Space Elevator Tether Taper Profile

Tether Material

Safety factor 1.5×

Counterweight altitude 1.5× GEO

Anchor cable diameter 10 mm

Readouts

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Taper ratio A(r_GEO) / A₀

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Taper ratio at counterweight

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Estimated tether mass

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How it works

A space-elevator tether can't have constant thickness. To hold the same tensile stress σ = T(r)/A(r) everywhere, its cross-sectional area A(r) must grow with altitude wherever the outward centrifugal pull exceeds gravity, and shrink where gravity still dominates. Balancing forces on a slice dr of the cable gives:

A(r) = A₀ · exp[ (ρ/σ) · ( ω²(r² − R⊕²)/2 + g₀R⊕²(1/r − 1/R⊕) ) ]

ρ  = material density        σ  = allowable tensile stress (÷ safety factor)
ω  = Earth's rotation rate   g₀ = surface gravity      R⊕ = Earth's radius

The exponent depends only on the material's specific strength σ/ρ — this is the single number that decides whether a space elevator is buildable. Push r out past geostationary orbit (r_GEO ≈ 35,786 km altitude, where centrifugal force exactly cancels gravity) and the exponent flips sign, so a counterweight anchored beyond GEO pulls the whole tether taut without a motor.

Material — sets ρ and σ. Steel and Kevlar have low specific strength, so the exponent (and the required taper) explodes to physically impossible values. Only a defect-free carbon nanotube fiber keeps the taper ratio in a buildable range — the real reason no space elevator has been built with today's mass-produced materials.
Safety factor — divides the allowable stress, directly multiplying the exponent (and the taper).
Counterweight altitude — how far past GEO the top anchor sits; more overshoot means more restoring tension but a taller, heavier structure.
Anchor diameter — the physical cross-section at the ground station, which sets the absolute (not just relative) mass of the whole cable.

The visualization renders the true taper shape (radius mapped to log₁₀ of the local area ratio so both ends stay visible on screen) and colors it from blue (thin, low-stress cross-section) to red (wide, high-stress cross-section).

Thin — low required area Wide — high required area GEO altitude ring

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