Space Elevator Coriolis Deflection

Climb Controls

Climber speed 360 km/h

Tether restoring period 5.0 h

Damping ratio ζ 0.30

Time acceleration 6000×

Live Readouts

Altitude

0 km

Elapsed

0.0 d

Tether deflection

0.00°

Coriolis accel.

0.00 mm/s²

Climber radius vs GEO

below GEO

How it works

The tether co-rotates with Earth at Ω = 2π / 86164 s. A climber moving outward at radial speed v_r in this rotating frame feels a Coriolis acceleration a_cor = 2Ω·v_r, directed tangentially (east–west) — it always pushes westward while ascending. The tether reacts elastically, so the whole rod tilts about its anchor by a small angle φ that obeys a driven, damped torsional oscillator:

φ'' = 2Ω·v_r / r(t)  −  2ζω₀·φ'  −  ω₀²·φ

r(t)   = climber's distance from Earth's center
ω₀     = 2π / T   (T = "restoring period" slider — stiffer tether ⇒ shorter T)
ζ      = damping ratio (how quickly tether sway is absorbed)

The driving term 2Ω·v_r/r shrinks as the climber gets farther out, so deflection is strongest low down and settles toward a smaller quasi-static value φ ≈ (2Ω·v_r/r)/ω₀² as altitude grows — exactly the mechanism real space-elevator engineering studies use to size the westward thrust or tether pre-lean needed to keep a climbing vehicle from swinging the whole structure out of alignment.

Climber speed — sets v_r; faster climbs mean a stronger, more sustained Coriolis push.
Restoring period — a stiffer (shorter-period) tether resists sway more and settles to a smaller deflection.
Damping ratio — how quickly any oscillation in the tilt dies out; near 0 the tether can overshoot and ring.
Time acceleration — a real climb takes days, so simulated time is sped up to watch the full ascent from surface to counterweight.

Below geostationary radius (≈35,786 km altitude) gravity dominates and the tether hangs in tension; beyond it centrifugal effects dominate and the counterweight keeps the cable taut outward — the "below/above GEO" readout tracks which regime the climber is in.

Tether & climber Earth (rotating frame) Counterweight

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