Are you using a tapering ration of 5 or 5^2 = 25 or possibly 5^3 = 125?

A simple ratio of 5 gives a ribbon that is 5 times as wide (or thick).
5^2 gives a ribbon that is 5 times as wide and 5 times as thick.

The following calculations assume that the ribbon remains 1 micron (1e-6 metres) thick.  

Strength wise once the ribbon has doubled in width its thickness can be doubled by halving the new width.  Iterate round until both width and thickness have increased by 5 times.



An increase in width by 5 times whilst keeping the thickness at 1 micron should be possible after 164 climbers.


Assumptions

1. Two mats are added to the counter weight side for every one added to Earth side.
2. The mats are added at GEO.
3. The climber is powered by laser.  (This is to make the calculations compatible rather than because I believe it.)
4. The first 5 climbers are used to install the insertion machinery and possibly a repair climber.
5. The insertion machinery is probably solar powered.
6. The weight of the climbers has to stay at 619 kg, including payload, until the “new” ribbon reaches Earth.  (I do not believe this one since the weak point is GEO and that is the first part strengthened.)
7. Excess cable is removed at Earth.
8. The counter weight cable just grows longer.  (The strength of this will have to be watched.)
9. The empty climbers are sent to the counter weight.
10. The initial cable is 5 cm wide at Earth and 11.5 cm at GEO.
11. The cable thickness stays at 1 micron (1e-6 metres).
12. CNT mats have a density of 1,300 kg/m^3
13. Each climber has a payload of 308 kg.  (The report assumed 288 kg new cable but the climber's dry mass included 40 kg for epoxy and splicing system.  The new assumption is that with out gluing 20 kg can be used for extra ribbon and 1 kg covers the splice and pin.)
14. The initial cable is 91,000 km in length.
15. GEO is at 36,000 km.  (35,786 km is more accurate.)

mat weight = length * width w * thickness * density
length = weight / (width w * thickness * density)

Since width is a variable

length = 308 kg / (w * 1e-6 * 1300 kg/m^3) = 236,923 / w metres
Rounding down and converting length to km gives
length = 236/w km.

Inserting 11.5 cm width mats
236/0.115 = 2052 km length mat

Using a 1.5 taper width 11.5 cm * 1.5 = 17.25 cm at GEO on reaching Earth
average width = (17.25 + 11.5)/2 = 14.375 cm

average mat length 236/0.14375 = 1640 km to 3 s.f.

Number of climbers to replacement cable = 3 * distance to GEO / average length
  = 3 * 36,000 / 1640
  = 65.9 climbers
Round up and add in machinery climbers

66 + 5 = 71 climbers using 1.5 tapering.

Since that is not sufficient to double the thickness of the cable.


Using a tapering of 5
 11.5 cm * 5 = 57.5 cm

average = (57.5 + 11.5) / 2 = 34.5 cm

 236 / 0.346 = 682 km

3 * 36,000 / 682 = 158.3 climbers
Rounding up and adding machinery

159 + 5 = 164 climbers

The cable length will be 91,000 + 2 * GEO distance = 163,000 km

If both width and thickness need to increase by 5 go round again using heavier climbers.

An alternative way of lifting using a double cable is to power the lift from the counter weight.  Use a winch to pull the counter weight down and then let the counter weight pull the ribbon back.  This pull back provides the power to the car.

Use two ribbons.  The first ribbon is static and provides the support.  The wheel on the ribbon should allow to ratcheted to only turn when going up.  The car is designed to place its weight on the support ribbon.

The second ribbon moves and provides the force.  A winch pulls the force cable down.  By winching for 7.1 hours the counter weight moves.  The force wheel on the car needs to permit the cable to descend freely but to clamp on the cable when it ascends.  This can be performed automatically by a ratchet.  The two ratchets on the car are set to allow wheel movement in opposite directions (the car only goes in one direction).

By transferring the weight to the force ribbon and reversing the ratchets a controlled descent can be made.

If the up and down times on the force ribbon are the same a 2 * 7.1 = 14.2 hour cycle exists.

From the By the Numbers: Reference Material.
A minimum speed of 200 km/h is needed.
The thickness T of CNT ribbon is 1 micron = 1 e-6 m.

Distance to be winched = 14.2 hours * 200 km/h = 2840 km

To do this in 7.1 hours 2 * 200 km/h = 400 km/h (250 mi/h) = 0.1111 km/s = 111 m/s
This is fast, about 3 times the speed of a normal winch, but not impossibly fast.

Circumference C = 2 pi r

The amount of length of material in a roll is average circumference / material thickness = C/2 / T

Allowing for a 10 cm core on the winch

length l in metres, l = ( (2 pi r1) – (2 pi r2) / 2) / T

( l T)/ p = r1 – r2
r1 = (l T)/ pi + r2

r1 = (2.840 e6 * 1 e-6) pi + 0.1 = 9.02 m

The maximum force on the ribbon must not exceed the breaking strain.
The reel out only needs to supply sufficient force to accelerate the ribbon and car to 111 m/s, overcome air resistance and friction.

When a car/climber is ascending or descending through the air it can be winched at a slower speed.


 v = u + a t
so t = (v – u)/a

At 144,000 km the counter weight has an attraction due to gravity of 0.002G and a centripetal acceleration of -0.08G giving a net -0.079G
G = 9.81 m/s/s

To gain full speed the ribbon would take (111 – 0)/(0.079 * 9.81) = 143.2 seconds (2.39 minutes)

For a shorter cycle smaller amounts can be winched in and standing waves setting up.  Stress calculations have to allow for half of the ribbon rising whilst the other half falls.  The amplitude would be up and down.

If there is a length of flexible material between the spacestation and the ribbon that is twice the length of the side to side thrashing then the slack can just absorb most of the thrashing.

There are a lot of conveyer belts around, there must be a standard solution.  The alignment function on the magnetic bearing was hinting at something.

Mat as in an oblong shaped carpet.

Here is an article describing belt splicing.
http://www.twinplantnews.com/issues/jan03/articleofmonth1.htm

I imagine CNT arriving folded to fit into the bottom of a climber.  The hooks at one end and the eyes/holes at the other.   The climber and its mat cargo are sent up the ribbons.  At GEO the insertion machine attaches one end to the existing cable and clamps the other end.  The existing cable is then unclamped pulling the new material into place.  When there is sufficient tension in the  ribbons the empty climber goes on its way to form part of the counter weight.  Repeat when the next cargo arrives.

The beginning and end of the mat may need reinforcing, as shown in photographs.  The hooks are probably metal but may be CNT and more than one row could be needed to take the weight.  The mat can be folded into a continuos Z shape so that it can be pulled out from either end.  There are designs of fasteners that are the same on both sides.

http://www.biscor.com/images/splices/bullnose.jpg
http://www.biscor.com/images/splices/nomexhook.jpg

http://www.biscor.com/biscorbelts/biscorbelts_nomexhook.htm

Off the shelf magnetic bearings can move rollers at 250 m/s
http://www.skf.com/portal/skf_rev/home

They may need 20W each.

Only near GEO.  The locomotive would only be lifted once.

That is not too hard, there are specialist belt splicing machines.  We would need to make one able to operate in space.  The separation in the ribbons never leaves the machine, so we do not even have to cut the ribbon just clamp the gap.  The splicing hooks and holes/eyes would be built into the mats on Earth.  The actual insertion will take less than 1 minute plus the run out time for the mat.

On time - everything in the new proposal is lifted to GEO and only to GEO (plus the length of a mat/segment).
On sticking a fibre to the side of the cable proposal the average fibre starts half way between Earth and GEO, goes through GEO and finishes half way to the counter weight.  Since it goes further this is likely to take longer, even more time if the climbers have to slow down to glue.  Conclusion mat insertion is probably faster.

Unfortunately true, more material will be needed.  We may not wish to recycle the material.  The material being cut out is the part that has been exposed to atomic oxygen, the atmosphere and the motorised pulley.  A simple way of removing the damaged material could be a benefit.

Reasons it is better –
The mat insertion machine stays at GEO so the climbers do not have to include a complex gluing and roll out machine.  Consequently each climber is simpler and can lift more CNT.  
The setting of the resin takes place on Earth, so there is no need to invent a glue that sets in a vacuum at both low and high temperatures.  
On Earth should the glue/resin clog the pipe there is a person around to unclog it.  
The ribbon to the counter weight gets bigger.
Ribbon damaged by the atmosphere is removed.
The mats can be quality inspected before being lifted.

When a wider mat arrives at the sea anchor heavier climbers can be used.  Depending on the pulling power of the longer weight cable and the breaking strain of the main ribbon it may occur earlier than that.

Do not worry about it.  Lensman is just using the old cheat of playing the man not the ball.

That particular thruster only produces 3 mN.  OK for station keeping but for main propulsion you need a motor that is stronger than gravity.
http://www.esa.int/gsp/ACT/propulsion/safe_test_overview.htm

There will soon be off the shelf thrusters that can produce 1 N (7.23 pdl) such as the Busek BHT-20K.
http://www.busek.com/halleffect.html

An alternative design to gluing fibre onto the side of the ribbon is to insert CNT mats at GEO.  The setting of the resin and quality inspection can occur on Earth.

The answer to this question depends on the design of the spacestation, climber, elevator and the distance between them.

One way of doing it is for the spacestation to transmit a radio (or laser) signal and for the climber to pick this up.  The climber is attached to the ribbon so can rotate around using a wheel and ordinary electric motor.  The climber rotates until the receiver shows that it is pointing at the spacestation and then throws the cargo into the net.

A similar technique can be used when launching cargos into orbit.  To change inclination they will normally have to be thrown due north (occasionally due south).  The pole star makes a good tracking point.  See the inertial stellar compass launched as part of the Space Technology 6 test satellite.
http://nmp.jpl.nasa.gov/st6/ABOUT/About_index.html

The US Government is not the only government with a space programme.  If the USA does not contribute large sums of money other governments, including the European Union, may.

During the first few years NASA is likely to be one of the smaller users of the Space Elevator.  Any attempted use is likely to upset the NASA's rocket departments, so most scientists will want to avoid years of arguments by not using the Space Elevator.

NASA plans five to ten years ahead.  Getting anything revolutionary through its thousands of committees takes that sort of time.  A crisis project may be able to do it – very short time scales, small budget and a tiny team located away from the main bureaucracy so joining is not seen as an immediate career boost.  Once the satellite is built and the launch contract signed LiftPort can hype the project to the entire world.

Alternative customers include:
* the Department of Defence.
* the British Ministry of Defence and its research agencies.
* the European defence ministries.
* various scientific research organisations.
* university researches.
* space companies – such as http://www.ee.surrey.ac.uk/SSC.
* contractors to NASA supplying space stations.
* refuelling GEO satellites.
* low cost launches to other planets.

After a few years the bigger SE can be used to launch big satellites and people which brings in a whole host of other customers.  Space stations with hotel accommodation.  Communication satellites able to handle thousands of Earth based subscribers.

The cable is not weight limited but force limited.

The limiting weight on the cable has be set at 1 metric ton.

F = m a

In the case of weight near the Earth surface the acceleration is gravity g = 9.81 m/s
A mass of 1 tonne (1,000 kg) is applying a force of 1,000 kg * 9.81 m/s = 9,810 N
Adding 10% on to that gives you a breaking strain of about 11 kN.
A decent winch can produce a lot more force than that.

To winch in 45 km you are either going to move a counter weight weighing several hundred tons or to stretch the cable.  Doing either whilst using less than 11 kN will be difficult.