Date: Thu, 06 Mar 2014 01:10:05 -0500
From: "Mike B." <yahoo at omniphile.com>
To: WSFA members <WSFAlist at KeithLynch.net>
Subject: [WSFA] Re: Could Partial Space Elevators Take Us Into Space?
Reply-To: WSFA members <WSFAlist at KeithLynch.net>

On 3/5/2014 8:26 PM, mark wrote:
> Just one small detail: orbital speed at geosync I see is 1.91miles/sec.,
> not the 5mi/sec for LEO. This suggests, to me, that you don't need to get
> into LEO, but rather just go up to the bottom of the elevator and dock...
> at well under half LEO speed. A quick calc says that's under 6700MPH,
> which sounds like jet/(scramjet/rocket assist), and ought to massively
> lower the cost and increase payload capacity.
>
I think you have a small error there.  Not with your orbital
speeds...those look reasonable...but with your idea that you need to get
up to geosych orbital speed to dock with a dangling tether.

The actual speed you need to reach to dock with the dangling tether,
relative to the surface of the Earth, is zero mps.  The dangling end
will stay below the center of mass (more or less...air may move it some
unless you counter it), which will be at geosync, and therefore not
moving with respect to the ground under it.  You could float up on a
balloon if it reaches low enough, but if you could get the docking point
that low, you might as well go the slight bit farther and go to the
ground (Geosync is at 22,300 miles, and a balloon is only going to be
able to get to about 180,000 feet, or 34 miles...if you've already
gotten a cable down the first 22,266 miles, going another 34 shouldn't
be too tough).  Spaceship One can get you to 68 miles, which isn't a lot
closer...and I don't think it can hover for docking, though I suppose
you could do a ballistic path that tops out right at the tether, and you
dock just before you start to fall back.

If you want a short tether, to deal with strength limits, you need the
rotating tether idea.  That is a double-ended tether with a cg in LEO,
that rotates such that the lower end is moving counter to orbital vector
of the whole thing...and therefore has a lower speed needed to dock with
it.  It accelerates you once docked (and it slows down of course...you
may be able to make up the momentum through electro-magnetic coupling
with the Earth's magnetic field if the cables are conductive and you run
current through them, or you could make it up by catching returning
spacecraft on the upper side and slowing them down.  Cable lengths for a
rotating tether can be much shorter...like 700 miles or so...long enough
to reach from LEO down to an altitude that your shuttle can reach.
Won't be able to use a balloon in this case, as the docking point will
be moving right along, even with the rotation subtracting some of the 5
mps orbital speed...you'd have to have a 1400 mile diameter double-cable
setup rotating at 14 RPM to subtract all of it...that's a bit much. If
you put the cg higher, you can lower the RPMs due to the slower orbital
speed and the longer "arms", but then you need stronger cables again.

If I remember correctly, the beanstalk strength requirements are
expressed in "equivalent cable lengths".  That is, how long you can make
a cylindrical cable (constant diameter) that can support its own weight
without breaking (an actual beanstalk will be thicker at the top, and
taper down, so longer for a given strength than a cylindrical cable).
To build a beanstalk to geosync you need an ecl of about 3600 miles.
The best steel has an ecl of about 900 (going from memory again...may be
off).  Kevlar is about 1500.  Spectra is a bit more, but still way short
of the needed value.  Carbon nanotubes may be a possibility, but there
are huge engineering obstacles to overcome before we'll be able to build
something that size with them.  The rotating tether idea may be possible
with current materials, but probably not with current transport vehicles
(the cable won't look like a crane cable...it will be *much*
bigger...think of a large skyscraper-sized structure 700 miles tall).
Getting it into LEO will be a trick...unless we make it up there from
materials already up there...see "asteroid mining").

-- Mike B.