The hoped for specific strength of carbon nanotubes gives them a breaking length of 4716 km so tapering may not be needed.  However a rope of that strength has not been made yet.
http://en.wikipedia.org/wiki/Specific_strength

Spectra fiber has a strength of 3510 MPa, density of 0.97 g/cm giving it a breaking length of 369 km.

The recharging stations are not in orbit.  They are being lifted by the same rope as the payload.  The mass of the payload has to be reduced simply because the recharging stations are present, even if they are not used.

140,000 feet is 42.6 kilo-metres.  A waystation at this hight would increase the mass of the payload the ribbon can lift and may permit the climber to open its solar panels.  Unfortunately the same strength of ribbon material is needed.  A self supporting waystation would need to be 500 miles high before the material strength can be halved.  There is no know way of self supporting anything at a hight of 500 miles which rotates at the same speed as the Earth.

Cambridge University in Britain is producing a continuous Carbon Nanotube (CNT) fibre that is half as strong as Kevlar.
http://news.bbc.co.uk/1/hi/sci/tech/7038702.stm

Kevlar is rated at 3 000 MPa so this fibre is about 1 500 MPa (1.5 GPa).  Since the fibre is made from spun CNT threads many of which are much stronger they hope to increase the strength by removing the defects.

Winching an object weighing 20 to 40 metric tons at a 100 miles per hour will generate a lot of heat.  The winch's drum will need water cooling.  This will also reduce the stress on the ribbon.

20 metric tons refers to the stress on the cable at the bottom.  The cable is actually force limited.

F = m a = 20,000 * 9.81 = 196,200 N


At 1000 km a = 7.28725 (using By the Numbers data)

m = F/a = 196,200 / 7.28725 = 26,923 kg

So if the 20 tonne climber does not go be low 1000 km we can have an extra 6 tonne underneath.

F = F1 + F2
ground mass m2 = (F - F1)/g

m2 = (196,200 - 16,000 * 7.28725 )/9.81 = 8,114 kg
Alternatively a 8 tonne atmospheric climber can dock to a 16 tonne space climber at 1,000 km.


At 3000 km a = 4.48554

m = 196,200 / 4.48554 = 43,740 kg

A 10 tonne atmospheric climber can dock with a (196,200 - 10,000 * 9.81 ) / 4.48554 = 21,870 kg
21 tonne climber at 3,000 km

There is the point that every ton the of weight removed from the bottom of the ribbon is an extra ton of payload.

An alternative is an interchange point between 1000 km (3/4 gravity) and 3000 km (1/2 gravity).  A light climber could be used as a taxi to get people to the full climber.  The light climber would not contain beds or a kitchen and only weak radiation shielding.

NASA is recruiting astronauts, but not pilots.
http://forum.nasaspaceflight.com/forums/thread-view.asp?tid=9866&posts=37&start=1

SpaceX is also looking for astronauts including pilots.
http://www.nasaspaceflight.com/content/?cid=5237


Personally I think NASA is being silly not using its own staff to act as test pilots for the various makes of COTS space capsules.  This may keep the unions happy but it will backfire badly.

The sling can be tested at various stages.

Its centre turns slowly so equivalent mass can be added permitting testing of the motor on the Earth.
The tip acceleration is designed to be safe for humans.  A much smaller one can turn faster on the Moon.
A tiny payload is possible.

The space elevator is still awaiting the invention of a sufficiently strong material.

If it is a slippage effect then 5 cm may work, possibly even 4.5 cm.  At least we are not orders of magnitude out.

On Earth Maglev is limited by air resistance, this major restriction does not apply on the Moon.

The speed effects can be tested in a vacuum chamber.  The 3g tangential acceleration on the track can be tested at a lower speed.  The 2.38 km speed could be tested in a smallish by locking the vehicle and spinning the track.

Not really. A lunar space elevator is something like 100,000 km straight down.  The Maglev track is 1209 km along the flat.  The reason we are using magnetic levitation is that wheels do not turn that fast.

The track could be made out of aluminium going around a crater whose diameter is 385 km +/- 10 km.
Aluminium is one of the main ingredients of lunar soil so it can be made on the Moon.

Lunar mountains go up to about 2 km tall.  So a 192.5 km sling would have a height to length ratio of 1:96
That is enormous, bridges have ratios of 1:10.  The length may be possible if the sling is turning whilst its tip is winched out.

Rotation time of sling is 2 pi * r / v = 2 * pi * 192.47 km / 2.38 km/s = 1 revolution per 508 seconds (1 rev 8.47 minutes)
or 0.118 revs/minute

4 cm nanotubes are sufficient to make a rope.  You just have to make a rope, this includes spinning the threads together to produce lengths hundreds of feet long.  See
http://en.wikipedia.org/wiki/Rope

Force = mass * acceleration
F = m a

The acceleration to rise has to be stronger than gravity say 1.1 g = 1.1 * 9.81
Mass of climber say 20,000 kg

Required force F = 20000 * 1.1 * 9.81 = 215,820 newtons or 216 kN

You are trying to solve the wrong weight problem with the cable.  The cable can be kept up by having a very heavy counter weight above 36,000 km.  The problem is that the cable will break under its own weight unless tapered.  To survive the pull up force you are proposing an even thicker cable is needed.