Editing Space elevator (section)

===Cable section===
Historically, the main technical problem has been considered the ability of the cable to hold up, with tension, the weight of itself below any given point. The greatest tension on a space elevator cable is at the point of geostationary orbit, {{convert|35786|km|mi|0|abbr=on}} above the Earth's equator. This means that the cable material, combined with its design, must be strong enough to hold up its own weight from the surface up to {{convert|35786|km|mi|0|abbr=on}}. A cable which is thicker in cross section area at that height than at the surface could better hold up its own weight over a longer length. How the cross section area tapers from the maximum at {{convert|35786|km|mi|0|abbr=on}} to the minimum at the surface is therefore an important design factor for a space elevator cable.

To maximize the usable excess strength for a given amount of cable material, the cable's cross section area would need to be designed for the most part in such a way that the [[Stress (mechanics)|stress]] (i.e., the tension per unit of cross sectional area) is constant along the length of the cable.<ref name="aravind" /><ref>Artuković, Ranko (2000). [http://www.zadar.net/space-elevator/ "The Space Elevator".] zadar.net</ref> The constant-stress criterion is a starting point in the design of the cable cross section area as it changes with altitude. Other factors considered in more detailed designs include thickening at altitudes where more space junk is present, consideration of the point stresses imposed by climbers, and the use of varied materials.<ref name="PhaseII"/> To account for these and other factors, modern detailed designs seek to achieve the largest ''[[Factor of safety#Margin of safety|safety margin]]'' possible, with as little variation over altitude and time as possible.<ref name="PhaseII"/> In simple starting-point designs, that equates to constant-stress.

For a constant-stress cable with no safety margin, the cross-section-area as a function of distance from Earth's center is given by the following equation:<ref name="aravind" />

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|cWidth = 330
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|Description = Several taper profiles with different material parameters
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{{block indent|<math>A( r ) = A_s \exp\left[ \frac{\rho g R^2}{T}\left( \frac{1}{R}+\frac{R^2}{2R_g^3}-\frac{1}{r}-\frac{r^2}{2R_g^3} \right) \right]</math>}}

where
{{block indent|<math>g</math> is the gravitational acceleration at Earth's surface (m·s<sup>−2</sup>),}}
{{block indent|<math>A_s</math> is the cross-section area of the cable at Earth's surface (m<sup>2</sup>),}}
{{block indent|<math>\rho</math> is the density of the material used for the cable (kg·m<sup>−3</sup>),}}
{{block indent|<math>R</math> is the Earth's equatorial radius,}}
{{block indent|<math>R_g</math> is the radius of geosynchronous orbit,}}
{{block indent|1=<math>T</math> is the stress the cross-section area can bear without [[Yield (engineering)|yielding]] (N·m<sup>−2</sup>), its elastic limit.}}

Safety margin can be accounted for by dividing T by the desired safety factor.<ref name="aravind" />