Project: "Black&White" TC for 10kVA+  (caps: 3 Maxwell 0.3uF/100kV)                    
Tesla Equations
Input value cells are yellow measured values are green
     Results are in blue beyond actual situat. extrapol.
Conversion factors Specific resistance at 20C Density
1 inch = 2,54 cm Aluminium  Al  (20C) 0,02857 Ohm mm2/m Acryl.Rho 1.18 1,18  kg/dm3
1  foot = 0,3048 m Copper Cu  (20C) 0,01786 Ohm mm2/m PVC Rho  1,4  kg/dm3
Tungsten  W  (20C) 0,055 Ohm mm2/m Al     Rho 2,702  kg/dm3
Brass 0,07 0,09 Ohm mm2/m Cu    Rho 8,93  kg/dm3
Bronce 0,018 0,056 Ohm mm2/m
Secondary Design:        
Dimensions:  D = diameter, B = length of windings, G = wire gauge, T = turns/inch or cm
AWG diameter wdg.length AWG turns/unit length length Approx. Weight of secondary
G D B G T of tube Dens.Rho  8,93  kg/dm3
20  inch 7,87 39,39 20,1 29,2 turns/inch 46,46 inch Former D 1,99 dm
enter value in [cm] 20,00 100,1 0,087 11,49 turns/cm 118,0 cm Former L 11,8 dm
diameter of wire, bare copper    = 0,800 mm        ( 0,503 mm2  cross.sect.) Former x 8[1] mm
diameter of wire, with insulation = 0,860 mm Former V 5,7 dm3
wire spacing between turns = 0,010 mm Former W 50,6 kg
Disks x 10[2] mm
Number of secondary turns = 1150,00 Circumference = pi * D Disks No. 4
Circum = 24,74 inch Disks V 1,2 dm3
Length of wire needed  =    2371 feet Radius = 3,94 inch Disks W 11,1 kg
722,6 m Circum = 62,83 cm Copper W 3,2 kg
Radius = 10,00 cm PU-Seal 4,5 kg
H/D aspect ratio = 5,00 Weight = 3,243 kg Cu Weight = 69,5 kg = calculated
d/s wire diam./spacing ratio = 0,92 DC Resistance =  25,67 Ohm        Space wound Sec' with Nylon-line Weight = 48,0 kg = measured
DC Resistance =  14,50 Ohm
RF Resistance of straight wire, with skin-effect =  32,69 Ohm
Coil RF Resistance with skin- and proximity effect =  101,19 Ohm Nylon f = 0,8715 mm
Q-factor, without considering of dielectric loss(=coil-former + sealing) Q =  309 interturn space s = 0,8715 mm
 
Wheeler Equation:  R = radius ", N = no.of turns, B = length of windings "
Date
L (uH) = (R^2 x N^2) / (9R + 10B) fmeas ########
Q kHz
L = 0,047746 H      L. = 47,7 mH L Meas.= 54,67 mH 23,2 1 14,8 Rv (Ohm)
Error in calculated L =  -12,7% 54,60 mH 2,9 0,12 14,2 Rv (Ohm)
An approximation to the Nagaoka inductance, 
accurate to 5 decimal places, was given by Lundin [1]. 
 a = radius, metres.  0,1
 b = length, metres. 1,0005
 N = number of turns 1150,00
 MU = 4*3.14159*1.0E-7 1,26E-06
 x = 4 * a*a/(b*b) 0,03996
 f = (1 + 0.383901*x + 0.017108*x*x)/(1+0.258952*x) 1,004969
 Ldc = MU*N*N*a*a*PI/b *(f - 8*a/(3*PI*b)) Henries. 0,048016 H
(Accurate to rather better than 1%.) Ldc =  48,02 mH    XL= 31313 Ohm
Error in calculated Ldc =  -12,2%
Counting turns, 30.3.00
  Turns DL [cm]
90 18,6
Medhurst Formula: Self Capacitance: C(pf) = K x D D = dia. in cm 100 21,3
100 21,3
K will automatically be determined by K from table K from fit 100 21,6
using H/D from a lookup table at the end 0,810 0,818  * ) 100 22,5
of this spreadsheet 100 22,0
from table from fit 100 21,9
Self capacitance of secondary: C(pf) = 16,2 pF 16,4 pF 100 22,0
23 4,7
* ) Setting x = H/D (with 1< H/D < 8 ) the fitted function for K may 813
be used in the form:  K = a+bx+cx^(1.5)+dlnx/x+e/x^2
or, if H/D < 1 or H/D > 8, by the fitted function for K,
in the form:     K = a+bx+cx^2lnx+dx^(2.5)+e/x^(0.5)
with the parameters a,b,c,d,e  in sheet "Medhurst". That's the way it is implemented.
Measurements 22.7.00 / Finn+Sk
  Resonance, coil with Toroid 1.6/0.4m
69 kHz outdoors
Self resonant frequency of secondary: manual trick trimming possibility of
total secondary capacitance Measurements 11.4.00 / Sk+Andi
f(khz) = 1/2pi(sqrt (L * C)) man.corr. 0 pF (normally 0) Resonance, bare coil, indoors
fo Scope
f = 180,5 kHz Unloaded by Toroid or Sphere formula: 119,00 kHz amplitude
  119,0 kHz Measured C top =  32,77  pF 119,51 kHz 60-70%, f+
Error in f =   51,6% calculated - measured 118,67 kHz 60-70%, f-
(the addition for C total is approx. only!) 0,84 kHz bandwidth ?
f = 103,8 kHz Loaded C total = 48,97  pF 141,7 Q
69,0 kHz Measured 288,5 Rv (Ohm)
Error in f =   50,4% calculated - measured In order to have a more realistic C total Higher f peaks
run Terry Fritz's great E-Tesla   for 309,82 kHz 2,603529 x fo
722,1 Lambda/4 [m] C total = 0,00 pF 448,00 kHz 3,764706 x fo
722,6 wire length [m] ( Fill and run sheet E-Tesla in order
  to automatically fill-in the value ! ) 119,40 kHz coil moved, ca. 1m
Readings on HP counter
Primary Design:  
Di = inner diameter , S = spacing between turns , n = number of turns, d = wire or tubing diameter
From Jim Lux, mail on 27th August 2000, Pupman
Di, S and d are in inches inn.dia. spacing wire dia angle # turns "calculating safe primary turn-to-turn distance"
Di S d a n The breakdown strength for air in a uniform field (not the case for
enter values:> inches 13,78 0,472 0,315 30 10 parallel wires) is about 31 kV/cm (70 kV/inch)
cm 35,0 1,20 0,80 30 10
D is center to center spacing of cylinders
w = width of windings on one side = 7,4 inches = 18,8 cm d is gap between cylinders
W = proj. of windings on one side = 6,4 inches = 16,3 cm r is radius of cylinders
h = height of windings = 3,7 inches = 9,4 cm
R = average radius = (1/2 * Di) + (1/2 * W) = 10,1 inches = 25,6 cm E = V * SQRT(D^2-4*r^2)/(2 * r * (D - r)*arccosh(D/2r))
w/(2*R) used as a replacement for H/D for proxieffect calc. =  0,366606
d/s for proxyeffect calc. =  0,4
Uprim = 8000 V
Total outside diameter of coil = 26,6 inches = 67,6 cm n used =   5 turns
V = 1600 V / turn 1600 V / turn
Lh. = 67,4 uH Lh(uH) = (R2 * n2) / (8R+11W ) D = 2,0 cm 2,0 cm
Lv  = 79,7 uH Lv(uH) = (R2 * n2) / (9R+10h ) d = 0,8 cm 0,8 cm
r = 0,4 cm 0,4 cm
L   = 70,7 uH L (uH) = sqr [ (Lv*sin(a))2 + (Lh*cos(a))2 ] D / 2r = 2,5
80,6 uH @ 9.37 Turns E = 1462 V/cm 1950 V/cm
Jim Lux's Küpfmüller P.86
(2 parallel cylinders)
calc.of trigonometric func's.
angle a
degrees 30
arc 0,523599
sine 0,5
cosine 0,866025
tangent 0,57735
cotangent 1,732051
Tubing or wire
Turn # w W h R Lh Lv L Turn # Dia. Dia. Length S Length
[inch] [inch] [inch] [inch] [uH] [uH] [uH] [inch] [mm] [inch] [m]
1[3] 0,315 0,273 0,157 7,026 0,8 0,8 0,8 1 14,33 364 45,00 1,14
2 1,102 0,955 0,551 7,367 3,1 3,0 3,1 2 15,69 398 49,29 2,40
3 1,890 1,637 0,945 7,708 6,7 6,8 6,7 3 17,05 433 53,57 3,76
4 2,677 2,318 1,339 8,049 11,5 12,1 11,7 4 18,42 468 57,86 5,23
5 3,465 3,000 1,732 8,390 17,6 19,0 17,9 5 19,78 502 62,14 6,80
6,45 4,606 3,989 2,303 8,884 28,6 31,9 29,4 6,45 21,76 553 68,35 8,54
6,97 5,016 4,344 2,508 9,062 33,2 37,4 34,3 6,97 22,47 571 70,58 10,33
8 5,827 5,046 2,913 9,413 43,3 49,8 45,1 8 23,87 606 75,00 12,24
9 6,614 5,728 3,307 9,754 54,6 63,8 57,1 9 25,24 641 79,28 14,25
9,37 6,906 5,980 3,453 9,880 59,2 69,4 61,9 9,37 25,74 654 80,87 16,31
11 8,189 7,092 4,094 10,436 81,6 97,7 85,9 11 27,96 710 87,85 18,54
12 8,976 7,774 4,488 10,777 97,4 117,9 102,9 12 29,33 745 92,13 20,88
13 9,764 8,456 4,882 11,118 114,8 140,3 121,7 13 30,69 780 96,42 23,33
14 10,551 9,138 5,276 11,459 133,9 165,1 142,3 14 32,05 814 100,70 25,88
15 11,339 9,820 5,669 11,800 154,8 192,3 165,0 15 33,42 849 104,99 28,55
16 12,126 10,501 6,063 12,140 177,4 222,1 189,6 16 34,78 883 109,27 31,33
17 12,913 11,183 6,457 12,481 202,0 254,5 216,3 17 36,15 918 113,56 34,21
18 13,701 11,865 6,850 12,822 228,5 289,7 245,2 18 37,51 953 117,84 37,20
19 14,488 12,547 7,244 13,163 257,1 327,6 276,4 19 38,87 987 122,13 40,31
20 15,276 13,229 7,638 13,504 287,7 368,6 309,9 20 40,24 1022 126,41 43,52
21 16,063 13,911 8,031 13,845 320,5 412,5 345,8 21 41,60 1057 130,69 46,84
22 16,850 14,593 8,425 14,186 355,5 459,6 384,2 22 42,97 1091 134,98 50,26
23 17,638 15,275 8,819 14,527 392,8 509,9 425,1 23 44,33 1126 139,26 53,80
24 18,425 15,957 9,213 14,868 432,4 563,6 468,7 24 45,69 1161 143,55 57,45
25 19,213 16,639 9,606 15,209 474,5 620,6 514,9 25 47,06 1195 147,83 61,20
26 20,000 17,321 10,000 15,550 519,0 681,2 564,0 26 48,42 1230 152,12 65,07
27 20,787 18,002 10,394 15,891 566,2 745,4 615,9 27 49,78 1265 156,40 69,04
28 21,575 18,684 10,787 16,232 615,9 813,4 670,7 28 51,15 1299 160,69 73,12
29 22,362 19,366 11,181 16,573 668,3 885,1 728,6 29 52,51 1334 164,97 77,31
30 23,150 20,048 11,575 16,914 723,6 960,8 789,6 30 53,88 1368 169,26 81,61
Total length of tubing  641,9 inches @ 10 turns
or wire, without ends for . 53,5 feet
connection to tank circuit. 16,3 m
length of tubing / wire, used in resistance calculations   5,4 m
Estimating Primary Copper-Loss: DC Resistance =  0,00441 Ohm (for  1 mm wall of Cu)
RF Resistance with skineffect =  0,018482 Ohm (for straight wire)
RF Resistance with skin- + proxyeffect=  0,024427 Ohm (for coiled wire)
Primary RF current (RMS), assumed = 14 A     ( DC  Cu-Loss = 1 Watt ---> for comparison with RF Cu-loss only )
         RF  Cu-Loss = 5 Watt  ( for RRF = see sheet "Skineffect"+"Proxi-eff." )
Remark: Proximityeffect is only a very raw guess: the primary is taken like a solenoid, even in case of a flat spiral !
The resistance is taken for the whole coil, even if the tap is set to fewer turns.
Preliminary calculation of winding supports: all dimensions are in [mm]
Please fill in the yellow fields,
and you will have a proposal for the
f total primary  = 681,8 first winding support and the length
of the strike-rail. = 2,126 m
f strike rail = 676,8 (circumf.= 2126 ) It must be remembered however,
that, depending on how many supports
you want to use (usually 4,6 or 8), you
Di = 350 155,9 5 will need to shift the grooves of the
No. of 8 following supports by an amount of
grooves 20 / (No of supports) 
10 toward the outside of the coil diameter,
distance in order to have a smooth groove path
20 to wind the coil. For  8
2,0 supports this is i.e. 2,5 mm
94,0 shift per each succeeding support.
6,0 Angle a
[deg] 152,0
30
162,9 5 The support sketch is for 'saucer' and
flat primaries, while helicals (a = 90deg.)
50 anyway need a different construction.
167,9
Calculate capacitor , knowing secondary frequency and primary value.  
Calculate L at  87%[4] of primary: L = 61,47 uH
If f in kHz and L in uH then:  C(nF) = 109 / (4p2 x f 2x L) C = 38,26 nF
Measured C =      109,40 nF @ 1kHz d=0.005
Measured C =      110,00 nF @ 120Hz d=0.003
Tip: manipulate XX% of primary by GOAL SEEK, in order to obtain your goal-value of C !
 
 
Calculate F  knowing C and L
C(nF) L(uH)
from above:  38,26 61,47
if C in nF, L in uH:
F(kHz) = 1000 / (2 x pi sqrt (L x C/1000))
F (kHz) = 103,79 (  primary at about 9,00 turns )
from fit to measured L = 8,00054 turns
best sparks experimental = 7,5 turns
 
Range of secondary frequencies with
various toroid sizes:   Enter your own
values for toroid sizes. (This is added to the 
self capacitance of the secondary as calculated above)
Toroid Name: C toroid C total f  l  l/4 
[pF] [pF] [kHz] [m] [m]
Galanis 1600/400 69,59 85,941 78 3826 957
Galanis 790/220 34,58 50,937 102 2946 736
Galanis 700/200 30,66 47,013 106 2830 708
Finn's 600/164 26,25 42,603 111 2694 674
Langenthal 515/120 22,25 38,606 117 2565 641
Langenthal 520/70 19,83 36,182 121 2483 621
Aluflex-duct 400/110 17,94 34,291 124 2417 604
Styropor-Adventskranz 300 10,79 27,144 139 2150 538
Calculate toroid capacitance: Equation courtesy of Bert Pool   For spheres: Csphere = er * ( 0.5* Dsphere ) / 9
Toroid:
Sphere:
d1 d2 s Dsphere
Enter values for toroid: > 750[5] 200[6] 0[7] mm 0[8] mm
29,5 7,9 0 inches
C toroid =  32,7720[9] pF C sphere =  0 pF
 
Calculations above use C top =  32,7720[10] pF
center-center diam.= 0,55 m
cord circumference = 0,628319 m
total outer surface = 1,085656 m2
metal volume = 0 ccm
metal density r = 2,6989 g/ccm
weight calculated = 0,0 kg 
weight measured = 13,5 kg 
s = thickness of metal sheet
Alternative toroids for evaluation (list of my toroids)
cord total outer metal metal weight weight
Toroid Name: d1 d2 s C toroid c-c diam. circumf. surface volume density r  calculated measured
[mm] [mm] [mm] [pF] [m] [m] [m] [ccm] [g/ccm] [kg] [kg]
Galanis 1600/400   1600 400 1 69,5865[11] 1,2 1,256637 4,73741 4725,567 2,6989 12,75 13,5
Galanis 790/220   790 220 1 34,5822 0,57 0,69115 1,237648 1232,023 2,6989 3,33 3,015
Galanis 700/200   700 200 1 30,6584 0,5 0,628319 0,98696 982,0256 2,6989 2,65  
Finn's 600/164   600 164 1,5 26,2482 0,436 0,515221 0,705716 1048,892 2,6989 2,83  
Langenthal 515/120   515 121 0,5 22,2513 0,394 0,380133 0,470524 234,2896 2,6989 0,63  
Langenthal 520/70   520 70 0,5 19,8269 0,45 0,219911 0,310893 154,3359 2,6989 0,42  
Aluflex-duct 400/110   410 112 0,2 17,9358 0,298 0,351858 0,329408 65,76394 2,6989 0,18  
Styropor-Adventskranz 300   247 65,5 0,2 10,7895 0,1815 0,205774 0,117332 23,39481 2,6989 0,06  
    .... End of TC calc ! ....  
 
 
 
 
 
[1]
Wall thicknessof Former  in [mm]
[2]
Thickness of disks in [mm]
[3]
Resonant L at tap:
Fractional values of turns can be entered, in order to attain a closer value for the tap point.
[4]

 Manipulate % of Primary by 'Goal seek' or 'Solver', in order to obtain your goal value of C [nF]
[5]
Outer extreme diameter of toroid (not center to center) in [mm]
[6]
Diameter of cross section (cord) in [mm]
[7]
Thickness of metal sheet [mm]
[8]
Diameter of sphere in [mm]

Leave blank or zero if you
dont have a spheric topload!
[9]
C[pF] = [1+(0.2781-d2/d1)] x 0.1102362 x sqrt{pi [(d1-d2) x (d2/2)]/2}
with d1,d2 in [mm]
[10]
C[pF] = [1+(0.2781-d2/d1)] x 2.8 x sqrt{pi [(d1-d2) x (d2/2)]/2}
with d1,d2 in [inches]
[11]
C[pF] = [1+(0.2781-d2/d1)] x 0.1102362 x sqrt{pi [(d1-d2) x (d2/2)]/2}
with d1,d2 in [mm]