Implications of Molecular Nanotechnology Technical Performance Parameters on Previously Defined Space System Architectures


This paper was presented at the
Fourth Foresight Conference on Molecular Nanotechnology


by

Thomas Lawrence 
McKendree

Molecular 
Manufacturing Shortcut Group

8381 Castilian Drive

Huntington Beach, CA  92646

USA



Nanotechnology Implications on Space Systems



PACS Classification Numbers

07.87     85.42





Table of Contents






List of Tables





List of Figures






Abstract

Molecular nanotechnology offers the prospect for significant increases in
various technical performance parameters, such as material strength and
density.  This performance would enhance the capabilities of many classes of
space systems.  To begin analyzing this effect, a first step is to take
previously defined space system architectures, not originally intended to use
molecular nanotechnology, and calculate how well those systems would perform
when simply using the MNT technical performance parameters.  This paper
discusses chemical rockets for putting payloads into Earth orbit, both single
stage and two stage architectures, synchronous and rotating skyhooks, solar
sails and solar electric ion engines, and large, inhabited space colonies.  In
all cases, MNT offers the possibility of significant system improvements.


1.
Introduction


Molecular nanotechnology (MNT) has been laid out as a vast, long-term project
[1], [2],
ultimately leading to a general ability to design and build products
to atomic precision, thus providing general applications (figure 1).  Research
along the development pathways are crucial to any realization of this vision.
That realization, however, will have dramatic consequences, requiring
significant foresight to properly handle [3].  Developing
the appropriate
foresight rests upon developing a sufficiently accurate and detailed
understanding of the actual capabilities MNT will provide.




Figure
1. Simplified roadmap of the effort to develop and apply molecular
nanotechnology (MNT).  From [2], used with permission.




1.1
Scope and Objectives


This paper develops early explorations of the capabilities MNT will provide in
the area of space operations.  It is an example of theoretical applied science
[1], examining what
sorts of applied capabilities are and are not feasible
within our current understanding of physical law.  The best example of
theoretical applied science in the area of molecular nanotechnology is [1],
which developed estimated technical performance parameters for molecular
nanotechnology (table 1).  This paper takes those parameters, and applies them
to models of previously defined space system architectures.  It also discusses
a methodology for extending, deepening and refining out understanding of the
actual capabilities molecular nanotechnology will provide, applicable to many
fields.


Table
1. Estimates used in this research for the technical performance
parameters of
MNT are taken from [1].






   

      Parameter
      Value
      Unit
   

   

      Product Tensile Strength
      5 x 10^10 
      Pa
   

   

      Corresponding Material Density
      3,510
      kg/m3
   

   

      Mechanosynthetic Device Operating Rate
      10^6
      Hz
   

   

      Marginal Manufacturing Costs
      0.1 - 0.5
      $/kg
   










1.2
Main Advances


Most of the space system architectures considered here were not developed to
particularly exploit the capabilities of MNT.  In particular, one of the major
benefits of MNT would be the novel function of a general purpose material
processing capability.  Since this is a novel function, however, it is not
included in previously defined space system architectures.

The capability of MNT which previously defined space system architectures do
take particular advantage of is the increased strength-to-density afforded by
MNT structural components.  The material properties assumed in the prior
analyses of space system architectures, and the comparable MNT values, are
shown in table 2 below.

Table
2. Values for material properties used in this research.





   

      Material
      Strength (Pa)
      Density (kg/m3)
   

   

      Aluminum (cold formed)
      3.52 x 10^8 
      2,650
   

   

      Steel (cold drawn)
      1.240 x 10^9
      7,800
   

   

      Titanium (cold formed)
      9.31 x 10^8
      4,540
   

   

      Graphite crystals
      2.1 x 10^10
      2,200
   

   

      MNT Structural Material (Diamondoid)
      5 x 10^10
      3,510
   








The
main conclusions of this research are that rockets can be made significantly
more efficient, and vastly more cost efficient, the feasibility of orbital
skyhooks is improved, interplanetary propulsion could have high performance,
and very large inhabited space colonies could be structurally sound.


2.
Methodology and Larger Goals


This research is meant to embed in a larger methodology, shown in figure 2
below.  That methodology has the larger goals of progressively developing a
better understanding of the future capabilities for space operations that will
be provided by MNT, at the system and mission level, and of progressively
developing an understanding of feasible and appropriate strategies for
operating with this unfolding capability.  The methodology can also help focus
ongoing efforts in the theoretical applied science of MNT, by defining which
uncertainties about MNT are operationally most significant.

While this larger methodology is expressed in terms of a focus on space
operations, it could be useful in all application areas for MNT.  The
methodology is based on a hierarchy of technical capabilities, system
architectures, operational concepts, and grand strategies.

MNT will make dramatically improved systems possible, and it thus is important
to develop and analyze system concepts using MNT [4].  Such systems must be
evaluated in their operating context.  MNT will so change the total
environment
of capabilities and actions, however, that it will transform the operating
environment context for doing the analysis.  This "chicken-and-egg" problem
requires an iterative analysis methodology to resolve.

Figure 2 describes such an iterative process, built around the hierarchy of
technical capabilities, system architectures, operational concepts, and grand
strategies.  Each level provides building blocks for assembling concepts at
the
level above.  Thus, one can think synthetically, combining building blocks
into
concepts at the next higher level.  Also, one can think holistically, using an
intuition or theory about what MNT can achieve at a particular level to
develop
a concept at that level.  In this latter case, one must then do a top down
analysis to make sure that the lower levels can actually support this new
concept, resulting in either a refutation or added confidence in the concept.
Another result of this top-down analysis likely to be additions to the menu of
building blocks at the levels below.




Figure
2. An iterative methodology for assessing system architectures using MNT,
likely to continue for years or decades by many researchers across many
research projects.


A first step in this methodology is to take a broad range of previously
defined
system architectures, and apply the Technical Performance Parameters of MNT to
those architectures.  This will provide an initial set of MNT-based system
architectures from which to launch further analysis.  Such system
architectures
are likely to be unbalanced, however, and thus will probably perform
significantly less well than system architectures designed to exploit the
particular capabilities of MNT.  The research is this paper is part of that
first step.


3.
Earth to Earth-Orbit Transportation


The standard concept for launching payload into Earth orbit is rockets,
although different staging architectures are often considered.  An alternative
approach which might better take advantage of the material strength-to-density
ratios offered by MNT are very long orbital cables, also called skyhooks and
orbital towers.  Both concepts are examined here.


3.1.
Chemical Rockets


[5] provides a typical top-level comparison of six different architectures for
transporting payloads from Earth using chemical rockets.  This paper assumes
LH/LOx engines with a 462 second specific impulse, and a 200 km circular
reference orbit inclined 51deg..  The six architectures examined are:


    

  1. Single Stage to Orbit (SSTO) with Horizontal Take Off (HTO) using an
undercarriage [SSTO(H)]; 

  2. SSTO with HTO using a sled [SSTO-SL]; 

  3. SSTO Air Launched from an aircraft at 8 km altitude, traveling at 180 m/s
[SSTO-AL]; 

  4. SSTO with ground-launched Vertical Take Off (VTO) [SSTO(V)]; 

  5. Two Stage To Orbit (TSTO) using an undercarriage [TSTO(H)];  and,

  6. TSTO with ground-launched VTO [TSTO(V)].


All stages in all architectures use horizontal landing, and thus have wings
and
undercarriages.  The wings and undercarriages are sized for the vehicle's
return, unless they are used in take off, as for example by 1) SSTO(H).  All
architectures are sized to a common take-off mass (GLOW) of 500 tonnes, but
their different architectures result in different payloads delivered to the
reference orbit (Table 3).

The primary means of taking advantage of MNT without changing these
architectures is to use diamondoid materials with much higher
strength-to-density ratios.  This will reduce the mass of the vehicles'
fuselages, wings and tails, undercarriages, and propulsion systems, roughly in
proportion to the relative strength-to-density of diamondoid to the materials
used.  (Many parts of the propulsion system, however, would require
appropriately coated surfaces, and external surfaces will require thermal
protection for re-entry.)  This research assumes that the systems were all be
built of titanium in the original paper.  The nature of the "on-board
equipment" is not clear described in [5].  It probably includes mass for life
support for pilots of the vehicles.  Since the exact nature of this mass is
unclear, the conservative assumption made here is that this mass could not be
reduced at all with the use of MNT.

By flying the same trajectories, the mass savings from applying MNT to the
vehicle's structure can be applied to the payload.  This occurs directly for
the SSTO vehicles and the second stages of the TSTO vehicles.  Mass savings on
the first stage of the TSTO vehicles are added proportionately to all
components of those vehicles second stages, including the payload.

The resulting vehicle and payload masses, and mass ratios, are shown in table
3
below.  The "Titanium" based numbers (first entry) are from [5].  The
"Diamondoid" based numbers are assuming MNT materials.  These results are
consistent with [6], which describes an MNT-based SSTO with a payload to GLOW
ratio of 1/6 and a ratio of payload mass to dry, empty vehicle mass of ~8.   


Table
3. Values for material properties used in this research. The difference
from
old to new is the use of MNT materials in the place of titanium.







   

      Architecture  Titanium/ Diamondoid
      "Dry, Empty Vehicle Mass"
      Payload Mass
      Mass Ratio
      "Payload to Dry, Empty Mass Ratio"
      Cost per kg to Reference orbit 
   

   

      1) SSTO(H)
      92.5 / 16.5
      -32 / 44
      -6.4% / 8.79%
      -35% / 267%
      NA / $5.19 / $375
   

   

      2) SSTO-SL
      57.3 / 10.5
      9.8 / 56.6
      1.96% / 11.33%
      17% / 541%
      $29k / $3.91 / $185
   

   

      3) SSTO-AL
      54.3 / 9.5
      17.0 / 61.8
      3.40% / 12.36%
      31% / 653%
      $16k / $3.54 / $153
   

   

      4) SSTO(V)
      57.4 / 9.4
      4.8 / 52.5
      0.96% / 10.50%
      8% / 540%
      $59k / $4.26 / $185
   

   

      5) TSTO(H)
      107.8 / 20.4
      17.0 / 49.5
      3.40% / 9.90%
      16% / 243%
      $31k / $4.55 / $412
   

   

      6) TSTO(V)
      70.4 / 14.5
      25.0 / 53.5
      5.00% / 10.70%
      36% / 368%
      $14k / $4.17 / $272
   








The
costs for the titanium systems were not in [5], but are based on a very simple
minded per mission cost estimate of $1000 per kg of dry, empty launch vehicle
mass, averaged over the life of the program.  This may be extremely
optimistic;
using traditional aerospace approaches it would require a tremendous number of
fleet missions conducted with low overhead.  The cost for the diamondoid,
MNT-based systems is based on the high end of the MNT manufacturing cost
estimate from [1], applied to
producing the vehicle and the fuel mass, and
assuming the vehicle is used once.  The third cost entry applies the per
mission cost estimate of $1000 per kg of dry, empty launch vehicle mass to the
diamondoid system masses.


3.2.
Skyhooks


A totally different architecture for placing mass into orbit is using very
long, orbiting cables.  The classic example is the synchronous skyhook [7], a
cable in geosynchronous orbit reaching down to be anchored at the planet's
surface, and extending upward so the entire structure is in tension.  It is
possible for a mass to climb this skyhook, gaining potential energy directly,
and taking momentum from the orbital momentum of the planet.  [8] discusses
another version, free-orbiting skyhooks counter-rotating to just cancel out
the
orbit and planet's rotation as the tip makes its closest approach.  Such a
skyhook can grab a payload, and pull it into orbit.

Skyhooks are generally much too long to support themselves if they are of
constant thickness.  The answer is to use cables tapered with the load so that
they experience constant stress over their length.  The ratio of the area of a
skyhook at distance r from the planet to the area of the skyhook tip at the
surface of the planet is expressed in equation (5) from [8]:


(1)

Where A(r) is the area of the skyhook at radius r from the planet's center,
A(rp) is the area of the skyhook at the planet's radius, rp is the planet's
radius, d is the skyhook material's density, t is the tensile strength, wo is
the orbital rate of the satellite, and ws is the rotation rate of the
satellite.  For a synchronous skyhook, ws = wo = wp (where wp is the planet's
rotational rate).  One particularly favorable concept is for a rotating
skyhook
roughly 1/3 the radius of the planet.  This can be designed to make its
closest
approaches near exactly six stable points on the surface.  It is also close to
the optimum rotating skyhook length.

One measure of skyhook feasibility is the taper ratio, the ratio between the
widest point in the skyhook and the tips.  The taper ratio is proportionate to
the exponent of the density to tensile strength ratio.  [8] derived taper
ratios, assuming graphite crystals and a substantial safety factor.  Properly
scaling those taper ratios based on the material properties achievable with
MNT, gives improved feasibility, as shown on table 4 below.


Table
4. Improved feasibility of skyhooks, using MNT materials.  Taper ratios
when
using graphite come from [8].




   

      Body
      Taper Ratio for Synchronous Using Graphite
      Taper Ratio for Synchronous Using MNT
      Taper Ratio for 1/3 Planet Radius Using Graphite
      Taper Ratio for 1/3 Planet Radius Using MNT
   

   

      Mercury
      2.22
      1.71
      1.42
      1.27
   

   

      Venus
      123
      25.2
      8.32
      4.13
   

   

      Earth
      100
      21.9
      10.1
      4.69
   

   

      Moon
      1.3
      1.19
      1.12
      1.08
   

   

      Mars
      2.41
      1.8
      1.56
      1.35
   

   

      Jupiter
      2.8 x 10^26
      5.3 x 10^17
      7.0 x 10^15
      4.1  x 10^10
   

   

      Saturn
      3.3 x 10^6
      2.3  x 10^4
      17,430
      695
   

   

      Uranus
      2,350
      182
      101
      22.1
   

   

      Neptune
      1 x 10^6
      1 x 10^4
      1,092
      168
   









4.
Interplanetary Propulsion


Once a payload is in space, it is then eligible for interplanetary transport.
The primary advantage of this is that the vehicle does not have to provide
direct lift against the planet's gravity, so propulsion systems with thrusts
much less than the vehicle's weights are quite acceptable.


4.1.
Performance of Systems in the Literature


In this area, some concepts have already been sketched out which are intended
to particularly exploit the capabilities of MNT.  [6] examines lightsails,
which are propelled by the light pressure from the sun on a large surface, and
solar-powered ion engines, which turn solar energy into electrical power and
use that power to accelerate ions to high exhaust velocities.  (The
accelerated
ions are neutralized before release so that the vehicle does not build up a
net
charge.)  As discussed, an unloaded sail 20 nm thick of aluminum will develop
an acceleration of up to 0.16 m/s2, depending on its solar angle,
at
one AU from the sun.  This is equivalent to a 0.08 m/s2
acceleration
with a payload mass equal to the sail mass, or a 0.04 m/s2
acceleration with a payload mass equal to three times the sail mass.  A major
advantage of solar sails (built with or without MNT) is that they can provide
this thrust continuously, without expending on-board reaction mass.

The ion engine discussed in [6] uses solar collectors with specific power on
the order of nearly 105 W/kg to drive ion engines with a ~250,000
m/s ideal exhaust velocity, providing ~0.8 m/s2 acceleration.  
[2],
suggests the specific power could be more than an order of magnitude
greater,
and a 1,000,000 m/s ideal exhaust velocity vehicle could provide ~9.8
m/s2 acceleration.  


5.
Space Colonies


Gerard K. O'Neill proposed housing citizens of a technological civilization in
large space stations he called "colonies," each with up to 20 million people
[9], [10], [11].  These O'Neill style colonies were large cylinders with
spherical end-caps, rotating to provide a standard 1 g of pseudogravity on the
inner surface.  O'Neill suggested that if made of steel such a colony might
reasonably be 3.2 km in radius, and 32 km long [10].


5.1
Maximum Radius of Space Colonies


The maximum radius of such an O'Neill style colony is limited by the hoop
stress of the spinning structure, and the tensile strength to density ratio of
the material.  The formula is


(2)

Where R is the radius, g is the acceleration of pseudo-gravity at the rim, and
G is the density.  MNT offers a 5 x 1010 Pa tensile strength. 
Using
the design rule of 50% safety factors for O'Neill style colonies [12], a 3.3 x
1010 Pa design tensile strength is reasonable.  The associated
material density is 3.51 103 kg/m3.  One goal of the
architecture is for g to equal 9.8 m/s2 [10],[12].  This all gives
a
possible space station radius of 9.6 x 105 m, or nearly 1000 km.
For comparison, the corresponding feasible radius for titanium is 14 km, and
even at its ultimate tensile strength with no safety factor, the titanium
limit
would be 23 km.

At the 9.6 x 105 m radius, the entire available strength (at the
safety factor) of the MNT-based material is being used to prevent the rotating
structure from bursting, and there is no strength left over to hold the space
station's contents, including an atmosphere.  To do so, a lower radius must be
set.


5.2
Mass of an Example Design


One approach would be to set the design goal of a station radius such that the
stressed skin structure would have a surface density of 5,000
kg/m2,
which is a mass required in any case to provide shielding against radiation
from space[12]. 

The mass of an O'Neill style colony can be first approximated as the sum of
mass of the structure, the mass of the furnishings, and the mass of the
atmosphere.  For the design sketched here, these sum to 1.6 x 1017
kg., or 1.6 x 106 kg per person.


5.2.1
Mass and Sizing of the Structure


The mass of a stressed skin shell for an O'Neill style colony is derived [12]
as:


(3)

Where s is the design stress, PA is the internal atmospheric pressure, G is
the
additional load for other contents, and a is the length to radius ratio of the
cylinder.  A typical a, used here, is 10.  [12] derives a requirement for 50.8
kPa internal atmosphere, and use a G equal to 16% PA.  Since the total area of
the structure is:


(4)

One can directly solve for the structure radius where the shell is 5000
kg/m2.  Using MNT materials, the structure will be 461 km in
radius.
For comparison, the equivalent number for titanium is 6.6 km, or for a
titanium
shell is at its ultimate tensile strength with no safety factor, 11 km.

A 461 km radius cylinder with endcaps, with a 4610 km long cylinder portion,
has a surface area on that cylinder portion of 1.22 x 1012
m2., half of which would be available for habitation (the other
half
being taken up with windows).  The [12] requirement of 87 m2 land
area per person (including land for agriculture) yields a possible population
for this structure of 76 billion people.  The stressed shell masses 8.0 x
1016 kg of carbon.


5.2.2
Mass of the Furnishings


The furnishings are defined as all the mass on the inner surface of the
colony,
excluding the atmosphere.  The G of 16% of PA (or 8,128 Pa) is the load of
these furnishings.  Since this load is providing a centripetal acceleration of
9.8 m/s2, the furnishings amount to 830 kg/m2, or 1.1 x
1016 kg for the entire colony.  (Note, if one assumes that no such
load is placed on the window areas, then the total mass for the furnishings is
halved.  This assumption is reasonable, but less conservative and not used
here.)


5.2.3
Mass of the Atmosphere


More difficult to supply could be the mass for the atmosphere.  The
structure's
volume is 3.5 x 1018 m3, which would require 2 x
1018 kg of atmosphere if evenly distributed, but it is not
necessary
to supply that full mass of atmosphere.  The pseudogravity of the station's
rotation will collect the bulk of the atmosphere close to the outer perimeter.
>From [10] one can derive a simple model of atmospheric density of


(5)

where r is any radius of interest within the cylinder, r0 is the atmospheric
density at the outer radius, and p0 is the atmospheric pressure at the outer
radius.  Integrating along r through the cylinder and spherical endcaps gives
a
total required mass of only 7.2 x 1016 kg, or roughly 3% of what
would be required to fill the cylinder uniformly.  Near 36 km above the
surface, the atmosphere will fall to only 1% of the surface density.  Thus,
each square meter of surface requires a roughly comparable mass of atmosphere
above it, whether that surface is in a very large open space station as
described here, or on the surface of Earth with real gravity.


5.3
An Alternate Design


Note, however, that in the previous design the atmospheric density at the
zero-g center of the colony is virtually zero.  This does not support the
secondary goal of allowing shirt-sleeve zero g activities [13].  Both [10] and
[12] state lower pressure limits for manned habitation is 1/2 atmosphere.  If
one sets the design goal of 1 atmospheric pressure at the outer radius
(101,350
Pa), and 1/2 atmosphere at the center, this gives a design radius of 11,700 m.
This can be achieved with the 50% safety factor by titanium, rotating as an
empty shell to simulate one g at the outer radius.  An aluminum structure
would
have a 16 % safety factor, and the safety factor for steel for this structure
would be 39 %.  While all three materials could survive as empty rotating
shells, they could not also hold the requisite atmosphere.  The MNT material
of
diamond satisfies this application, including holding the atmosphere and the
internal station furnishings, with a shell thickness of 4 cm.  Adding the
additional design goal of 5 kg/m2 thick structural material yields
a
3,783 % safety factor for diamond.


6.
Conclusion


The substantial increases in low level technical capabilities MNT will provide
implies significant increases in space system capabilities.  Example system
architectures for Earth-to-Orbit and interplanetary transport, and large space
colonies, have been examined.

The two most obvious extensions of this work would be to analyze the
performance of other previously defined space system architectures when using
the technical performance parameters of MNT, and to take these system
architectures, and refine them to better take advantage of the estimated
capabilities MNT will offer.

Further extensions should include designing example missions using estimated
MNT space system capabilities and designing novel missions and systems to
particularly exploit the technical capabilities of MNT.  The ultimate goal
should be to develop foresight on future capabilities for space operations
adequate to make appropriate plans in the context of a developing molecular
nanotechnology.


References

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