# [extropy-chat] Space elevator numbers II

Keith Henson hkhenson at rogers.com
Wed Feb 14 02:11:14 UTC 2007

```snip

>So the lift power required is in the range of 2/3rds of a Gw.

>Climbers using beamed power and electrical motors to go up a cable are
>in the range of 1% efficient.  Which means something like 66 Gw of power
>would be required to lift the parts for a 5 Gw power sat every 5
days.  That's
>not impossibly bad, the power sat would pay back its lift energy cost in
>66 days.

Still, 1% efficient is awful.  Plus the space elevator has to carry a great
deal of extra weight in the climbers from photo voltaic cells and motors
plus the fact that motors would be slow so it would take a truly massive
cable to get high throughput and the transit time would be a week or ten days.

Mechanical drives are close to 100% efficient.  They have been considered
but it takes cable strength exceeding 63 Gpa to run the cable over a pulley
at GEO.  Most designs have assumed lower strength tapered cables.  Last
summer it occurred to me that pulleys could give step taper in the number
of strands while using a constant diameter cable.   This allows the use of
cables with strength in the range of 10-15 Gpa and a closed loop of cable
in the range of 100 times the 22,500 mile distance to GEO.  If the cable
can be moved at 1000 mph, then trip time to GEO would be under a day and
cable replication in the range of 100 days.

There are *many* technical details which would need to be worked out.  Bare
cable can probably go up and down through the atmosphere at 1000 mph (a 31
foot diameter driver wheel turning at 900 rpm), but material loads and
personnel cars probably will have to go up on a variable speed cable to a
50 mile transfer station because of excessive supersonic drag.

Fortunately Coriolis force will keep the up and down strands well
separated.  It may take spraying static charge on the cables to keep them
from tangling.  The pulleys will need to have the ability to slightly
adjust in diameter to keep them at the right altitude.

For 1000 mph the driver wheel at the bottom would be 31 feet in diameter
turning at 900 rpm.  This is a bit faster and a bit larger than the design
of the Rotary Rocket engine (720 rpm, 22 feet).  Bearings in electrical
turbo generators operate for decades at speeds 4 times this high.  The g
force at the rim is roughly 2700 g.  (If I calculated it right.)  The cable
is so light and under so much tension that slipping should not be much of a
problem.

The diameter could be doubled in size, reducing the g forces by half, but
increasing the air resistance on the driver wheel.

Materials have a characteristic rim velocity that has been investigated in
the context of rotary pellet thrusters.

http://www.star-tech-inc.com/papers/asteroids/asteroids.pdf

1000 mph is about .44 km/sec, which certainly well within the range of
common materials.

Incidentally, 1000 mph is  arbitrary.  But the faster the cable moves, the
shorter the replication time for hauling up more cable and the higher the
throughput.  Also the number was picked to make the transit time to GEO
under a day.

To be continued

```