Project Cyclops, A Design... - Department of Earth and Planetary ...

where r = "Ym/'rs- If we let
o-_--o----_
+ --
Nef f = n + (kr - l)P,_n (L7)
c_
c
-------o--,_ ---3_ ----o_- _----o
be the effective number of side tunnels of length s, then
we have simply
C = SNell7 s (L8)
For the tunnel pattern shown in Figure L-la, k = I,
and N m is twice the nearest inleger to as/S = x/)T/rr- i/2.
Thus,
Aim= ,.l_ntd7 ) (L9)
Pattern
2(a)
where "int" means "the integer part of." Substituting in
equation (L7) we find
_, \ / /
_, \ ,_ \, [ / / ,,
Nla = n + 2(r- 1) int _ (LI0)
For the tunnel pattern of Figure L-!b, k = VC2-and
N m is ]bur times the nearest integer to (as/SW_) - 1.
Thus,
.....
Nlb = n + 4(Vr}-r - 1) int (LI 1)
9
For the tunnel pattern of Figure L-2a, k = _v/-ff/2 and
n m is twice tile nearest integer to 2ah/X/3s. Thus,
/ / /), \ ,,
Pattern
2(b)
3,'2a = ,
(L12)
Figure L-2. Tunnel patterns fi_r hexagonal lattice array.
If we divide N by n to obtain the .:_l_ern factor
f= N/n, we can express the tunneling cost simply as
Finally, for the tunnel pattern of Figure L-2b,
k = 2 anti N m is six times the nearesl integer to
(% - s_3/2)/es.
C = J'nSTs = fnC u (LI 4)
N2b = n+6(2r-ltint-- i _J4 / F,/v n +l-v/-3 )
Ll _)
where Cu = cost of a unit side tunnel. Table L-3 !isis the
pattern factors for the tunnel pattern of Figures l.-I and
L-2 for various sizes of array, and for r = l _
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