LS.AC%MIT-EECS@sri-unix.UUCP (11/02/83)
From: A. J. Courtemanche <LS.AC at MIT-EECS> This talk of space elevators is pretty neat, but does anyone know what sort of technology we would need to implement such a device? Specifically, do we currently have materials that can be used to build a tall (80 miles? 100 miles? 200?) structure that won't destroy itself under it's own weight? Also, what sort of structures will be needed to make sure the elevator doesn't topple over? -------
REM%MIT-MC@sri-unix.UUCP (11/09/83)
From: Robert Elton Maas <REM @ MIT-MC> When actually finished, it won't topple under its own weight because it'll be hanging from its orbital point (hanging both up and down from there) rather than supported at the bottom. During construction, however, if it's built bottom-up, it'll have to support its own weight nitially. But more likely it'll be constructed in orbit and then deorbited at one end, so it'll never have to support its own weight by pushing from the bottom, even during construction. Note, it'd be widest at the middle, at the orbital point, and taper narrower both towards the ground and out to space. Alternately the very bottom part could be supported from the bottom, so it'd taper like the Eiffel Tower at the bottom, then reverse-taper up to the orbital point and back down above it as in the first paragraph. But the very bottom part would be infitesimal (a half mile?) compared to the rest (20,000 miles or more). Although there are some designs for having a tower supported from below, there's a problem in putting so much weight on a single point on Earth. I rather doubt the ground would hold. It would be embarassing to build such a tower only to have the whole island it's located on be sunk into the Earth by all that weight.
eder@ssc-vax.UUCP (Dani Eder) (11/13/83)
x 6 November 1983
Unfortunately, current materials technology does not allow the
construction of a reasonable geo-synchronous tower. But you can do
some interesting things with current structural materials.
The key concept to understand in dealing with tall structures
is 'scale height'. In a tower made of a given material, it is
the maximum height a constant section column can be built, and can
be found by dividing the compressive strength (lb/in**2) by the
density (lb/in**3). The result is in inches. In a cable hanging
from the sky, it is the maximum length a constant section cable
can be before breaking, and is found the same way.
Some examples: Steel 240,000 psi , .3 lb/in**3 = 800000 in = 12.6 mi
Kevlar 3650 MPa , 1500 kg/m**3 , 9.8 m/s**2 (note, 1 gravity
is assumed in english units, must be explicit in metric) = 248 km
If you want to build a minimum weight structure taller than one
scale height, you taper the column or cable by a factor of e (2.718...)
per scale height. One interesting material is graphite reinforced epoxy,
which we use here at Boeing in commercial airplanes. The scale height,
allowing a factor of saftey for real world design, is 50 km. It is
quite possible to build a tower that reaches into low earth orbit.
Fortunately, as you get away from the earth's surface, gravity
is less, so the scale length increases. Unfortunately, the number
of scale lengths to GEO, even for kevlar, is 26. This means the tower
has to weigh e**26 = 1.45x10**11 times the 'payload'. If we could
grow saphhire fibers, with a theoretical strength of 2.8 million psi,
then the tower would only weigh 5000 times the payload, which would
make it a feasible transportation system.
Dani Eder
Boeing Aerospace