Why must the tether be thickest in the middle?

Each piece of tether holds up the net weight of everything below it. In the rotating frame the net force points down below GEO and outward above it, so tension peaks at GEO. If the stress is to be the same everywhere (constant-stress design), the cross-section has to grow as A(r)/A₀ = exp(Φ(r)·ρ/σ), where Φ is the effective potential difference in the rotating frame, about 48.4 MJ/kg from Earth's surface to GEO. That ratio is the taper ratio.

Why do people say only carbon nanotubes would work on Earth?

The exponent in the taper ratio is 48.4 MJ/kg divided by the specific strength σ/ρ. Kevlar manages about 2.5 MJ/kg, giving a taper ratio of about e¹⁹, some 260 million; steel is astronomically worse. Only materials with tens of MJ/kg bring the ratio down to a few or a few dozen and the tether mass to something sane. Single nanotubes and graphene qualify in theory, but long fibres made from them are much weaker today, so the tool marks those values as theoretical or hoped for.

What happens if you let go at different heights?

A released object keeps the elevator's sideways speed ωr. Below GEO that is slower than circular orbit speed, so the release point becomes the apogee; below about 23,500 km the perigee dips into the atmosphere or the ground. At GEO it just stays put. Higher up the speed exceeds circular speed and the release point becomes the perigee; beyond about 46,700 km (r = (2μ/ω²)^(1/3)) it reaches escape speed and can head for the Moon or the planets with no rocket.

How much energy and time does the climb to GEO take?

In the rotating frame the motor only has to beat the effective potential, about 48.4 MJ or 13.4 kWh per kilogram, around $1.30 at $0.10 per kWh. In the inertial frame the payload also gains about 2.6 kWh/kg of kinetic energy, which comes from Earth's rotation through the sideways tether tension that supplies the Coriolis force. At 200 km/h the climb to GEO takes about 7.5 days.

Are elevators on the Moon or Mars easier?

Much easier. Mars has 38% of Earth's gravity, a stationary orbit about 17,000 km up and a potential depth of about 9.5 MJ/kg, though Phobos orbits at about 6,000 km and would cross the tether. The Moon spins so slowly that its stationary orbit lies outside its gravitational reach, so a lunar elevator runs from the Earth-facing side to the Earth–Moon L1 point about 58,000 km up. In the rotating Earth–Moon frame that is only about 2.7 MJ/kg deep, and existing fibres such as Kevlar or Dyneema give taper ratios of just a few.

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🗼Space Elevator Calculator - Taper Ratio, Materials, Climb & Release Orbits

In the frame that rotates with Earth, a space elevator tether feels gravity pulling down and centrifugal force pulling out, and the two cancel at the geostationary altitude of 35,786 km. The tool plots the net acceleration with altitude, works out how much a constant-stress tether must thicken from the ground to GEO, and compares steel, Kevlar, Zylon, carbon fibre, carbon nanotubes and graphene. An animated climber rises and lets go at a chosen height: below about 23,500 km it falls back, above about 46,700 km it escapes Earth. You can also explore the counterweight trade-off and compare elevators on the Moon and Mars.

Free · No sign-up · Runs in your browserLast updated: 2026-10-29

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How to use Space Elevator

1On Tether & materials, choose a material, safety factor and design load and read the taper ratio, breaking length and tether mass
2On Climb & release, set the climb speed, release altitude and tether end, then press Start climbing
3Read the climb time, motor work and the orbit after release (perigee, apogee or escape speed)
4Drag the tether end on Counterweight, and compare the three bodies on Moon / Mars

FAQ

Why must the tether be thickest in the middle?: Each piece of tether holds up the net weight of everything below it. In the rotating frame the net force points down below GEO and outward above it, so tension peaks at GEO. If the stress is to be the same everywhere (constant-stress design), the cross-section has to grow as A(r)/A₀ = exp(Φ(r)·ρ/σ), where Φ is the effective potential difference in the rotating frame, about 48.4 MJ/kg from Earth's surface to GEO. That ratio is the taper ratio.
Why do people say only carbon nanotubes would work on Earth?: The exponent in the taper ratio is 48.4 MJ/kg divided by the specific strength σ/ρ. Kevlar manages about 2.5 MJ/kg, giving a taper ratio of about e¹⁹, some 260 million; steel is astronomically worse. Only materials with tens of MJ/kg bring the ratio down to a few or a few dozen and the tether mass to something sane. Single nanotubes and graphene qualify in theory, but long fibres made from them are much weaker today, so the tool marks those values as theoretical or hoped for.
What happens if you let go at different heights?: A released object keeps the elevator's sideways speed ωr. Below GEO that is slower than circular orbit speed, so the release point becomes the apogee; below about 23,500 km the perigee dips into the atmosphere or the ground. At GEO it just stays put. Higher up the speed exceeds circular speed and the release point becomes the perigee; beyond about 46,700 km (r = (2μ/ω²)^(1/3)) it reaches escape speed and can head for the Moon or the planets with no rocket.
How much energy and time does the climb to GEO take?: In the rotating frame the motor only has to beat the effective potential, about 48.4 MJ or 13.4 kWh per kilogram, around $1.30 at $0.10 per kWh. In the inertial frame the payload also gains about 2.6 kWh/kg of kinetic energy, which comes from Earth's rotation through the sideways tether tension that supplies the Coriolis force. At 200 km/h the climb to GEO takes about 7.5 days.
Are elevators on the Moon or Mars easier?: Much easier. Mars has 38% of Earth's gravity, a stationary orbit about 17,000 km up and a potential depth of about 9.5 MJ/kg, though Phobos orbits at about 6,000 km and would cross the tether. The Moon spins so slowly that its stationary orbit lies outside its gravitational reach, so a lunar elevator runs from the Earth-facing side to the Earth–Moon L1 point about 58,000 km up. In the rotating Earth–Moon frame that is only about 2.7 MJ/kg deep, and existing fibres such as Kevlar or Dyneema give taper ratios of just a few.

Features

Gravity, centrifugal and net acceleration vs altitude in the rotating frame, with the stationary orbit found automatically
Closed-form constant-stress cross-section A(r)/A₀ = exp(Φρ/σ) and a taper-ratio table for eight materials
Inertial-frame animation: the elevator turns with Earth and the released climber follows RK4 two-body motion
Release outcome (impact, ellipse or escape) with the lowest safe release height and the escape release height
Counterweight, tether and total mass vs tether length
Earth, Mars and a lunar elevator through Earth–Moon L1 compared by potential depth and taper ratio

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