[The following is an excerpt from a letter to Allen Meece]
[Updated 4 September 2002]>
I expect the tether to recoil violently if broken. True,
the amplitude of the compression wave created by snapping a Spectra cable with a
given tension is less than that of snapping a bungee cord with the same
tension. However, if the potential energy due to tension is the same in
each case, then the energy released by snapping the tether is the same
either way, too. If the energy can't go into a compression wave, then it
will go into a transverse wave instead -- like a whip, rather than a
slingshot. Now, that energy may be insufficient to carry that wave all the
way up the tether despite damping, but it still goes somewhere. If the
tether breaks, the resultant wave is headed straight for the platform. It
doesn't really have anyplace else to go.
The same thing is observed in steel chains and cables.
They don't elongate much either, but you don't want to be standing next to one
when it goes. Of course, they also have more inertia than Spectra and are
therefore less subject to damping forces. So the recoil of the VBP tether
should be less than with a heavier rope breaking under the same load.
Also, I'm coming to the conclusion that tapering the
tether is a bad idea. There will be brief periods, especially during
the initial ascent, when we can expect the line tension at the bottom to exceed
the line tension at the top of the tether. As the platform approaches the
tropopause, wind drag will cause more tension than weight will. It doesn't
dramatically affect the wind drag to increase the tether diameter by a few
millimeters, as long as we can lift the extra weight. Also, we will
find it cheaper to have the tether manufactured with a uniform thickness.
My current estimate for best tether thickness is 20mm, not
16mm. This is able to resist 45 tons of force, which is my computed worst
case scenario. (To reach this kind of drag, the VBP has to start out
in 7m/s ground winds, which increase exponentially all the way up to 20km,
with no fall-off in wind speed past the tropopuase or anywhere
else. This is the equivalent of deploying in a 16 mph wind with a 20T
platform and encountering artificially exaggerated winds all the way
up. Physically impossible, but not too many times worse than we
may ask of it from time to time.) The 20mm
tether has more than twice the minimum strength of the 16mm, enough to
increase our safety margin to respectable levels. Of course, at twice
the strength it also has twice the weight: 19 tons.
It's a shame the Technora-blend stuff wears better. I
was looking at the New England Ropes page and noticed that the straight, single
braid Spectra has a higher modulus and lower weight than the T-900 double
braided rope we'll be using. With that stuff, we could get by with the
18mm rope, which would only weigh 11 tons. Of course, the folks at
New England Ropes say it's unsuitable for winches because it abrades too
easily. I do have an estimate for the brittleness temperature of high
density polyethylene: -100C. I think Spectra rope should remain intact at
higher temperatures, being chemically the same material, but don't quote me on
that. I'm still looking.
I don't think we're going to have much luck shaving weight off
of the rope, so we should start toying with ideas to take it off the
platform. Reducing the platform weight could also lower the drag, allowing
us to thin out the rope again, so it's important to consider.
I'm looking at supporting the platform and tether mount in much the same way as the
gondola is supported beneath a conventional hot air balloon. Ropes do all
the work.