Determining the Number of Innerducts Contained in Outerducts

Determining the Number of Innerducts Contained in Outerducts
Table 1. Number of Circles, n, Contained in Complete Layers of Circles and Diameter of
Enclosing Circle
Arrangement of Innerducts in Center Pattern (see Fig. I)
n "A" "B" "C" "D" "A" "B" "C" "D"
No. of Innerducts, N, Enclosed Diameter, D, of Enclosing Outerduct*
0 1 2 3 4 d 2d 2.155d 2.414d
1 7 10 12 14 3d 4d 4.055d 4.386d
2 19 24 27 30 5d 6d 6.033d 6.379d
3 37 44 48 52 7d 8d 8.024d 8.375d
4 61 70 75 80 9d 10d 10.018d 10.373d
5 91 102 108 114 11d 12d 12.015d 12.372d
n****************
* Diameter D is given in terms of d, the diameter of the enclosed circles.
** For n complete layers over core, the number of enclosed circles N for
"A" center pattern is 3n^2+3n+1; for "B," 3n^2+5n+2; for "C,"
3n^2+6n+3; for "D," 3n^2+7n+4; while the diameter D of the enclosing
circle for "A" center pattern is (2n+1)d; for "B," (2n+2)d; for "C,"
(1+2(n^2+n+1/3)^.5)d; and for "D," (1+(4n^2+5.644n+2)^.5)d.
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