Page 52 - Vertical City

52 the vertical city

The theoretical model comprises nxn identical buil-
dings, square in plan BxB, with i levels each of height h
(H = ih) located on a square grid which orthogonal axes
are distant of Lx = L+B.

The network connects the i floor and every ground
floor horizontally to the city center.

Whatever the value of n, the total volume contained
in the conduits of the network is minimum when, from
the city center, four main conduits (in the layout of a
cross) feed (each) n/2 secondary conduits serving each
n/2 buildings, all of a length of (n/2-1)Lx.

Each main conduit so links n²/4 buildings [figure 16].
The conduit with a section Ω at the highest level i
of each building has a section of iΩ at the ground floor.
The volume contained in the vertical conduit on
the height (i-1)h between level i and the ground floor
is thus 2 i(i-1)Ωh/2 for each building and i(i-1)n²Ωh/2 for
the n² buildings.
The section at the end of a horizontal secondary
conduit being iΩ, each horizontal secondary conduit
presents a section that increases from iΩ at the outs-
kirts of the city to (n-2)iΩ/2 for its last section, passed
the building n/2-1, where it connects to the main hori-
zontal conduits at building n/2.

∑2 i-1 k(Ωh) = i(i-1)Ωh/2
k = 1