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# How do i determine the number of coil winding/size in a axial flux generator ? Answered

i am building a axial flux wind turbine, i have built a small one, now want to move onto a bigger one. but i couldn't find any information on how to calculate the size of coils for the required power output. example i want to make a 48v 5kw generator, how would i calculate how many turns is required, the wire thickness, how many coils per phase. can someone please explaining the process in determining all this?

all the resorces online just give me numbers, example 72 turns of 1mm wire to get 48v, they dont tell me how to calculate it myself for different voltages or different power power output.

any help would be appreciated

thank you

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## Discussions

Predicting voltage and power from an arrangement of coils and magnets, is mostly based on Faraday's law, for predicting the induced voltage in each coil, and also Ohm's law, which tells us the electrical resistance in each winding, which limits how current, and thus power, the coil can supply to a load.

The open circuit voltage of any particular coil is,

Vcoil = N*(dPhi/dt)

where N is the number of turns on the coil, and (dPhi/dt) is the time rate of change of the magnetic flux enclosed by those turns.

That equation by itself suggests a large number of turns N is good for making a coil deliver more voltage. While that is true, making N larger, for a given volume of space in which N turns must fit, will require wire that is thin and long, which will increase the coil's total resistance. This conundrum is explained in words and equations, in the paragraphs that follow.

Regarding coil resistance, that is what determines the maximum current a coil can supply, which is the short circuit current, just

Isc = Vcoil/Rcoil

Although in the shorted condition, zero useful work is done, and all the work goes into heating the coil itself.

A more useful equation might be something like:

with this equation suggesting you want to make Rcoil smaller than Rload, to the extent you want to put more power into the load than into the resistance in the coil.

Regarding ways to predict, or design, coil resistance, if you know in advance the shape of your coil and how big it is, then you know its volume (e.g. in cubic centimeters), and you know that volume is going to be filled with copper magnet wire.

Volume = (1/f)*A*L, L = (Volume*f)/A, A = (Volume*f)/L

where A is the wire's cross-section area, and L is its total length.

This variable f, is a "packing fraction", a number slightly less than 1, which accounts for how well the wire fills the space; e.g. circles with their centers on a square grid (f=pi/4~=0.7854), e.g. circles on a hexagonal grid (f=3^0.5*pi/6~=0.9069).

Some expressions for the ratio (L/A), and (A/L), in terms of just L, or just A:

(A/L) = (Volume*f)/(L^2) = (A^2)/(Volume*f)

(L/A) = (L^2)/(Volume*f) = (Volume*f)/(A^2)

Coincidentally, those variables {A, L}, the wire's cross-section and its length, are what determine the coil's resistance. The variable rho is bulk resistivity of the wire material. In practice, this wire material is almost always electrical grade copper.

Rcoil = rho*L/A = (rho/Volume*f)*(L^2) = (rho*Volume*f)*(1/A^2)

And this not unexpected. If you use thicker wire (larger A), you will get a coil with less resistance. Also thicker wire causes the total length of wire L, in each coil, to be smaller, since Volume*f=constant=L*A.

Also thicker wire means you will get fewer turns, since the total number of turns N depends on the total length of wire in the coil, since

L = N*(average turn length)

I am trying to think of a good variable name for, "average turn length". Maybe use capital "C" like for the word, "circumfrence", plus a subscript "avg" signifying an average value over all N turns.

L = N*Cavg; N = L/Cavg

and I am expecting "Cavg" is constant for a particular coil shape and size, much the same as the total "Volume" remains constant for a particular coil shape and size.

Anyway, the point of all this math, is to show you there is kind of a trade-off between induced voltage Vcoil, which requires large N, number of turns, and making a coil with low resistance Rcoil, since more turns, for a given coil volume, make the wire longer and thinner, and that tends to increase the resistance.

If you need both low resistance Rcoil and big voltage Vcoil, probably the only way to do that is by scaling up the volume of the coil, and the magnets too. You know, make everything bigger, and heavier, and more expensive too!

What is the cliche about bigness? Go big or go home? Ha!
;-)

Or buy an alternator from someone. Although that is a SEDIFY (somebody else does it for you) approach, when you maybe wanted to do it yourself, DIY.

Anyway, I am hoping this explanation can give you kind of an overview, since you said "all the resources online..." fail to explain to you how to go about designing a permanent magnet alternator.

I am guessing that my explanation will fail you too, because it has too many abstract equations, and too much hand waving, but not enough real examples. Ha!
;-)

If it would be all that easy we would not bother to buy motors or generators anymore ;)
Without knowing all the specs for the apperature it is simply impossible to tell you what you need.
Don't know what your base is either, a DC motor? A salvage generator that needs to be rewired?

For a basic DC motor you just need to check that the thing runs close to or above the rated RPM's to get the stated voltage back out - minus some losses here and there.
In the example you gave the wire needs to be able to handle well over 100A.
I would go for 120A by checking the common wire gauge tables for copper wire.
Even at less power it is a true pain to wire your own generator or motor properly - not for the beginner IMHO.