The Rocket/Skyhook Combination
Burke Carley
949 Golden Beach Blvd.
Indian Harbour Beach, Fl 32937
Hans Moravec
Robotics Institute
Carnegie-Mellon University
Pittsburgh, Pa 15213
Copyright 1982 by F. Burke Carley and Hans P. Moravec
Why you should read this article
The task of delivering 50 million kilograms of payload to low
earth orbit would require almost 1700 launches of the Space Shuttle if
done in a straightforward manner. Judicious use of a large satellite
incorporating a high specific impulse engine and a long tapered Kevlar
cable, itself transported to orbit in multiple shuttle flights, could
cut the total number of launches, including the satellite construction
phase, to about 300.
Dream on
A relatively new class of proposals for travel to and through
space involves the idea of very long, very strong, tapered cables,
spinning so that their tips move at or near orbital velocity.
Although the concept has promise of being one of the simplest and
cheapest for massive orbital commuting in the long run, and could be
used today for travel in space and on the moon if there were call for
it, present strength of materials limitations make the simplest
variants of the idea infeasible for the most immediate need, namely
transporation to and from earth.
Two major types of earth orbital cable (sometimes called
skyhook) have been investigated in the literature. The simplest, but
also largest, has a filament dropped to the surface from synchronous
orbit, counterbalanced by one extending outwards. Anchored to the
ground and kept taut by a ballast at the far end, this structure could
be used as the backbone for an orbital elevator system (Figure 1). It
has been rediscovered on at least three separate occasions
@cite(Artsutanov60) @cite(Isaacs66) @cite(Pearson75) and is the
central theme of two science fiction novels @cite(Clarke78)
@cite(Sheffield79). The second kind is newer, but has also been the
subject of rediscovery @cite(Artsutanov69) @cite(Moravec77). It
involves a much smaller cable in low orbit which rolls in its orbital
plane and whose ends brush the earth with the rotational motion
cancelling the orbital motion at ground level. It is as if the cable
were two spokes of a giant wheel that rolled along the ground (Figure
2). Payloads could be picked up on a spoke touchdown, and launched a
half rotation later with greater than escape velocity. The momentum
lost by the cable in this process could be returned slowly by high
specific impulse engines at its center, or by capturing and landing
payloads in a reverse of the launch process. With the latter approach
the energy cost of orbital commuting becomes vanishingly small.
Dupont needs more spinach
The problem with the above schemes is that the taper and mass
required by the cables is exponential in the square of the
weight/strength ratio of the cable material, and is astronomical if
the material is too weak. The strongest commercially available
material is Dupont's Kevlar synthetic fiber, which is five times
stronger for its weight than steel. A synchronous skyhook of Kevlar
would weigh 10@+(13) as much as it could support at one time, while an
optimally sized Kevlar rolling cable would be 10@+(7) times as massive
as its payload. A material only five times as strong as Kevlar would
bring these numbers into the range of the feasible. With such a
material the synchronous cable would mass 10,000 as much as its
payload and the rolling cable only 100 times its lifting capacity.
Since the cables can move such payloads repeatedly, they could
ultimately transport many times their own mass.
Although five times the strength of Kevlar is well within the
theoretical bounds for normal matter, and strengths of this magnitude
have been observed in the laboratory in small samples of several
substances, the timescale for commercial availability of such strength
in bulk materials is uncertain.
Half a skyhook is better than none
For a given material, the required mass of a spinning cable is
exponential in the square of the desired velocity of the cable tips.
Similarly the mass ratio of a rocket is exponential in the velocity it
must achieve. These facts suggested to us that a combination of
rocket and skyhook, each providing about half the velocity needed for
earth orbit, might be superior to either alone. A spinning cable in
low earth orbit would catch a rocket-accelerated payload moving at
about half orbital velocity and accelerate it to full orbit, in a
lower energy version of the rolling skyhook maneuver (Figure 3).
Besides giving an overall mass advantage, combining a rocket
with a skyhook makes it practical to use weaker materials in the
skyhook. Our analysis of a number of situations using the space
shuttle as the rocket and Kevlar as the skyhook construction material
lead us to the following encouraging results.
Encouraging results
With the rocket/skyhook combination any large task of delivery
to space can be accomplished with less material than with either
method alone.
We chose to minimize the number of launches of the Space
Shuttle to deliver 50 million kilograms to orbit. This task would
require 1695 launches of the rocket alone.
Instead we imagine a cable grown upward from an initial
orbital altitude of 185 km. As construction proceeds the shuttle
docks with the lower end of the growing skyhook. As the skyhook
lengthens, its center of mass moves into higher orbits, and its lower
end moves more and more slowly with respect to the ground. The shuttle
can thus arrive and dock at lower and lower velocity, with
correspondingly greater payload per trip. The payloads would then be
ferried up the cable, elevator style.
We also considered two similar schemes. In one a shorter
cable in low orbit spins so that its lower tip moves at reduced
velocity, in a small scale version of the rolling skyhook mentioned
earlier. This variant results in the least number of necessary
launches, but provides the least time and highest g forces for
docking. The third possibility involves a cable that oscillates about
ninety degrees from the vertical in each direction, under influence of
the vertical gravity gradient. This "rocking" cable can transport
payloads to orbital velocity without being climbed, and is
intermediate in its properties between the vertical and spinning
vatieties.
The skyhook structure, whichever variety, incorporates a power
plant and a propulsion system to boost the upper end of the growing
skyhook into the correct orbit, and to replace orbital momentum
transferred to the shuttle payloads on each docking. The power plant
was assumed to have a power density of 10 kilograms per kilowatt and
the propulsion system a thrifty specific impulse of 5000 seconds,
about the numbers for solar electric ion engines suggested for comet
missions.
The skyhook can be looked upon as an energy and momentum
storage system by which an ion engine operating for long periods can
accumulate its effect for the short, high intensity, spurts needed in
an earth launch.
Summary
The following table summarizes the results for a range of
possibilities. The strength column gives the strength to weight ratio
of potential materials, in units of "specific length", which is
tensile strength divided by density times one gravity. Intuitively
specific length is the length of material fashioned into a uniform
rope that can just support itself when suspended from one end in a
uniform 1 g field. Kevlar has a nominal specific length of 200
kilometers, but if the cable is built assuming this strength there
would be no allowance for unexpected loads or for slight deterioration
of the material. An assumed strength of 100 km lets the skyhook
operate at a stress equal to half of Kevlar's strength, and 50 km
would give us a very conservative safety factor of four. We have
included an entry for 400 km to allow for near future advances in
materials.
Skyhook
Type Strength Length Payload Total Launches
shuttle alone 0 1 1695
vertical 50 km 1530 km 3.1 653
rolling 50 km 700 km 4.5 464
vertical 100 km 2300 km 4.2 510
rolling 100 km 1010 km 6.5 336
vertical 200 km 3470 km 6.0 387
rolling 200 km 1500 km 10.5 233
vertical 400 km 5280 km 8.8 291
rolling 400 km 2190 km 18.3 160
Figures
Figure 1: The Synchronous Skyhook (or beanstalk or orbital tower).
This is the simplest and most elegant of all the cable-to-orbit
schemes. It is also the largest, most demanding and most expensive.
A 150,000 kilometer cable is grown upwards and downwards from
synchronous orbit. When the lower end reaches the ground it is firmly
anchored. A ballast which keeps the entire cable in tension (by vitue
of centrifugal force produced by the earth's rotation) is flown and
attached to the far end. The cable can then be used to support
climbing and descending payloads.
Figure 2: The Rolling Skyhook. This diagram shows the area swept out
during one orbit. The cable length shown (about one third the earth's
diameter) is optimal in the sense that this length minimizes the
skyhook mass for a given lifting capacity. The skyhook touches down
six times during each two hour orbit. Near the touchdowns the cable
tip moves vertically, and the tip, with a constant upward acceleration
of 1.4 g comes to a momentary stop. It could pick up payloads during
these encounters, and release them a half rotation later with enough
velocity to take them to the orbit of Saturn. Such launches subtract
orbital momentum from the cable.
Figure 3: A Rocket/Skyhook Combination. A (relatively) short orbiting
cable is spun moderately so that its tips move at about half orbital
velocity. A (also relatively) small suborbital rocket able to achieve
half orbital velocity delivers a payload to the skyhook tip, which
then accelerates it to full orbital speed and beyond. This variant
could be built today.