[extropy-chat] Space elevator numbers II

[Keith Henson]

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