A Mechanical Drive for the Space Elevator, the "Reel to Reel Drive"

Part 1: A primitive, possible, but not very advisable method
Part 2: Pulling up with many ropes running over many reels

Abbreviations:

CNT = Carbon nanotubes
s= tensile strength in Newton per square meter (= Pa = Pascal)

CSA = cross-sectional area
1 GPa = 1 billion Pa = 1000 000 000 Pa
1kN = 1000 Newton

GEO = geo synchronous orbit
?= density in kg per cubic meter

L = breaking length (L = s:?)
?= specific weight in Newton per cubic meter (? = ?g)

Taper ratio = maximum CSA divided by minimum CSA (at ground)

Part1:

Would it be possible to lift the cabins ("climbers") of the space elevator like in any other elevator hanging them on a cable which is wound up by a motor? You would need (in addition to the cable, that is fastened to the ground, the "guiding cable") a second cable of the same dimensions, that has to carry its own weight too and hoist up the payload. Up in the end-station it is wound up on a giant winch. The counterweight must be moved accordingly. For a payload of 10t you have to hoist up about 100t CNT (carbon nanotube) cable.

Its weight is much less (with a taper ratio of 1:4 it is 40t) and decreases on the way up because the gravity decreases. The volume of the hoist cable would be 130 cubic meters, therefore a spool of about 6m diameter would do. Acceleration and speed on the way up can be as high as the winch can manage. The energy for hoisting up could come from solar panels (the GEO Station has full solar power nearly all the time) and must be stored by an appropriate method (electrolytic hydrogen and fuel cells, flywheel, etc.).

You can't let the hoist cable at the top run over a pulley like in usual elevators, going down on the other side, because the cable is tapered, and on the other side the thick part would hang under the thin part and it would be torn by its weight.

To bring the cabin back to earth from top-station let gravity do its turn, you just have to brake in time and you can even win energy back by using the motor as a generator. Only at the start you have to use an external force (maybe a tug climber running on the guiding cable), because the weight is only 2% and even this little bit is neutralized by the centrifugal force.

The disadvantages of this construction are a) the need for 2 of these very expensive cables, one of them flexible enough to be wound up on a spool and b) a very low transport capacity: Just one cabin can go up and then down at the time. But the travel time can be shortened with a powerful motor. If you start upwards with comfortable 0.5g acceleration, your weight seems to be 150% of normal. To continue with the same subjective load you can increase the acceleration as the gravity decreases till at some point you have to switch to deceleration. Your seat should swing 180° around, as the gross force now shows upwards. The deceleration can be as much more than 1.5g as your remaining weight and declines to 1.5g at the top station (in or near GEO). The travel time from ground to top would then be about 1 hour.

The travel time downwards depends on the power of the climber tug and over what distance he will haul cabin and hoist cable. The weight of a conductor that brings energy from GEO to the tug is very little up there, but the electric resistance of several 1000km is getting too high. By the way: CNT (carbon nanotubes) is said to be a very good conductor, so the electric current could flow through guiding and hoisting cable to the climber. As soon as the tug leaves, the acceleration will drop to rather low values: about 1%g at 30Mm (1Megameter = 1000km) above ground ("near" GEO-station), 4.4%g at 20Mm, 14%g at 10Mm and at last 1g at 0Mm - a long-time journey.

Part 2:

It would be so much simpler if the hoist rope were endless and could run over rolls/reels/pulleys at top and ground station. But that is impossible because the cable tapers as said before. Cables of constant diameter can be used only if they are shorter than the "breaking length" L, the maximum length of a cable of constant CSA hanging down in 1g gravity without tearing under its own weight. L is the quotient of sand ?. For very good steel with s= 2 GPa and ?= 77 kN per cubic meter (since the density ?is 7.85 gram per cubic centimeter), you get L = 26 km. For carbon nanotubes (CNT) values of sfrom 30 to 120 GPa are given (but due to lattice imperfections and notch effects it's certainly considerably less) and ?is about 13 kN/cubic meter (?= 1.3), hence L is between 2400 and 9600 km. With s= 46 GPa for instance you get L = 3600km. The distance to GEO is 10 times more, so if gravity would be 1g all the way up, the CSA would have to increase by the factor exp10 (e to the 10th power) which is ca. 22 000 and the diameter by the factor 150. Fortunately the gravity decreases strongly, so that a taper ratio from 4:1 to 5:1 will do. The diameter, which has to be some millimeters at ground to carry payloads of some tens of tons will only double on its way to the top.

Back to the untapered cables that can go up and down like a paternoster. Imagine a CNT cable of several mm thickness that can hold its own weight of L = 3600 km length or 20t suspended, or 10t and its weight of 1800 km (or 5t on 2700km or 15t on 9000km etc.) So if there is a motor driven pulley on the ground and another one 1800km higher fixed on the cable of the space elevator and the constant diameter cord running around these pulleys, you could hoist up a 10t payload 1800km high (and simultaneously 10t downwards, which would make it much easier for the motor). In fact you could go even higher, because in 1800 km altitude gravity is already down to 60%. The pulley up there is coupled to another one and from there goes another cord up to the next pulley which can be located several 1000 km higher, because the breaking length up there is much longer (because of the lesser gravity). And so in ever larger steps you get at last to the top station, all the cords and pulleys driven by the motor on the ground.

There are some minor problems, which competent engineers could certainly solve, e.g. how the climbers will change from one cord to the next one. A little more difficult: how to accelerate and decelerate them. Either the cords run with different velocities managed by appropriate gear ratios between the coupled pulleys. Or, if there is only one climber on its way up (and/or one down) all the ropes are accelerated for a while simultaneously and decelerated later.

Steffen Kummerow studied physics at the Universities of Hamburg and Karlsruhe, got his diploma at the Nuclear Research Center of Karlsruhe KFZK and worked in future research and in teaching. He has been a dedicated follower of serious and hard core Science Fiction all his life.

You can find more considerations about the future and the universe on his website http://www.future-universe.com/

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