Page 54 - Vertical City

54 the vertical city

The volume contained in each horizontal principal
conduit 4 is thus: n²(n-2)iΩLx/16; and for the four: n 2(n-2)
iΩLx/4.

This leads to a volume V = n²Ωi[(n-2)Lx+(i-1)h]/2
contained in the whole system of vertical and horizon-
tal conduits deserving a gross floor area of P = n²B²i,
it may also by expressed by V = n²Ωih[i(n-2)(L/H+B/
H)+(i-1)]/2.

The ratio V/P measures the financial load of the
network of conduits to each build gross square
meter: V/P = Ωh[i(n-2)(L/H+B/H)+(i-1)]/2B² or with
n = (P/(iB)²)1/2:

2V/ΩP = ɣ = h{i[1-2(L/H+B/H)]+(iP/B²)1/2(L/H+B/H)-1}/B².

For a given value of P and in function of the chosen
rule (being either L/H or L/B), indifferent to n, it
depends only of i.

Choosing the rule L/H = α = constant:

ɣ = h{i[1-2(α+B/ih)]+(iP/B²)1/2(α+B/ih)-1}/B²

Figure 17 and table 1 with B = 30 m and h = 3,3 m
provide the corresponding values of ɣ with regard to i
for L/H = 2 et P respectively 2 million m² for the small
city and then 20, 80 and 320 million m².

∑4 n - 1 k(niΩ Lx/2) = n2(n-2)iΩLx/16
2
k = 1