Coilers Club #1 : Coil Ratio

Coiling Ratio .

Kenneth Henrik Olsen

Oslo 12.01.2019

An attempt to have all measures for a coil, in one unit . I have developed a conveniant method for doing so . By writing 3 numbers. And knowing the wire diameter or AWG. Thin wire for high voltages, and thick wire for Ampere load . The temperature determine the performance of the coil, limited by Ampere and the wire crossection. Designing a coil with temperature and current in mind, is the better . If the coil is very hot after use, too low resistance. If the coil is cool after operation, too much resistance .

1. N Turns per layer
2. N Layers
3. Radius_hole . The donut hole in the middle of the coil .

N turns : N Layers : R_hole

Coil Lenght : Coil Radius : Radius hole

Y1 L_coil : X2 R_coil : X1 R_hole

Both X1 and X2 are horizontal radial lenghts on the same axis . These would be the same on the Z axis, since a radial lenght describe 2 axis at once . I call this the fancy name of Reduced Dimensional Set . For you can model a 3D object, with only 2 values. Radius and Lenght . A sphere is even better, and is modelled, with only one Radial value ! Saving you 2 integers numbers and 2 operands ( + - * / ) .  A square, or a qube, the most regarded shape in out society, needs a minimum of 3 integers for definition ( X Y Z axis ).

X3 = outer radial measure of the last outer turn layer .
C3 = outer circumference
Lenght Y1 = distance between the disk cylinder faces .

1 : 1 : 1
2 : 1/2 : 4

I first start with the desired number of Turns . Lets say 10 000 turns .
I square the number to find a "Block size" That is equal in Turns * Layers .
SQRT 10 000 = 100 turns * 100 layers

I then say
Coil Lenght = R_Hole
1*100 turns : 1 *100 layers: 1*100 units long

I need the diameter of the wire AWG given in millimeter
AWG30 = 0.25 mm diameter with no insulation .
AWG30 = 0.3 mm diameter with insulation .

( 100t * 100 * 100 ) * AWG30 . 0.3mm
30mm Y1 : 30 mm X2 : 30mm X1

meter = mm / 1000
centimeter = mm / 10 = 3cm * 3cm * 3cm
cm to inch = 3cm / 2.54 = 1.1 inch

Ohm of wire
Turns : Layers : C2 Coil Inner Circumference
D1 = X1*2 = 3*2= 6 cm
C2 = D1 * pi = 2*X2 *pi = 2pi * 3cm  = 18.8 cm

Wire lenght cm and meter
282 turns * 282 layers * 18.8cm Circumference = 1495051 cm / 100 = 14950 meter

AWG30 Ohm per meter = 0.338 ohm / m

14950 * 0.338 = 5053 ohm / 1000 = 5k Ohm

As it appears, the coil pick up the Magnetic B-field by VOLUME, via induction, field coppling. But pick up the electro static E-field, by Surface AREA . The Electric field vibrations is mirrored and refracted just like optics. But the magnetic field is neither reflected nor refracted. Optics may relate directly to the transmission of the Electric field . Optics and E-field have capacitive effects, concerning surfaces charging the atmosphere . Magnets create an Ampere drift on copper . Lenz law, Eddy currents, Facoult currents .

It also may be . The Electric field stimulate the ELECTRON on the atom. Where the magnetic field stimulate the NEUTRONS inside the atom core . Displacing the electrons by creating a "well" or dip in the atomic core substance that create a path for the electrons to descend . Electrons are deflected with magnets in an Oscilloscope ... anyways .

The Coil Ratio can be split into halvs and quartes easily, to increase the surface area, decrease the volume, but retain the number of turns. Changing the circumference changes the ohm per turn, so the wire is longer per turn on the outer layer . Doubling wire crossection,  and retaining the number of turns . That doubles the volumetric size and doubles the wheight . If the coil has a hollow core, the minimum size of the inner diameter or R_hole, is where the coil arcs over its diameter onto itself . Voltage too high, diameter must be increased . 

For better accuracy on the ohm.

Average of inner and outer layer . 

3 cm : 2 * 3 cm : 3 cm

C2 = 18.8 cm

C3 = D2 * pi
R2 = 3 cm
X1 = 3 cm
X2 = 3 cm
X3 = X1+R1

C3 = X3 * 2pi = X3 * 2pi = 6 cm * 2pi = 37.7 cm

Wire lenght Average = (18.8 + 37.7) / 2 = 28.24 cm

Wire length average = 282 * 282 * 28.3 = 2250529 cm / 100 = 22505 meter

ohm average = 22505 * 0.338ohm/m= 7606 ohm / 1000 = 7.6k Ohm

Ohm Differance between Coil 1 and Coil 2

coil 1 = 5 kOhm

coil 2 = 7,6 kOhm

diff = 7.6 - 5 = 2.6 kOhm

With coiling wire I prefere to use Wire diameter and not the crossection . The wire diameter is measured with a Micrometer .
wire crossection = 1 mm^2
wire R = SQRT ( 1mm / Pi ) = 0.5641 mm
wire D = 1.1283 mm ... that matches AWG#17
wire O_circumference= D * Pi = 3.5449 mm
wire C_crossection = Pi * R^2 = 3.14 * 0.5641^2 = 0.999 = 1 kvadrat

The coils weight is important.
Lets say the coil has 1000 turns . The coil changes lenght and diameter, with the wire increase of crossection . Thus retaining equal distribution of Turns * Layers . Block Coil Fashion .

SQRT 1000 = 31.6

AWG 24 = 0.511 mm wire diameter
R_hole + Lenght = 31.6 * AWG24 0.511 = 16.5 mm
D coil = 32 mm
Weight = 277 gram

AWG17  = 1.15 mm wire diameter
R + L = 31.6 * AWG12 1.15 = 37.16
D coil = 74 mm
Weight = 3.2 kg


AWG 12 = 2.050 mm wire diameter
R + L = 31.6 * AWG12 2.050 = 64.8 mm
D1 coil inner turn = 129 mm
D2 coil outer turn = 2R1
O1 = Pi * D1 = 129*pi = 405 mm
O2 = C3 = X3 * 2pi = pi * D2 = 129 mm * 2pi = 814 mm
O3 average = 405 + 814 / 2 = 609 mm per turn avg
Wire lenght mm and meter
31.6 turns * 31.6 layers * 609 mm Circumference / 1000 = 608 meter
AWG12 weight per meter = 0.0294 kg per meter
Weight coil = 0.0294 kg/m * 608 m = 17.87 kg

If you have a square coil.
Translate the Circumference by dividing
O3 / 4 = 609 / 4 = 152 mm all 4 lenghts on the square.
The constructor select the width of the coil by measure, lets say 20 mm parallell planes. I name them Xa1 and Xa2.
Remaining lenghts on the rectangle is
Xa1 + Xa2 - O3 = 20 + 20 - 609 = -569 mm
Ya1 & Ya2 = 569 / 2 = -284 mm
Rectangle circumference = 20 + 20 + 284 + 284 = 608 mm