The Construction and Utilization of Space Filling Polyhedra for Active
Mesostructures
By Forrest Bishop
Dec. 7, 1995
1. Introduction.
An "Active Mesostructure"
(PDF) is a collection of mesoscopic, similar machines, built by nanotechnology
methods (1). "Active" means each machine has the capacity to
exchange power and signals with the other machines, and to interact with
the external environm ent. An example of this is J. Storrs Hall's "Utility
Fog" (2). This paper concerns another type of system, discussed in
(3) and developed independently by this author. These machines are generally
envisioned as cubes, though other types are entertained.
This is a system composed of identical, connected, space filling
polyhedra (cells), each capable of moving with respect to its adjoining
neighbors, singly or in groups. The cells are connected face-to-face.
The scale of the cells (the "cell metric") is a ssumed to be
on the order of 100 nanometers (mesoscopic), though much of the discussion
would apply to cells of any metric. The simplest to conceive and design
for are the parallelepipeds, specifically the cube. This is the example
used for the purpose of illustration. Much of this discussion would also
apply to non-cubical cells, of which the square plate (a "cut down"
cube) is of interest for reasons of manufactureability. Some aspects of
this discussion are specific to the cube and to its permitted degrees
of freedom.
This article touches on methods of modeling, constructing, and
programming a structure composed of many such cells. A general solution
for transforming a large aggregate of cells from one arbitrary configuration
to another is outlined. A few examples of applications and unusual devices
are given. As we are speaking here of a machine that c an radically alter
its shape and surface composition, most applications haven't even been
dreamed of. The "Terminator T-1000" from the movie "Terminator
2" (4) is used to illustrate some of the concepts. The T-1000 machine
is a somewhat reasonable depiction of a nanotechnological, mesoscopic
version of the system outlined below.
2. General Description.
There are several geometries of interest for a space filling cell.
Besides the cube, the hexagonal prisms and the slant parallelepipeds are
capable of making the necessary face-to-face joining. These forms may
be of interest when specific crystalline materials are desired for application
or manufacturing reasons.
A distinction is drawn in the method of interfacing the cells between
cells that can only slide apart, and cells that can either slide or simply
detach from one another.
A right regular hexagonal prism is of interest from a manufacturing
standpoint, as some single crystals form this shape naturally (i.e. they
self-assemble - see figure. The resulting aggregate
is constrained to movement perpendicular to the hexagon plane, which is
useful in some products. A hexagonal prism with a width comparable to
a cubical cell metric, and having standard interfaces at one or both ends,
can also serve as a structural element in an otherwise cubical system.
There are two variations on the cubical theme of particular interest.
The first is a cube with mechanical interfaces on each of the six faces,
that are capable of sliding two connected cubes in one of the two directions
parallel to the joined faces, and parallel to the edges of those faces.
The two faces of each sliding cube that are parallel to the motion and
perpendicular to the join plane remain flush to the corresponding faces
on the other cube. The cubes are unable to detach the two joined face
s by movement normal to the plane of the joint. They can only move in
one of the two permitted directions at a time, and must be aligned with
four faces flush in order to change direction. These are "XY cubes".
The second type of cube has the same specifications as an XY cube,
but with the additional capability to detach faces normally (3). These
are "XYZ cubes". This distinction leads to a number of differences
in how the cell can move in an aggregate, as well as differences in manufacture.
In neither case do the cubes rotate in any way with respect to one another.
The XY cube requires a maximum of two extra moves to uncouple two
faces normally as do XYZ cubes. The first move is to slide {the cube to
be detached from} sideways, at which point the desired cube is free to
move. The second extra move is to slide {t he cube that was detached from}
back to its original position. This can be seen by tracing the trajectories
in the five cube configuration space, for example (figure
4.). This adds complications in various situations (see Extraction
under Modes of Motion).
In either case, the standard cube (active cell) has, in addition
to the mechanical interfaces, methods of receiving and transmitting power
and signals from any face, to any face, along with the necessary interfaces
for this on each face. Power and si gnals may be electrical, chemical,
mechanical, acoustic, electromagnetic radiation, etc. Drive mechanisms
on each face are required to move the cells. Cells in motion with respect
to the power supply need to be able to continue receiving power in order
to carry out some of the maneuvers listed below. This is accomplished
with sliding contacts for the electrically powered type. Each active cell
should have some onboard digital processing capability.
When the cells are aligned, they can be locked into position by
the equivalent of a sliding pin in one cell engaging a hole in the other.
A nanotech version may use something more subtle than this, like twisting
the sliders or effecting a reversible electrochemical reaction.
Construction Methods.
The desired material for a nanotech cell structure is of course
diamondoid (5), but other interim options should be entertained. Silicon
chip and microstructure fabrication is currently the most mature transitional
technology. It might be feasible to build active XY cells with a few extensions
of these techniques (This technology is also mentioned in (3)). XY cells
are mechanically simpler than XYZ cells, as well as having an inherently
stronger cell-to-cell joint.
One idea is to fab the individual faces using ordinary photolithography
processes. A silicon wafer is bonded to a removable substrate. Undercuts
(T-slots) are made for the XY mechanical joints. Pinion racks are cut
into the faces, to be engaged by a pinion on the facing cell. Through-holes
are made to the substrate. Dovetails are side cut on the edges. A 3D template,
or chaser, can be run over these various cuts to true them up. Perhaps
diamond film is deposited. Conductors are masked and deposited.
The wafer is give a new, removable substrate on top. This is either
made of active cells of the same design, or a cut template that can be
slid onto the wafer from the side as a cell would do. The bottom substrate
is removed, and various cuts made for mounting motors, gears, locking
pins and drivers, and a microprocessor with the interface switch. More
conductors and bonding pads are added. The individual faces are now removed
from the substrate. This is easy if other active cells of the same metric
a re used here. The internal parts are made in separate processes that
are already extant. The cubes are assembled using active cells (the first
ones obviously aren't).
This produces cells on the order of a 1mm, or perhaps .1mm, metric,
a far cry from 100nm. The size limiting factor seems to be the microcontroller
die size. These would be very expensive, but useful.
Another similar technique is to make the entire body of silicon,
hollowed out with five faces built in. This may be a square plate, instead
of a cube. The innards are added and the sixth face is put on as a lid..
In order to make trillions of active nanotech cells, some sort
of replication is needed. As these are not inherently self-replicating
(except as Von Neumann's robot in a warehouse of its parts), it is therefore
necessary to replicate the factories th at make them. A proposed means
of doing this is in (1). Perhaps the two methods can be combined.
Power can be either from an external supply, or a special module(s)
with standard interfaces. Corridors of various integer multiples of the
cell metric can be formed to transmit electromagnetic energy from one
part of an extended structure to another. These waveguides can be for
either RF or optical wavelengths. Existing quantum well laser arrays can
be incorporated on a cell face for transmission.
Energy might be stored in chemicals, batteries, capacitors, superconducting
ring waveguides or wires, strain energy, mesoscopic flywheels, and so
forth.
Waste heat removal has many options as well, including scaled down
versions of existing cooling methods.
Keeping the interfaces clean is critical to the operation of a
mesoscopic active cell. One of the advantages of using XY cells is their
natural tendency to wipe the interfaces clear of foreign matter when they
move (see Square Wheels). This action can be enhanced by some sort of
flexible shields at the edges of the cell. In addition, XY cells avoid
the problem XYZ cells have of entrapping debris during a normal attachment.
Specialty Cells (pixels). (See
Fig. 2.)
There is a need for special purpose cells, where one or more faces
aren't standard, and therefore not able to interface. Special surfaces
can include optical effects, chemistry labs, environmental surfaces, sensors,
tools, and so forth. These units may have a volume of several standard
cells. In any case, they will require extra attention (see Extraction
under Modes of Motion).
Hangars and other multi-cellular structures
In order to store pixels and structural members when they aren't
in use, a hangar of some kind is needed. This can be simply a box made
of standard cells, or a special purpose cavity based on the same cell
metric and the same standard interfaces. A special hangar would save on
system resources, increasing structural integrity at the expense of internal
mobility. Because the cubes cannot change their relative attitude, pixels
are designed for each one of the (six) possible orientations In addition
there can be edge (eight kinds) and corner (eight kinds) pixels, if required.
This means a pixel hangar has to have racks facing in several directions
to accommodate the various types of pixels, or that several differently
oriented hangars are used.
Supercomputers for "master" control can be contained
in a larger structure. These "mother ships" roam the interior
and coordinate large groups of cells.
Structural cores, exoshells.
It isn't always necessary for the entire structure to be composed
of active cells. There can be other, extended elements (again based on
the same cell metric) incorporated for more specific applications. The
active cells might only be a small percentage of the total mass (or volume).
These extended structures can be backbones, frameworks, exoshells, and
so forth. Active cells can also form the interface between these larger
structures.
3. Figure games
For a given number of connected cells (an aggregate), there is
a finite number of possible configurations. This set is referred to here
as configuration space. For any give initial configuration [A], there
are one or more possible paths to transform the cell aggregate into a
final configuration [B]. This is the [A]->[B] problem. Note that different
orientations of the same configuration are treated as separate entities.
This is because the aggregate is assumed to be operating in the real world,
where this matters.
These paths are trajectories in the configuration space, or figure
games (Figures 3.&4.).
The line connecting one figure to another is a "motion primitive",
consisting of a single cell move (light lines) or a single block move
(heavier lines). So then, a connected sequence of motion primitives forms
a figure game.
As can be seen from figure (4.),
there can be many possible figure games to get from [A] to [B], but only
a small subset of these are minimal. It's my guess that at between 100
and 200 cells in an aggregate, the total number of possible figure games
exceeds the number of possible chess games.
This type of analysis is therefore intractable for even small numbers
of cells. It can however provide some insight and guidance into partial
solutions to the general problem. For example, in (figure
3.) there is one configuration that separate the space into two distinct
regions. To get from one side to the other requires passing through this
gateway or terminus. It would simplify the master software to establish
artificial termini, or rest configurations, which the cell agregate has
to pass through Although this may cause certain configurations to no longer
be attainable, it also decreases the permissible number of figure games.
These configuration space diagrams can also be of use in discerning
rules for generating minimal figure games. As a simple example, fivecube
shows that to move from squarelike to rodlike, the block move should be
made first. This principle may be extensible to the general case, and
is used implicitly below.
If these solvable configuration diagrams are applied to the entire
aggregate, a constrained general solution of [A]->[B] might proceed
as follows: (this is [A]->[X]->[B] )
1) Use the figure games for 8 cells (this is a solvable set) to
assemble 2x2x2 cubes, then 4x4x4 cubes, etc. (these are artificial termini,
or composite cells). This requires an addition choosing algorithm to decide
which cells should go to which composite cell. The issue should be computable
at the current local level. Cells that are already in larger composites
do not participate until the process reaches the scale of their composite
cell.
In addition, there is the connectivity problem: which surfaces
of which composite cells should mate? I think this solves itself on the
way up to [X], but there are extra moves {out of the 8 cell figure game
and then back in to the same point} in order for XY composite cells to
effect the joining. These extra moves often require sending a request
down a line for a single row, slab, or block move.
Let the excess cells remain on exterior surfaces. Slab move or
block move them as and when needed to finish other large cells. This requires
a more global programming approach, but again at a level commensurate
with the current operating scale.
2) At the point where this produces a solvable (meaning a complete set
of figure games is available), arbitrary configuration of large composite
cells ( [X] ), reconfigure the aggregate in the most [B]-like shape. This
is done with a 3D pattern matching program. Slab or block move the remainder
cells to enhance the [B]-ness (this is carried out at all applicable scales
in turn also).
3) Again, use the figure games for 8 cells to refine the structure at
smaller scales. At each scale, refer to the [B] configuration file to
select configurations most like [B]s morphology at that scale. Connectivity
of the composite cells is more computation intensive in this phase of
the transformation, as [B] is not arbitrary.
This description doesn't include such details as larger embedded
structures, internal voids, and pixels. These would require application
specific software. There may be less brutish ways to determine trajectories
than the figure game analysis given above, perhaps based on search algorithms
and interaction rules.
In (4) there is a scene in which a {humanoid shape [A]} transforms
into a {facsimile of the linoleum floor [B]} it's standing on. A transformation
based on the above algorithm might look something like this: First, the
pixels are retracted to their hangars. The smooth surfaces of [A] give
way to a grainier, cubical geometry. The cubes merge to create larger
cubes, repeating the process until a stack of cubes (say 40) resembling
a blocky snowman is created (this is [X]). The master program compares
{"flat plate on floor"} to the 3D configuration space of 40
cells, and deduces the best match to be a slab of 39 cubes with the 40th
cube sitting on top. Using its map of the figure games, it now rearranges
[X] into this configuration, following a minimal trajectory (this is the
[B-like] shape). These 40 composite cells now disassemble into 160 composite
cells arranged as 280 cubes in a slab with 40 cubes sitting on top. The
process continues until the desired thickness is reached, then the remaining
cubes on top are brought into the main slab, which is more like a film
by now (this is [B]). Optical/environmental pixels are expressed on the
top surface, and display a picture of a linoleum floor.
For the case of arranging cells that possess individual identities,
there exists a general solution, extensible to n-dimensions (6). The puzzle
in which 15 squares are in a 4x4 array with one empty cell can demonstrate
this. As it is an energy intensive algorithm, its utility is limited,
but useful in certain circumstances. More generally, these kinds of games
can help develop rules and algorithms for dealing with large aggregates.
Another possible solution to [A]->[B] is the "free for
all". This is more akin to cellular automata, in which each cell
follows a few rules of interaction. The cells in [A] are sent their new
[B] addresses, and then let loose. I'm not at all sure this would work,
and even if it could, it would be very energy intensive.
4. Modes of Motion. (Figure 5.)
For engineering design, the above methods have limited utility.
A more useful approach is to define certain types of group movement, preferably
as distinct from one another as possible. These tools then provide a descriptive
language for the design engineer, as well as a simplification of the programming.
The modes of motion set presented below is not particularly orthogonal,
and certainly not exhaustive. It is, I think, a step in the right direction.
XYZ only Modes
1) normal detachment (These are motion primitives as well.)
2) normal joining
XYZ and XY Modes
0) A single cell move.
1) Single row extrusion.
a) Internal: Two or more moving surfaces contact the aggregate.
b)External: only one surface of the row contacts the aggregate.
2) Block Move. A one, two, or three dimension group on an exterior surface.
Note that Mode 1b) is a subset.
3) Slab Move. Like 2), except two or more moving surfaces in contact
with the aggregate. Note Mode 1a) is a subset.
Cascaded Modes.
By simultaneously making basic moves in a concatenated, or cascaded
fashion, various unusual mechanisms can be built (see Dodging Bullets)
and very high relative speeds attained
(see Addendum: Space Probe Launcher).
4) Telescope.
5) Cascaded Block Move.
6) Cascaded Slab Move.
Methods of changing a group's members. All three of these are illustrated
in the Red Cell Filter /Pump.
7) Deposition. Cells are sheared off in XY fashion, and left on a "fixed"
part of the aggregate.
8) Acquisition. Cells are slid onto a "moving" group. Note
this is the complement of 7), and the definition depends on what part
is considered fixed.
9) Exchange. This move allows two separate
structures to appear to pass through each other.
10) Coordinated Array Moves. All of the above modes can be carried out
as simultaneous or sequenced array moves on an extended aggregate. Examples
are Tank Treads, Systolic Pump, and density variations.
11) Move with Stop and Feed. Any of Modes (1-6), and 10) can be stopped
so that additional cell can be added (or removed) before resuming the
mode.
12) Extraction. This is a combination of several simpler modes and primitives,
used to bring a pixel to an exterior surface (express a pixel). The generic
pixel is assumed not to have a standard interface on the face closest
to the surface. The specific combination of moves is highly dependent
on the type of cell. For an XYZ cell, a row detachment and slab move to
form a corridor, followed by a single or double-cell extrusion, suffices.
There are 24 possible slab moves that can form this corridor for the pixel-
four to each face. Only the four slabs associated with the pixel face
are useful here. When the pixel reaches the (presumably flat) surface,
either an extra cell has to be present on the surface to receive it (only
if it has side interfaces), or a second cell attached behind it forms
an elevator and unloading dock. With the pixel(s) expressed, the rest
of the procedure is reversed to restore the internal structure.
For an XY cell, no row detachment is possible. A single row extrusion
is required, which has to turn and move across the surface until the pixel
comes up. The array has to be kept out of the way of the single row. The
pixels move across the surface, out of the way of the single row, and
the row retracts. This would also work for XYZ cells, of course. This
method imposes some interesting restrictions on how the array is constructed.
To return the pixels to their hangars, the procedure is simply
run in reverse.
Example: Humanoid into linoleum floor.
By using these modes with some sort of expert system to determine
what to do, the aforementioned [A]->[B] example might proceed roughly
like this:
First retract the pixels. Use the 8-cell figure games as above
to collect stray cells into some (small) composite cell size. Now the
telescope mode is used on the vertical portion, and the cascaded block
move for the horizontal. At the base of the blob, a transition is needed.
This is done with stop-and-feed. The interior telescope sections move
first, and form the first layer of blocks against the floor. Square Wheels
are used to move across the floor. The next layers out form a cascaded
block on top of the floor layer, and so forth. As the cascading blocks
move away from the ex-humanoid, downward and crossways feeds are made
to fill in the “cross” that would otherwise form. As things are settling
down, pixels are expressed and display a picture of a linoleum floor.
This method would appear much like the depiction in (4).
5. Devices.
Cube Pump. (Figure 6.)
This was one of the first (1991) widgets the author devised. As
the working cubes are moving around a lot, they're subject to premature
wear. Perhaps special cells should be used here, or the working cubes
can be time changed.
In operation, it is like a piston pump, with the cube performing
as valves as well as pistons. The drawing shows a near minimal XY cube
version, but in practice the bore and stroke can be varied independently
to produce a pump with a 2x3 bore and a 50 cell metric stroke, for example.
This device could also operate as an internal combustion piston
engine.
Tank treads. (Figure 7.)
A synchronized array block move looks a lot like the treads on
a military tank, and on some conveyor belts.
Systolic Pump (Figure 8.)
By incorporating tank treads inside of a corridor, fluid can be
entrained and moved in the manner of a systolic pump. Another method is
to use out-of-phase cascaded slab moves.
Square Wheels. (Figure 9.)
These are out-of-phase, synchronized slab and block moves with
feeds. If it's actually being used as a wheel, one or more wiper cells
can be added to help keep it clean.
Red Cell Pump. (Figure 10a.,
Figure 10b.)
This was designed in response to T. Toth-Fejel's draft article.
It demonstrates a lot of the basic modes and variations on them.
Space filling structures. Density variations.
By making array moves, a variety of unpacked structures can be
formed (see Minsky Robot Bush).
Dodging Bullets.
For a military or space AMS (or a Terminator), it may be possible
to detect and track incoming projectiles, and rearrange the internal structure
to form a corridor for the objects to pass through.
A little calculation: Say a 1cm bullet traveling towards the AMS
at 500 m/s. Say an onboard micro-array radar, 10m range, less than 1cm
resolution (I think this device already exists). Add a 100 GigaFLOPS (why
not?) DSP for extra comfort. The time in which the AMS has to react is
then 10m-s/500m, or .02sec, less processing time at signal aquisition.
The distance that the material has to move out of the calculated target
zone is ~1cm for a 2cm square corridor. The required maximum average radial
velocity is then 1cm/.02s, or 50cm/s! Note that most of the material doesn’t
need to move the full 1cm. In addition, consider that an AMS of this kind
would probably operate at less than a fully packed density, for increased
internal mobility, and that the modes of motion can be cascaded slab-on-slab,
and I don't think this is such a far-fetched notion.
6. Conclusion. That's it. Bye bye!
Glossary
[A], etc.: A specific configuration of a given aggregate.
[A]->[B]: Change the shape of an aggregate from [A] to [B].
Active Cell: A standardized machine, capable of interfacing and interacting
with identical units.
Active Mesostructure: A collection of interacting, mesoscopic machines
(Ref. (1)).
Aggregate: A fixed number of standard cells connected together
by their mutual interfaces.
Cell Metric: The lengths, edge angles, and face angles of the smallest
cell of a particular system.
Composite Cell: A group of cells that form a larger cell similar
to the cell metric.
Configuration: An arrangement of the cells in an aggregate in which
all cells are centered and aligned at the cell metric.
Configuration Space: All of the possible configurations of an aggregate.
Motion primitives form the links between configurations. There are three
types of mutually exclusive spaces comprising one, two, and three dimension
aggregates.
Express (pixel): Remove a pixel from its hangar and move it to an exterior
surface with its property face(s) facing out .
Figure Game: A permitted trajectory in configuration space, from
one configuration to another. A set of linked motion primitives between
two arbitrary configurations.
Figure Game Set: All possible figure games for a given aggregate
size.
[A]->[B] Figure Game Set: For any two configurations, the set
of all possible trajectories between them.
Fully Packed: No internal voids in the aggregate- all cell positions
occupied.
Group: A subset of an aggregate.
Mesocell: An active cell of mesoscopic proportion, consisting of
roughly 10^7 to 10^10 atoms.
Microcell: Bigger than a mesocell. Based on microtech rather than
nanotech.
Microtech: Engineering objects on a scale of roughly .1 micron
to 1mm. Many of the atoms are imprecisely positioned, compelling a high
degree of structural redundancy.
Mode of Motion: A method of moving a group or groups of cells in
an aggregate.
Motion Primitive: (a)A single cell move of one cell length in an
allowed manner, or (b) a block or slab move of one cell length.
Pixel: A cell with one or more non-standard faces, used for surface
property expression.
Point Probe: The leading spacecraft in a space probe convoy. It
is a sacrificial mass for clearing a corridor in space of ambient particles.
Rest Position, Rest Configuration: The configuration an aggregate
or a group might assume when it's not doing anything.
Standard Interface, Standard Face: The mechanical, power, and signal
interfaces on a particular surface of a standardized active cell. Note
that the interface is different for each different face orientation.
Terminus: A configuration that an aggregate, or part of an aggregate,
has to assume (by necessity or by design) at some point in a figure game.
References
1) Tihamer T. Toth-Fejel, "Active MesoStructures, Kinetic Cellular
Automata, and Parallel NanoMachines", to be published in "Tools
for the Next Millenium: The Promise of Molecular Nanotechnology",
Lance Chambers, Ed.
2) J. Storrs Hall, "Utility Fog", Extropy #13, 3rd Quarter,
1994
3) Joseph Michael, "Shape Changing Robot Construction Theory &
Application Notes", 1995, available via anonymous ftp.demon.co.uk
in directory /pub/ibmpc/dos/apps/graphics/pm as file pm5.zip (MS-WORD
2.0 document).
4) "Terminator 2: Judgment Day", Directed by James Cameron,
a Pacific Western production in association with Lightstorm Entertainment
5) K. Eric Drexler, "Nanosystems: Molecular machinery, Manufacturing,
and Computation" 1992 Wiley
6) Prof. Marvin Minsky, private conversation, June 18, 1995
7) "Thermodynamic Study of Phase transitions of Monolayer N2 on
Graphite" M.H.W. Chan, et al. Physical Review, Sept. 1, 1984
Addendum
Space Probe Launcher:
The cascaded telescope mode might be used in a space based launch
system. This study design launches one milligram (active mesocell aggregate)
microprobes at 10 km/sec.
The launcher, when in its rest position, looks like a thinwall
cylinder one meter long, 10cm diameter, and massing on the order of 100
grams (7). It is almost entirely made of nested, coaxial carbon Bucky
tubes, able to slide longitudinally with respect to one another. Each
tube, or stage, is composed of two or more nested and interlinked Bucky
tube layers for various amounts of tensile strength, and for accommodation
of circuitry and superconductors. Each stage can move at a maximum velocity
of one meter per second with respect to its two nested neighbors. Each
stage has superconducting, sliding electrical contacts to receive its
power, and to transmit power to the tubes nested within it. There are
10000 nested stages. The microprobes are attached to the forward inner
surface of the innermost stage, and have a total mass of one milligram
(~10^10 mesocells). The outermost tube is fixed to the rest of the launch
system.
The relative acceleration between any two stages is one meter/sec^2.
The motive mechanism can be molecular-mechanical, linear electrostatic
motors, wave-guided RF EM radiation, cascaded chemical reactions, etc.
Friction losses have to be very low, as there is no way to absorb the
heat.
Before launching the probes, the telescoping sections are extended
rearward 5000 meters. To do this, each stage moves 50 cm with respect
to its two adjacent stages. This is like pulling back a slingshot.
To effect a launch, all the stages are powered and accelerated
simultaneously for one second.
After a one second boost phase, the telescoped stages are back
in the rest configuration. Each stage has moved 50 cm with respect to
its neighbors, and is moving at the rated one meter per second per stage.
The innermost stage is moving at 10000 meters per second relative to the
outermost, fixed stage. At this time, the payloads are released, and the
stages decelerate. The energy produced by deceleration is fed back to
the fixed launcher as regenerative braking.
The stages are extremely thin walled tubes subject to tension loading
on their long axes.
It should be noted that 1) there are always at least two tubes
nested during the boost phase, 2) the maximum load is on the outermost
tube, which has the largest diameter, and the largest number of Bucky
tube laminations (about 380). The first 475 stages have 2-lamination stages.
Another lamination is added every 25 stages. The methods of linking and
propelling the laminations in a stage may have to be coupled to distribute
the tensile load over all of the laminations. In addition, it might be
necessary to terminate the tube with annular diamondoid caps linking the
laminations together.
Buckling:
It may be possible to internally pressurize the stages during the
first part of the boost with waveguided RF EM momentum introduced at the
forward end. The radiator would then have to move out of the way before
the 10 km/sec stages reach it. A superconducting reflector capping the
inner stage may be useful for this and for the prelaunch extension.
Wandering:
Any lateral departures from linearity during boost would quickly
produce a mess. The launcher is most vulnerable to external perturbations
when in the extended, prelaunch configuration. Any sideways motion has
to be eliminated before boosting. One method is to extend and retract
various stages out of phase with the induced "snaking". The
acceleration profiles for different stages can also be actively varied
to achieve the same effect during boost. An alternative is a guide wire
or tube.
Power Dissipation:
Power required is about 10 megawatts for one second. The power
distribution and energy conversion have to be nearly perfect, as there
is essentially no available thermal mass to absorb losses. If any superconductor
in the 100 gram launcher mass were to go over its critical temperature,
for example, the launcher would explode. Regenerative braking is a requirement.
Construction:
The tubes are gigantic in comparison to today's Bucky tubes. In
addition, the interlinking (which may reduce the strength of the carbon
sheet), superconductors, and so forth, add extra complications not dealt
with here. It could be that Bucky tubes are superconducting themselves,
which may or may not be a good thing here. The superconductors may consist
of 1-2-3 ceramics plated onto the carbon tubes. It might be feasible to
build a carbon fiber version of lesser performance.
A slightly larger version of the study design (say 30 km/s), onboard
an Earth satellite, could send microprobes to any point in the Solar System.
It has been evident for quite some time that the first workable
star probes will be nanotech based machines massing less than one gram.
This gizmo might be scaleable to speeds of interest (some decent fraction
of c) to interstellar probe designers, at least for the initial boost
(the probe's cells then rearrange to form a maser sail). A reasonable
launch turnaround time is required, since point probes are sent first
to bore a corridor in the interstellar medium, followed by the science
probes.
Acknowledgments:
Thanks to:
Extropians, for thinking the thinkable.
Jeffrey Soreff, for providing the right answer at the right time.
Tihamer Toth-Fejel, for encouraging me to write this up.
David Schanen, the Webmaster.
Current Webmaster: Gina "Nanogirl"
Miller
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