User Manual

Determining the Number of Innerducts Contained in Outerducts
Outerducts enclosing a given number of innerducts based on volume. --four of many
possible compact arrangements of circles within a circle are shown at A, B, C, and D in
Fig. 1.
1. Arrangements of Center of Core Innerducts: the four most common arrangements of
center or core innerducts are shown cross-sectioned in Fig 1. It may seem that the “A”
pattern would require the smallest enclosing outerduct for a given number of enclosed
innerducts, but this is not always the case since the most compact arrangement will, in part,
depend on the number of innerducts to be enclosed.
ABC D
Fig. 1
2. Diameter of Enclosing Outerduct: Successive, complete layers of innerducts may be
placed around each of the central cores, Fig. 1, of 1, 2, 3, or 4 innerducts as the case may be.
The number of innerducts contained in arrangements of complete layers around a central core
of innerducts, as well as the diameter of the enclosing outerducts, may be obtained using the
data in Table 1.
Thus, for example, the “A” pattern in Fig. 1 shows by actual count, a total of 19
innerducts arranged in two complete “layers” around a central core consisting of one
innerduct. This agrees with the data shown in the left half of table 1 for n = 2
To determine the diameter of the enclosing outerduct, the data in the right half of
Table 1 is used. Thus, for n = 2 and an “A” pattern, the diameter D is 5 times the
diameter d of the enclosed innerducts.
3. Number of Innerducts, N, Enclosed by an Outerduct: The diameters of innerduct
and outerduct are already known and use the data in the left half of Table 1 is used.
Thus, for example, if D = 16” and d = 1.66”, and an “A” pattern, we would divide
16/1.66 (D/d) which gives an answer of 9.64. Truncating the decimal portion gives 9.
Therefore, D is 9 times larger than d (D= 9d). Look in the right half of Table 1 and
find in the “A” pattern the value “9d.” Follow the row across to the “A” pattern in the left
half of the table to obtain the No. of innerducts, which is 61.
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