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== Parameters for two pulley elevators == || || Launch Loop || SE1000 || unit || || Height || 68 || 1000 || km || || pulley diam || 40 || 40 m || m || || speed || 400 || || m/s || || altitude0 || 4 || 0 || km || || altitude1 || 72 || 1000 || km || || g0 || 9.79 || 9.81 || m/s^2^ || || g1 || 9.59 || 7.33 || m/s^2^ || || Tension 0 || 200000 || || N || || Tension 1 || 420000 || || N || || Material || Kevlar 49 || CNT || || || Density || 1440 || 1300 || kg/m3 || || Modulus || 127 || 630 || GPa || || strength || 3.6 || 150 || GPa || || safety || 2.0 || || || || area || 2.33 || || cm^2^ || || diameter || 1.72 || --- || cm || || width || --- || || || || thickness || --- || || || || mass || 46000 || || kg || |
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| The launch loop uses round cables for the elevator. The electric field $ E_0 $ will be highest at the edge of the cable: $ E_0 = 2 \pi \epsilon_0 \lambda / r_{cable} $ Where $ \lambda $ is the charge density in Colombs/meter and $ \epsilon_0 = $ 8.85 E-12 farad/meter is the permittivity of vacuum (and air, to a good approximation). Alternately, for a given maximum electric field (say, 100KV/m, 3% of the breakdown field of air) then $ \lambda $ is given by: $ \lambda = r_{cable} * E_{max} / 2 \pi \epsilon_0 $ The actual voltage on the cables might be a few hundred kilovolts, depending on the geometry of the bottom pulley in relation to ground. If both cables have the same voltage, then they will have the same charge, and repel. The repulsion force per length $ f $ is given by the charge density times the electric field at the spacing distance $ r_{space} $ : The space elevator uses wide and very thin strips. The limiting fields will we quite high at the edges |
Pulley Elevators
for the Launch Loop and the Space Elevator
A pulley elevator is a simple-appearing way to provide both support and lift in a space elevator or a launch loop. The vehicle can be passive, containing no more than some kind of automatically actuated clamp so that it can release from one moving elevator cable and clamp onto another.
Real life is never that simple. The main drawback for an elevator cable is that if it is tall enough and the cables are closely spaced, then they can easily come close enough to abrade each other. The design must prevent this. The other problem is the same as all long cables, where force changes are rapid compared to the speed-of-sound propagation time; the analysis is complicated, and involves not just the static stretch of the cable, but the inertia and mass flow rate.
Megastructure cables and elevators face yet another complication; their interaction with a nonlinear gravitational field in a rotating frame. Very long cables may move in ways not anticipated by a designer focused on elasticity and strength of materials, particularly movements radially from the expected straight-line path. Electrostatic repulsion may also play a role.
Parameters for two pulley elevators
|
Launch Loop |
SE1000 |
unit |
Height |
68 |
1000 |
km |
pulley diam |
40 |
40 m |
m |
speed |
400 |
|
m/s |
altitude0 |
4 |
0 |
km |
altitude1 |
72 |
1000 |
km |
g0 |
9.79 |
9.81 |
m/s2 |
g1 |
9.59 |
7.33 |
m/s2 |
Tension 0 |
200000 |
|
N |
Tension 1 |
420000 |
|
N |
Material |
Kevlar 49 |
CNT |
|
Density |
1440 |
1300 |
kg/m3 |
Modulus |
127 |
630 |
GPa |
strength |
3.6 |
150 |
GPa |
safety |
2.0 |
|
|
area |
2.33 |
|
cm2 |
diameter |
1.72 |
--- |
cm |
width |
--- |
|
|
thickness |
--- |
|
|
mass |
46000 |
|
kg |
Limiting Case - a moving cable without external tension
More Later
Limiting Case - a non-moving cable around pulleys
More Later
Electrostatic Repulsion
The launch loop uses round cables for the elevator. The electric field E_0 will be highest at the edge of the cable:
E_0 = 2 \pi \epsilon_0 \lambda / r_{cable}
Where \lambda is the charge density in Colombs/meter and \epsilon_0 = 8.85 E-12 farad/meter is the permittivity of vacuum (and air, to a good approximation). Alternately, for a given maximum electric field (say, 100KV/m, 3% of the breakdown field of air) then \lambda is given by:
\lambda = r_{cable} * E_{max} / 2 \pi \epsilon_0
The actual voltage on the cables might be a few hundred kilovolts, depending on the geometry of the bottom pulley in relation to ground. If both cables have the same voltage, then they will have the same charge, and repel. The repulsion force per length f is given by the charge density times the electric field at the spacing distance r_{space} :
The space elevator uses wide and very thin strips. The limiting fields will we quite high at the edges
More Later
The Steady State General Case - moving cables around pulleys, without velocity change
More Later
The Dynamic General Case, with velocity change
More Later