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Supplementary Information for
Grover's Inductance Calculations
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Inductance Calculations: Working Formulas and Tables
F W Grover, 1946 and 1973. Dover Phoenix Edition 2004. ISBN: 0 486 49577 9. Dover Publications. Dr Frederick W Grover's monograph for engineers and scientists engaged in the accurate calculation of self and mutual inductance. The book is based on the work carried out by E B Rosa and F W Grover during their distinguished careers at the American National Bureau of Standards during the first half of the 20th Century. Much of the information is given in tabular form; as befits the calculation methods used at the time, but source material is fully referenced, and most of the generating functions are presented and explained. |
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Chapter Headings: 1. General principles. 2. Methods of calculating inductances. 3. Geometric Mean Distances. 4. Construction of and method of using the collection of working formulas. Part 1: Circuits whose elements are straight filaments. 5. Parallel elements of equal length. 6. Mutual inductance of unequal parallel filaments. 7. Mutual inductance of filaments inclined at an angle to each other. 8. Circuits composed of combinations of straight wires. 9. Mutual inductances of equal parallel polygons of wire. 10. Inductance of single-layer coils on rectangular winding forms. Part 2: Coils and other circuits composed of circular elements. 11. Mutual inductance of coaxial circular filaments. 12. Mutual inductance of coaxial circular coils. 13. Self-inductance of circular coils of rectangular cross section. 14. Mutual inductance of a solenoid and a coaxial circular filament. 15. Mutual inductance of coaxial single-layer coils. 16. Single-layer coils on cylindrical winding forms. 17. Special types of single-layer coil. 18. Mutual inductance of circular elements with parallel axes. 19. Mutual inductance of circular filaments whose axes are inclined to one another. 20. Mutual inductance of solenoids with inclined axes and solenoids and circular coils with inclined axes. 21. Circuit elements of larger cross sections with parallel axes. 22. Auxiliary tables of functions which appear frequently in inductance formulas. 23. Formulas for calculation of the magnetic force between coils. 24. High frequency formulas. |
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Errata and Supplementary Information: Errors and their corrections are shown below in the form of scanned pages marked in pencil. Most of these were discovered through the careful work of Rodger Rosenbaum.  Active links lead to documents giving corroborative information. |
.Pages 19-22.
 A
complete re-calculation
of tables 1, 2, and 3 (pages 19-22) has been given by
Rodger Rosenbaum. See [Grover_p19-22.pdf].
Most of the errors are small except for the one shown above,
which should be marked on any working copy. |
.Page 34.
| The above contains a simple arithmetic error: 0.002 x 304.8 x 3.6889 = 0.7162 |
.Chapter 15, p122-141.
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Mutual inductance of coaxial single-layer coils: A discussion of the accuracy of Grover's tabular calculation method is given in ref [27]. Claims made in that paper relating to inaccuracies in Grover's method may however be flawed, due to the unsubstantiated assumption that FEEFC calculations are equivalent to actual measurements. At time of writing (4th April 2009) Rodger Rosenbaum is investigating this matter, and a report will follow; but apart from changes in the last digit of some tabulated values, no errors have been found in Grover's work. |
.Pages 143-147.
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Formula 119, p143, is Coffin's formula truncated, which is in
turn an extended version of the Rayleigh-Niven formula (see [Sci169,
p116-117], formula 69 and formula 71). The second term in
the series should be: . . . + (β²/8)[ln(4/β) +
1/4] - . . . Consideration was given to the possibility that Grover might be correcting errors in the 1911 document, but a comparison against Lundin's formula [5] indicated that 1/4 was the best choice for the term in question. Rodger Rosenbaum has since compared the formula against Lorenz's exact expression, and confirms this conclusion (see: p143err.gif). Note however, Grover's comment above: "For values of β as large as 1/4 three terms will suffice for an accuracy better than 1 part in 1000". As is confirmed by Rodger's calculation, even with the error, this statement is correct. Rodger comments: "When you look at the plots, it is clear that 1/4 is the right value. The error as β gets small descends right down to the round-off error of the arithmetic for a value of 1/4, but not for 1/8. The fact that the error is better than 1 part in 1000, as Grover says, even with 1/8, suggests that he did some calculations with the 1/8 value, and noticed the error was 1 part in 1000, failing to notice that with 1/4 the error would be much smaller." Rodger has also calculated the exact values of Nagaoka's coefficient K as they should appear in tables 36 and 37 (p144-147), (see tables036-37.gif). Some minor differences occur, and the tables may be amended using the data provided. |
.Pages 149-150.
| A recalculation of Rosa's mutual inductance correction factor H (Table 39, p150) to 10 decimal places, and a discussion of the GMD method, is given in [Weaver 2008]. Grover's table has no errors greater than 1 in the last digit, but the more accurate information may be preferred. Weaver's article also provides information on the coding of calculation routines. A one-line continuous formula which gives H with a maximum absolute error of better than ±0.000 000 02 is given in [TA3.2]. |
.Page 151.
| A comma has been inserted instead of a decimal point: p = 30.5510 |
.Page 156.
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Arithmetic error: -0.0023 x
7051 = -16.2173 7051 - 16.2 = 7034.8 |
.Page 161.
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On page 161, the last line in formula 134 reads: a=2.451b But this has to be 2a=2.451b The number "2" is missing. For confirmation, see line 1 of formula 134: 2a/b=2.451 Thomas Heckel |
.Page 164.
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Here the error can be seen by looking back at formula 135 (p163);
Grover used the diameter (12 inches) instead of the radius (6
inches). The above should read: ΔL = 0.004 π (20)(6 x 2.54)(-0.2453) = -0.9396 µH, and the inductance of the helix is: L = 70.71 - (-0.9396) = 71.65 µH. |
| David Knight & Rodger Rosenbaum, April 2009. |
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