Alternative Energy – How to Calculate the output of a DIY Alternator

This Article premiered January 31, 2011 at our Website: http://www.watchman2012.com
It put us on the WORLD map, and the rest is history. A year and a half later, we believe it’s time to post it here.
The Blackhats may scrape the content, however the world knows that this first of it’s kind information
 
ASSIGNMENT: MATHEMATICALLY MODEL
THE POWER OUTPUT OF THIS:
  
 
Easier Said than DONE !
 
However, a reasonable model for PERFECT conditions can be made using known
principals of PHYSICS and MATHEMATICS !
 
I have been working this out for over two weeks,
12 hour dayze, just to wrap my head around this.
Just to let you know,
I have not done it alone, I have had the VERY patient
help of a real Physicist,
to be able to present for the FIRST time on
the WEB, a METHOD that everybody can use !!
 
MANY, MANY, THANKS GOES TO OUR DEAR PHYSICIST AT:
Their E-mail address is:
 
They have in house Mathematicians and Physicists who will answer questions using the latest
science,
known principals, and apply it to your question with logic and humor.
Their site is a great read, and fun for everyone, I encourage you to visit !
 Their prompt response(s) to me (seen below) allowed me to sleep again at night !
 
YOUR RESOURCE FOR LED, LED LIGHTING, INFORMATION, ALTERNATIVE ENERGY, WIND, SOLAR, ~ Please leave a comment we value your input watchman2012.comwatchman2012.com Energy & Survival Science, Boldly doing Math,
news, information and opinion stories of interest
on a wide range of topics from DIY, politics, culture, Energy,
Energy Conservation, faith and family.
 
I have had at least four false starts to this final presentation page,
as inevitably I would get bogged down in either a variable or an equation.
 
My new best friend, the Physicist says:
“Don’t feel self conscious about the math stuff. 
A “good” understanding of E and M requires vector calculus, and almost no one gets that far.
I’d guestimate somewhere around 1 in 1,000, and of those very few come away with a decent understanding.”
 
As for me, if it wasn’t for their help, I’d still be dreaming of calculations -literally.
 
Diving right in, I will lay out the physical facts of our device, lay out the underlying equations, and
then
plug in the pertinent variables and show the results,
for our mathematical model of this Alternator.
 
It is a “potential” model, and as such may or may not represent reality,
as the variables can change in real life but it does give a method for all the DIY folks
who build these to “build” them on the blackboard FIRST
Then fabricate the device and
hopefully come close to the model.
 
My main reason for undertaking this was that most of the sites are sorta backwards in that
they have years of experience building and testing the devices, and as such they have a feel
for what is going to work.
But they don’t go far enough for my taste in the math and science behind WHY it works.
 
I wanted  to totally understand WHY it works, and
WHAT happens when you change a variable such as:
  1. the size of a coil,
  2. the number of turns in the coil,
  3. the strength of a magnet,
  4. the gap between the rotor and stator of the alternator,
  5. the fifth “element”:  speed/frequency of it’s spin.
The load you attach it to also effects it’s output.
 
 It is AMAZING how much is really involved with the Alternator/Generator.
 
TESLA was brilliant in being able to build on other’s work and envision the generator.
VERY few improvements on his fundamental work have come about since he first introduced the
world to it,  that says a LOT about how elemental his work was !
 
Here we go:
 
As my DEAR Physicist says:
“Set it up however you like, just keep in mind that magnetic flux is the name of the
game.  
Picture the magnetic field as flowing water, and the coils as a hoop.  
The goal is to get as much water to flow through the hoop as possible
(and then switch the direction over and over).”
 
Electromagnetic induction:
Electromagnetic induction is the production of voltage across a conductor moving through
a magnetic field.
It underlies the operation of generators, all electric motors, transformers, induction
motors,  synchronous motors, solenoids, and most other electrical machines.
 
Michael Faraday is generally credited with the discovery of the induction phenomenon in 1831
though it may have been anticipated by the work of Francesco Zantedeschi in 1829.
Around 1830 to 1832 Joseph Henry made a similar discovery, but did not publish his
findings until later.
 
Magnetic flux through an open surface:
Faraday’s law of  induction
A vector field F ( r, t ) defined throughout space,
and a surface Σ bounded by curve ∂Σ moving with
velocity v over which the field is integrated.
While the magnetic flux through a closed surface is always zero, the magnetic flux through
an open surface need not be zero and is an important quantity in electromagnetism.
For example, a change in the magnetic flux passing through a loop of conductive wire will cause
an electromotive force,

and therefore an electric current, in the loop.

The relationship is given by Faraday’s law:

 
 
where :
\mathcal{E} is
the “Electromotive force” -EMF,
Φm
is the flux through a surface with an opening bounded by a curve
∂Σ(t),
∂Σ(t) is a closed contour that can
change with time; the EMF is found around this contour, and the
contour is a boundary of the surface over which Φm
is found,
d is an infinitesimal vector
element of the contour ∂Σ(t),
v is the velocity of the segment d,
Eis the electric field,
B is the magnetic
field.

 

Simplified for our purpose:

The induced voltage depends on the diameter (area) of the coil
and the number of turns of the coil.
The power is determined as
well by the resistance of the coil.
Faraday’s law will give
you the induced emf in the coil:
 

 
That is the potential energy per unit charge in the coil.
If the coil is connected to a load, there will be energy consumed.
The current will be I = V/R. The power is 
 
OR:
 
 
Where:
N=the number of turns in the coil
A=area
B is the
magnetic field
dt=time
ΦB is the magnetic flux in Webers or Tesla
( our Physicist suggests sticking with SI units to avoid conversion issues, the SI unit is TESLA)
 
The EMF generated by Faraday’s law of induction due to relative movement of a circuit and a magnetic field is
the phenomenon underlying electrical generators.
 
When a permanent magnet is moved relative to a conductor, or vice versa, an electromotive force is created.
If the wire is connected through an electrical load, current will flow, and thus electrical energy is generated,
converting the mechanical energy of motion to electrical energy.Although Faraday’s law always describes the working of electrical generators,the detailed mechanism can differ in different cases.
 
When the magnet is rotated around a stationary conductor, the changing magnetic field creates an electric field, as described by the Maxwell-Faraday equation, and that electric field pushes the charges through the wire. This case is called an induced EMF
 
On the other hand, when the magnet is stationary and the conductor is rotated, the moving charges experience a magnetic force (as described by theLorentz force law), and this magnetic force pushes the charges through the wire. This case is called motional EMF.
 
An electrical generator can be run “backwards” to become a motor. (AND VICE VERSA !!)
 
 
watchman2012.com Energy & Survival Science, Boldly doing Math,news, information and opinion stories of intereston a wide range of topics from DIY, politics, culture, Energy,Energy Conservation, faith and family.
 
Whew !
 
So there we have it, all or most of the tools to adequately determine the potential output of our alternator.
What we need now is data about the physical properties of the alternator, reduce that to variable data and begin to plug in the equations !!
 
 
These are our test magnets:
 
and             
1″ dia. x 3/8″ thick                         
1″ dia. x 1″ thick    
Grade N52 – Nickel Plated  NdFeB,
Grade N52
Axially Magnetized                           
Axial (Poles on Flat Ends)
Surface Field: 4440 Gauss     
 Surface Field: 6619 Gauss   2051.5 @ .5 distance  1/2″   
           NO noticeable drop off at .5″  (1/2″) 
3986.8 @ .25 distance 1/4″               
3586.8 @.75  3/4″

   37.65 lbs  force                               
61 lbs Force

 
http://www.kjmagnetics.com/ A GREAT SOURCE !
 
              
 
  
 Field’s strength drops off as distance increases
 
 
FACTS:
14 gauge wire 0.0641 diameter inches (1.628 diameter MM ) 
{ not an important variable, just a fact }
72 turns per coil
1″ SQUARE Rotor Plate  “winding post”
12 inside coils
12 outside coils
 
Our “design” RPM = 60 RPM  { DESIGN is another way of saying
“HIGH HOSEY”, “cuz we said so”… }
we need a number to plug in so we say 60 rpm could be close for
an intermittent windturbine,
I will also include a set of calculations for the classic powered
GENERATOR of 3600 RPM.
Our “design”  R, for LOAD/resistance is
a 100 watt lightbulb: 144 Ω (ohms) (ohm=SI unit as well)
 
Our “design”  GAP between the rotor and stator is 1/2 inch = .5″
this gives us the greatest Gauss/TESLA, magnetic flux
It increases the magnetic flux the closer (smaller) the gap is, so bear that in mind, the opposite is true too, it drops off with distance.
 
Now, in my previous attempt in plugging the information in there were several variables that were off
I had read the Gauss ratings for the magnets from a “general” table and not specifically for the magnet itself,  I found the specific table for them this time.
There is some difficulty with the site’s calculator in determining drop off Gauss results for the larger magnets IE: the calculator says you are inside the magnet for a .25 distance, either that or the Gauss is equal to it’s surface (which I will use as a plug in)
 
To Convert Gauss to T(esla):
 {One tesla is equal to 104 gauss}
OR
{1 Gauss = .0001 Tesla, or 1 Tesla = 10,000 Gauss}
 

Original Article at: http://www.watchman2012.com

 
For our 3/8″ thick magnet and gap of .5″
the Gauss =2051.5  T= 2051.5 X .0001 = 0.20515T
For our 3/8″ thick magnet and gap of .5″
the TESLA Unit = 0.20515T
 
For our 1″ thick magnet and gap of .5″
the Gauss = 6619 
T=6619 X .0001 = 0.6619T
For our 1″ thick magnet and gap of .5″
the TESLA Unit = 0.6619T
 
 
Finally, I was missing the cross sectional
area of A, of each coil
 
From our Dear
Physicist:

A = (pi*D2)/4 where D is the diameter of that pipe.

If you were to wrap it around a pipe, then
A= (pi*D2)/4 where D is the diameter of that pipe.
 
You mentioned that the coils were square.
The area for a square is just A=D2
Also, make sure to always use SI units. 
So, A = (1″)2 = (0.0254m)2 = 0.00064516 m2.
THE EQUATIONS:
 
So we have a simple yet eloquent equation of:
 
V = (dΦ / dt) = N x A x ( dB / dt)
 
Where:
V = Voltage
dΦ = the magnetic flux
dt = time
equals:
N = the turns in the coil
A = the cross sectional area of the coil
dB = the magnetic flux
dt = time
 
Our physicist transposes this for us:
 
The magnetic field in the coils should be roughly sinusoidal. 
Definitely not exactly, but close enough. 
There will be higher harmonics, but they shouldn’t make a huge difference.
 
B = aSin([2 pi]fT)
 
Where:
“a” is the amplitude of the field,
“f” is the frequency in Hz, 
“T” is time.
The time derivative of this is:
 dB/dt = 2*pi*f*a Cos([2pi] fT)

 
The “T” in the Cos is just time, not a particular amount of time. 
It’s saying that, as time goes on, Cosine is going to go up and
down. 
There’s nothing for you to plug into it.
For example:
The voltage coming out of a wall socket would be
V=170 Sin(2*pi*60 T). 
Knowing the T is only important if you want to know what the
voltage is “right now”. 
But it’s not useful, because it’ll be completely different in a
couple hundredths of a second.
 
AC power goes up and down a lot (how much is exactly is just the
frequency). 
So, you don’t concern yourself with the moment-to-moment power
output, and focus instead on the average power output. 
 
Happily, the average of Sin2 and Cos2 is
1/2, (.5)  which makes things easier.
 
I grabbed this from wiki, it shows the
relationship nicely:

Here begins my second and third tangents LOL
I happily went assigning values for variables, and for the first time
ever, switched my microsoft desktop calculator to “scientific” !
I guessed correctly, I might add, what the various buttons do LOL and
went about going thru a great number of calculations to
square variables, multiplication and sum things up for BOTH the 3/8″
magnets, and the 1″ magnets.
 
What I calculated took me over 12 hours to complete !
It looked VERY cool
 
I was precisely wrong LOL
 
 
 
I had quickly phoned my friend to warn him to be extremely careful when running experimental tests because if my math and understanding was correct, he was generating HIGH voltage and Amperage.
It wasn’t correct, but caution is advised anyway, since one-tenth of an Amp,  for one-tenth of a second can stop your heart !
I could see that something was off, and made several more hours of
calculations to see if I could change the results.
I must say I had great fun doing it.
It’s why blackboards come with erasers LOL
 
So I wrote my Dear Physicist again, and asked more detailed
questions about the equations as I was not seeing the
logic in some of them, and mis-applying Cosine, not knowing that
the pretty sub-equation was there for VERY minute moments in time.
 
 
Skipping over the incorrect equations and right into the CORRECT
equations for each magnet size with each coil
I now have THE DEFINITIVE method
to calculate the POTENTIAL power of a magnet/coil pair:
 
The boiled down facts/variables:
 
Magnets are:
B = 1″ dia. x 3/8″ thick =2051.5 Gauss @ .5 ” =0.20515T squared = 0.0420865225
and:
B = 1″ dia. X 1″    thick =6619 Gauss    @ .5″ = 0.6619T  squared = 0.43811161
 
N = 72 turns per coil
A = 0.00064516of each coil =0.0000004162314256
R = 144 Ω (ohms)
f  = frequency in Hertz (Hz)
 
The FINAL EQUATION:
 
Here is our Dear Physicist’s example of the full blown, final
equation @60 RPM (1 Hz) :
 
P = (7220.000645162/144) (2*pi*1*0.6619 Cos(2*pi*1*T) )2 =
(722*0.000645162*22*pi2*0.66192/144) [Cos(2*pi*1*T)]2 =
0.000259 (Cos(2*pi*1*T))2
 
So to make a blank, fill in the variables, equation,  we start with:
 
P = ( N2  x A2 / R)  ( 2 x pi x f x B Cos(2 x pi x f x T) )
(N2  x A2 x 22 x pi2 x B2 / R) [ Cos( 2 x  pi x f x  T ) ]2
 
Further:
since we know the Happy average of Sin2 and
Cos2 = 1/2 = .5
 
We simplify it to:
P = ( N2  x A2 / R)  ( 2 x pi x f x B x .5)   =
( N2  x A2 x 22 x pi2 x B2 / R) x .5
 
( N2  x A2 x 22 x pi2 x B2 / R) x .5  <—– THIS is INTERNET GOLD for ALL DIY WINDTURBINE DESIGNERS !!!!!!

Original Article at: http://www.watchman2012.com

 
WHERE: 
N = Number of turns in the coil squared 
A = The cross sectional Area of the coil squared in: (m2 ) an SI Unit 
pi = pi2 = YUMMY ! 
B = Magnetic flux of the magnet in T(esla) Units – Squared  
R = The Resistance of the connected load in Ω (ohms) an SI unit 
.5 = our Happy average of Sin2 and Cos2 
 
AGAIN:
MANY, MANY, THANKS GOES TO
OUR DEAR PHYSICIST AT:
Their E-mail address is:
 
They have in house Mathematicians and Physicists who will answer questions using the latest science, known principals, and apply it to your question with logic and humor.
Their site is a great read, and fun for everyone, I encourage you to visit !
 
Their prompt response(s) to me allowed me to sleep again at night !
 

YOUR RESOURCE FOR LED, LED LIGHTING, INFORMATION, ALTERNATIVE ENERGY, WIND, SOLAR, ~ Please leave a comment we value your input watchman2012.com

watchman2012.com Energy & Survival Science, Boldly doing Math, news, information and opinion stories of interest
on a wide range of topics from DIY, politics, culture, Energy,
Energy Conservation, faith and family.
 

Original Article at: http://www.watchman2012.com

 
 
The Calculations:
 
For the 1″ x
3/8″
magnet coil pair @ 60 RPM:
P = ( 5184 x 0.0000004162314256 x 4 x 9.865881 x
0.0420865225 / 144) = (0.000024887213527721514387891264 x .5) =
0.00001244 Watts per coil
P = 0.00001244 Watts per coil
 
x 12 coils =0.00014932 Watts @ 60 RPM
x 120 Volts = 0.0000012443 AMPERES
===================================================
For the 1″ x 1″ magnet coil pair @ 60
RPM:
 
P = ( 5184 x 0.0000004162314256 x 4 x 9.865881 x
0.43811161 / 144) = (
0.000259 x 0.5) =
 0.0001295 Watts per coil !!!!!!!!!!!!
P = 0.0001295 Watts per coil
 
x 12 coils = 0.001554 Watts @ 60 RPM
x120 Volts = 0.00001295 AMPERES
===================================================
 
For the typical Generator Speed of
3600 RPM (60 Hz) :
We need to adjust the
equation for the increased Hz:
 
( N2  x A2 x 22 x pi2 x 602 x B2 / R) x .5 
 
( 60 RPM = 1 Hz, so you take a Hz reading of YOUR alternator, Multiply by 60, then Square it to plug into the equation ) 
 
 
For the 1″ x 3/8″ magnet coil pair @ 3600 RPM:
P = ( 5184 x 0.0000004162314256 x 4 x
9.865881 x 3600 x 0.0420865225 / 144) =
(0.0895939686997974517964085504 x .5) =
0.0447969843498

P = 0.0447969843498987258982042752 Watts per
coil

 
x 12 coils  = 0.5375638121987847107784513024 Watts @3600 RPM
x 1 HOUR  = 32.253828731927082646707078144Watts
x120 Volts = 0.0044796984 AMPERES
x 1 HOUR  = 0.268781904  AMPERES

====================================================

For the 1″ x 1″ magnet coil pair @ 3600 RPM:
 
P = ( 5184 x 0.0000004162314256 x 4 x 9.865881 x 3600 x
0.43811161 / 144) = (0.9326538649839237318887998464 x .5) =
0.4663269324919618659443999232
P = 0.4663269324919618659443999232 Watts per coil
 
x12 coils   = 5.59   Watts @ 3600 RPM
x 1 HOUR  = 335.755391 Watts
x120 Volts = 0.0466326932 AMPERES
x 1 HOUR  = 2.797961592  AMPERES
 
You will note that I plugged in a
design 120 Volts to calculate the Amperes of the coils, just to show
what COULD potentially be produced.
It is NOT actual Amperes produced.
I also added a possible hourly output for giggles.
 
 
ACTUAL INITIAL TESTS:
 
So, we initially jury rigged a spinning
perimeter rotor:
 
 
To COMPLICATE matters we ADDED the 1″ magnets
on TOP of the 3/8″ magnets to increase the magnetic flux.
 
A Close-up:
 
 
The Second 1″ magnets were added as we were
concerned that the field may not reach the inner coils
properly.
 
Here’s what the unfinished ring with just the
3/8″ magnets looks like:
 
 
Although not scientific we did a metal filing
on paper over JUST the 3/8″ magnets and the field looks like
this:
 
Note the three “DOTS” of filings stuck to the
inside of the ring where the magnets are placed.
The filings give a good view of what the
field looks like.
 
And we measured it for giggles to see if it
would reach the inner coils:
This determined that it WAS touching the
inner coils, but we wanted it stronger
and so added the 1″ magnets on top of the
3/8″ magnets to increase the field strength
for meter readings.
 
We then attached a drill to the hub of the
trailer axel and spun that puppy up !
 
Let there be LIGHT !!
 
 
This one shows the motion:
 
 
The initial results:
 
With three coils wired together in Series we get the
following:
 
SPUN BY HAND:
 
Just the 3/8″ magnets: 2 Volts,  1 Ampere @ 20Hz(1200RPM)
BOTH MAGNETS      : 2.5 Volts, 1.12 Ampere @ 20 Hz (1200RPM)
INNER COILS read:      2.9 Volts  1.18 Ampere @ 20 Hz (1200 RPM)
 
DRILL ATTACHED, BOTH MAGNETS:
 
OUTER COILS:   7.25 VOLTS 1.88 AMPERES @ 62 HZ ( 3720 RPM)
INNER COILS     8.12 Volts   2.0 AMPERES    @ 65 Hz ( 3900 RPM)
 
I could redo the calculations to match the flux and Hz, so we
have a good comparison of calculated vs actual
I may do that later,
these tests were done before I finished getting a lesson from my
Dear Physicist !
The next tests will be closer to our design model calculations
for comparison.
 
When I say “we” lol, I mean my friend, I am just the calculator…
He is currently fabricating a Parallel Rotor Plate to go in FRONT of the stator
using just the 1″ magnets so we can see how that effects the induction.
We can control the gap a tad better and ultimately will have a rotor that looks more like the traditional DIY rotor so we can test it against this Stator configuration
 
It will look something like this:
The yellow dots being the magnets….
 
 
 
 
Costs so far: 
 
5 pounds of 14 ga. Enameled Wire = $300 
(12) 1″ N52 Magnets = $200 
Steel Plate (to make up the 16 plates of the stator) =$100 (and plenty left to make more !) 
Total: $600 
 
Ok, you may say kind of expensive for an alternator that you could buy at a store. 
However, the FUN in building it, the Science discovery, and the original intention of: 
making a wind turbine = Priceless ! 
 
The NEXT designs will be even better now that we KNOW what EVERYthing does 
and once built they are rugged, and will withstand HEAT better than resin impregnated coils ! 
 
Obviously, from the testing and calculations this puppy screams: MECHANICAL POWER (rather than wind) 
 
JUST WAIT UNTIL YOU SEE THE STEAM ENGINE WE ARE BUILDING FOR IT !! 
 
-Watchman 
 
 
PS. If you read this far, Please leave a comment ! 
 
PPS. I have been authorized to say that the plates and completed stator are available for sale ! 
Contact us for price and availability here 
 

YOUR RESOURCE FOR LED, LED LIGHTING, INFORMATION, ALTERNATIVE ENERGY, WIND, SOLAR, ~ Please leave a comment we value your input watchman2012.com

watchman2012.com Energy & Survival Science, Boldly doing Math,
news, information and opinion stories of interest
on a wide range of topics from DIY, politics, culture, Energy,
Energy Conservation, faith and family.
 
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