That 1% of the cable can easily weigh more than the rest of the cable, particularly in the case of SE1.  The part exposed to the atmosphere could easily have extra mass due to having a metal lightning conduct running down it, a protective coating, be painted in warning colours and carry flashing lights.

The cable between the earth and the balloon may even have a reusable climber able to carry 2 or 3 people.  This section is so short that its climber does not need to be laser powered - a major advantage when dealing with the part subject to fog, mist, sea spray, storm and cloud.  Stronger/extra motors to deal with the enormous air drag would be nice – it is not accidental that loaded lorries do not go at 200 km/h.

An alternative to constant speed climbers is constant force climbers.  These will naturally slow down in the atmosphere.

Over simplifying

60 km/hour sea to 140 km =  2 hours 20 minutes
200 km/hour 140 km to 800 km = 3  hours 18 minutes
243 km/ hour 800 km to GEO =  144 hours

A total time of approximately 150 hours (6 and a quarter days).

Very little that will be carried by the Space Elevators is likely to be speed sensitive but a lot may be force (acceleration) and time sensitive.

You are being over simple on this one.

v = u + at

Where required final velocity v = 0
a = acceleration due to moon's gravity (function rather than a constant)

If the moons gravity is accelerating you to the left there is a velocity u to the right at which the two will cancel out.  Such a landing is possible on a perfectly smooth ball, pity there are mountains on the moon - one of which is bound to get in the way.

LEO to Earth may work but look at the problems returning moon missions have.  The SE are catchable near GEO because a now orbiting spacecraft can have more than one go.

This may depend on your definition of efficient (91.27 vs 10.6 tonne).  SE1 can lift the load but journeys lasting longer than a year may not be very popular.

Using the proposed Ion_Trunk to move 5.5 metric tons from GEO to solar retrograde orbit (270°) at 800 km LEO by spiralling down.  Time 362.4 days and 1,315 kg of Xenon/krypton fuel.  Total mass just over 10.3 metric tons.

To move 5.5 tons to 180° (full retrograde) at 500 km takes 451 days and 1,637 kg of fuel.  Total mass 10.6 metric tons.

Assumptions.

6 off HiPEP thrusters each generating 0.670 N.   Total 6 * 0.67 = 4.02 N or 29 pdf
Each thruster weights 49.5 kg, needs 40 kW and 7 mg/s propellant.
The main structure weights 1 metric ton and the empty fuel tank 2 metric tons.
The 240 kW of electricity is generated by 1333.3 square meters of solar panels weighing 173.3 kg (optimistic for 2010).
Solar cells exposed to sun light for 2/3 of each orbit.  The thrusters are switched off in darkness.
The zero-thrust-propellent used starting and stopping the thrusters is negligible (unrealistic at 90 minute intervals).
No atmospheric drag (unrealistic for these time scales).
The average acceleration is approximately 4E-7 km/s/s.

As part of the now cancelled Project Prometheus NASA was developing more powerful thrusters.  Unfortunately I do not have the mass, thrust, energy and propellent usage details needed to model them.

Once the initial SE has reached ground LiftPort can legitimately take deposits for climbs.  The two to three year delay will allow customers time to make their satellites.

The electronics industry has successfully used learning curve pricing to recover its development costs, such depreciation pricing may apply to the Space Elevator's ribbon.  $10 mass produced chips can have an initial sample price of $1,000.  Rocket launches of GEO satellites and interplanetary probes cost a lot more than LEO launches since an extra stage is involved.  There is only a small cost difference to the SE, so it will be able to match per pound prices earlier.

There are many satellites in GEO that have run out of fuel.  Extending their life for a few years by attaching an extra ion drive and propellent may be worth while.  These refuellers may be sufficiently small that even the thin elevator can lift them.

The resources required to perform a climb are only weakly correlated with payload weight, so other than as a way of making comparisons with rocket launches easier weight charging may be inadvisable.  A customer with a quarter ton satellite is unlikely to want to pay the lifting cost for a 5 ton Stage 2.

A shopping list may contain.

1.Standard launch fee.
2.Time on ribbon in half days, includes power for lasers.
3.Single use fee in half days – heavy loads may require the entire ribbon to be emptied.
4.Climber – various options.
5.Stage 2 rocket – various options.
6.Fuel/propellent for stage 2 rocket.
7.Clean room assembly.
8.Special engineering costs.

Different customers will want different options for instance NASA has its own clean rooms and Boeing may want to use its own rockets.  If several customers wish to share a climber and launch the additional cost to LiftPort is tiny.

I gave comparisons with existing satellite launching systems in the postings of 6-13-2006 10:26 PM and 6-20-2006 02:36 AM.

The first stage of the Pegasus rocket is an aircraft.  The Ariane is all rocket.

Note: the obvious limitations apply when comparing a simulation of a proposed system with measured results on a rival real system.

Be careful here to distinguish between the Space Elevator's ribbon and things attached to the ribbon.  The Earth's spin is used to support the ribbon, to get this effect the ribbon needs to be very, very long.

The proposed Climbers will use electric motors to go up and down the ribbon.  The electricity will be generated using solar panels.

http://www.elevator2010.org/site/primer.html

To complete the set I run simulations of placing a 5.5 metric ton object in south polar LEO orbit and the full retrograde (180°) LEO orbit.

When thrown in LEO the total stage 2 weights were 77 and 91.27 metric tons.  Only the later versions of the Space Elevator and climbers can lift these rockets.



____________________ Testing effect of launching a satellite from the Space Elevator

Satellite into retrograde Sun Synchronous (polar) Orbit

Satellite is to be thrown at a height of 961.800 km whilst raising at a speed of  0 km/h or 0 km/s.
Moving climber to  961.8 km takes  0 days  5 Hours and  48 minutes at 200 km/h

Aiming satellite at a final height of  800 km and an inclination of  270 degrees.
Therefor orbital velocity needs to be 7.452 km/s
The Pay Load weighs 5,500.0 kg, fuel 70,146.0 kg and the structure  1374 kg.
Total mass at launch is 77,020.0 kg.
Thrust of rocket 726 kN and fuel burn rate 219 kg/s.

Location of Space Elevator makes initial inclination  0 degrees and rotational velocity 0.535 km/s.

Semi-Major axis (a) 3,679.605 km  Semi_Minor (b) 377.445 km  Eccentricity 0.995
Periapsis - Min distance 19.410 km (height -6,358.590 km) and Max velocity 202.394 km/s
(A negative height means it will crash into the Earth.)
Apoapsis  - Max distance 7,339.800 km (height 961.800 km) and Min velocity 0.535 km/s


Command types
F = Freefall for 'Value' seconds
I = Change Inclination by 'Value' degrees.  Negative to go south
P = Pitch angle of 'Value' degrees. 0 = rocket is horizontal, 90 = straight up
S = Thrust to Slow down for 'Value' seconds or until the fuel runs out
T = Thrust for 'Value' seconds or until the fuel runs out


Time (s) 0            Velocity 0.535 km/s  Inclination  0 degrees  Up velocity  km/s  Height 961.800 km

__________ F 4            Freefall for 4 + 1 seconds to prevent harm to cable
Time (s) 4            Velocity 0.535 km/s  Inclination  0 Degrees  Up velocity -0.029 km/s  Height 961.741 km.
;;;                   Orbital velocity for current height is 7.369 km/s  Fuel 70146.0 kg.

__________ P 15.35        Select vertical flight angle
Time (s) 5            Velocity 0.535 km/s  Inclination  0 Degrees  Up velocity -0.037 km/s  Height 961.708 km.
;;;                   Orbital velocity for current height is 7.369 km/s  Fuel 70146.0 kg.

__________ I -90          Fly to the new orbit of -90 degree (South Polar) inclination
Time (s) 77           Velocity 0.535 km/s  Inclination  -90 Degrees  Up velocity -0.370 km/s  Height 946.915 km.
;;;                   Orbital velocity for current height is 7.377 km/s  Fuel 54378.0 kg.

__________ T 248          Use Thruster to gain required orbital speed
Time (s) 325          Velocity 7.452 km/s  Inclination  -90 Degrees  Up velocity 0.032 km/s  Height 800.270 km.
;;;                   Orbital velocity for current height is 7.452 km/s  Fuel 66.0 kg.

__________ P -90          Bring the satellite to a vertical halt
Time (s) 326          Velocity 7.452 km/s  Inclination  -90 Degrees  Up velocity 0.032 km/s  Height 800.301 km.
;;;                   Orbital velocity for current height is 7.452 km/s  Fuel 66.0 kg.

__________ T 10000        Fire thruster
Time (s) 327          Velocity 7.452 km/s  Inclination  -90 Degrees  Up velocity 0.000 km/s  Height 800.317 km.
;;;                   Orbital velocity for current height is 7.452 km/s  Fuel 0.0 kg.

__________ F 5            Verify that satellite is still in orbit 5 seconds later
Time (s) 332          Velocity 7.452 km/s  Inclination  -90 Degrees  Up velocity 0.000 km/s  Height 800.318 km.
;;;                   Orbital velocity for current height is 7.452 km/s  Fuel 0.0 kg.

Fuel left  0 kg.

*END





____________________ Testing effect of launching a satellite from the Space Elevator

Satellite into retrograde Orbit - the hardest to get to

Satellite is to be thrown at a height of 761.500 km whilst raising at a speed of  0 km/h or 0 km/s.
Moving climber to  761.5 km takes  0 days  4 Hours and  48 minutes at 200 km/h

Aiming satellite at a final height of  500 km and an inclination of  180 degrees.
Therefor orbital velocity needs to be 7.613 km/s
The Pay Load weighs 5,500.0 kg, fuel 84,400.0 kg and the structure  1374 kg.
Total mass at launch is 91,274.0 kg.
Thrust of rocket 726 kN and fuel burn rate 219 kg/s.

Location of Space Elevator makes initial inclination  0 degrees and rotational velocity 0.521 km/s.

Semi-Major axis (a) 3,578.436 km  Semi_Minor (b) 352.182 km  Eccentricity 0.995
Periapsis - Min distance 17.373 km (height -6,360.627 km) and Max velocity 213.956 km/s
(A negative height means it will crash into the Earth.)
Apoapsis  - Max distance 7,139.500 km (height 761.500 km) and Min velocity 0.521 km/s


Command types
F = Freefall for 'Value' seconds
I = Change Inclination by 'Value' degrees.  Negative to go south
P = Pitch angle of 'Value' degrees. 0 = rocket is horizontal, 90 = straight up
S = Thrust to Slow down for 'Value' seconds or until the fuel runs out
T = Thrust for 'Value' seconds or until the fuel runs out


Time (s) 0            Velocity 0.521 km/s  Inclination  0 degrees  Up velocity  0 km/s  Height 761.500 km

__________ F 4            Freefall for 4 + 1 seconds to prevent harm to cable
Time (s) 4            Velocity 0.521 km/s  Inclination  0 Degrees  Up velocity -0.031 km/s  Height 761.438 km.
;;;                   Orbital velocity for current height is 7.472 km/s  Fuel 84400.0 kg.

__________ P 18.5         Select vertical flight angle
Time (s) 5            Velocity 0.521 km/s  Inclination  0 Degrees  Up velocity -0.039 km/s  Height 761.403 km.
;;;                   Orbital velocity for current height is 7.472 km/s  Fuel 84400.0 kg.

__________ I 180          Fly to the new orbit of 179 degrees the worst permitted retrograde orbit
Time (s) 118          Velocity 0.521 km/s  Inclination  180 Degrees  Up velocity -0.591 km/s  Height 725.007 km.
;;;                   Orbital velocity for current height is 7.491 km/s  Fuel 59653.0 kg.

__________ T 1000         Use Thruster to gain required orbital speed
Time (s) 391          Velocity 7.612 km/s  Inclination  180 Degrees  Up velocity 0.000 km/s  Height 500.418 km.
;;;                   Orbital velocity for current height is 7.612 km/s  Fuel 0.0 kg.

__________ F 5            Verify that satellite is still in orbit 5 seconds later
Time (s) 396          Velocity 7.612 km/s  Inclination  180 Degrees  Up velocity 0.000 km/s  Height 500.419 km.
;;;                   Orbital velocity for current height is 7.612 km/s  Fuel 0.0 kg.

Fuel left  0 kg.

*END

Your mental picture of what is going on is wrong.  The Space Elevator is not a tower on the top of the Earth supported from below but a string on the side of the Earth being dragged up from the top.  The spin of the Earth is pulling it round and “refuels” the drag.  To obtain this spin we have to built the SE on the equator rather than at the North Pole.

I have drawn a picture of an ion rocket that could be used to lower satellites into 400 km orbit from GEO.  See Ion_Truck

http://uk.geocities.com/am.swallow@btopenworld.com

There is an enormous saving of fuel by using ion thrusters but it is very slow.

A half ton payload takes 90.03 days and 327 kg propellant.

Limiting the total weight SE1's maximum weight of 15 metric tons including a one tonne climber, a 10.53 metric ton payload takes 317.5 days and 1,152 kg propellant.

(I repeated this calculation, the 2.5 tonne of structure was for a Mars rocket with 64 thrusters, the small space tug with 6 thrusters is unlikely to need more than 1 metric ton of structure.)

Is the velocity of an item dropped at 20,000 km 10 km/s or 1.9 km/s?

The cable rotates the earth once a day = 86,164 seconds (removing the extra time due to solar orbit)
Velocity is circumference of circle / time
Circumference = 2 pi r

v = 2 pi (Earth radius + height) / true day
   = 2 pi (6,378 + 20,000) / 86,164
v = 1.924 km/s

Objects on the space elevator are supported by the ribbon rather than being in free fall.

I reran the polar satellite with only 1 degree inclination.  It saved 27,080 kg of fuel.  A saving of 27 tonnes is worth while.

The saving is only a third of the fuel used because the orbital plane is changed before the satellite is accelerated to orbital velocity.