[robertpaulsen]

Lateral speed at the surface of the Earth: 1000mph
Lateral speed at 62,000 miles: 17,300mph

How do we go up and increase lateral speed without bending the cable into a big "C" shape?

Lateral speed is everything. Taking an object up the elevator and pushing it out the door at 100 miles in altitude (shuttle orbiting height) will do no good. It doesn't have orbital speed to stay there. At any elevator height.

[The_Victor]

Lateral speed at the surface of the Earth: 1000mph Lateral speed at 62,000 miles: 17,300mph

How do we go up and increase lateral speed without bending the cable into a big "C" shape?

A little basic physics. A point on the outside of a tire moves faster that a point toward the rim. The speed increases linearly with the radius distance from the point of rotation.

w=vr Angular (rotational velocity) is velocity time radius

You put the termination point at geostationary orbit where the speed needed to maintain orbit is equal to the rotation of the earth.

[Smokin' Joe]

How do we go up and increase lateral speed without bending the cable into a big "C" shape?

Just one problem. Really. How do you anchor the darned thing?

[Gorjus]

How do we go up and increase lateral speed without bending the cable into a big "C" shape?

That's the biggest issue.

The concept behind the space elevator is that the string is acually moving in synch with the earth's rotation, which means you have orbital velocity at geostationary altitude (22,300 miles). Most of the designs I've seen go up to about 36,000 miles, at which point the terminus is at earth escape velocity (in order to keep up with rotation). Letting go of something at that point would fling it off into interplanetary space. As you pointed out, though, at 100-200 miles altitude, the string is moving at much less than orbital velocity and anything released there would fall back to earth quite quickly.

However, anything rising up the cable would need to be accelerated to keep up with the string - and that would slow the string, eventually leading to collapse. Something would need to be done to replace that angular momentum - every time the 'elevator' went up. That would take as much momentum transfer (fuel) as it would take to orbit the same amount of mass using conventional means, unless you could recover and de-orbit as much as you're lifting into orbit. Right now, there's no concept on how to do this.

It's also not trivial to produce the required strength. Actually, carbon nano-tubes are about an order of magnitude less than the required strength-to-weight, and they're nano-tubes. Just a bit short for the job. Carbon-carbon bonds, as used in the nano-tubes, as also the strongest bonds known within current chemistry/physics. Getting that extra order of magnitude is not a job for engineers, it's a job for basic science - a breakthrough in theory, not just a refinement of technology.

Nonetheless, I believe both problems can be solved. I'm not sure the economics will ever work out, though. Like a lot of problems, it's more social than technical.

[RightWhale]

There have been thorough threads on this every year for at least four or five years. It's all there if somebody wants to search the archives.