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I'm a curious person that knows only basic physics, and I want to craft a homemade power generator (eolic, magnetic or hydroelectric, the origin of the energy doesn't matter yet).

I would like to find formulas to determine the possible output in volts and watts. I think these will tell me all the variables like the wire gauge, the number of turns + diameter of the coil, the size/shape/strength of the magnet, etc. Where can I find formulas like these?

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  • \$\begingroup\$ See Maxwell's equations. Otherwise experiment. \$\endgroup\$ Commented Apr 14, 2015 at 18:25
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    \$\begingroup\$ @OlinLathrop Why not just start with experiment? Shoulders of giants be damned. \$\endgroup\$
    – Samuel
    Commented Apr 14, 2015 at 20:01
  • \$\begingroup\$ @Sam: Under the heals of giants? \$\endgroup\$ Commented Apr 15, 2015 at 13:04
  • \$\begingroup\$ thx @Greg d'Eon :D \$\endgroup\$ Commented Apr 15, 2015 at 18:10

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Depend on the design of your dynamo (such as the number of poles and inductor circuits). Here is the general formula for dynamos:

V=FnN(P/a)(1/60)

F= Magnetic flux of each pole (Wb) n= inductor amount of circuits (serial connected) N= rotation speed (r.p.m) a= inductor amount of circuit pairs p= amount of poles pairs

For the case you explain of a simple coil circuit with a magnet, I think this is the formula you are looking for:

V(t)=NBAw sin(wt)

N= number of spires of your coil

B= Magnetic field (Tesla)

A= spire area

w= rotation frequency (rad)

t = time

The output must be rectified.

The size of the wire is defined according the current that the coil will managed and it depends on the load you will add to the circuit and the voltage output. For this you must calculate the V(t) max ( dV(t)/dt=0) and with the load (impedance) of your external circuit you will have the current that will flow in your coil, now you can determinate the theoretical gauge for your wire. I say theoretical because it is recommended to use a wire significant bigger to reduce the heat due to the Joule Effect.

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  • \$\begingroup\$ this seems to be what i was looking for, i'll do some research on it, thank you very much \$\endgroup\$ Commented Apr 15, 2015 at 19:25
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Looking at websites of people who have much experience in this area is an excellent start. The few example sites I mention below vary in how much theory and alternator design they offer but some are reasonably good. I have not looked at any of them in any detail for some while, but some will get into flux, magnet sizes versus field depth, core materials / laminations / "ironless", axial and radial flux alternators, air gaps, saturation, phases, cut in speeds, ... . Many sites major on the mechanical aspects but there is enough of the theory on this sort of site to get you going. After that there are any number of academic papers available - many for $ but some free.

An excellent cross section of ideas, practice and theory can be found at Hugh Piggot's Scoraig Wind site. And here

This gives you an idea of the sort of things he deals with

Also good is The Back Shed

You are probably thinking of a HAWT as per Piggot's products, but VAWTs are worth a look for various reasons.

A good performing not too hard to built is the "Lenz" design.

An example Lenz VAWT - do not be fooled by the appearance. Also do not believe the categorisation of this as a drag turbine. It's a hybrid with TSRs of over 2 in some situations.


The term "axial flux" is an excellent one for finding related articles as while it is not limited solely to this field it is the major area where the term is used. The web search "axial flux" design produces many useful leads.

As elsewhere - quality varies but much is useful. eg

Thesis 2005 DESIGN OF AXIAL-FLUX PERMANENT-MAGNET LOW-SPEED MACHINES AND PERFORMANCE COMPARISON BETWEEN RADIAL-FLUX AND AXIAL-FLUX MACHINES - and I get to learn a new place name (from Lappeenranta University of Technology, Lappeenranta, Finland)

IEEE. For $. Abstract. Just reading the abstracts shows you what you may wish to know. Electromagnetic design of axial-flux permanent magnet machines

And another. Design and Analysis of 42-V Coreless Axial-Flux Permanent-Magnet Generators for Automotive Applications

Even a design "axial flux" image search looks like a gold-mine (or a Barium Strontium Titanate ....?)


Searching Youtube for "axial flux" and "radial flux alternator" produces many leads and you can soon decide what to follow from there. Information provided is variable and "uneven" and many major on the practical rather than theoretical, but much can be found that is good.

A word of advice - anything that uses the words "overunity", "free energy", "... magnets ..." as a key title should, at most, probably be put aside for another occasion. Almost all such sites//articles are provided by people who either do not understand what you are trying to learn about or who arecon-men (there do not seem to be too many con-women in this field).

This will give you some ideas

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  • \$\begingroup\$ I thought the OP is asking about the generator part, and not about what will be turning the generator. I interpreted the question as wanting to know how much volts/amps he gets with this strong a magnet moving that fast past a coil with N turns of wire in each of M windings, etc. \$\endgroup\$ Commented Apr 14, 2015 at 20:16
  • \$\begingroup\$ @OlinLathrop :-) - the sites I mention vary in how much theory and alternator design they offer but some are reasonably good. Having started to write this I realise I could or should have put some of this in my response. I'll do so. I have not looked at any of them in any detail for some while, but some will get into flux, magnet sizes versus field depth, core materials / laminations / "ironless", axial and radial flux alternators, air gaps, saturation, phases, cut in speeds, ... . \$\endgroup\$
    – Russell McMahon
    Commented Apr 15, 2015 at 2:07
  • \$\begingroup\$ @OlinLathrop Added to answer. Removed reference to you. Shifted focus more towards alternator aspects. \$\endgroup\$
    – Russell McMahon
    Commented Apr 15, 2015 at 2:36

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