Rosa mutual inductance correction for round wire solenoids.
Developing a correction coefficient which takes pitch angle into
account. D W Knight. 24th Oct. 2012.
Dataset for fitting. 133 rows x 239 columns = 31787 points.
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
Parameter sets were determined using fitting template on sheet
2.
p / D
0.000000
0.0000004
0.0000007
0.000001
0.000002
0.000004
0.000007
0.000010
0.000015
0.000020
0.000025
0.000030
0.000040
0.000050
0.000060
0.000070
0.000080
0.000090
0.000100
0.000115
0.000130
0.000145
0.000160
0.000180
0.000200
0.000220
0.000240
0.000260
0.000280
0.000300
0.000320
0.000340
0.000370
0.000400
0.000430
0.000460
0.000500
0.000530
0.000560
0.000600
0.000630
0.000660
0.000700
0.000730
0.000760
0.000800
0.000830
0.000860
0.000900
0.000930
0.000960
0.001000
0.001050
0.001100
0.001150
0.001200
0.001250
0.001300
0.001350
0.001400
0.001450
0.001500
0.001550
0.001600
0.001650
0.001700
0.001770
0.001840
0.001920
0.002000
0.002100
0.002200
0.002300
0.002400
0.002500
0.002600
0.002700
0.002800
0.002900
0.003000
0.003100
0.003200
0.003300
0.003400
0.003500
0.003600
0.003700
0.003800
0.003900
0.004000
0.004200
0.004400
0.004700
0.005000
0.005200
0.005400
0.005700
0.006000
0.006200
0.006400
0.006700
0.007000
0.007200
0.007400
0.007700
0.008000
0.008200
0.008400
0.008700
0.009000
0.009200
0.009400
0.009700
0.010000
0.010200
0.010400
0.010700
0.011000
0.011200
0.011400
0.011700
0.012000
0.012200
0.012400
0.012700
0.013000
0.013400
0.014000
0.014400
0.015000
0.015400
0.016000
0.016400
0.017000
0.017400
0.018000
0.018400
0.019000
0.019400
0.020000
0.020400
0.021000
0.021400
0.022000
0.023000
0.024000
0.025000
0.026000
0.027000
0.028000
0.029000
0.030000
0.031000
0.032000
0.033000
0.034000
0.035000
0.036000
0.037000
0.038000
0.039000
0.040000
0.041000
0.042000
0.043000
0.044000
0.045500
0.047000
0.048500
0.050000
0.052000
0.054000
0.056000
0.058000
0.060000
0.062000
0.064000
0.066000
0.068000
0.070000
0.072000
0.074000
0.077000
0.080000
0.083000
0.086000
0.090000
0.093000
0.096000
0.100000
0.105000
0.110000
0.115000
0.120000
0.125000
0.130000
0.135000
0.140000
0.145000
0.150000
0.160000
0.170000
0.180000
0.190000
0.200000
0.210000
0.220000
0.230000
0.240000
0.250000
0.260000
0.270000
0.285000
0.300000
0.320000
0.340000
0.360000
0.380000
0.400000
0.425000
0.450000
0.475000
0.500000
0.540000
0.580000
0.620000
0.660000
0.700000
0.750000
0.800000
0.900000
1.000000
1.400000
2.000000
3.141593
5.441398
10.000000
100.000000
1000.000000
pitch / coil diameter
/
0.000000
0.0000073
0.0000128
0.000018
0.000036
0.000073
0.000128
0.000182
0.000274
0.000365
0.000456
0.000547
0.000730
0.000912
0.001094
0.001277
0.001459
0.001641
0.001824
0.002097
0.002371
0.002644
0.002918
0.003283
0.003648
0.004012
0.004377
0.004742
0.005107
0.005471
0.005836
0.006201
0.006748
0.007295
0.007842
0.008389
0.009119
0.009666
0.010213
0.010943
0.011490
0.012037
0.012766
0.013314
0.013861
0.014590
0.015137
0.015685
0.016414
0.016961
0.017508
0.018238
0.019150
0.020062
0.020973
0.021885
0.022797
0.023709
0.024621
0.025533
0.026445
0.027357
0.028269
0.029180
0.030092
0.031004
0.032281
0.033558
0.035017
0.036476
0.038299
0.040123
0.041947
0.043771
0.045595
0.047418
0.049242
0.051066
0.052890
0.054713
0.056537
0.058361
0.060185
0.062009
0.063832
0.065656
0.067480
0.069304
0.071127
0.072951
0.076599
0.080246
0.085718
0.091189
0.094837
0.098484
0.103955
0.109427
0.113074
0.116722
0.122193
0.127664
0.131312
0.134960
0.140431
0.145902
0.149550
0.153197
0.158669
0.164140
0.167787
0.171435
0.176906
0.182378
0.186025
0.189673
0.195144
0.200615
0.204263
0.207910
0.213381
0.218853
0.222500
0.226148
0.231619
0.237090
0.244385
0.255328
0.262623
0.273565
0.280860
0.291802
0.299097
0.310040
0.317335
0.328277
0.335572
0.346514
0.353809
0.364751
0.372046
0.382988
0.390283
0.401225
0.419462
0.437699
0.455936
0.474172
0.492409
0.510645
0.528882
0.547118
0.565354
0.583590
0.601826
0.620061
0.638297
0.656533
0.674768
0.693003
0.711238
0.729473
0.747708
0.765943
0.784177
0.802411
0.829762
0.857113
0.884464
0.911814
0.948280
0.984745
1.021209
1.057673
1.094136
1.130598
1.167059
1.203519
1.239978
1.276436
1.312893
1.349349
1.404031
1.458710
1.513386
1.568060
1.640954
1.695621
1.750285
1.823166
1.914258
2.005340
2.096412
2.187474
2.278525
2.369564
2.460591
2.551606
2.642607
2.733596
2.915531
3.097407
3.279221
3.460969
3.642647
3.824252
4.005779
4.187227
4.368590
4.549865
4.731050
4.912139
5.183588
5.454803
5.816041
6.176816
6.537099
6.896864
7.256083
7.704299
8.151568
8.597839
9.043061
9.753112
10.460150
11.163982
11.864417
12.561274
13.427042
14.286609
15.985890
17.656787
24.019370
32.481637
45.000000
60.000000
72.559406
88.200592
89.820001
pitch angle / degrees
Last km
0.33787676
0.33787660
0.33787646
0.33787631
0.33787579
0.33787476
0.33787320
0.33787163
0.33786902
0.33786641
0.33786379
0.33786118
0.33785595
0.33785072
0.33784548
0.33784025
0.33783502
0.33782979
0.33782455
0.33781670
0.33780886
0.33780101
0.33779316
0.33778269
0.33777223
0.33776176
0.33775130
0.33774083
0.33773037
0.33771991
0.33770944
0.33769898
0.33768329
0.33766759
0.33765190
0.33763621
0.33761529
0.33759961
0.33758392
0.33756301
0.33754732
0.33753164
0.33751073
0.33749505
0.33747936
0.33745846
0.33744278
0.33742710
0.33740620
0.33739053
0.33737485
0.33735395
0.33732783
0.33730172
0.33727560
0.33724949
0.33722338
0.33719728
0.33717117
0.33714507
0.33711897
0.33709288
0.33706678
0.33704069
0.33701460
0.33698852
0.33695200
0.33691549
0.33687377
0.33683205
0.33677992
0.33672779
0.33667568
0.33662357
0.33657148
0.33651939
0.33646731
0.33641525
0.33636319
0.33631114
0.33625911
0.33620708
0.33615506
0.33610305
0.33605105
0.33599906
0.33594708
0.33589511
0.33584314
0.33579119
0.33568731
0.33558347
0.33542777
0.33527216
0.33516847
0.33506480
0.33490938
0.33475404
0.33465052
0.33454704
0.33439188
0.33423680
0.33413346
0.33403015
0.33387525
0.33372043
0.33361726
0.33351413
0.33335949
0.33320492
0.33310192
0.33299896
0.33284457
0.33269026
0.33258742
0.33248463
0.33233049
0.33217643
0.33207376
0.33197113
0.33181724
0.33166342
0.33156092
0.33145845
0.33130481
0.33115124
0.33094659
0.33063986
0.33043553
0.33012928
0.32992527
0.32961949
0.32941580
0.32911050
0.32890712
0.32860228
0.32839922
0.32809485
0.32789209
0.32758818
0.32738573
0.32708228
0.32688013
0.32657714
0.32607275
0.32556912
0.32506623
0.32456409
0.32406269
0.32356202
0.32306208
0.32256288
0.32206439
0.32156663
0.32106959
0.32057326
0.32007765
0.31958275
0.31908855
0.31859506
0.31810226
0.31761017
0.31711877
0.31662807
0.31613806
0.31564874
0.31491604
0.31418488
0.31345525
0.31272715
0.31175870
0.31079293
0.30982983
0.30886937
0.30791156
0.30695637
0.30600379
0.30505380
0.30410640
0.30316158
0.30221931
0.30127960
0.29987479
0.29847566
0.29708217
0.29569429
0.29385246
0.29247756
0.29110816
0.28929081
0.28703273
0.28478965
0.28256144
0.28034801
0.27814924
0.27596502
0.27379527
0.27163988
0.26949875
0.26737181
0.26316013
0.25900416
0.25490327
0.25085687
0.24686437
0.24292525
0.23903896
0.23520500
0.23142288
0.22769211
0.22401224
0.22038280
0.21503225
0.20979273
0.20297694
0.19635269
0.18991676
0.18366595
0.17759711
0.17026218
0.16320056
0.15640609
0.14987256
0.13994592
0.13064488
0.12194253
0.11381136
0.10622341
0.09745932
0.08944465
0.07544624
0.06380972
0.03393649
0.01504649
0.00461719
0.00096958
0.00016132
0.00000016
0.00000000
N = 10^7 value
kinf
3.02E-07
2.51E-07
2.42E-07
2.36E-07
2.25E-07
2.13E-07
2.04E-07
1.98E-07
1.91E-07
1.87E-07
1.83E-07
1.80E-07
1.75E-07
1.71E-07
1.68E-07
1.66E-07
1.63E-07
1.61E-07
1.60E-07
1.57E-07
1.55E-07
1.54E-07
1.52E-07
1.50E-07
1.48E-07
1.47E-07
1.45E-07
1.44E-07
1.43E-07
1.41E-07
1.40E-07
1.39E-07
1.38E-07
1.37E-07
1.35E-07
1.34E-07
1.33E-07
1.32E-07
1.31E-07
1.30E-07
1.29E-07
1.28E-07
1.27E-07
1.27E-07
1.26E-07
1.25E-07
1.24E-07
1.24E-07
1.23E-07
1.23E-07
1.22E-07
1.21E-07
1.21E-07
1.20E-07
1.19E-07
1.18E-07
1.18E-07
1.17E-07
1.16E-07
1.16E-07
1.15E-07
1.15E-07
1.14E-07
1.13E-07
1.13E-07
1.12E-07
1.12E-07
1.11E-07
1.10E-07
1.10E-07
1.09E-07
1.08E-07
1.07E-07
1.07E-07
1.06E-07
1.05E-07
1.05E-07
1.04E-07
1.04E-07
1.03E-07
1.02E-07
1.02E-07
1.01E-07
1.01E-07
1.00E-07
1.00E-07
9.95E-08
9.91E-08
9.86E-08
9.82E-08
9.74E-08
9.66E-08
9.55E-08
9.45E-08
9.38E-08
9.32E-08
9.23E-08
9.15E-08
9.09E-08
9.04E-08
8.96E-08
8.89E-08
8.84E-08
8.80E-08
8.73E-08
8.67E-08
8.62E-08
8.58E-08
8.53E-08
8.47E-08
8.43E-08
8.40E-08
8.34E-08
8.29E-08
8.26E-08
8.23E-08
8.18E-08
8.13E-08
8.10E-08
8.08E-08
8.03E-08
7.99E-08
7.96E-08
7.93E-08
7.90E-08
7.86E-08
7.81E-08
7.73E-08
7.69E-08
7.62E-08
7.57E-08
7.51E-08
7.47E-08
7.41E-08
7.37E-08
7.31E-08
7.28E-08
7.22E-08
7.19E-08
7.14E-08
7.10E-08
7.06E-08
7.02E-08
6.98E-08
6.90E-08
6.83E-08
6.76E-08
6.70E-08
6.64E-08
6.58E-08
6.52E-08
6.46E-08
6.41E-08
6.35E-08
6.30E-08
6.25E-08
6.20E-08
6.16E-08
6.11E-08
6.06E-08
6.02E-08
5.98E-08
5.94E-08
5.90E-08
5.86E-08
5.82E-08
5.76E-08
5.71E-08
5.66E-08
5.60E-08
5.54E-08
5.48E-08
5.41E-08
5.36E-08
5.30E-08
5.24E-08
5.19E-08
5.14E-08
5.09E-08
5.04E-08
4.99E-08
4.95E-08
4.88E-08
4.81E-08
4.75E-08
4.69E-08
4.62E-08
4.56E-08
4.51E-08
4.44E-08
4.36E-08
4.28E-08
4.20E-08
4.13E-08
4.06E-08
3.99E-08
3.93E-08
3.87E-08
3.81E-08
3.75E-08
3.64E-08
3.53E-08
3.44E-08
3.34E-08
3.26E-08
3.17E-08
3.09E-08
3.02E-08
2.94E-08
2.87E-08
2.80E-08
2.74E-08
2.65E-08
2.56E-08
2.45E-08
2.34E-08
2.24E-08
2.15E-08
2.06E-08
1.96E-08
1.86E-08
1.77E-08
1.69E-08
1.56E-08
1.45E-08
1.34E-08
1.24E-08
1.15E-08
1.05E-08
9.61E-09
8.04E-09
6.76E-09
3.55E-09
1.56E-09
4.77E-10
9.99E-11
1.66E-11
1.68E-14
1.68E-17
difference between N=10^7 value and extrapolated value for
kminf
maxerr
0.00000002
0.00000011
0.00000017
0.00000023
0.00000038
0.00000060
0.00000086
0.00000105
0.00000131
0.00000153
0.00000168
0.00000184
0.00000209
0.00000237
0.00000282
0.00000331
0.00000379
0.00000424
0.00000467
0.00000536
0.00000600
0.00000662
0.00000724
0.00000803
0.00000877
0.00000952
0.00001025
0.00001093
0.00001157
0.00001218
0.00001280
0.00001341
0.00001426
0.00001504
0.00001578
0.00001651
0.00001740
0.00001802
0.00001859
0.00001932
0.00001985
0.00002035
0.00002097
0.00002139
0.00002178
0.00002226
0.00002259
0.00002290
0.00002327
0.00002353
0.00002383
0.00002419
0.00002459
0.00002495
0.00002526
0.00002553
0.00002576
0.00002596
0.00002613
0.00002627
0.00002638
0.00002647
0.00002654
0.00002658
0.00002663
0.00002671
0.00002678
0.00002682
0.00002683
0.00002679
0.00002671
0.00002657
0.00002653
0.00002653
0.00002650
0.00002643
0.00002634
0.00002623
0.00002609
0.00002594
0.00002576
0.00002557
0.00002537
0.00002515
0.00002492
0.00002467
0.00002442
0.00002416
0.00002389
0.00002361
0.00002305
0.00002264
0.00002200
0.00002136
0.00002094
0.00002051
0.00001989
0.00001927
0.00001886
0.00001846
0.00001787
0.00001728
0.00001690
0.00001651
0.00001595
0.00001544
0.00001512
0.00001480
0.00001432
0.00001384
0.00001353
0.00001322
0.00001277
0.00001232
0.00001202
0.00001172
0.00001125
0.00001074
0.00001037
0.00000997
0.00000936
0.00000880
0.00000887
0.00000889
0.00000890
0.00000894
0.00000893
0.00000886
0.00000879
0.00000867
0.00000860
0.00000852
0.00000844
0.00000837
0.00000834
0.00000822
0.00000808
0.00000782
0.00000777
0.00000770
0.00000770
0.00000777
0.00000778
0.00000776
0.00000766
0.00000751
0.00000733
0.00000712
0.00000688
0.00000661
0.00000632
0.00000613
0.00000597
0.00000582
0.00000567
0.00000551
0.00000536
0.00000523
0.00000509
0.00000494
0.00000480
0.00000464
0.00000449
0.00000435
0.00000419
0.00000404
0.00000383
0.00000361
0.00000341
0.00000321
0.00000295
0.00000271
0.00000249
0.00000227
0.00000207
0.00000189
0.00000172
0.00000156
0.00000142
0.00000129
0.00000117
0.00000107
0.00000094
0.00000085
0.00000077
0.00000072
0.00000069
0.00000067
0.00000066
0.00000064
0.00000062
0.00000058
0.00000054
0.00000049
0.00000043
0.00000036
0.00000029
0.00000021
0.00000014
0.00000009
0.00000017
0.00000029
0.00000040
0.00000049
0.00000056
0.00000061
0.00000064
0.00000066
0.00000066
0.00000066
0.00000065
0.00000063
0.00000059
0.00000055
0.00000049
0.00000044
0.00000038
0.00000033
0.00000029
0.00000024
0.00000020
0.00000016
0.00000014
0.00000010
0.00000008
0.00000006
0.00000004
0.00000003
0.00000003
0.00000002
0.00000001
0.00000001
0.00000000
0.00000000
0.00000000
0.00000000
0.00000000
0.00000000
0.00000000
maximum error magnitude for empirical fitting function
np4kinf
analytical
4
9
13
14
16
17
18
16
15
19
17
20
19
20
21
20
18
19
20
19
20
16
19
20
22
21
22
23
21
22
20
21
24
21
24
23
24
25
26
number of data used in regression analysis for kminf
kinf
0.33787707
0.33787686
0.33787670
0.33787654
0.33787602
0.33787497
0.33787340
0.33787183
0.33786921
0.33786659
0.33786398
0.33786136
0.33785612
0.33785089
0.33784565
0.33784042
0.33783518
0.33782995
0.33782471
0.33781686
0.33780901
0.33780116
0.33779331
0.33778284
0.33777237
0.33776191
0.33775144
0.33774098
0.33773051
0.33772005
0.33770958
0.33769912
0.33768342
0.33766773
0.33765204
0.33763635
0.33761543
0.33759974
0.33758405
0.33756314
0.33754745
0.33753177
0.33751085
0.33749517
0.33747949
0.33745858
0.33744290
0.33742723
0.33740632
0.33739065
0.33737497
0.33735408
0.33732796
0.33730184
0.33727572
0.33724961
0.33722350
0.33719739
0.33717129
0.33714519
0.33711909
0.33709299
0.33706690
0.33704080
0.33701472
0.33698863
0.33695211
0.33691560
0.33687388
0.33683216
0.33678003
0.33672790
0.33667578
0.33662368
0.33657158
0.33651950
0.33646742
0.33641535
0.33636329
0.33631125
0.33625921
0.33620718
0.33615516
0.33610315
0.33605115
0.33599916
0.33594718
0.33589520
0.33584324
0.33579129
0.33568741
0.33558357
0.33542787
0.33527226
0.33516856
0.33506490
0.33490947
0.33475413
0.33465061
0.33454713
0.33439197
0.33423689
0.33413355
0.33403024
0.33387534
0.33372052
0.33361735
0.33351421
0.33335957
0.33320501
0.33310201
0.33299904
0.33284465
0.33269034
0.33258751
0.33248471
0.33233057
0.33217651
0.33207384
0.33197121
0.33181732
0.33166350
0.33156100
0.33145853
0.33130489
0.33115131
0.33094666
0.33063993
0.33043561
0.33012935
0.32992535
0.32961957
0.32941588
0.32911057
0.32890719
0.32860236
0.32839929
0.32809492
0.32789216
0.32758825
0.32738580
0.32708235
0.32688020
0.32657721
0.32607282
0.32556919
0.32506630
0.32456416
0.32406275
0.32356209
0.32306215
0.32256294
0.32206446
0.32156670
0.32106965
0.32057333
0.32007771
0.31958281
0.31908861
0.31859512
0.31810232
0.31761023
0.31711883
0.31662813
0.31613812
0.31564879
0.31491610
0.31418494
0.31345531
0.31272720
0.31175875
0.31079298
0.30982988
0.30886943
0.30791161
0.30695642
0.30600384
0.30505385
0.30410645
0.30316163
0.30221936
0.30127965
0.29987484
0.29847571
0.29708222
0.29569434
0.29385251
0.29247760
0.29110820
0.28929086
0.28703277
0.28478969
0.28256149
0.28034805
0.27814928
0.27596506
0.27379531
0.27163991
0.26949879
0.26737185
0.26316016
0.25900419
0.25490330
0.25085690
0.24686441
0.24292528
0.23903899
0.23520503
0.23142291
0.22769214
0.22401227
0.22038283
0.21503228
0.20979276
0.20297697
0.19635272
0.18991678
0.18366597
0.17759713
0.17026220
0.16320058
0.15640611
0.14987257
0.13994593
0.13064489
0.12194254
0.11381137
0.10622342
0.09745934
0.08944466
0.07544625
0.06380973
0.03393650
0.01504649
0.00461719
0.00096958
0.00016132
0.00000016
0.00000000
extrapolated value for kminf obtained by regression
analysis.
