Maximum climber capacityThroughput (at maximum capacity)
Performance vs. maximum power
Maximum climber capacityThroughput (at maximum capacity)
Performance vs. maximum speed
Maximum climber capacityThroughput (at maximum capacity)
Table vs. altitude
Table vs. launch period
Table vs. maximum power
Table vs. maximum speed
Equatorial tether, static in the frame rotating with the Earth. The effective gravity
g(r) = GM/r² − ω²r includes the centrifugal term; it vanishes at GEO
and is negative (outward) above it.
The unloaded tether carries the working stress σ = σmax/FoS everywhere (uniform-stress design),
so its unstrained cross-section is proportional to its tension. The material is strained by ε = σ/E,
so a stretched metre of tether contains only 1/(1+ε) m of material. This makes the tether lighter
and less tapered than a rigid model would predict; the “mass if strain were ignored” output shows the difference.
The tether has the given strained length and ends in a counterweight that supplies the tension at the top.
Tensions are labelled in kg using the effective gravity at the base, g0,
so a climber of m kg sitting at the base removes exactly m kg of base tension.
Each climber of total mass m climbs at v = min(vmax, P/(m g)),
with all power going into lifting against effective gravity. One climber is launched every launch period;
the worst-case loading has one climber at the base and climbers at every launch-period interval up to GEO.
Climbers above GEO would increase base tension, so they are ignored.
Climber payload = total mass − fixed mass − (mass per MW)·P − (mass per km/h)·vmax
− (mass per kg)·total mass. The base climber mass is total mass minus payload. Throughput is shown both for
total climber mass and for payload; curves stop where the payload would be zero or negative.
A climber at radius r lowers the tension everywhere below it by m g(r). The base tension
fraction plot shows |g(r)|/g0: the effect of a climber at that height on the base
tension relative to the same climber at the base.
Sizing: the tether is scaled so that, fully loaded, the base tension is the minimum tension fraction times the
unloaded base tension. In “specify climber total mass” mode this gives the tether capacity; in “specify capacity”
mode the largest climber total mass satisfying the condition is found. The performance plots keep the tether
capacity fixed and vary one climber parameter at a time.
Elastic changes in tether length caused by climber loads are neglected.
Reel-in: the tether material that sat between the ground and the given design altitude is pulled onto a
drum at the base; the design (material and counterweight) is unchanged. The new static equilibrium is solved
with linear elasticity: along the unstretched length s, dr/ds = 1 + T/(A0E)
and dT/ds = ρA0g(r), with the counterweight balancing the top tension
and the bottom held at the ground. The counterweight moves down, so the base tension (and with it the climber
capacity) drops. Reeled-in curves are dashed; the reeled tether's capacity uses its own unloaded base tension
and the same minimum tension fraction.