LSE Phase I Final Report

Table of Contents

Section

Page

Executive

Summary

Introduction

Vision

Lunar Space Elevator Design

Basic

Considerations

Configurations

Vertical Design with Counterweight

Balanced Design without Counterweight

Uniform Design “Conveyer Belt”

Curved Design for Polar Access

Tramway for Polar Access

Materials

Use of Existing Composites

Fail-Safe Design for Safety, Reliability, and Repair

Improved Materials and Carbon Nanotubes

System

Components

Climber System Design

Orbit Transfer Vehicles

Tramway Construction and Vehicles

Key Technology Challenges

Lunar

and

Advanced

Materials 24

Robotic Construction Using Lunar Resources

Dynamics

and

Control 25

Autonomous

Operations

Operations, Economics, and Payoffs

Operational

Concept

Payload

Flows

LSE Cost Analysis

Launcher Cost Projections

Orbital Transport

Elevator Mass and Transport Cost

Development Cost

Lunar

Space

Elevator

Payoffs 29

Building the Lunar Space Elevator

Steps

Construction

Using

Lunar

Resources

Launching

Lunar

Materials

Material

Forming

and

Fabrication

Construction

Techniques

Conclusions

Feasibility

Impact

Development

Phase

Plans

Appendix

References

List of Figures and Tables

Figure

Title

Page

Lunar Space Elevator System Concept

Lunar Space Elevators about L1 and L2

Required Tapers for Earth, Mars, and Moon Space Elevators

LSE Ribbon and Counterweight Mass vs. Height

Tension Profile of a Two-Segment Balanced LSE

Mass of the Balanced LSE vs. Height

L1 and L2 Space Elevators with Polar Support Tower

Maximum Latitude vs. Material Strength

Lunar

Space

Elevator

and

Tramway

10.

Maximum Tramway Spans vs. Support Tower Height

11.

Multiple-Ribbon

Fail-Safe

Design

12.

Robotic

Climbing

Vehicle

13.

Drive Motors, Attitude Control, and Ribbon Interface

14.

Solar

Arrays

and

Climber

Structure

15.

Structural Arrangement for Controlling Center of Gravity

16.

Details of Tires and Ribbon Interfaces

17.

Perigee Radius vs. Height of Payload Release on LSE

18.

Clementine Mosaic of Lunar Polar Hydrogen

19.

Structural Concept to Route Tension Forces

20.

Lunarcrete

Block

with

Wire

Tension

Insert

21.

Wiring

Multiple

Blocks

Together

22.

Lightweight

Towers

for

Tramway

Support

23.

Encapsulating Lunar Regolith with Fused Aluminum 37

24.

Truncated Octahedrons as Space-Filling Blocks

25.

Blocks

with

Threaded

Aluminum

Inserts

26.

Habitat Constructed with Either of These Systems

Table

Title

Page

Candidate Materials for LSE Compared with Carbon Nanotubes 15

iii

Nomenclature

cross-sectional area of space-elevator ribbon

gravitational

acceleration

L tether

length

selenocentric radius vector

geocentric radius vector

radius of the Moon

arclength along the unstretched tether

T tether

tension

t time

circular orbital velocity at the lunar surface

transverse wave velocity in the tether

tether inclination to the local horizon

non-dimensional parameter, v

gravitational parameter of the Earth

gravitational parameter of the Moon

tether mass per unit length

angular velocity of the orbital motion of the Moon

Abbreviations and Acronyms

CW counterweight
GEO  geostationary Earth orbit
HEO  high Earth orbit
LEO  low Earth orbit
LLO  low lunar orbit
LSE lunar

space

elevator

collinear Lagrangian point between Earth and the Moon

collinear Lagrangian point beyond the Moon

SE space

elevator

taper ratio, cross-sectional area at L1/cross-sectional area at base

Performance and Cost

A lunar space elevator using existing high-strength composites with a lifting capacity of
2000 N at the base equipped with solar-powered capsules moving at 100 km/hour could
lift 584,000 kg/yr of lunar material into high Earth orbit. Since launch costs may be about
$1,000/kg then, this material would be worth more than half a billion dollars per year,
resulting in greatly reduced costs and creating a new paradigm for space development.

Technology Challenges

To build the lunar space elevator and to operate it successfully will require that we
identify and address some key enabling technologies.  One key technology is the
application of advanced composites with better strength/density values, and the potential
use of lunar materials. A second technology is the use of robotic construction on the
lunar surface, preferably using indigenous materials, to reduce the cost of construction.
A third is mastering the dynamics and control of the lunar space elevator structure itself.
Finally, to make the system cost effective, the operation of the LSE and its components
must be autonomous, to minimize the requirements for human operation or intervention.

Building the Lunar Space Elevator

The construction system creates adaptable sets of identical geometric shapes of small
blocks and wires made from locally available lunar materials, using automated block
assembly and wire forming to construct complex shapes. This architecture is a new way
to create a lunar base for robotic and human operations on the surface.

Vision and Significance

Lunar space elevators will revolutionize the way we operate in cislunar space, and can
be a key piece in the development of the Moon and the use of its resources for
advanced space development. It can contribute greatly to the new vision for a Moon-
Mars initiative by:

•

Providing lunar materials in Earth orbit at less cost than launching from the Earth

•

Providing an unlimited supply of construction material in Earth orbit

•

Providing for continuous supplies to lunar installations

•

Providing the basis of a new paradigm for robotic lunar construction and

development

•

Supporting astronomical observatories on the lunar farside

Conclusions

The results of this phase I effort demonstrate that the lunar space elevator is feasible,
and can be constructed of available materials to fit in the timeframe of the NASA Moon-
Mars initiative. The lunar space elevator requires only technology advances
commensurate with current plans for return to the Moon. It will provide unlimited
amounts of lunar material for constructing large solar power satellites and shielded
habitats space complexes in Earth orbit. With the use of lunar polar ices, the lunar
space elevator can also provide large quantities of propellant in Earth orbit for use by
vehicles bound for the Moon or Mars. The lunar space elevator also provides a low-cost
means for transporting infrastructure components from Earth orbit to the lunar surface.

In Phase II, we will create a detailed development plan for this revolution in the future of
cis-lunar space.

Introduction

The space elevator is a connection between the surface of a planet and a terminus
beyond the stationary orbit radius, where a counterweight maintains the structure in
tension and in balance between its synchronous orbit velocity and the planet’s
gravitational attraction. The space elevator was invented first by Leningrad engineer
Yuri Artsutanov

in the 1960’s, but was not noticed by the Western spaceflight

community until the Principal Investigator Jerome Pearson

invented it independently

and published in

Acta Astronautica

. For a planet or single body, the space elevator can

be balanced about any point in the geostationary orbit. For a moon, however, the three-
body dynamics dictates that a lunar space elevator must be balanced about one of the
collinear Lagrangian points L1 or L2. The lunar space elevator was invented first by the
PI

, followed independently by Artsutanov

. According to Levin, the lunar space elevator

was mentioned much earlier by Tsander

in a Russian language publication.

The space elevator must be constructed of extremely strong, lightweight materials,
because it is tapered exponentially with of the planet’s gravity field and the
strength/density of the building material. Compared with the Earth space elevator, lunar
space elevators are far less demanding of materials. Rather than waiting for carbon
nanotubes to be developed into structural materials, we can use existing high-strength
materials such as T1000G carbon fiber, or, with protective coatings, Spectra 2000,
Zylon, or Magellan M5. These all have breaking lengths of several hundred kilometers
under 1 g, and would require taper ratios of less than ten between the base and the
Lagrangian balance points.

Brad Edwards

received NIAC funding to examine an Earth space elevator using carbon

nanotubes. There are annual space elevator symposia and sessions at the IAF
Congress this year in this rapidly changing field. The Earth space elevator concept has
now been advanced in the construction system, the cargo lifting system, and especially
in materials

. However, there are two very difficult problems to be overcome in building

the Earth space elevator—the necessity for a material such as carbon nanotubes, which
may not be available for construction for decades, and the problem of interference with
all other spacecraft and debris in Earth orbit. Because the space elevator is a fixed
structure that extends from the equator to beyond the geostationary orbit, every satellite
and every piece of debris will eventually collide with it, typically at greater than orbital
velocity. This means that for safety the Earth space elevator must be constantly
controlled to avoid these obstacles, or they must be removed, requiring an enormous
space cleansing.

Shorter rotating tethers have been proposed by Moravec, Carroll

, and by Hoyt and

Forward

as propulsion systems for transporting masses to and from the Moon, but there

are several difficulties in achieving their visions. They are based on momentum
exchange tethers, catching and throwing masses from their tips, and touching down
instantaneously at several points on the lunar surface. This requires precise control of
the tether tip, precise rendezvous with the target masses, and precise catching of the
incoming masses from another rotating tether. The low lunar orbit rotating tether’s orbit
must be carefully controlled and adjusted to precisely touch the surface. Also, the
rotating tethers require that the mass flow be balanced between Earth and the Moon, or
they must make up the momentum by other means, usually by solar power and electric
propulsion. Finally, the incoming masses are on hyperbolic orbits, so if a catch is
missed, the payload is lost; there is no second chance.

Vision

Lunar space elevators will make possible the development of lunar resources and their
availability for large-scale operations in cislunar space. The lunar space elevator
architecture, shown schematically below, consists of three systems: a lunar construction
system, a lunar space elevator system, and a cislunar transportation system.

The construction system is a unique and streamlined method for creating the basic
building blocks for lunar and orbital construction. The space elevators use both
Lagrangian points to provide access to nearside and farside equatorial regions and the
polar regions as well. Solar-powered vehicles climb the space elevators to take
payloads beyond the Lagrangian points with excess orbital energy. From there, small
robotic space tugs complete the cislunar transportation system to take them to high
Earth orbit for use in construction, shielding, habitats, and solar power satellites.

L-2

L-1

COUNTERWEIGHT

CARGO CAPSULES

POLAR BASE

COUNTERWEIGHT

EQUATORIAL BASE

HEO

TRAMWAY

Figure 2. Lunar Space Elevators about L1 and L2

Two types of lunar space elevator are proposed, balanced about the L1 and L2
Lagrangian points. L1 is 58,021 ± 3183 km from the center of the Moon toward the
Earth, and L2 is 64,517 ± 3539 km from the center of the Moon away from the Earth.
The variations are due to the 0.055 eccentricity of the lunar orbit. The L1 LSE is slightly
easier to build and is constantly visible from the Earth; the L2 LSE is slightly better for
launching masses into Earth and lunar orbits.

These space elevators can also support development of the lunar maria resources on
the near side, and support an astronomical observatory on the far side, away from the
Earth’s electromagnetic interference. The poles may be the key to lunar resource
development. The Clementine and Lunar Prospector missions indicated that there may
be valuable deposits of hydrogen ices in permanently dark craters near the poles.
These could be invaluable as a source of rocket propellant for propulsion in cislunar

space. There may also be permanently sunlit mountain peaks near the lunar poles,
allowing for the generation of continuous solar power, even through the 14-day lunar
night. This could greatly assist a mining base near the pole.

To access the poles, the space elevators must have a different form—with non-vertical
segments that curve away from the equator and toward the poles, connecting the
resources near the lunar poles with the transportation system. The maximum latitude
that can be reached is limited by the material strength/density, which was demonstrated
theoretically by one of us (Levin

). Depending on how close our tether building material

allows the base to be moved toward the pole, it will be necessary to provide a certain
length of a tramway-like connection to reach the polar mining base.

As the lunar space elevator is constructed, extending from the L1 or L2 balance point,
the lower tip of the space elevator ribbon will naturally reach the surface at the equator.
Additional strands can then be lowered and towed by a surface vehicle toward the poles,
and anchored at convenient mountain peaks at the latitude where they are tangent to the
surface. These additional ribbons not only make the lunar space elevator redundant and
fail-safe, but they will be extended from lunar mountain peak to peak until they reach
mining bases near the poles. This would create direct connections between the polar
mining and refining bases and the launch stations beyond L1 and L2.

Significance

We expect lunar mining, refining, and construction plants on the surface, with useful
objects constructed from lunar resources, carried up the lunar space elevators by solar-
powered cargo capsules, and dropped from the tip of the space elevator into high Earth
orbit for use in the next phase of space development. Lunar space elevators will
revolutionize the way we operate in cislunar space, and will greatly reduce the cost of
getting building material into Earth orbit.

The lunar space elevator can be a key piece in the development of the Moon and the
use of its resources for advanced space development, and it can contribute greatly to
the new vision for a Moon-Mars initiative announced by President Bush in January of
2004. We propose to take advantage of these positive attributes by demonstrating the
paradigm shift that lunar space elevators could make in our next moves back to the
Moon, to Mars, and on into deep space.

In addition, the lunar space elevator can be a stepping stone to the Earth space elevator.
Lunar space elevators do not require super-strength materials, and do not endanger all
Earth satellites. Lunar space elevators are twice the length of the Earth space elevator,
but because of the Moon’s much smaller mass they can be constructed of existing
materials. In addition, there are few satellites in lunar orbit, no man-made debris, and
fewer meteoroids are expected. The Earth space elevator and the lunar space elevator
both need traveling vehicles to carry cargo along their ribbons of material, and they are
both orders of magnitude longer than any structure yet constructed in space. For these
reasons, the lunar space elevator is an excellent testbed for examining many of the
technology challenges of the Earth space elevator, including the dynamics and stability
of long structures in space, control of the lateral and longitudinal oscillations, and
vehicles climbing rapidly along their great lengths.

The lunar space elevator allows us to re-discover the Moon for space habitats, after the
romance in the 1970s with space colonies at L4 and L5. The Moon’s polar regions may

Lunar Space Elevator Design

Basic Considerations

Unlike the Earth space elevator, balanced about any point in geostationary orbit, the
lunar space elevator can be balanced only about the L1 or L2 Lagrangian points. In
addition, because of the peculiarities of the three-body system, the balanced lunar space
elevator is longer than the balanced Earth space elevator, and the lunar space elevator
requires a larger counterweight for the same relative distance beyond the balance point.

Because of the Moon’s small mass, lunar space elevators are far less demanding of
materials than Earth space elevators; they can be constructed of existing composites.
This is also true for Martian space elevators, as shown in Figure 3. The required area
taper ratio between the balance point and the surface is plotted in terms of the
characteristic height of the material, which is the maximum length of a hanging cable of
the material under a 1-g gravity field. Current composites have characteristic heights of
a few hundred kilometers, which would require taper ratios of about 6 for Mars, 4 for the
Moon, and about 6000 for the Earth. The mass of the Moon is small enough that a
uniform cross-section lunar space elevator could be constructed, without any taper at all.

100

1000

100

1000

10000

Characteristic Height, km

equire

a Ta

r R

Moon

Mars

Earth

Figure 3. Required Tapers for Earth, Mars, and Moon Space Elevators

Configurations

These design requirements allow several possible configurations for the lunar space
elevator. It can take the classic vertical, exponentially tapered form, extending above
the L1 balance point to a counterweight that provides balance. It can be a balanced
design without a counterweight, by extending far enough above the Lagrangian point. It
can be curved, and touch down at latitudes away from the equator. And in the case of
the Moon, it can be uniform in cross-section, built in the form of a conveyer belt with the

We would like to connect the Lagrangian points directly to the lunar poles, but that is
impossible, even for an infinitely strong material. Curving the space elevator to anchor it
away from the equator takes additional strength from the material, and there is a latitude
limit at which the ribbon becomes horizontal. In a paper at the 3

Space Elevator

Conference, Anders Jorgenson calculated the maximum latitude for an Earth-based
space elevator to be 47 degrees. Blaise Gassend

calculated the path of climbers on

non-equatorial cables, and found that vibration may be dangerous.

Ivan Bekey suggested using a tall tower at the pole, and allowing the ribbon to hang
from the tower without extending below the surface level. Figure 7 is a sketch of the
concept, with the ribbon just grazing the lunar surface. However, even with carbon
nanotubes, the polar tower would have to be hundreds of kilometers high. This seems
impractical at present.

To L2

To L1

Support

Tower
At Pole

max

Moon

Figure 7. L1 And L2 Space Elevators With Polar Support Tower

To reach a non-equatorial base, the cable would have to be dropped from L1, touch the
lunar surface at the equator, towed by a ground vehicle to the pole, and raised to the top
of the tower, or at least to a tower located at

max

, from which another section can be laid

to the tower at the pole.

max

is a function of the tension and the maximum stress in the

cable, and increasing it will increase the taper ratio and the total mass required for a
given material. This means there is a trade-off between the ribbon mass and the
number and height of the towers required.

Geoff Landis

proposed a space elevator based on a tower in compression combined

with an upper cable in tension, and showed that the combination was lighter than the
simply tensile or the simply compressive design. Similarly, using lunar towers allows
reaching higher latitudes.

Eugene Levin (see Appendix) calculated the maximum lunar latitude achievable as a
function of the characteristic height of the ribbon material, which allows us to calculate
the tower heights necessary. This also gives some insight into the tradeoffs between
stronger materials and higher towers. These calculations are more complicated than the
Earth space elevator, because of the 3-body problem of the Earth-Moon system.

However, this takes a large fraction of the material strength, as shown in Figure 8. In
this figure, the abscissa is

, the ratio of the square of the transverse wave velocity of

the material, v

= T/

, to the square of the circular velocity at the lunar surface, v

For M5 fiber with a safety factor of 2,

≈

Maxim um Latitude

Eta = vt2/v02

ati

, D

= vt

⁄

Figure 8. Maximum Latitude as a Function of Material Strength

Using a ribbon of M5 fiber, the LSE bottom end could be towed to a latitude of about 36
degrees and retain about half its strength for lifting payloads. The maximum latitude
attainable by M5 is 52.5 degrees, but that takes all its strength, leaving no margin for
lifting payloads. Even carbon nanotubes could reach a latitude of only 76 degrees,
which still leaves a distance of 426 km overland to the pole. This means that a tramway
will be required to reach the poles, no matter what the material.

However, taking half the stress limit to reach 36 degrees saves only about 1000 km of
tramway, but it halves the throughput of the entire system. Much higher productivity can
be obtained by just using a vertical configuration, and taking the tramway the entire
2700-km distance from the equator to the pole.

Tramway for Polar Access

These results show that curving the LSE is possible, but that it significantly increases the
tension, reduces its carrying capacity, and cannot reach all the way to the poles. These

0.00

0.20

0.40

0.60

0.80

1.00

Latitude Span, Deg

Groun

d C

learance/

ight

h=1 km
h=2 km
h=3 km

Figure 10. Maximum Tramway Span vs. Height of Support Tower

Materials

Use of Existing Composites

The space elevator must be constructed of extremely strong, lightweight materials, to
support its weight over the tens of thousands of kilometers of length; even then, for
minimum mass it must be tapered exponentially as a function of the planet’s gravity field
and the strength/density of the building material. The table below shows some
candidate materials for lunar space elevators, with density, stress limit, and the breaking
height (the longest cable that can be suspended in 1 g). Lunar space elevators require
much lower material strengths than the Earth space elevator, which will require carbon
nanotubes (shown in Table 1 for comparison). All these materials, save the carbon
nanotubes, are available now.

Table 1. Candidate Materials for LSE Compared with Carbon Nanotubes

Material

Density

kg/m

Stress Limit

GPa

Breaking height

h =

g, km

SWCN*

2266

2200

T1000G† 1810

6.4

361

Zylon PBO‡

1560

5.8

379

Spectra 2000¶

970

3.0

316

M5**

1700

5.7 (9.5)

342 (570)

Kevlar 49††

1440

3.6

255

*Single-wall carbon nanotubes (laboratory measurements) †Toray Carbon fiber
‡ Aramid, Ltd.Polybenzoxazole fiber ¶Honeywell extended chain polyethylene fiber
** Magellan honeycomb polymer (with planned values)

†† DuPont Aramid fiber

Our baseline material for the ribbon is M5 fiber, which is advertised now, and may be
improved. We expect a 50% increase in the M5 fiber capabilities by the time the lunar
space elevator is constructed, which seems reasonable in light of past progress. Note
that the LSE does not depend on the availability of carbon nanotubes for the building
material.

Fail-Safe Design for Safety, Reliability, and Repair

Micrometeoroid damage is a major consideration in lunar space elevator survivability.
We have determined that a ribbon shape provides the greatest protection against
severing by meteoroids, while still allowing the wheeled climbers to grip the material.
However, a single ribbon would not be fail-safe. A break would result in a catastrophic
loss of the entire system. Even though a break near the surface or near the top would
allow time for an adjustment of the balance through moving masses at L1, the wave
propagation velocity in the high-strength material would result in a destructive tensile
impulse that seems too difficult to overcome.

For this reason, we have decided upon a multiple ribbon system. With interconnections
every so often, if one section is severed, the parallel section can take the load until
robotic repair vehicles can replace the missing ribbon. The multiple ribbons are more
versatile than the multi-strand tether proposed by Forward and Hoyt

. The

interconnections might be on the order of 100 km apart, small enough that a repair
climber could carry the mass of 100 km of replacement ribbon. Multiple ribbons also
naturally allow two-way traffic up and down the elevator. This makes it easier to carry
payloads from Earth down the ribbon to the Moon, at the same time that lunar materials
are being carried up the ribbon for launch to Earth orbit.

The lunar space elevator multiple ribbons would be connected at intervals by cross
members, as shown in the sketch of Figure 11. The nominal safety factor varies with the
number of parallel ribbons, as shown in the table. A 3-ribbon design may be the best
choice, as pointed out by John Oldson.

Number of Ribbons, n 2 3

Safety Factor, f

4 3 2.7 2.5 2.4

Figure 11. Multiple-Ribbon, Fail-Safe Design

The risk of meteoroids has been addressed by Levin

and by Carroll

in the NASA

Guidebook for Analysis of Tether Applications. From Levin, the mean time in years
between meteoroid cuts for a ribbon h mm wide and L km long is:

T = 6 h

2.6

A 200,000 km, 30 mm ribbon will be cut in 2.5 months, 50 mm in 9 months, and 100 mm
in 4.6 years. Multiple ribbons reduce this risk. The probability of having a 20 km 30 mm
ribbon cut in a month (the duration of a typical repair mission) is 4x10

-5

. The probability

of having two parallel sections cut in a month is 2x10

-9

. We have 10

sections. The

probability of losing a dual-line LSE is thus equal to 2x10

-5

. This is close to failsafe, but

damaged sections must be replaced every few months. This can be done from way
stations with repair climbers and spare ribbon sections.

Multiple ribbons and regular replacement of ribbon sections has another advantage: the
speed of the climbers could be increased, raising throughput directly. We could accept
the increased wear on the ribbon, and replace worn sections the same way we replace
broken sections. Higher climber speeds would also reduce the time required for a
payload to be carried up the entire 200,000-km length of the extended lunar space
elevator; at 30 m/s, they could cover the distance in less than 3 months.

Improved Materials and Carbon Nanotubes

There is considerable research going on in the United States, Japan, and Europe in
trying to develop carbon nanotubes into practical composite materials. In the next few
years, we may see significant advances in this area, with either conventional composites
that are augmented with fibers of carbon nanotubes, or perhaps even a complete carbon
nanotube material that has much higher stress limits. Either of these advances would be
very significant for the capability of the lunar space elevator. Since carbon nanotubes
have about four times the stress/density ratio of M5 fibers, a lunar space elevator built
with even de-rated carbon nanotubes would have much higher throughput. This would
significantly reduce the cost per kilogram of lunar materials delivered into Earth orbit.
During Phase II, we will assess this progress, and evaluate the chance of such materials
being available in the 2025 time frame.

System Components

There are several distinct types of vehicles that will be used in the construction and
operation of the lunar space elevator. During the construction phase, we will need high-
Isp orbit transfer vehicles to carry the initial ribbon mass and the ground installation
mass from LEO to L1 or the lunar surface. We will then need construction vehicles to
erect the tramway and to build the surface mining and refining installations. During the
operational phase, we will need ribbon climbing vehicles, which can also carry payloads
along the tramway ribbon. We will also need smaller OTVs to carry the lunar payloads
to LEO and Earth materials to the Moon. We examined the climbers in some detail
during the Phase I study.

Climber System Design

The maximum speed of the climbers on the ribbon is a critical parameter, because it
largely sets the maximum throughput of the system. The operational speed is also

velocity of 15 m/s would require 10 kW at the surface, but drops to less than 100 watts at
just 7% of the way to L1. Climbers equipped with just 2 kW of power, achievable from
modest-sized arrays, could start slowly, then accelerate as their weight dropped, and
exceed the average velocity at heights where the friction and load on the ribbon is much
lower.

The climber solar arrays will be in the shade on the lower part of the ribbon for half of
each month. However, because of the 5

inclination of the lunar orbit to the ecliptic, the

maximum shade reaches just 29% of the distance to L1 at new moon, and there is no
shade during the half of the orbit between first quarter and last quarter. By launching the
climbers during the daylight, the long-term average of 100 climbers on the ribbon can be
maintained. Since each climber takes about 50 days to reach L1, there would be two
groups of climbers on the ribbon, with a gap between them. Alternatively, laser light
could be beamed from the base of the ribbon, as proposed for the Earth space elevator.

To alleviate the problems of lack of sunlight and high required power near the base of
the ribbon, the climbers might be launched from the base with a certain velocity, and at
the apex of their trajectories, attach to the ribbon. We have not examined the dynamics
of this situation, but it can be addressed in Phase II. Also, it may be possible to provide
the climbers with magnetic levitation to reduce the wear on the ribbon, if conductive
inserts could be incorporated into the ribbon material. Finally, each way station might be
able to sling the climbers up to the next station, without touching the ribbon at all. Or the
climbers might be equipped with mechanical devices to interact with thicker sections of
the ribbon every 100 m or so, to provide the impetus of velocity to fly to the next section.
Above L1, and on the downward ribbon, this same device would keep the speed of the
climber reasonably small.

The climbers will bow the ribbon due to the Coriolis force from their velocity. With the
ascending ribbon on the west and the descending ribbon on the east, this force will
separate instead of entangling the ribbons. The climbers will also tend to twist the
ribbons. To handle this problem, gyroscopic precession might be used; the mechanism
illustrated in Figure 13 on the next page shows the concept. Precession produces a
force at right angles to the force applied to it. If the climber in the illustration is going up
and the flywheel is rotating in the same direction as the drive wheel, twisting the flywheel
in the direction shown will result in a force around an axis parallel to the ribbon. With
flywheels in both wheels the combined force would be about the centerline of the ribbon.
In this example it would be counterclockwise when viewed from the rear.

The split field coil design shown may be more complex than is really needed. In reality,
a standard motor and actuator would work and most likely need to move only in the
plane shown. Torque applied to the flywheel is countered by torque on the drive wheel,
probably an undesirable steering input. Two or more sets of drive wheels in a train may
be necessary to resist this force. The flywheel need not be powered unless it is to be
used. If a twist is detected, it is powered up, moved to a new position until the desired
effect is achieved, then straightened out and turned off. Changing speed changes the
force during the process. The drawing scales to a tire one meter in diameter and grids
that appear in various views are one meter divided by lighter half meter lines. The ribbon
shown is 10 cm wide.

The view on the left shows the situation that arises when multiple ribbons come together
in space. The resulting “X” shaped connections require clearance to the side as well.
The battery pack has been shortened and the solar array is turned sideways as the
vehicle passes over one of the ribbon junctions. A much longer battery pack can be
used with a single ribbon and the solar panel is never in conflict. That condition is
shown with a ghosted underlay on the right and in most of the other illustrations.

Figure 16 shows a detail of how the large tires spread the load on the ribbon, reducing
the added stress due to the climbing and improving traction. The deformable tires are
supported by curved springs that distribute the force and accommodate variations in
ribbon thickness when the vehicle passes over a patch or a support tower. The inset in
the upper right corner of Figure 13 shows a “Tweel”, a non-pneumatic experimental
tire/wheel from Michelin that demonstrates the principle. The deformable tire approach
allows steering by tilting the wheel relative to the ribbon which reduces the rolling radius
on one side of the tire. The actuator shown in blue would regulate the pinching force
between the tires or spread them apart if a climber needs to be removed from the ribbon.
An orange flange is shown on one of the wheels that could trap the ribbon like the
flanges on a railroad truck. However, the ribbon would have to be stiff enough to accept
pressure on its edges. Alternately, the rings could also serve as a sensor that corrects
steering if it detects ribbon contact. A system that minimizes contact with the ribbon is
preferred. We have incorporated a binocular camera system borrowed from the Mars
rovers that could sight down the ribbon, tracking lateral alignment relative to the wheels
and detecting approaching supports, damaged sections or a stalled climber. We
anticipate a semi-autonomous system with the computer handing over to a human when
it detects a problem.

Figure 16. Detail of Tires and Ribbon Interface

A space-frame chassis design is illustrated. The various tubes could be carbon fiber and
a system devised to disconnect them at the joints. The wheel assemblies are identical
at both ends and the solar panels are interchangeable. This approach provides

maximum flexibility. The climbers can be delivered in pieces and assembled, plus parts
can be salvaged as components fail. Presumably, the climber could run on only one of
the four motors in an emergency.

This design attempts to demonstrate a credible solution with an emphasis on simplicity
and non-exotic mechanical solutions. In Phase II we can consider a greater range of
possibilities. Perhaps the most exotic might be a climber that uses only one side of the
ribbon, clinging to the surface by exploiting van der Waals molecular forces. In theory a
force of100 kN/m

could be achieved this way. Another area that needs thought

concerns lunar dust. We might need to devise an electrostatic device to repel it from the
ribbon or it might be immaterial.

Orbit Transfer Vehicles

Orbit transfer vehicles will be required to carry the lunar payloads from the upper
elevator to Earth orbit, and to carry Moon-bound payloads back from Earth orbit. The
climber vehicles can provide the power from their solar arrays, and a high-Isp propulsion
system can be mated with the climber to provide the delta-V to reach Earth orbit. This
propulsion system may just shuttle between Earth orbit and L1, while the climbers move
over the entire course, from polar mines or equatorial bases to LEO and back.

Tramway Construction Vehicles

Since the climbers can adjust for horizontal or vertical ribbons, they can move the entire
length of the ribbon, from L1 to the pole. Being solar powered, they will face the same
problem of being in the shade for about half of each month. However, the horizontal
motion along the tramway will require far less power than the lifting portion of the trip up
the vertical ribbon, so it may be possible to fit them with batteries to store energy. It may
also be possible to provide a conductor on the tramway to provide power to the vehicles.

During the tramway construction phase, a robotic vehicle will be required for erecting he
support towers and stringing the ribbon between them. In this phase, ribbon is carried
overland by a lunar rover, which also doubles as a tower-building system. Using
construction materials from the lunar surface factory, the vehicle would build the towers
from the bottom up, and raise them vertically, without the need for erecting them by
rotating them from horizontal to vertical. As each new structural part is inserted in the
bottom of the tower, the top rises until it reaches the required height. As we mentioned,
a total of about 30 towers would be sufficient to reach from the equator to the pole.

Key Technology Challenges

Lunar and Advanced Materials

The strength to density ratio of the elevator ribbon is the primary parameter in the
elevator design, with a high value critical for making the system cost effective. Currently,
materials such as M5 and Spectra have the highest strength to density ratio, but a lunar
elevator made from these materials, while technically possible, would not be cost
effective. An advanced version of M5 was selected in Phase I as the baseline material.
However, carbon nanotube based materials have the potential to dramatically improve
the performance of the LSE. We expect to see great progress in developing higher
strength composites in the next decade, because their use would revolutionize many
aspects of military and space operations, enabling lighter air vehicles and perhaps even
single-stage-to-orbit launch vehicles. The progress in this field will be monitored under
this task, as well as any new high strength materials.

There has been some examination of the use of lunar materials to make composites,
and we expect that in the next 5-10 years there will be additional advances made, as
soon as the new robotic lunar explorers start their operations around 2008. The
observations of these vehicles, coupled with ground experiments on artificial lunar soil
and the Apollo samples, may lead to credible ways to mine and fabricate spun lunar
basalt for the lunar space elevator ribbon. This would greatly reduce the cost of
launching additional ribbon material from the Earth.

Robotic Construction Using Lunar Resources

There will be many operations on the lunar surface necessary to build and operate the
lunar space elevator. There will be mining operations near the pole for lunar ices and at
different locations along the tramway for exploiting mineral deposits. It will be necessary
to provide power plants, perhaps with large solar arrays on mountain peaks near the
pole. And the construction of the tramway, with its tens of support towers, will require an
extensive operation on the lunar surface. All of these operations will be vastly improved,
and reduced in cost, by the use of robotic vehicles, and the use of as much indigenous
lunar materials as possible.

Cost efficient development of this large infrastructure will need a high degree of robotic
or telerobotic (some remote human control) operation for low-cost construction.
Advances in telerobotic capabilities (with a large time delay) have been demonstrated by
the Spirit and Sojourner Mars rovers. Telerobotic operations on the lunar surface should

be much easier than Mars, with constant visibility from Earth and time delays of only
seconds.

With successful robotic and telerobotic operation, the remaining key to the construction
process is the use lunar resources. The overwhelming example of lunar resource use
will be in the expected water ice near the lunar poles. Using this resource will not only
provide life support to the manned bases on the moon, but will also become probably the
most important lunar export to Earth orbit for propellant depots for space vehicles
leaving Earth orbit. The use of lunar materials for construction of the equator-to-pole
tramway support towers will also be of great importance in reducing the overall cost of
lunar space elevator system development.

Dynamics and Control

The lunar space elevator will be the longest structure ever built in orbit. It will even
exceed the length expected for the Earth space elevator. There are several dynamics
issues that need to be addressed in building such an extremely long structure. Because
of its great length, the LSE will have very low frequencies of lateral vibration; higher
modes will have higher frequencies, but all the modes will probably have low natural
damping, and therefore be prone to forced excitations. There will be forced oscillations
induced by the libration and orbit eccentricity of the Moon; traveling waves induced by
the motion and release of the climbers; and even oscillations induced by the gravitational
effects of the sun. The natural frequencies and mode shapes of these vibration modes
must be analyzed and understood, as well as the dynamics of the capture and release of
payloads traveling between the LSE and Earth orbit.

The solutions to these dynamics problems will likely require the use of active control.
The natural damping of the space elevator ribbon can be augmented by active damping
introduced at the way stations, at L1, and on the lunar surface to absorb traveling waves.
It may also be possible to modulate the speed or acceleration of the climbers to provide
active damping suppression.  Whatever solution or solutions are selected, they will be
necessary for the successful and safe operation of the lunar space elevator.

Autonomous Operations

The ideal for the lunar space elevator is to have every aspect of operations, from mining,
refining, power production, tramway vehicles, climbers, and catch and release of
payloads, completely autonomous, with very little human intervention. Maximum
autonomy is a requirement for cost effective operation many proposed systems to be
deployed in space in the decades to come, in addition to the LSE. The elevator must be
able to operate effectively with no onsite human presence, of course, but it may be cost
effective to have supervisory control by humans on Earth, given that the maximum time
delay for teleoperations will be about 2.5 seconds. To repair micrometeoroid damage,
including actual cuts, autonomous or teleoperated repair capability will be needed.
Lunar surface operations will probably require minimal onsite human intervention.

The key enabling technologies of advanced materials, robotic construction with lunar
materials, control of the dynamics, and autonomous operations, will all be addressed in
our Phase II program; these key technologies appear to be difficult, but certainly not
intractable. Overcoming these potential obstacles can help ensure the success of the
lunar space elevator program.

Operations, Economics, and Payoffs

Operational Concept

The lunar space elevator operational concept is to carry material from the lunar equator
and the poles to Earth orbit and from Earth orbit to the Moon. This allows lunar-derived
construction materials and propellants to be delivered into Earth orbit, and allows Earth-
launched supplies and equipment to be delivered to lunar bases and installations.

The lunar space elevator will function like a “highway” between Earth orbit, L1, and
points on the lunar surface. Materials from the lunar highlands and from the maria will
be used as raw materials in producing building materials, shielding, and a variety of
structural shapes that can be launched via lunar space elevator to HEO, GEO, and LEO.
Payloads to different orbits can be launched by simply choosing the point on the LSE for
their release. The resulting orbit is highly elliptical, with perigee at the desired altitude,
and apogee near the end of the lunar space elevator. These orbits can then be
circularized by low-thrust, high-efficiency propulsion systems. The chart of Figure 17
shows the Earth-orbit perigee attained by release from different heights on the LSE.
Releasing from high up on the lunar space elevator allows the payloads to reach
perigees in LEO. Payloads in LEO can be lifted by low-thrust propulsion to rendezvous
and dock with the LSE, and then travel down the elevator ribbon to the surface.

Figure 17. Perigee Radius vs. Height of Payload Release on LSE

= R

/ (2 R

- R

)

= R

- L,

= Moon's orbit radius

Payload Flows

Lunar materials shipped to Earth orbit will consist of a variety of lunar resources:

•

Lunar regolith to HEO for shielding and general construction

•

Lunar plagioclase, feldspar, anorthite, etc., for Earth-orbit construction

•

Lunar water, oxygen, aluminum, and sulfur to LEO for propellant depots

•

Lunar water from the poles to lunar bases for life support

Earth payloads shipped to the LSE and the lunar surface will include potential
counterweight masses for LSE construction, return of lunar climber solar arrays to the
surface for re-use, and Earth-launched materials bound for the Moon. Note that the LSE
is like a pipeline, with large but slow throughput, so it will not carry human cargo.
However, the LSE could carry a large quantity of materials and supplies to complement
the human passengers who will move by faster chemical rockets to and from the Moon.
The result will be a large reduction in the cost of moving payloads from LEO to the
Moon, and the availability of lunar materials at a reasonable cost in Earth orbit.

To carry this large tonnage, we could use a fleet of 50 tugs, using ion rockets or
electrodynamic thrusters, to take the Earth supplies from LEO to the LSE and bring the
lunar products back to LEO. Each tug would consume about 10-20 kW of solar power,
produce 0.5-1 N of thrust, and transfer 500-kg payloads in about 2 months. Each tug
could move 1.5-2.5 tons per year, and 50 tugs could move 75-125 tons per year, or a
million kg per decade.

To support the tugs, we would need to launch 10 tons each month to LEO, of which 10%
is fuel for the tugs. The tugs will be departing daily; for the first few years, they will be
carrying only LSE parts, but later some of them could deliver lunar fuel to other
spacecraft. The tugs could be scaled to the most efficient size and power, which might
be as high as 300 kW in some scenarios.

LSE Cost Analysis

The performance of the lunar space elevator depends on the carrying capacity of the
ribbon material, which is a function of the available material strength and the total mass
of the ribbon. The cost of the lunar space elevator depends on Earth-orbit launch costs,
orbital transfer to lunar trajectories, and the cost of developing and operating the system.

Launcher cost projections

A simple spreadsheet cost model for the lunar space elevator was developed, using a
strategy from Nock

et al. in their work on Moon-Mars transport economics. Launch

mass to LEO is used as the standard parameter for costing. Rather than attempting to
project launch costs to LEO well into the future, we use three values, low ($0.3M/t),
medium ($1M/t), and high ($3M/t), to convert launch mass to cost. The high end of this
range is based on the published cost and performance of the Falcon V launch vehicle,
currently under development by SpaceX (

www.spacex.com

), and scheduled for launch

during the second quarter of 2006. The current estimated cost is $15.9M plus range
fees, and the payload to a Cape Canaveral inclination, 200 km altitude circular orbit is

6020 kg, which gives a cost per tonne of $2.64M. Allowing a modest amount for range
fees, we round this up to $3M/t. Taking this cost as the upper end of the range seems
reasonable, but actual demonstration of flights at these rates is needed. Note this is a
big reduction from the $10M/t of current launchers, which was the value used by Nock.
Given the published goal of SpaceX founder Elon Musk to develop even lower cost
vehicles, assuming the midrange of $1M/t to LEO is probably a conservative cost for the
time frame of the LSE. The low end is consistent with the ambitious goals of various
paper studies of advanced launchers, but is not out of line looking two or three decades
in the future.

Orbital Transport

A magnetoplasmadynamic (MPD) thruster system currently being developed at JPL

assumed for the LEO-to-L1 leg. The assumed Isp was 4000 s, with an efficiency of
about 82% and a thrust of 12.5 newtons. A total mass/power ratio of 10 kg/kW was
assumed for sizing the inert mass of the system. The payload and inert mass were
sized at 20 and 2 t, respectively, and performance computed with these numbers.
Round trip transit time, returning empty to LEO, is about 6 months.

Two additional components must be added: The mass required on the lunar surface,
and the transport needed to go from L1 to the lunar surface. It is somewhat less costly,
in terms of total mass in LEO, to use high Isp electric propulsion to low lunar orbit, then
switch to a chemical rocket needed for a soft landing, However, for simplicity, we chose
to use oxygen/hydrogen chemical rockets for the entire trip. An Isp of 465 s was
assumed for an RL-10 class engine. Also, return trip propellant was assumed to be
available on the lunar surface, where it would be derived from polar ice. Larger or
smaller use of lunar derived propellants could change the mass required for this leg by
significant amounts, but lunar propellants would only have a major impact overall if they
are available in LEO for the transport to L1.

The Delta-V’s used are based on Earth to escape and Moon to escape, and are
therefore a bit conservative. Actual systems would have losses not accounted for which
would balance out these assumptions.

The orbit transfer delta-V’s assumed were:

LEO to L1 high thrust: 3350 m/s
LEO to L1 low thrust: 7800 m/s
L1 to lunar surface: 2640 m/s (includes some margin for soft landing)

Elevator Mass and Transport Cost

The current mass estimate for the lunar elevator, with an added 10% margin, is just over
6100 t, plus an additional 100 t on the lunar surface. Adding in the xenon propellant for
the cargo transport, plus oxygen-hydrogen chemical propellant for the lunar surface
transport, gives a total LEO mass of 8000 t. Multiplying by the assumed range of
transport costs gives a total cost for launch of 2.4 B$ at the low end, to 24 B$ at the high
end.

Development Cost

With the original assumptions of a higher range of launch costs, we felt development
costs could be ignored relative to launch cost. With the lower range used here, this is no
longer the case, and it is likely that development costs will dominant at the lower end of
launch cost. On the other hand, a mature industry for carbon nanotube products,
sustained by the much larger terrestrial and traditional aerospace markets, could pay for
all development of the main component of the system, the elevator ribbon. As a rough
estimate, we would put the development cost range at $1-10 B, or roughly comparable
to the launch cost range. This number is completely dependent on the system details
and the technology available decades in the future, and must therefore be regarded as
very rough.

No discounted economics were used, for a couple of reasons. The revenue stream
being discounted is not well defined, and the LSE will probably be part of a larger
government funded program not driven by standard cost accounting.

Lunar Space Elevator Payoffs

Potential Impact on Long Term NASA Plans

NASA is currently undergoing a major transformation, explicitly due to the radical change
in the stated goals of the agency put forward by President Bush early in 2004. Follow-on
documents, including the Aldridge Report

in 2004 and the NASA FY 2006 Budget

Request and the companion report “The New Age of Exploration” (both available on the
NASA website) give a broad view of the goals of this “Moon-Mars Initiative,” possible
timelines, and major developments needed to bring about the goals. The goal is to send
humans back to the Moon no later than 2020, followed by human exploration of Mars
sometime afterwards. Along the way, key supporting technologies will be deployed.
Specifically cited is the use of in situ space resources, such as the probable lunar polar
ice deposits.

The LSE fits into this new vision from several standpoints. First, it can serve as a focal
point for the development and deployment of advanced autonomous systems, but close
enough to Earth to allow monitoring and some near real time control. Second, it can
serve the infrastructure needs of the lunar base activity, currently planned as a precursor
for the Mars missions, by moving cargo down to the surface and water for propellant up
to L1. If the lunar activities grow to include more ambitious plans for radio or optical
telescopes, the savings from the LSE is even higher. Third, the clearest quantitative
benefit comes from serving the large demand for propellant inherent in recurring human
missions to Mars, and related unmanned activities on Mars and beyond. Once the mass
flow leaving LEO reaches this level, the benefits of having oxygen and hydrogen
available in quantity in LEO and high Earth orbit are clear.

Finally, there is a new underlying sense in the new vision that one fundamental purpose
of the space program is to inspire, as well as create the needed infrastructure for a bold
exploration program. The LSE could do more than just lower the cost for achieving this
vision—it could be a visible inspiration to all the people of Earth, whenever the Moon is
in the sky, of the new realm of humanity.

Building the Lunar Space Elevator

Steps in Construction

These are the basic steps required for development of the LSE infrastructure.

1. Launch ribbon to LEO, and then to L1, with large launch vehicles and ion rockets
2. Maintaining balance about L1, extend ribbon upward and down to the lunar surface
3. Launch mining equipment to pole
4. Launch mining equipment, tower builders, factory, and climbers to lunar equator
5. Construct 2-way catenary from equator to pole with tower builder
6. Test complete operation

Using Lunar Resources

As part of the development of the concept of the lunar space elevator, we looked at the
requirements for construction on the lunar surface, the possibility of using lunar
resources for construction, and the methods that could be used to build the system. It
appears that the major lunar product will be the building materials and raw materials that
are widely available in the lunar regolith. The one key mineral resource that is localized
is the water ice expected in craters near the poles. The other natural resource is the
nearly continuous sunlight available at mountain peaks very near the poles. Thus our
focus was on mining and refining the lunar regolith to produce blocks and wires, and
potentially fibers for reinforcing the space elevator itself, and strengthening it for carrying
larger loads.

One potential lunar resource is solar power. There are two ways to enjoy essentially
continuous sunlight in cislunar space. The first is using stabilized spacecraft or elevator
stations at L1 and L2. The L1 sunlight will be invaluable in the initial space elevator
construction. The initial construction phase will begin with a vehicle launched from Earth
to L1, and maintained in position near the balance point with thrusters. The vehicle
could easily have 100 kW of power from thin-film solar arrays, and have power
continuously, except during eclipses. Even those could be eliminated by using a
controlled halo orbit about L1 that would take only a small thrust to maintain, using Hall
thrusters powered by the solar arrays.

The second way to achieve nearly continuous sunlight is on mountain peaks at the
poles. Substantial work has been done on the topography of the lunar polar regions,
following the success of Clementine and Lunar Prospector. The sun as seen from the
Moon librates 1.5 degrees in elevation, making “winter” the worst time of the year for
illumination.

The paper by Bussey, Spudis and Robinson

summarizes their work on well-lit locations

as well as permanently dark locations at the lunar south pole. They found that the pole
itself, located on the rim of the crater Shackleton, was the best location in the south,
receiving 80% sunlight in winter. A second location 10 km away receives about 73%
illumination, and together the two sites receive 98% illumination (presumably in winter).

Since topographic databases

now exist for the polar regions, it should be possible to

review these findings, extend them to the north polar area, and do the calculation of how
high a tower would need to be to receive a certain increase in sunlight, or conversely,
how fast and far a mobile solar array would need to go to stay in sunlight most or all of

location, and capture it into L1 for the counterweight. That may be the final CW, while
the initial counterweight could be composed of space debris, external tanks, or lunar
materials.

Kirk Sorensen of NASA MSFC also suggested that we could build the counterweight
from lunar materials by having a mass driver on the Moon or a rotating tether on a tower
to throw materials to L1. A 1990 paper by Bob Zubrin discusses the concept, in the
context of launching LOX tanks into lunar orbit, for use by lunar landers from Earth for
the delta-V for the lunar landing and takeoff. They could refuel both going to the Moon
and returning, reducing their required mass and increasing their payload.

Eugene Levin analyzed the use of a lunar sling for launching materials into lunar orbit for
use by the lunar space elevator.

Material Forming and Fabrication

Blocks and Wires

We developed structural concepts that would route tension forces from all three
Cartesian axes through the same block, but systems of interlocking blocks could handle
tensions in the X, Y, and Z directions independently. Both approaches have yielded
systems that seem to solve the problem. They are all interlocked mechanically and have
the potential of being made entirely from lunar materials. The concepts are based on
research by Wykes

XYZ Geometry

Figure 19. Structural Concept to Route Tension Forces

The image at the left in Figure 19 shows an array of colored columns in which green
represents the X direction, violet represents Y and orange represents Z. This
composition may be repeated indefinitely but it creates cube shaped voids in the
structure. These cube shaped voids have six faces, each on the surface of a different
column. By attaching a pyramid shape to these surfaces the void is filled. A cube with a

pyramid on either end is called a pencil cube. This system modifies that shape by
adding two half cubes to two of the sides. The resulting blocks can be connected in
chains at these faces and completely fill the space.

Lunarcrete is widely accepted as a lunar construction material and would work for us as
well. T. D. Lin has proposed a Dry-Mix/Steam-Injection procedure for casting concrete
in space. We envision an automated system of molds like ice cube trays. Dry cement
and aggregate would be exposed to 180° steam for 18 hours and finished parts would
emerge with no additional curing required. Concrete created this way develops a
compressive strength of 700 MPa, more than twice the performance achieved with
conventional casting without the 28 day cure cycle. The creation of traditional solid
concrete structures on the moon with this process would be a daunting challenge. The
universal blocks we are proposing are a few centimeters long and an automated
production factory might be delivered to the moon by a single spacecraft. This central
factory on the lunar surface could distribute the universal blocks anywhere on the moon
that an extensive tramway system could reach.

Figure 20. Lunarcrete Block with Wire Tension Insert

A Wire Tension Insert

Figure 20 shows two views of a Lunarcrete block with an insert molded-in. Concrete
requires reinforcement if it is to be exposed to any substantial tensile loads. In this
example two roughly U-shaped wires are welded where they intersect and configured so
the projecting loops will overlap the loops of adjacent blocks. Molded into the concrete
they create a system that allows the blocks to be joined into a continuous column.

This concept carries the tensile loads down the center of each block column. A quarter-
turn key is proposed which can be placed between overlapping loops and rotated by a
robotic arm. The space between the loops is wider than it is long so that an oblong key
clears the wires when inserted but stretches and tensions the wires when rotated 90°.

The final design may have a slight concavity to keep the wires centered and it may need
a wider head that contacts the block when twisted. A symmetrical version with a head
on both sides would allow disassembly from either side. We can roll the shape into a
wire then cut and cold-head the pieces. Alternately, they can be cast in an investment
material or reusable ceramic mold. The wires and the key may be heat treated after
forming if we need to get greater strength or toughness. Case hardening is also a
possibility.

The wires in this example are .060” but could be considerably larger if required. This
seems about right for mild steel. By welding two relatively imprecise pieces we can
control the critical length to establish the desired pre-load on the assembled column.
We will need to study potential structures to decide what this value should be, but if we
assume a structure with an internal pressure of 15 psi and blocks with a 1” cross
sectional area we would need to generate 60 pounds of force between blocks in each
chain to keep them from separating under the load.  Since this is 30 pounds/wire it
seems like a reasonable number and there is no absolute requirement that the blocks
stay in contact under all conditions.  In fact, absolute precision of fit is not likely and we
may need to keep the blocks slightly undersize. Compression loads will pass through
the faces that do contact each other and the structure would shift slightly under load,
which may be good. It would be a “self-designing structure.” It may actually mimic the
behavior of a metallic solid.

Figure 21 shows how multiple blocks would be wired together. Fasteners have been
proposed that would facilitate attachment to the ends of each chain of blocks. The
design in the center is created entirely from wire and might be produced at the site.
Alternately, a thin titanium sheet can be formed into shapes which bridge two block
columns and accept conventional fasteners. A design like this may be beyond the limits
of lunar manufacturing but they are relatively light and can be stacked very compactly for
shipment.

Figure 21. Wiring Multiple Blocks Together

Wire Element Forming and Welding

capsules are formed by impact extrusion like a soft drink can or by electro-deposition.
They are filled with a mixture of regolith and aluminum particles, preheated to a
temperature just below melting and compressed. The metal fuses and the result is a
block with a metallic skin that should not require additional reinforcement. The process
is illustrated in Figure 23.

DROP HAMMER

.003Ó MIN.
(SODA CAN)

ALUMINUM
PELLET

EXTRUDED ALUMINUM
FORMS CAPSULE HALVES

REGOLITH PARTICLES

Figure 23. Encapsulating Lunar Regolith with Fused Aluminum

The Truncated Octahedron

A second block system is based on the truncated octahedron, one of several all-space
filling solids. It is also symmetrical in the Cartesian planes. It lends itself to compression
molding and might be formed by the encapsulation process. One interesting property is
shown below. When the square faces of the blocks are joined a matrix is formed in
which the spaces are identical to the blocks. A structure would have the option of being
50% open or solid. If it’s solid it would actually consist of two independent systems of
blocks that are interlocked but need not be attached.

Figure 24. Truncated Octahedrons as Space-Filling Blocks

The blocks may be joined in a variety of ways. Small conical bumps in the center of
each face could be fused by an electrical discharge (projection welding) or adhesives
might be used. Acrylic adhesive systems that coat one surface with a resin and the
other with a catalyst are found in industry and various other systems might be adapted

Towers, Vehicles, and Potential Lunar Material Ribbons

A review of the literature on lunar derived tether materials, mainly the late 1970’s and
early 1980’s, shows that one group spun actual glass using an Apollo 12 basalt
simulated composition, but did not report properties

. It seems likely that some

processing will be required to achieve an optimum lunar based fiber material, and there
is literature discussing general chemical processing, including a sodium hydroxide basic
and HF acid leach for separation of various components

One interesting candidate is fused silica fibers. Produced in lab quantities, fused silica in
vacuum has remarkable properties, but one major drawback. The mean tensile strength
under vacuum and at room temperature reported in Kelly and MacMillan

is 9 GPa, with

a density of 2.2, but a modulus of 73.5 GPa. This is an elongation of over 10% at
failure, but corresponds to a characteristic height of 417 km with no de-rating. (Further
strength increases occur at lower temperatures, but the modulus remains the same.)
Making and using this material would be a challenge, but it has a high potential benefit.

It is not yet clear what the optimum amount of processing and desired product is, if any,
in this context. However, the cost savings of being able to use lunar materials are
obvious, and they are certainly candidates for the large counterweight mass.

Lin, a Portland cement expert, suggests hydrogen reduction of lunar ilmenite.  He also
suggests a steam process which produces a finished product in 18 hours.  Most of the
water associated with concrete production is needed because of the wet casting process
and must be dried out of the finished product to achieve any strength.  A relatively small
percentage is the "water of hydration" and actually involved in the chemical reaction.
Such schemes could be adapted to “sulfurcrete,” sintered aluminum dust, etc., assuming
that lunar water could be obtained from the ices near the poles.

Alternate Fibers Based On Lunar Materials

One method for reducing the overall cost of the lunar space elevator is to use

in situ

lunar materials to make fibers that are strong enough to reinforce the initial ribbon. This
could greatly increase the carrying capacity of the LSE, and also greatly reduce the
amount of material that must be lifted out of the Earth’s gravity well.

Lunar aluminum, silicon, iron and titanium are abundant. Aluminum has a relatively low
density, is relatively abundant and can be used to create high strength fibers. Its
strongest form seems to be sapphire, which can be grown as long single crystals or
whiskers. The processes involved might even benefit from the microgravity environment
at L1. Perhaps we could grow continuous crystal strands that could go directly into the
ribbon assembler. Sapphire whiskers are almost as strong as graphite whiskers,
although they are more than twice as heavy.

Another material which compares favorably is quartz whisker. Silicon is plentiful and if
we can generate whiskers in space they would be many times stronger than glass fibers
made from the same element. Fibers in a metal matrix are also currently popular, and
an application might be sapphire whiskers in glassy aluminum foil. Glass fibers with
metal coatings might be used, since there is no water or oxygen problem.

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