Space Elevator—A Revolutionary Space Transportation System
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1000 GPa, and the theoretical value for its maximum tensile strength is 130 GPa.
If the maximum strength of the ribbon material was only 70 GPa, its characteristic
height would be 2,762 km using a safety factor of about two (σ 0 = 35.2 GPa), and
the variation in area of cross section would be as shown in Fig. 6).
The nominal tension in the ribbon may now be expressed as
T 0 (s) = σ 0 A(s) = σ 0 A m exp[F(s)]
(19)
The mass of the ribbon is given by
m t = γ A m
L 0
0
exp[F(s)]ds
(20)
Through manipulation of Eq. (17), the required counterweight may be expressed as
m c = γ A m ¯
h
exp
F(s)| s=L 0
R E
R G
2
R E +L 0 (1+ε 0 )
R G
−
R G
[R E +L 0 (1+ε 0 )]
2
(21)
Fig. 7 Mass (per mm 2 of maximum cross-sectional area) of space elevator components versus
nominal ribbon length