll have double the voltage so you're right about that part.  If you were building an anemometer type instrument that would not draw any significant current from the coils then yes, you'd double your voltage.

What I was getting at is in order to extract power from the generator you have to draw current from it.  In your example to line up the coil legs with the magnets you have to "stretch" the coil legs apart twice as far.  

Let's assume for example you have square coils with 4 ohms resistance.  That's 1 ohm for each leg and 1 ohm each for the top and bottom sides that connect the current producing legs.  Making the top and bottom sides twice as long doubles their resistance so now your coil has 6 ohms total resistance.  Power lost to heat is proportional to resistance to your losses go up by 50%.  The effect is the same if the total resistance/coil is less than 1 ohm.

Also since you still have the same number of magnets going past the same number of coils in one revolution, the total power produced is the same (minus the additional losses).  Remember, even though your magnets go twice as fast, there's twice as much gap between them where no power is produced.

Bottom line, voltage output is directly proportional to face velocity of the magnet to the coil but other factors come into play when talking about power rather than voltage.

I hope this helps.

[wil]

RP, thanks for your patience on this...

I'm trying to understand why your distorting the coil:

"you have to "stretch" the coil legs apart twice as far" - why?

Are you saying that one coil's leg is required to be touching the next coil's leg?

"even though your magnets go twice as fast" - No, the velosity is the same.

"there's twice as much gap between them where no power is produced" - This is part of the concern in my thoughts, and what role this "dead" moment plays. However, I thought this spot would be inbetween the coils and not between the legs of 1 coil.

Thanks,

Wil

[RP]

"you have to "stretch" the coil legs apart twice as far" - why?

Generally you want each radial leg of the coil to be over a magnet at the same time (one north pole and the other south for instance).  With alternating magnets having the same spacing as the center to center width of the coil, each leg will see an alternating north, south, north and the same time the other leg is seeing south, north, south.  If you double the radius of the magnets, they wil be spaced twice as far apart like the spokes on a wheel are farther apart out at the edge of the wheel than they are near the hub.  To make the coil legs line up with them, the coil must also be wider so that the distance between the radial legs matches the spacing of the magnets.

"even though your magnets go twice as fast" - No, the velosity is the same.

No, the actual face velocity is faster.  To see this imagine standing in a clear area holding a stick 1 foot long  with a baseball attached to the end of it and rotating on your heel at 1 revolution/second.  If someone steps in front of the baseball they'll say "what was that?".  Now imagine your stick is 30 feet long and you're spinning at the same speed.  The baseball is now traveling at over 90 mph and they're going to be pretty upset if heot with it.  As the radius doubles the velocity past the fixed coils doubles.

"there's twice as much gap between them where no power is produced" - This is part of the concern in my thoughts, and what role this "dead" moment plays. However, I thought this spot would be inbetween the coils and not between the legs of 1 coil.

Think of the extreme case:  Picture a magnet rotor with only one magnet on it facing a stator with one coil.  For most of a revolution nothing will happen then you'll get one pulse of power, then nothing again untill the magnet swings round past the coil again.  This is the point i was getting at.  As you increase the diameter of the magnet rotor but without adding magnets or increasing their size you have all these dead spots where nothing is happening because your magnets are nowhere near your coils.

I hope this is helping

[finnsawyer]

It's not just velocity.  It also involves the amount of flux.  According to Faraday's Law it is the time rate of change of the total flux that is passing through the the coils at any time.  Most people seem to have trouble understanding what this means.  If you take an existing three phase alternator and simply double the rotor diameter using the same magnets and coils you will find that your coils no longer can extend over two adjacent magnets.  In a proper three phase alternator design the maximum voltage out for a coil or phase occurs when that configuration is reached.  The time rates of change of flux from the two neighboring magnets then add.  With the coils between the magnets of the doubled rotor there will be no flux through the coils of that phase.  This will cause a lower voltage than the original alternator, which voltage will go to zero as the rotor diameter is increased.  That is, eventually the coils will be in a dead zone with no change in flux for a time.

So, what needs to be done is to scale up the magnet size and coil size as you increase the rotor diameter.  For instance, if you double the rotor diameter, then you need to double both the magnet length and width.  You scale up the coils accordingly.  With the same number of windings in the coils you will get eight times the voltage out since you have increased the flux by a factor of four and the velocity by a factor of two.  Note, however, that to get the same number of windings in the coils you now use heavier wire, since the coils are also wider.  You need four times the amount of copper in total, and each turn, on average, is twice as long as before.  You could get this by laying down two strands of the original wire and connecting them in parallel.  The result with twice the length of each winding is that you have the same resistance as before.  Potential power output is now 64 times the smaller alternator, since it depends on voltage squared divided by resistance.

It might help your understanding of Faraday's Law to check out the alternator design that I propose in my diary.  

[wil]

RP - I really appreciate your time here however the velocity is not faster. In your example it is faster, but not in my original example.

The origninal rpm was 120 and in the second the rpm is 100. If my math was correct with the given diameters the velocity only changed about .01 fps.

The point of "dead" spots is an issue that I didn't really think about and I do appreciate that point comming out.

I haven't really played with where the magnets would be oriented with the coils when the diameter changes, I just assumed that since both diameters changed at the same rate the magnets would still be oriented in the same position over the coils as the smaller diameter.

So in the end, what we would really like to see in coil orientation is for them to be as close together as possible. Would that be correct?

If that is correct then is the physical construction/design centered around the geometry of the coils?

Thanks,

Wil

[wil]

finsawyer,

"The time rates of change of flux from the two neighboring magnets then add.  With the coils between the magnets of the doubled rotor there will be no flux through the coils of that phase.  This will cause a lower voltage than the original alternator, which voltage will go to zero as the rotor diameter is increased.  That is, eventually the coils will be in a dead zone with no change in flux for a time"

This is one of the (in my mind) unseen variables that I was hoping to find by asking this question.

I know showing extreme examples help in the understanding of what happens but what is the tolerance?

When a person designs an alternator where do you say to yourself: "that is not likely to work because the coils are too far apart."?

If I add 12 coils and 16 magnets(on one plate) to my original example and when I increase the diameter to 14.375", the coils are now .5" further apart. Is this a good exmple of a bad tolerance or would this be an acceptable tolerance?

Thanks,

Wil

[RP]

"The origninal rpm was 120 and in the second the rpm is 100. If my math was correct with the given diameters the velocity only changed about .01 fps."

Sorry about that.  You're right, I got lost in the mechanics of it and forgot the original question.  Yes the voltage will be the same.  

I haven't really played with where the magnets would be oriented with the coils when the diameter changes, I just assumed that since both diameters changed at the same rate the magnets would still be oriented in the same position over the coils as the smaller diameter.

In an air core alternator you treat each coil leg as a generation point rather than the whole coil.  With an iron stator the flux changes on the whole coil at once but with an air core the flux can affect one leg at a time so the thinking is a little different.

So in the end, what we would really like to see in coil orientation is for them to be as close together as possible. Would that be correct?

Well... You want to use as much of the available space as possible so yes if your coils are touching then you have no wasted space.

If that is correct then is the physical construction/design centered around the geometry of the coils?

You want the coil width (leg to leg) to match the distance between magnets and you want the magnets to be spaced with a gap about 1/2 of the width of the magnets to minimze flux leakage directly from magnet to magnet.  Also the coil layout depends on whether it's to be a single phase, 3 phase ,etc. machine.  It all ties together really.

The way I learned about all this was reading the board here.  Click on the "Everything" link at the top of the page and start scanning the stories.  There are some real experts here and many of the postings have excellent drawings that show the relationship of the magnets to the coils for various design rules.

[finnsawyer]

If a single coil passes over a single magnet you will get a voltage pulse of one polarity followed by an identical voltage pulse of the opposite polarity the magnitude of which will be proportional to the speed at which the coil passes the magnet.  Knowing the form of this twin pulse one could then find the output from a particular coil or phase by adding the pulses created as the coil passes over each magnet in turn.  Some pulses will overlap and reinforce as I indicated before.  When you increase the rotor size you will increase the pulse amplitudes and the angular widths of the pulses will decrease.  That is, the pulses will last a shorter time at the same RPM.  So, increasing the magnet separation means you will be forming the output voltage off of the wrong parts of the pulses as the part of the coil leaving a magnet has lost more flux before the coil starts moving over the next magnet than is ideal.  For your case of a small change it's probably a wash, but you could try analyzing the case for wedge shaped magnets where the flux through a turn of a coil is a simple matter of the area covered.

To muddy the waters some more, a greater separation between magnets will reduce leakage flux if the air gap doesn't change.  This would tend to give a greater output voltage.

[wil]

RP,

Thanks for all your comments they were all very helpful. I also appreciate the good rule-of-thumb in your satement:

"You want the coil width (leg to leg) to match the distance between magnets and you want the magnets to be spaced with a gap about 1/2 of the width of the magnets to minimze flux leakage directly from magnet to magnet."

At this point I'm only interested in 3 phase, air core alternators. I have been on and off the board (mostly reading) for about a year and a half. I have been building spreadsheets based on what I have read on the board and in Hugh's books.

I'm in the final stages of constructing one of Hugh's 12' machines. A good pile of questions arose when I tested the output, first by hand and then I attached an 8hp Briggs and took several different measurements.

In Hugh's book the data says that I should reach cut-in at 120 rpm. I don't remember the exact rpm I measured, but I was off by quite a bit. Another look at the stator and outter magnet plate showed that the gap as 1/4" out on one end of the magnet plate.

I re-adjusted and paid more attention to what was happening as I tightend the nuts down on the plate.

In the end I ended-up with amost the same data that was in the book...whew!

The cut-in speed is actually 127 rpm so thats not too bad.

Thanks,

Wil

[wil]

finsawyer,

Thanks for your comments. I'm going to have to agree with you in that your last statement DID muddy the waters a little.... It almost sounded like what I was asking about in the original post...However I do recoginze the other issues to be considered.

I often wondered if round or wedge shaped magents would out-perform the rectangular shaped magnets. I have seen several posts with round magnets and fewer with wedge shaped magnets.

"That is, the pulses will last a shorter time at the same RPM"

Understood. This is because the travel speed is higher, and so the frequency increases.

"For your case of a small change it's probably a wash" - I suspected this, but was uncertain. OK, now for a dangerous statement...In this case I could actually lower the cut-in speed of this alternator from 120 to 100 rpm.

I googled Farady's Law and found a few sites that I will be studying. I suppose when I have a better understanding of this I will be able to recognize a fair tolerance.

Thanks,

Wil

[RP]

Excellent work!

Ed at windstuffnow.com has some really good diagrams explaining the layouts for 3 phase and how they work here: http://www.windstuffnow.com/main/3_phase_basics.htm

[finnsawyer]

Well, with the larger diameter the peak voltage will increase, but it will last for a smaller part of a cycle due to the added 0.5 inch spacing.  So, the question becomes whether the increase in voltage (and peak power) is enough to offset the shorter duration when rectified.  So, reducing the RPM should get you the peak voltage you're looking for, but at less average power.  If you're trying to reduce the cut-in RPM this might be acceptable.

Existing wedge shaped magnets are not exact. They don't have the necessary arcs built in, and you can't bend wire to follow a sharp corner and such an arc anyway.  The circular magnet is the only one that could be analyzed exactly, as its geometry and the coil geometry are exact.  One could, in principle, find the rate of change of flux through the coil using calculus. It also has the least wire and hence least resistance for a given number of turns of any shape.  The circular shape also would tend to reduce leakage flux somewhat.  But, I don't believe it makes much difference what shape magnets people use.  They get good results in most cases.  It would be nice if people would report their results in detail, and if the site would set up a data base showing what people have achieved with the different magnets and variations.  Well, good luck and have fun!    

[wooferhound]

Here is a story by a guy that actually built and tested what you are talking about.

http://www.fieldlines.com/story/2006/1/5/23847/16961

[Flux]

It's angular velocity that matters, not linear velocity.

You will achieve little by spacing the same magnets on a larger diameter, the mean volts will remain the same, but you can alter the waveform and reach a higher peak voltage. Beyond a certain point you will just add extra resistance.

To use larger discs effectively you can use larger magnets ( and increase flux) or use more of the same magnets and increase frequency.

The mean voltage is proportional to flux per pole, frequency and number of turns.

Number of poles and angular speed determine frequency.

Save yourself a lot of bother and forget linear velocity in rotating electrical machines. That old V=BLV equation is very confusing once you progress beyond a wire moving linearly through a field.

Flux

[Seaspray0]

Don't think of it as the velocity of the magnet passing the coil.  It's the rate of change in the magnetic field that goes through the coil that generates the voltage.  In this case, it's how fast you change from north to south (next magnet to pass) and how strong the magnets are.  You can vary the coils and magnet size/spacing to some extent and end up with a skewed sine wave, but I don't think you'd see any power improvement.  Sine waves without all the harmonic distortions transmit much better over power cables.

[wil]

Flux,

Sorry I haven't reply very quick I've been a little busy a work the last three days.

What is the difference between angular velocity and linear velocity?

How does one find the angular speed?

Since my last post I downloaded a copy of some CAD software so I could create a scale drawing, to get a good look at the placement of the coil legs over the magnets.

This drawing is based on the dimensions in Hugh's book. I can already see that if there is very much movement outward there is going to be a fairly large reduction of the magnets area over the leg of the coil.

I'm sure that will have an effect on the flux per pole as you've stated.

"Save yourself a lot of bother and forget linear velocity " - I will but now I'm interested in angular velocity.

Thanks,

Wil

[Flux]

Linear velocity is the speed in ft/sec or similar units that a magnet passes the coil.

What matters is the number of magnets per second passing. That is relater to the number of poles and the rotational speed in revs/sec ( or rpm).

For a given number of poles and a given rpm, the poles /sec is constant, but the linear velocity increases with radius.

Regarding your drawing, you can keep the legs in the right place with a larger diameter by making the coils wider, but the larger coils will have more resistance. You will have the same voltage so you loose out. You can now use the space more effectively by using thicker wire and things are partly self compensating. there is an optimum ratio of magnet width to space between magnets, it is not sharply defined, but large departures from the normal will make a less cost effective machine.

Roughly with the 12/9 type winding things work best when the mean gap between magnets is about the magnet width. Crowding increases leakage flux and reduces winding space, requiring thinner wire ( more resistance). Very wide spaces result in excessive turn length and associated resistance that is not compensated by the possibility of thicker wire.

Flux

[finnsawyer]

Linear velocity is the product of the angular velocity times the radial distance to the point of interest.  Well, strictly speaking that would be the linear speed as velocity is a vector, which for a point rotating around a center constantly changes direction.  It seems to me that focusing on angular velocity only makes sense if you are scaling everything about the alternator up or down by the same ratio.  In reality one has no such restriction. Besides, Faraday's Law doesn't involve angular velocity.  Personally, I prefer to stay with the basics rather than introduce a quantity that hides the physics.  Perhaps, with the 3:4 designs one finds here using angular velocity may be a handy crutch, but I don't think it would be of much use in a design like the 3:2 arrangement that I propose, where the coil diameters can have any value, such value, in turn, determining the rotor diameter along with the magnet size.  Well, maybe its a case of six of one, half a dozen of the other, since the two are so closely linked.

[wil]

Flux,

"the speed in ft/sec or similar units that a magnet passes the coil"

Some of the info I have found so far speaks of using degrees or radians as the unit of measure.

"For a given number of poles and a given rpm, the poles /sec is constant"

I can see this.

"but the linear velocity increases with radius"

Ok, but I dont see this yet. I guess, in my case there are 16 magnets(1 plate) and 12 coils, the magnet plates are 14" diameter. So if in 1 rpm 16 magnets pass 1 coil then could you say rpm * magnets = magnets per second?

Where is the relationship to radius?

Sometimes I get confused when I've read posts regarding poles. I'm fairly certain that 1 pole = 1 magnet.

"there is an optimum ratio of magnet width to space between magnets, it is not sharply defined"

What is the rule of thumb? (would it be 1 magnet width?)

"Roughly with the 12/9 type winding"

What is the 12/9 type winding?

"the mean gap between magnets is about the magnet width"

I've seen this before on the board, but I thought it was the magnet thickness.

Given the 1x2x.5 magnets, and if it where the width, then there should be roughly a 1" gap between the magnets from one plate to the next. Is that correct?

The gap in the alternator I assembled is .700", and the magnets are .500" thick.

Thanks,

Wil

[wil]

"Linear velocity is the product of the angular velocity times the radial distance to the point of interest"

So would the following be correct: (fps = av * rd) & (av = fps/rd)

By radial distance do you mean the radius of the circle or the radians traveled?

Thanks,

Wil

[Flux]

Yes angular velocity is often given in radians/ second.

For most type of machine, poles does equal number of magnets. For the dual rotor axial there are 2 magnets for each pole, it is the flux paths that determine poles and in this case there are 2 magnets in series to produce each flux path.

Your 16 magnets on a dual rotor would be 16 pole in the case where each disc has 16 magnets.

You are happy with the fact that for a given speed and a given number of poles, the poles/sec is constant. Now for the radius bit, at any radius the angular velocity, poles/sec, radians/sec or whatever is constant. Linear speed is distance per second if you like. The distance for a rotating device is the circumference of the circle and is pi x diameter, so obviously the distance travelled will be greater at a larger radius. Any one magnet will travel further in a single rotation if it is at a larger radius. so its speed is greater if we regard it in the conventional way. it's not strictly linear speed when moving in an arc but you get the idea.

What Faraday said and what the law normally attributed to him is taken to mean may be different, but what it basically comes down to is the fact that the voltage is proportional to the rate of change of flux, or the flux linking a turn per second.

This comes back to be dependent on the flux per pole and the number of poles per second for a single turn. For a given magnet, the flux is fixed so it is the number of poles per second passing a coil that matters, the actual speed of the magnet in conventional terms is irrelevant. if the magnet is at a large radius it will travel faster, but in any rev it will only pass that coil once.

This holds true for mean volts. If you start considering rms, peak or any other voltage then things change with the interval when the magnet is over a coil leg compared with when it is not.

Sorry about confusing you with the 12/9 thing. The type of winding usually used with the dual rotor axial alternators has 3 coils (one per phase) for every 4 magnets. The common 12 magnet rotor would have 9 coils. (12 coils for your 16 magnets)

Magnets 1" wide would typically have 1" gap between them, you can squeeze it below 1" near the centre without much effect or you can go up to 1" spacing at the centre for a less compact machine with a bit more output.

1/2" thick magnets will work reasonably effectively with an air gap a bit under 1". Many make the coils 1/2" thick. With resin , glass and a reasonable mechanical clearance this works out to a gap of about 3/4". With leakage and grade N35 magnets you have about 600mT flux density in the gap and is probably the best compromise between winding space and total flux.

I hope this clears things up,

flux

[wil]

"but in any rev it will only pass that coil once"

Ok, I see why rpm or rps would be more relevant than fps.

Below GeoM said: "Linear velocity is the product of the angular velocity times the radial distance to the point of interest"

That would be: (fps = av * rd) or (av = fps/rd)

If we put some numbers to this where:

Diameter = 12"

rpm = 120

fps = 6.28

Then the angular velocity is 1 radian per second. (correct?)

"Magnets 1" wide would typically have 1" gap between them"

The alternator in Hugh's plans ended up with about 1 3/8" gap between the the center edges.

"you can squeeze it below 1" near the centre without much effect or you can go up to 1" spacing at the centre for a less compact machine with a bit more output."

So a person should really make an effort with 1" wide magnets to keep as close as possible to 1" spacing between magnets.

Thanks,

Wil

[Flux]

"Then the angular velocity is 1 radian per second. (correct?)"

Mathematicians will correct me if I am wrong, but I think there are 2pi radians in a circle. 120 rpm is 2 rps so you would have 4pi radians/sec at 120 rpm.

"So a person should really make an effort with 1" wide magnets to keep as close as possible to 1" spacing between magnets."

Within reason, there is nothing exact about it, but if the 1" spacing worked out for a 12" disc there would be no point in using 14" ones. The gain would be small for a large increase in weight and cost.

The time to use bigger discs is when you want a more powerful alternator, in which case you would use more magnet material ( bigger magnets or more of the cost effective 2 x 1 x 1/2 size).

Flux

[finnsawyer]

I failed to mention that the angular velocity is in radians per second.  It is obtained from the RPMs by dividing by 60 to get revolutions per second and then dividing that by 2Pi (6.28 - there are 2Pi radians in a complete circle).  The radial distance is the distance from the center of rotation to the point of interest on the rotor.  Points farther away from the center move faster.

[finnsawyer]

Oops! Multiply by 2Pi, don't divide.  Flux is right.  Two revolutions per second is 4Pi radians per second.

[wil]

Ok thanks for your patience. I may have become confused with GeoM's post.

Anyway, it should be like this:

revolutions per second * 6.28 = angular velocity.

The whole point in this venture was to learn more about how to design the alternator and why the components are placed as they are; I believe I did learn the answers and I'm right on the edge of designing an alternator for my next wind turbine.

A fair rule of thumb for magnet placemet is approximately 1 magnet width, with maybe 10% to 30% tolerance. Which, in-turn, will help determine the diameter of plate and placement of the coils.

Most of the time the wind here is from 5 to 15 mph, but on days like yesterday...

My anemometer says we had an average of 13 and hi of 34 mph. (unusual, but par for some of the winter wind here.)

Yesterday, a properly designed wind turbine, should have given me around 600w to 12kw with an 18' turbine.

I would prefer a lower cut-in speed to capture as much as possible around 7 or 8 mph and is probably going to be the target for the next turbine, and the blade diameter will be at least 18' if not more. I haven't really decided on the what the maximum wind speed and cut-in should be yet. I may shoot for low and mid-range speeds on the next 2 turbines..

Thanks guys, I really appreciate your time.

Wil