Brendon
01-27-2009, 02:44 PM
Who wants to get this sucker cooking at 64% the speed of light? Quite a long article. Sorry about the margins and all. This is from this website (http://www.magicdragon.com/ComputerFutures/SpacePublications/STAR.html).
ABSTRACT
Spacecraft constructed from cryogenic hydrogen (or deuterium
and tritium) ice can use the same material for structure,
shielding, coolant, and fuel. This type of "autophage"
(self-consuming) spacecraft achieves an extremely low dead-weight
fraction, which is a critical parameter for optimizing the
performance of interstellar spacecraft.
To reduce the volatility of hydrogen ice, a particular
self-refrigerating structure is presented. Hydrogen ice by itself
is imperfect as a structural element; various methods of
stiffening by the admixture of carbon or boron fibers are
discussed. Other cryogens relevant to specific fusion reactions
are considered, including deuterium, tritium, boron-11, and
saturated solutions of lithium in anhydrous ammonia.
A quantitative analysis is presented of the relativistic
kinematics of multi-staged interstellar iceships. In the limiting
case of a 5-stage deuterium ice fusion spacecraft on a one-way
mission with no deceleration at the destination, a dead-weight
fraction of 10-1 for each stage, and a total payload fraction of
10-5, then the final burnout velocity of the 5th stage is 0.64c,
which at constant 0.0485 g acceleration would reach Alpha Centauri
in 12.81 years, and at 1-g acceleration would get a probe zipping
through the Alpha Centauri system in 6.7 years.
Appears in:
the Proceedings of ÒPractical Robotic Interstellar Flight:
Are We Ready?Ó, New York University, New York City,
29 Aug-1 Sep 1994,
and in Journal of the British Interplanetary Society, April 1996
__________________________________________________ __
1 C.E.O., Computer Futures Inc.; Active Member: British
Interplanetary Society, National Space Society, World Space
Foundation, Space Studies Institute, Planetary Society
TABLE OF CONTENTS
Title page, Abstract, Table of Contents 1
1.0 Introduction 2
2.0 Design of Hydrogen Ice Spacecraft 3
2.1 Thermal Analysis: Here Comes the Sun 6
2.2 Lithium or Boron in Hydrogen: Icy Isotopes 7
3.0 Relativistic Kinematics 10
3.1 Five-Stage Scenario:MultipleInstrumentPackages/Arrivals
13
4.0 Future Research 15
5.0 Summary & Conclusions 16
6.0 References 17
__________________________________________________ __
1.0 INTRODUCTION
For innovative space exploration missions, unusual
requirements are levied on the structural components of the
spacecraft. In many cases, the preferred solution is the
utilization of unusual materials. Spacecraft constructed from
cryogenic hydrogen (or deuterium or tritium) ice can use the same
material for structure, shielding, coolant, and fuel.2,3,4,5,6,7
This type of "autophage" (self-consuming) spacecraft achieves
an extremely low dead-weight fraction (fraction of non-payload
mass remaining after all fuel is expended), which is a critical
parameter for optimizing the performance of interstellar
spacecraft.9 At the same time, hydrogen is ideal in having a
minimum molecular weight of exhaust material. This dead-weight
consideration is even more important for multi-staged rockets.
To reduce the volatility of hydrogen ice, at a temperature of
5o Kelvin, we have to keep it cool while the vehicle is being
assembled and fueled near planet Earth, and to keep it cool during
the flight despite heating from exhaust radiation, interstellar
dust impact, and stellar ultraviolet radiation. A particular
self-refrigerating structure is presented below. Hydrogen ice by
itself is imperfect as a structural element; various methods of
stiffening by the admixture of carbon or boron fibers are
discussed. Other cryogens are considered, including a saturated
solution of lithium in anhydrous deuterated ammonia.
For uranium fission rockets12,16, the fraction of mass
converted into energy is roughly 7 x 10-4;
for deuterium fusion, it is roughly 4 x 10-3.
Assume that we have a deuterium fusion engine with conversion
fraction (epsilon) = 4 x 10-3; the details are left to the
engineers. Assume that the spacecraft structural material is the
fuel, namely frozen deuterium. Assume a one-way unmanned probe
with no powered deceleration at the destination (a one-way probe
with deceleration at the destination would require squaring the
mass ratio). Assume as in the classical case per Subotowicz 19
that each stage has the same mass ratio and exhaust velocity.
Then, as we shall see in the section on relativistic
kinematics, appreciable burnout velocities can be achieved if we
can keep the dead-weight fraction as low as 10-1 for each stage,
i.e. only one-tenth of non-payload mass remains after all fuel
(former structural element) is expended. For example: in the
limiting case of a 5-stage deuterium ice fusion spacecraft, if the
payload fraction is 10-5, then the final burnout velocity of the
5th stage is 0.64c, which at constant 0.0485 G acceleration would
reach Alpha Centauri in 12.81 years, and at 1 G acceleration would
get a probe zipping through the Alpha Centauri system in roughly
6.7 years.
A quantitative analysis is presented of the relativistic
kinematics of multi-staged interstellar iceships. A particular
five-stage multiple instrument packages/multiple arrivals scenario
is calculated. Future research considerations are outlined.
Summary and conclusions are presented. 43 references are listed.
2.0 DESIGN OF HYDROGEN ICE SPACECRAFT
James B. Stephens of JPL first proposed (in 1984 and 1985,
while in communication with this author) banking hydrogen fuel in
Low Earth Orbit without a tank, based on his 20 years of studying
icy comet nuclei. He began to add ancilliary benefits, as
detailed below, including using hydrogen ice in orbit to cool "old
fashioned" (low temperature) superconducting electronic systems
for low-noise, low-power long-range sensors. Jim Stephens
presented his idea to NASA and the Department of Defense in the
early 1980s, but received little interest. This author then
advanced the concept of interplanetary and interstellar spacecraft
constructed from cryogenic hydrogen ice that can use the same
material for structure, shielding, coolant, and fuel.2,3,4,5,6,7
The ideal spacecraft can be lightweight, inexpensive, and
fuel efficient by using balls of hydrogen ice as both structure
and fuel. Hydrogen may be "exotic" in its structural function,
because it has the tensile strength of butter, but it accounts for
over 75% of all matter in the universe and costs under $10 per
pound. The material can be stiffened with the admixture of carbon
or boron fibers, or various particulates.
Balls of modified hydrogen ice first serve as structure, then
are detached, liquified or turned into slush, and channeled into a
fusion reactor as fuel. In this way, almost all non-essential
parts of the spacecraft are consumed during the mission. This
author considers the scenario conceptually similar to the scene in
the Marx Brothers' film Go West where Groucho, Harpo, and Chico
feed the furnace of a steam locomotive with boxcar slats, then
furniture, and then demolish and burn the caboose. There is a
similar scene in Around the World in 80 Days,8 where Phogg burned
parts of the steamship Henrietta for fuel to complete the last
stage of his journey.
This type of "autophage" (self-consuming) spacecraft achieves
an extremely low dead-weight fraction, which is a critical
parameter for optimizing the performance of interstellar
spacecraft.9 More recently, but more conservatively, Aston10
proposed that thrusters use spent nuclear fuel as propellant.
Nordley11 extends Aston's notion to say that "The current
generation of ion thrusters uses as heavy a propellant atom as
possible to maximize the mass-to-charge ratio in the ion
generation part of the thruster, and thus minimize its size and
weight. This is less of a concern in a very high exhaust velocity
interstellar application because the engines require less mass
flow per unit power. Indeed, use of a lower mass propellant atom
would reduce the voltage requirements of accelerator stages for a
given exhaust velocity.... [Aston's] philosophy could be extended
to parts of the spacecraft structure as well. Singly charged
aluminum or silicon atoms would achieve [in an ion electric
propulsion system] about 4.7 time the velocity of a singly charged
xenon atom and about 8.7 times the velocity of singly charged
uranium atoms in the same [electric] field." The hydrogen ice
autophage concept takes Aston's and Nordley's approach to a
logical extreme.
To reduce the volatility of hydrogen ice, a particular
self-refrigerating structure was invented by James Stephens,
analyzed quantitatively by James Salvail at the University of
Hawaii, illustrated in Figure 1, and described below.
_________________________________
[get from mac disk, or scan in picture here]
Figure 1: Self-refrigerated Ice Sphere
__________________________________________________ ________________
Concentric spheres of very thin metal (i.e. lithium) or
metallized mylar coating thicker concentric spherical shells of
hydrogen ice are connected to each other by at least two rods made
of a material that has very low thermal conductivity. This is
necessary so that the spheres above the instantaneous level of the
subliming ice surface do not move relative to each other. The
outer shells are highly reflective, thick enough to provide
reasonable structural integrity. The inner spheres are made of
the same materials, but much thinner (is much less than 0.1 cm), as they are
merely radiation shields.
The radiation shields and outer hulls must contain enough
sufficiently sized holes or pores so that sublimed hydrogen
molecules are quickly lost into space. The evacuated spaces
between the slowly receding ice surface and the outer hulls thus
have negligible gaseous heat conduction because the gas is very
rarified. Gas flux is small enough that heat convection is also
negligible.
Under these conditions, the escaping sublimed hydrogen
expands and refrigerates the remaining concentric spheres,
maintaining a temperature well below the 20o K melting point of
hydrogen; the nominal system temperature is 5o K.
The system as a whole as conceived by James B, Stephens
includes: (1) ice embedded insulation, (2) vapor cooled
insulation, (3) isomer conversion catalyst integral with
insulation, (4) Infrared photon reflective and vapor conductive
insulation, (5) vapor cast crystalline hydrogen ice using nuclear
magnetic resonance heating of non-crystalline ice, (6)
self-forming filamentary insulation from dispersed particles in
the ice that cohere due to ice cleaning.
The attributes of the system include: (1) unitized design --
hydrogen ice is the cryogen, propellant, shielding, absorber,
power source, window, and insulation support during launch; (2)
superconducting temperature cryostat (less than 5o K for hydrogen); (3)
self-insulating solid cryogen; (4) long lifetime in Earth orbit;
(5) low cost material (less than $10/pound); (6) low cost fabrication
(casting process); (7) low launch cost (withstand high
acceleration forces); (8) low cost operation (efficient
superconducting solid state system); (9) acoustically quiet (no
moving parts); (10) thermally stable (large thermal capacity well
insulated); (11) high density ice vapor cast and used at same
temperature avoiding shrink stresses in insulation and components
embedded in ice.
Stephens also emphasized neutron absorbing properties of
hydrogen ice, microwave reflection or absorption, laser-tough
shielding, neutral and charged particle beam tough shielding,
radar stealth, and a wide range of capabilities for embedded
avionics, including: phased-array radar, solar-powered ion rocket
and superconducting magnet power generator/storage, and
superconducting guidance and control.
As the concept was extended by this author (see Figure 2),
individual hydrogen ice spheres can be orbited by small boosters,
and later assembled into a large spacecraft. Solid hydrogen is
inherently safer than liquid hydrogen. The spheres can have
embedded avionics, providing distributed redundant capability for
the spacecraft at superconducting temperatures. Once assembled,
the low accelerations typical of ion, fission, or fusion
propulsion would not endanger the inherently low compressive and
tensile strength of hydrogen ice as a structural material. An
acceleration of 0.0485 gravities is used in Section 3.1. The
hydrogen ice spheres would be between the payload (or crew) and
the nuclear propulsion, providing neutron-absorbant shielding at
no extra cost.
_________________________________
Figure 2: On-Orbit Iceship Assembly
[get from mac disk, or scan in picture here]
_______________
__________________________________________________ ________________
Earlier articles by this author suggested space exploration
missions including: (1) sungrazer, (2) outer planet explorer, (3)
interstellar precursor 1000 AU mission (TAU), (4) subterranean
radar mapping of planets, (5) manned Mars mission, (6) propellant
transfer and storage for Space Station refueling depot.
This author then proposed experiments of detonation wave
propulsion/attitude control with alternating layers of hydrogen
ice and oxygen ice, and made detailed suggestions for utilization
of cryogen ices on the Moon, Mercury, and Mars.25,26,27
2.1 Thermal Analysis: Here Comes the Sun
James Salvail's thermal analysis2,3,4 by computer simulation of
the system of differential equations showed that at 1 AU from the
sun, a 50-layer hydrogen ice sphere of 1 meter radius remained
nearly isothermal at the initial temperature of 5o K, with a
negligible temperature gradient and a near-constant mass flux of
17.8 nanograms/cm2-sec. After a simulated 10 years, the hydrogen
ice component had shrunk to 21 inches in radius, and the total
lifetime was 12 years. Reducing the the radiation shields from 50
to 10 had no effect. Painting the outer surface black (for
stealth) gave a tripled mass flux of 53.8 nanograms/cm2-sec, a
surface temperature of 5.2o K, and a reduced lifetime of 4.2 years.
Obviously, for our spacecraft, reflectivity and long lifetime are
preferred to stealth (which the DOD might prefer).
Even at 0.1 AU from the sun, far inside the orbit of Mercury,
a 50-shield 1 meter shiny sphere stays at 5.81o K, with a mass flux
of 1.06 micrograms/cm2-sec, and a lifetime of 75 days.
At 0.1 AU from the sun, a 10-shield 1 meter shiny sphere stays at
6.39o K, with a mass flux of 10.5 micrograms/cm2-sec, and a
lifetime of 35 days. The radiation shield effects are important
for larger thermal loads, such as would occur if the hydrogen ice
spacecraft mission began with a gravity assist swingby close to
the sun.
The effects of a fission or fusion explosion near the
spacecraft, as might happen with temporary malfunction of a
nuclear rocket engine, or of catastrophic failure of one of
several co-travelling redundant spacecraft, was simulated as a
temporary change from heliocentric deistance of 1.0 AU to 0.01 AU,
where the radiative equilibrium temperature for a black body is
2808o K, for 20 seconds. If the outer coat does not melt at the
maximum temperature attained (2361o K), then the hydrogen ice
adjacent to the outer surface peaks at 8.73o K, with a gas flux of
4.7 milligrams/cm2-sec, decreasing after 10 minutes to 5.85o K
(50-shield) or 5.79o K (10-shield), at which time the ice had
receded 2.5 cm.
All things being equal, the lifetime of a self-refrigerated
hydrogen ice sphere was found to be directly proportional to the
first power of its initial radius. Thus, a 2 meter radius sphere
has a 24 year lifetime at 1 AU, and 2 years at 0.1 AU. For deep
space missions, loss becomes extremely small for spheres several
meters in radius.24
Similar thermal analysis has been performed for slab and
cylindrical geometries.24
Hydrogen ice by itself is imperfect as a structural element;
various methods of stiffening by the admixture of carbon or boron
fibers have been explored, as well as admixtures of particulates
such as montmorillonite clay.
A survey of cryogenic ices and slushes has been presented in
an earlier article by this author.4 For this paper it suffices to
note that hydrogen ice has a density of 70.6 g/l at -262o C, melts
at 20o K to become a liquid with density 70.8 g/l at -253o C, and
that slush is intermediate in density but has various advantages
over both solid and liquid.
For proposed antimatter propulsion29,30 it is suggested that
there be a significant excess of hydrogen to anti-hydrogen for
optimization. In such a case, the spacecraft would be constructed
of hydrogen ice as before, but with small very carefully suspended
and shielded units of anti-hydrogen, for which the
self-refrigeration concept is most definitely not appropriate.
Antimatter propulsion requires several breakthroughs.
Fission propulsion does not, and requires only ordinary hydrogen
as a propellant, heated by whatever fission reactions take place
in whatever reactor/engine. Fission power is not emphasized in
this paper. Fusion propulsion does require breakthroughs.31
Assuming the existence of adequate space-rated fusion reactors, we
must turn our attention from ordinary hydrogen ice to more unusual
materials.
2.2 Lithium or Boron in Hydrogen: Icy Isotopes
In one sense, ordinary hydrogen (protium) is the ideal
structure/fuel, as it is extremely cheap and has the lightest
molecular weight of any material exhaust. But the fusion reaction
attainable 20 with ordinary hydrogen fuses two protons to produce a
deuteron (deuterium nucleus), a positron (anti-electron), and a
neutrino, at an energy of 0.42 Mev (million electron volts). This
yields 2.0 x 1013 Joules per kilogram of fuel.
p + p -> D + e+ + v
But this is irrelevant, since the reaction involved is not
true nuclear fusion. As revealed by the emission of the neutrino,
this is a "weak force" reaction, rather than a "strong force"
reaction. Too much of the energy is carried away by the neutrino.
The reaction is too difficult to initiate. The total energy yield
is (relatively) low. And for little more effort, with more
sophisticated fuel, we can get better results.
If our hydrogen ice is made of equal proportions of protium
and deuterium, we can fuse the two to produce Helium-3 and a gamma
ray, with 5.49 Mev energy, corresponding to 1.75 x 1014 Joules per
kilogram of fuel.
p + D -> He3 + gamma
But this is not a good idea either. The gamma rays would be
emitted in all directions, and tend to fry the payload. We might
as well eliminate protium completely, and use either pure
deuterium ice or a deuterium/tritium mixture.
Pure deuterium ice would result in two different reactions,
yielding a combination of Helium-3, tritium, protons, and
neutrons.
D + D -> He3 + n 3.27 Mev (7.8 x 1013 J/kg)
D + D -> H3 + p 4.03 Mev (9.65 x 1013 J/kg)
Deuterium is easily obtainable in massive quantities, since
it makes up roughly 1 part in 6,000 of the hydrogen in water here
on Earth.23 Deuterium oxide, D2O, heavy water, costs from $0.06 to
$1/gram depending upon quantity and purity.23 The
deuterium-deuterium fusion reaction is moderately easy to
initiate, requiring a temperature in the 10 million degree range.
But the neutrons in the output are nasty. Since they are
uncharged, they tend to fly in all directions, uncontrollable by
electric or magnetic fields, frying and/or rendering the payload
radioactive. Nonetheless, this is the reaction and fuel used by
default throughout the remainder of this paper.
An energetic deuterium-tritium reaction seems at first to
have certain advantages. This is the most studied reaction today,
because of the low ignition temperature of roughly 10 million
degrees.
D + H3 -> He4 + n 17.6 Mev (3.37 x 1014 J/kg)
This is actually the easiest fusion reaction to ignite, and
may thus be the first used for terrestrial fusion power. But
tritium is quite radioactive, decaying in about a decade, and that
neutron is still trouble.
There are several interesting reactions involving Helium-3 in
the fuel, but we disregard them here for two reasons. First, it's
hard to obtain, although it might be extracted from the upper
centimeter of lunar regolith where it has accumulated from solar
wind. Second, the self-cooling approach described in my articles
for hydrogen doesn't work as well for helium isotopes, which have
to be cooled to below the background temperature of the universe.
Frozen helium is just too volatile.
This leaves us with several more exotic reactions. We
consider Lithium. Lithium occurs in nature21 with an abundance
ratio of 7.39% for the isotope Lithium-6 (Li6) to 92.61% for
Lithium-7 (Li7). Lithium melts at 180o C, and boils at 1,326o C.
If we built the spacecraft out of equal proportions of protium and
pure Lithium-6 isotope, we have:
p + Li6 -> He4 + He3 3.90 Mev (5.53 x 1013 J/kg)
We would be using hydrogen ice with lithium foil in the
self-refrigerating concentric structure, plus walls and girders of
lithium. Lithium is a soft metal, but at cryogenic temperatures
(and away from water) it is strong enough without brittleness to
suffice for structural purposes. Unfortunately, this is a
difficult reaction to ignite.
We get somewhat more bang for the buck if we use isotopically
pure Lithium-7, for a reaction yielding an electromagnetically
focusable stream of alpha particles.
p + Li7 -> He4 + He4 17.00 Mev (2.0 x 1014 J/kg)
Again, this is a hard reaction to ignite.
We can use deuterium ice and pure Lithium-6, again getting an
all-alpha output:
D + Li6 -> He4 + He4 22.30 Mev (2.67 x 1014 J/kg)
Or even consider protium plus Boron-11 for the so-called
Boron-fission reaction:
p + B11 -> He4 + He4 + He4 8.80 Mev (7.0 x 1013 J/kg)
But this is even less studied, and also extremely difficult
to ignite, requiring perhaps 1,000 times the ignition temperature
of Deuterium. Lithium or Boron fusion might be initiated by
incoming protons from interstellar space when rammed into at over
0.02 c, which might be useful for upper stages of a staged
interstellar spacecraft.28
If we use fibers of Boron-11 to stiffen deuterium or tritium
ice, it might be okay to let those boron fibers go right into the
rocket engine, vaporize, and partly engage in nuclear reactions.
The unreacted boron would reduce the energy yield somewhat, and
merely be expelled as part of the reaction mass.
There is a clever way to get the lithium mixed in with the
hydrogen. Lithium is very soluble in anhydrous ammonia (NH3 with
no water). The resulting solution is the lowest density liquid
known at room temperature, with a density of only 0.511 g/l.22
Regular ammonia, NH3, has a molecular weight of 17.03, a density of
0.7710 g/l, and melts at -77.7o C, while Trideutero ammonia,
ammonia-d3, ND3, has a molecular weight of 20.05 and melts at -74o
C.23 Lithium solutions in ammonia have metallic conductivities
above 9 Mole percent metal. There is a eutectic at 22 Mole
percent metal at 88o K., and at lower temperature is a stable solid
compound, perhaps Li(NH3)4.
We can mix up batches of Lithium-6 or Lithium-7 in ordinary
anhydrous ammonia, or Lithium-6 in fully deuterated anhydrous
ammonia, freeze the stuff in the concentric perforated
lithium-foil configuration, and build our spaceship out of that
lithiated ammonia ice. This does leave us with a certain amount of
useless nitrogen, which would contaminate the fusion reaction,
unless separated out and expelled as unreacted exhaust mass. But
lithiated anhydrous ammonia might be worth investigating as an
exotic chemical fuel for liquid oxygen combustion.
Where does this leave us? We don't have a clear idea of a
spacecraft fusion reactor that burns lithium or boron.31 So we may
have to bite the bullet on the neutron radiation problem and build
our spacecraft out of deuterium or mixed deuterium-tritium ice.
The rest of this paper makes that assumption. Nordley32 points out
"that as soon as the main reaction happens, the products become
available for side reactions. While the output of particles from
these side reactions may be several orders of magnitude below the
output of the main reaction, and thus not worthy of interest
regarding the kinematics, they will still be very significant
(especially the neutrons) to electronics and biological components
at the power levels needed for interstellar flight."
We note that Lithium can trap neutrons, heating up, and
transferring that heat to melt or slushify hydrogen ice. Future
considerations include analysis of the limits of neutron-hardened
payloads through redundancy, self-repair, or even nanotechnology.33
3.0 RELATIVISTIC KINEMATICS
Spacecraft constructed from cryogenic hydrogen ice can use
the same material for structure, shielding, coolant, and
fuel,2,3,4,5,6,7 but more importantly, from the kinematic viewpoint,
that means that very little of the spacecraft's mass is wasted as
non-productive non-payload.
This type of "autophage" (self-consuming) spacecraft achieves
an extremely low dead-weight fraction (fraction of non-payload
mass remaining after all fuel is expended), which is a critical
parameter for optimizing the performance of interstellar
spacecraft.8 At the same time, hydrogen is ideal in having a a
minimum molecular weight of exhaust material, and hence maximum
exhaust velocity.
As Spencer & Jaffe report,9 "the earliest studies of
relativistic rocket mechanics by Ackeret,12,13 Tsien,14 Bussard,15
and others made two implicit assumptions that severely limit
performance of the rockets considered. They assumed that
nuclear-energy rockets are limited to a single stage and that the
available energy corresponds to a fixed fraction of the final
vehicle mass. The latter assumption apparently arose from the
thought that spent nuclear fuel would be either retained on board
or dumped, rather than exhausted at high velocity. These
assumptions are neither necessary or desirable.
"More recently, interstellar travel has been considered by
Sanger16 and Stuhlinger.17 They realized that the limitation
regarding the amount of energy available being a function of the
propellant mass rather than the final mass was unnecessary;
however, they did not consider staging the vehicles as is done
with chemical rockets. They concluded, therefore, that
interstellar travel using nuclear reactions as an energy source
was impossible because of fundemental limitations on the amount of
energy available for rocket propulsion. In contradiction, the
analysis presented [by Spencer and Jaffe9] shows that nuclear
fission or fusion rockets can be considered for interstellar
travel."
The equations of Spencer and Jaffe have been used for the
relativistic kinematic calculations in this paper. These include
the correct relationship first given by Sanger 16 and Huth 18
between fraction of mass converted into energy (epsilon) and
exhaust velocity relative to vehicle (w), and between fraction of
mass converted into energy (epsilon) and specific impulse (I),
namely:
w/c = [epsilon(2-epsilon)]1/2
I = (c/g)[epsilon(2-epsilon)]1/2
For a one-stage vehicle, the burnout fraction (xi) is the
ratio of the rest mass of the vehicle at burnout to the rest mass
of fuel consumed:
xi = Mb / Mf
and the rest mass of fuel consumed is the sum of the rest mass of
fuel exhausted (Mex) and the rest mass of fuel converted to kinetic
energy
Mf = Mex + (epsilon)Mf
As Spencer & Jaffe pointed out, the performance of a
multi-staged interstellar spacecraft is very sensitive to the
dead-weight fraction (beta) and the overall payload fraction
(phi). In particular, for an n-stage vehicle, the final burnout
velocity of the payload (nth stage) in terms of over-all payload
fraction, deadweight fraction, and fraction of mass converted to
energy is
{Clyde: insert scanned in printout of nicely rendered equation
here}
[(1 + beta)/(beta + phi1/n)]^{2n[epsilon(2-epsilon)]1/2} - 1
un / c =
-------------------------------------------------------
[(1 + beta)/(beta + phi1/n)]^{2n[epsilon(2-epsilon)]1/2} + 1
and the over-all mass ratio is
delta = [(1 + beta)/(beta + phi1/n)]n
Then, if the payload fraction is 10-1 we have the following
relationship between dead-weight fraction (beta), number of
stages, and fraction of light velocity of payload:
Dead-weight Fraction Number of Stages Fraction of Light Velocity
(Beta) (n) (un / c)
____________________ ________________ ____________________
0.1 1 0.15
0.1 2 0.17
0.1 3 0.177
0.1 4 or 5 0.18
0.2 1 0.125
0.2 2 0.15
0.2 3 0.155
0.2 4 0.16
0.2 5 0.162
0.3 1 0.105
0.3 2 0.13
0.3 3 0.14
0.3 4 0.146
0.3 5 0.148
If the payload fraction is 10-3 we have the following
relationship between dead-weight fraction (beta), number of
stages, and fraction of light velocity of payload:
Dead-weight Fraction Number of Stages Fraction of Light Velocity
(Beta) (n) (un / c)
____________________ ________________ ____________________
0.1 1 0.20
0.1 2 0.37
0.1 3 0.44
0.1 4 0.46
0.1 5 0.47
0.2 1 0.16
0.2 2 0.30
0.2 3 0.37
0.2 4 0.41
0.2 5 0.44
0.3 1 0.14
0.3 2 0.26
0.3 3 0.32
0.3 4 0.36
0.3 5 0.38
If the payload fraction is 10-5 we have the following
relationship between dead-weight fraction (beta), number of
stages, and fraction of light velocity of payload:
Dead-weight Fraction Number of Stages Fraction of Light Velocity
(Beta) (n) (un / c)
____________________ ________________ ____________________
0.1 1 0.22
0.1 2 0.40
0.1 3 0.53
0.1 4 0.61
0.1 5 0.64
0.2 1 0.16
0.2 2 0.30
0.2 3 0.42
0.2 4 0.50
0.2 5 0.55
0.3 1 0.14
0.3 2 0.26
0.3 3 0.36
0.3 4 0.44
0.3 5 0.48
The assumption has been made in this paper that there is no
rocket-based deceleration of the payload at its destination. To
provide such deceleration, the mass ratio must be squared. To
decelerate at the destination, accelerate back to Earth, and
decelerate at the return would require raising the mass ratio to
the 4th power. But several proposals have been made20 (pp.116-7)
for interstellar spacecraft braking by solar sail, magnetic sail,34
or electrical deflection of interstellar plasma. It remains to be
seen whether any of these approaches are feasible at velocities
above 0.01 c.
3.1 Five-Stage Scenario: Multiple Instrument
Packages/Arrivals
Hartman35 in reviewing an earlier draft of this paper,
considered the time it would take for the limiting-case 5-stage,
10-5 payload fraction, 0.1 dead-weight fraction spacecraft. That
earlier (19 August 1994) draft was distributed as a pre-print at
Practical Robotic Interstellar Flight: Are We Ready?, 29 Aug-1 Sep
1994, New York University, New York City, and at ConAdian: The
52nd World Science Fiction Convention, 1 Sep-5 Sep 1994, Winnipeg,
Manitoba. In it, I had imprecisely claimed that the vehicle in
question would reach the Alpha Centauri system in "roughly 6
years."
As Hartman comments, "the lowest acceleration that will give
you a final velocity of 0.64 c by the end of the trip to Alpha
Centauri [assumed to be 4.1 light years] would be approximately
0.0485 gravities. That would require a constant acceleration for
the entire journey, and would take roughly 12.81 years [12 years,
294 days]. Any lower acceleration, and you would need more
distance (and time) to reach the proposed final velocity. With a
full one gravity acceleration the probe would reach 0.64 c in 0.62
years [0.622], while covering just under two-tenths of a light
year [0.199]. It would then coast for 3.9 light years [3.901],
thus taking about 6.7 years [6.717] for the trip."
He correctly observes that with low accelerations, little
structural strength is required, hence the plausibility of
hydrogen ice. "Will the probe's structure stand up to even 1/20
G? If not, the final velocity will be lower." The various
stiffening methods suggested for hydrogen ice may not be valid for
1 G, but are almost surely effective for 0.0485 G = 47.5 cm/sec2.
Hartman then elaborates on an aspect of my scenario which had
not been spelled out in the earlier draft. As he puts it, "all
five of the stages would reach Alpha Centauri in a reasonable
length of time. The fifth stage, if you use 0.0485 gravities,
would reach its goal in 12.81 years [accelerate full time, 4.1
light years], the fourth in 13.19 years [accelerate 4/5 time, 2.6
light years, and coast 1.5 light years], the third in 14.51 years
[accelerate 3/5 time, 1.48 light years, and coast 2.62 light
years], the second in 18.60 years [accelerate 2/5 time, 0.65 light
years, and coast 3.45 light years], and the first in 33.30 years
[accelerate 1/5 time, 0.165 light years, and coast 3.935 light
years].
"If higher accelerations are used, these times would be
compressed, ranging from 6.72 years to 32 years. If each stage
carried its own instrument package, the probe would return much
more data, and the additional packages would add little to the
massive lower four stages. Since the fifth stage would pass
through the target system at nearly two-thirds the speed of light,
it could take only a hasty peek at its goal. The following stages
could take longer looks, though only the first and perhaps the
second stages could benefit from directions influenced by the
fifth stage's information."
The following numbers, calculated by Hartman, apply to the
arrival after the nominal payload of four successive instrument
capsules. These figures assume no braking. A consensus reached
at Practical Robotic Interstellar Flight: Are We Ready? was that
payloads should be equivalent to a Hubble Space Telescope in order
to adequately image destination planets and to maintain an optical
communication link with Earth.
__________________________________________________ ________________
Stage Arrival Velocity Arrival Time Signal Return
5 0.640 c 12 years + 295 days 16 years + 331 days
4 0.512 c 13 years + 68 days 17 years + 105 days
3 0.384 c 14 years + 185 days 18 years + 222 days
2 0.256 c 18 years + 219 days 22 years + 256 days
1 0.128 c 33 years + 111 days 37 years + 148 days
__________________________________________________ ________________
4.0 FUTURE RESEARCH
This paper is a conceptual study, backed by quantitative
analysis. Future research is needed to develop the concept into
the systems design phase. The following are some of the important
considerations yet to be performed:
¥ Geometry: should the spacecraft be a "cluster of grapes"
configuration of spheres, or a more conventional cylindrical
configuration, still using the self-refrigerated hydrogen ice
concept?
¥ Attach/Detach: how are the spheres attached to each other,
and how are they detached to be used as fuel? If robotically,36,37
what is the deadweight fraction of that robotic mechanism, and is
it less than the tankage requirements for conventional liquid
fuel? Are robots chewed up and vaporized as reaction mass?
¥ Fuel Processing: how is hydrogen ice melted or slushified;
how separated from the metal concentric shields, stiffening fibers
or particulates, and insulating rods; how pumped or introduced
into the reaction chamber?
¥ Centroid: as spheres are plucked and moved, the
center-of-mass of the spacecraft shifts. How is attitude
corrected to maintain the proper thrust vector?
¥ Payload: should there be (one to five) centralized payloads
as such, or does a distributed array of superconducting avionics
embedded in multiple spheres suffice for operations at the
destination? If so, what science data can be captured and
returned?38
¥ Radiation: How much can payload be hardened against nuclear
engine neutrons and cosmic rays by redundancy, self repair, and
nanotechnology?33 I suspect that the optimum payload is the size
of a heavily shielded bacterium, able to build a useful
sensor/communication package from in situ material, but that is
outside the scope of this paper.
¥ Stages: how many stages should there be, given the
diminishing returns for additional stages in terms of coasting
velocity, at great expense in terms of mass ratio? The trade-off
should consider the multiple instrument package/arrival time
scenario of Section 3.1, above.
¥ Parameters: What are specific parameters of mass and thrust
for selected configurations of multi-stage fission and fusion
hydrogen ice spacecraft and specific stellar destinations?
¥ Destination: What should be the target star system for such
an intersetllar probe? I suggested in a separate presentation at
Practical Robotic Interstellar Flight: Are We Ready? the value of
fixing the date of arrival of probe transmissions at 2045 A.D.
(the Centenary of the United Nations) or 2076 A.D. (American
Tricentennial), so that a given destination and average velocity
fully determines the launch date, allowing scenarios to be more
easily compared.
¥ Ignition: can Lithium or Boron fusion be ignited by
incoming protons at above 0.02 c?28
¥ Braking: can the payload be decelerated at the destination
by solar sail, magnetic sail,34 or electrical deflection of
interstellar plasma?
¥ Hybrid: can this hydrogen ice concept be effectively
combined with other technologies, such as laser propulsion,39 solar
sails,40,41,42 ion propulsion, mass drivers, anti-matter43, pellet
streams (or streams of heavy ions such as, I suggest,
buckminsterfullerenes), and the like?
¥ Cost: what does such a spacecraft cost?
¥ Schedule: when are such spacecraft likely to be feasible;
what precursor missions are likely (i.e. Solar Gravitational Focal
Zone, Kuiper Belt, Oort Cloud); how does hydrogen ice spacecraft
development fit in with other aspects of space transportation
infrastructure?44
Many basic questions remain. The author hopes that the
"hydrogen ice spacecraft for robotic interstellar flight" concept
itself stimulates interesting answers.
5.0 SUMMARY & CONCLUSIONS
Spacecraft constructed from cryogenic hydrogen (or deuterium
and tritium) ice can use the same material for structure,
shielding, coolant, and fuel.2,3,4,5,6,7 This type of "autophage"
(self-consuming) spacecraft achieves an extremely low dead-weight
fraction (fraction of non-payload mass remaining after all fuel is
expended), which is a critical parameter for optimizing the
performance of interstellar spacecraft, especially multi-staged
spacecraft.9
To reduce the volatility of hydrogen ice, a particular
self-refrigerating structure invented by James B. Stephens of JPL
and quantified by James Salvail (U. Hawaii) and D. Hustvedt for
Earth orbit operations,24 was extended by this author to
interplanetary25,26,27 and interstellar applications. With
self-refrigeration, hydrogen ice lasts surprisingly long (1 meter
radius sphere at 1 AU lasts 12 years). Hydrogen ice by itself
(butter-soft) is imperfect as a structural element; various
methods of stiffening by the admixture of particulates or carbon
or boron fibers are proposed.
Ordinary hydrogen ice is an ideal fuel for fission and
anti-matter propulsion.29,30 Other cryogens are considered relevant
to fusion propulsion,20,31 including deuterium, tritium, Lithium-6,
Lithium-7, Boron-11, and a saturated solution of lithium in
anhydrous ammonia.21,22 Specific fusion reactions are discussed in
terms of fuel, radiation, energy, and ignition.
A quantitative analysis is presented of the relativistic
kinematics of multi-staged interstellar iceships. The relativistic
multi-stage equations of Spencer and Jaffe9 are utilized, and the
insights and errors of earlier authors noted.12,13,14,15,16,17,18,19
Tables are presented for fusion propulsion scenarios with
dead-weight fractions of 0.1, 0.2, and 0.3; payload fractions of
10-1, 10-3, and 10-5; and number of stages from 1 to 5; yielding
payload velocities of 0.15 to 0.64 c.
In the limiting case of a 5-stage deuterium ice fusion
spacecraft on a one-way mission with no deceleration at the
destination, a dead-weight fraction of 10-1 for each stage, and a
total payload fraction of 10-5, then the final burnout velocity of
the 5th stage is 0.64c, which at constant 0.0485 G acceleration
would reach Alpha Centauri in 12.81 years (with earlier stages
arriving with their own instrument packages at later dates), and
at 1 G acceleration would get a probe zipping through the Alpha
Centauri system in roughly 6.7 years.
This paper is a conceptual study, backed by quantitative
analysis. Future research is needed to develop the concept into
the systems design phase. There are some important considerations
yet to be performed, involving: Geometry, Attach/Detach,
Robotics,36,37 Fuel Processing, Centroid, Payload, Sensors,38
Radiation, Nanotechnology,33 Stages, Parameters, Destination,
Ignition,28 Braking,34 Hybridization (laser propulsion39, solar
sails40,41,42, antimatter43), Cost, and Schedule.44
Many basic questions remain. The author hopes that the
"hydrogen ice spacecraft for robotic interstellar flight" concept
itself stimulates a new set of interesting questions and
interesting answers.
ABSTRACT
Spacecraft constructed from cryogenic hydrogen (or deuterium
and tritium) ice can use the same material for structure,
shielding, coolant, and fuel. This type of "autophage"
(self-consuming) spacecraft achieves an extremely low dead-weight
fraction, which is a critical parameter for optimizing the
performance of interstellar spacecraft.
To reduce the volatility of hydrogen ice, a particular
self-refrigerating structure is presented. Hydrogen ice by itself
is imperfect as a structural element; various methods of
stiffening by the admixture of carbon or boron fibers are
discussed. Other cryogens relevant to specific fusion reactions
are considered, including deuterium, tritium, boron-11, and
saturated solutions of lithium in anhydrous ammonia.
A quantitative analysis is presented of the relativistic
kinematics of multi-staged interstellar iceships. In the limiting
case of a 5-stage deuterium ice fusion spacecraft on a one-way
mission with no deceleration at the destination, a dead-weight
fraction of 10-1 for each stage, and a total payload fraction of
10-5, then the final burnout velocity of the 5th stage is 0.64c,
which at constant 0.0485 g acceleration would reach Alpha Centauri
in 12.81 years, and at 1-g acceleration would get a probe zipping
through the Alpha Centauri system in 6.7 years.
Appears in:
the Proceedings of ÒPractical Robotic Interstellar Flight:
Are We Ready?Ó, New York University, New York City,
29 Aug-1 Sep 1994,
and in Journal of the British Interplanetary Society, April 1996
__________________________________________________ __
1 C.E.O., Computer Futures Inc.; Active Member: British
Interplanetary Society, National Space Society, World Space
Foundation, Space Studies Institute, Planetary Society
TABLE OF CONTENTS
Title page, Abstract, Table of Contents 1
1.0 Introduction 2
2.0 Design of Hydrogen Ice Spacecraft 3
2.1 Thermal Analysis: Here Comes the Sun 6
2.2 Lithium or Boron in Hydrogen: Icy Isotopes 7
3.0 Relativistic Kinematics 10
3.1 Five-Stage Scenario:MultipleInstrumentPackages/Arrivals
13
4.0 Future Research 15
5.0 Summary & Conclusions 16
6.0 References 17
__________________________________________________ __
1.0 INTRODUCTION
For innovative space exploration missions, unusual
requirements are levied on the structural components of the
spacecraft. In many cases, the preferred solution is the
utilization of unusual materials. Spacecraft constructed from
cryogenic hydrogen (or deuterium or tritium) ice can use the same
material for structure, shielding, coolant, and fuel.2,3,4,5,6,7
This type of "autophage" (self-consuming) spacecraft achieves
an extremely low dead-weight fraction (fraction of non-payload
mass remaining after all fuel is expended), which is a critical
parameter for optimizing the performance of interstellar
spacecraft.9 At the same time, hydrogen is ideal in having a
minimum molecular weight of exhaust material. This dead-weight
consideration is even more important for multi-staged rockets.
To reduce the volatility of hydrogen ice, at a temperature of
5o Kelvin, we have to keep it cool while the vehicle is being
assembled and fueled near planet Earth, and to keep it cool during
the flight despite heating from exhaust radiation, interstellar
dust impact, and stellar ultraviolet radiation. A particular
self-refrigerating structure is presented below. Hydrogen ice by
itself is imperfect as a structural element; various methods of
stiffening by the admixture of carbon or boron fibers are
discussed. Other cryogens are considered, including a saturated
solution of lithium in anhydrous deuterated ammonia.
For uranium fission rockets12,16, the fraction of mass
converted into energy is roughly 7 x 10-4;
for deuterium fusion, it is roughly 4 x 10-3.
Assume that we have a deuterium fusion engine with conversion
fraction (epsilon) = 4 x 10-3; the details are left to the
engineers. Assume that the spacecraft structural material is the
fuel, namely frozen deuterium. Assume a one-way unmanned probe
with no powered deceleration at the destination (a one-way probe
with deceleration at the destination would require squaring the
mass ratio). Assume as in the classical case per Subotowicz 19
that each stage has the same mass ratio and exhaust velocity.
Then, as we shall see in the section on relativistic
kinematics, appreciable burnout velocities can be achieved if we
can keep the dead-weight fraction as low as 10-1 for each stage,
i.e. only one-tenth of non-payload mass remains after all fuel
(former structural element) is expended. For example: in the
limiting case of a 5-stage deuterium ice fusion spacecraft, if the
payload fraction is 10-5, then the final burnout velocity of the
5th stage is 0.64c, which at constant 0.0485 G acceleration would
reach Alpha Centauri in 12.81 years, and at 1 G acceleration would
get a probe zipping through the Alpha Centauri system in roughly
6.7 years.
A quantitative analysis is presented of the relativistic
kinematics of multi-staged interstellar iceships. A particular
five-stage multiple instrument packages/multiple arrivals scenario
is calculated. Future research considerations are outlined.
Summary and conclusions are presented. 43 references are listed.
2.0 DESIGN OF HYDROGEN ICE SPACECRAFT
James B. Stephens of JPL first proposed (in 1984 and 1985,
while in communication with this author) banking hydrogen fuel in
Low Earth Orbit without a tank, based on his 20 years of studying
icy comet nuclei. He began to add ancilliary benefits, as
detailed below, including using hydrogen ice in orbit to cool "old
fashioned" (low temperature) superconducting electronic systems
for low-noise, low-power long-range sensors. Jim Stephens
presented his idea to NASA and the Department of Defense in the
early 1980s, but received little interest. This author then
advanced the concept of interplanetary and interstellar spacecraft
constructed from cryogenic hydrogen ice that can use the same
material for structure, shielding, coolant, and fuel.2,3,4,5,6,7
The ideal spacecraft can be lightweight, inexpensive, and
fuel efficient by using balls of hydrogen ice as both structure
and fuel. Hydrogen may be "exotic" in its structural function,
because it has the tensile strength of butter, but it accounts for
over 75% of all matter in the universe and costs under $10 per
pound. The material can be stiffened with the admixture of carbon
or boron fibers, or various particulates.
Balls of modified hydrogen ice first serve as structure, then
are detached, liquified or turned into slush, and channeled into a
fusion reactor as fuel. In this way, almost all non-essential
parts of the spacecraft are consumed during the mission. This
author considers the scenario conceptually similar to the scene in
the Marx Brothers' film Go West where Groucho, Harpo, and Chico
feed the furnace of a steam locomotive with boxcar slats, then
furniture, and then demolish and burn the caboose. There is a
similar scene in Around the World in 80 Days,8 where Phogg burned
parts of the steamship Henrietta for fuel to complete the last
stage of his journey.
This type of "autophage" (self-consuming) spacecraft achieves
an extremely low dead-weight fraction, which is a critical
parameter for optimizing the performance of interstellar
spacecraft.9 More recently, but more conservatively, Aston10
proposed that thrusters use spent nuclear fuel as propellant.
Nordley11 extends Aston's notion to say that "The current
generation of ion thrusters uses as heavy a propellant atom as
possible to maximize the mass-to-charge ratio in the ion
generation part of the thruster, and thus minimize its size and
weight. This is less of a concern in a very high exhaust velocity
interstellar application because the engines require less mass
flow per unit power. Indeed, use of a lower mass propellant atom
would reduce the voltage requirements of accelerator stages for a
given exhaust velocity.... [Aston's] philosophy could be extended
to parts of the spacecraft structure as well. Singly charged
aluminum or silicon atoms would achieve [in an ion electric
propulsion system] about 4.7 time the velocity of a singly charged
xenon atom and about 8.7 times the velocity of singly charged
uranium atoms in the same [electric] field." The hydrogen ice
autophage concept takes Aston's and Nordley's approach to a
logical extreme.
To reduce the volatility of hydrogen ice, a particular
self-refrigerating structure was invented by James Stephens,
analyzed quantitatively by James Salvail at the University of
Hawaii, illustrated in Figure 1, and described below.
_________________________________
[get from mac disk, or scan in picture here]
Figure 1: Self-refrigerated Ice Sphere
__________________________________________________ ________________
Concentric spheres of very thin metal (i.e. lithium) or
metallized mylar coating thicker concentric spherical shells of
hydrogen ice are connected to each other by at least two rods made
of a material that has very low thermal conductivity. This is
necessary so that the spheres above the instantaneous level of the
subliming ice surface do not move relative to each other. The
outer shells are highly reflective, thick enough to provide
reasonable structural integrity. The inner spheres are made of
the same materials, but much thinner (is much less than 0.1 cm), as they are
merely radiation shields.
The radiation shields and outer hulls must contain enough
sufficiently sized holes or pores so that sublimed hydrogen
molecules are quickly lost into space. The evacuated spaces
between the slowly receding ice surface and the outer hulls thus
have negligible gaseous heat conduction because the gas is very
rarified. Gas flux is small enough that heat convection is also
negligible.
Under these conditions, the escaping sublimed hydrogen
expands and refrigerates the remaining concentric spheres,
maintaining a temperature well below the 20o K melting point of
hydrogen; the nominal system temperature is 5o K.
The system as a whole as conceived by James B, Stephens
includes: (1) ice embedded insulation, (2) vapor cooled
insulation, (3) isomer conversion catalyst integral with
insulation, (4) Infrared photon reflective and vapor conductive
insulation, (5) vapor cast crystalline hydrogen ice using nuclear
magnetic resonance heating of non-crystalline ice, (6)
self-forming filamentary insulation from dispersed particles in
the ice that cohere due to ice cleaning.
The attributes of the system include: (1) unitized design --
hydrogen ice is the cryogen, propellant, shielding, absorber,
power source, window, and insulation support during launch; (2)
superconducting temperature cryostat (less than 5o K for hydrogen); (3)
self-insulating solid cryogen; (4) long lifetime in Earth orbit;
(5) low cost material (less than $10/pound); (6) low cost fabrication
(casting process); (7) low launch cost (withstand high
acceleration forces); (8) low cost operation (efficient
superconducting solid state system); (9) acoustically quiet (no
moving parts); (10) thermally stable (large thermal capacity well
insulated); (11) high density ice vapor cast and used at same
temperature avoiding shrink stresses in insulation and components
embedded in ice.
Stephens also emphasized neutron absorbing properties of
hydrogen ice, microwave reflection or absorption, laser-tough
shielding, neutral and charged particle beam tough shielding,
radar stealth, and a wide range of capabilities for embedded
avionics, including: phased-array radar, solar-powered ion rocket
and superconducting magnet power generator/storage, and
superconducting guidance and control.
As the concept was extended by this author (see Figure 2),
individual hydrogen ice spheres can be orbited by small boosters,
and later assembled into a large spacecraft. Solid hydrogen is
inherently safer than liquid hydrogen. The spheres can have
embedded avionics, providing distributed redundant capability for
the spacecraft at superconducting temperatures. Once assembled,
the low accelerations typical of ion, fission, or fusion
propulsion would not endanger the inherently low compressive and
tensile strength of hydrogen ice as a structural material. An
acceleration of 0.0485 gravities is used in Section 3.1. The
hydrogen ice spheres would be between the payload (or crew) and
the nuclear propulsion, providing neutron-absorbant shielding at
no extra cost.
_________________________________
Figure 2: On-Orbit Iceship Assembly
[get from mac disk, or scan in picture here]
_______________
__________________________________________________ ________________
Earlier articles by this author suggested space exploration
missions including: (1) sungrazer, (2) outer planet explorer, (3)
interstellar precursor 1000 AU mission (TAU), (4) subterranean
radar mapping of planets, (5) manned Mars mission, (6) propellant
transfer and storage for Space Station refueling depot.
This author then proposed experiments of detonation wave
propulsion/attitude control with alternating layers of hydrogen
ice and oxygen ice, and made detailed suggestions for utilization
of cryogen ices on the Moon, Mercury, and Mars.25,26,27
2.1 Thermal Analysis: Here Comes the Sun
James Salvail's thermal analysis2,3,4 by computer simulation of
the system of differential equations showed that at 1 AU from the
sun, a 50-layer hydrogen ice sphere of 1 meter radius remained
nearly isothermal at the initial temperature of 5o K, with a
negligible temperature gradient and a near-constant mass flux of
17.8 nanograms/cm2-sec. After a simulated 10 years, the hydrogen
ice component had shrunk to 21 inches in radius, and the total
lifetime was 12 years. Reducing the the radiation shields from 50
to 10 had no effect. Painting the outer surface black (for
stealth) gave a tripled mass flux of 53.8 nanograms/cm2-sec, a
surface temperature of 5.2o K, and a reduced lifetime of 4.2 years.
Obviously, for our spacecraft, reflectivity and long lifetime are
preferred to stealth (which the DOD might prefer).
Even at 0.1 AU from the sun, far inside the orbit of Mercury,
a 50-shield 1 meter shiny sphere stays at 5.81o K, with a mass flux
of 1.06 micrograms/cm2-sec, and a lifetime of 75 days.
At 0.1 AU from the sun, a 10-shield 1 meter shiny sphere stays at
6.39o K, with a mass flux of 10.5 micrograms/cm2-sec, and a
lifetime of 35 days. The radiation shield effects are important
for larger thermal loads, such as would occur if the hydrogen ice
spacecraft mission began with a gravity assist swingby close to
the sun.
The effects of a fission or fusion explosion near the
spacecraft, as might happen with temporary malfunction of a
nuclear rocket engine, or of catastrophic failure of one of
several co-travelling redundant spacecraft, was simulated as a
temporary change from heliocentric deistance of 1.0 AU to 0.01 AU,
where the radiative equilibrium temperature for a black body is
2808o K, for 20 seconds. If the outer coat does not melt at the
maximum temperature attained (2361o K), then the hydrogen ice
adjacent to the outer surface peaks at 8.73o K, with a gas flux of
4.7 milligrams/cm2-sec, decreasing after 10 minutes to 5.85o K
(50-shield) or 5.79o K (10-shield), at which time the ice had
receded 2.5 cm.
All things being equal, the lifetime of a self-refrigerated
hydrogen ice sphere was found to be directly proportional to the
first power of its initial radius. Thus, a 2 meter radius sphere
has a 24 year lifetime at 1 AU, and 2 years at 0.1 AU. For deep
space missions, loss becomes extremely small for spheres several
meters in radius.24
Similar thermal analysis has been performed for slab and
cylindrical geometries.24
Hydrogen ice by itself is imperfect as a structural element;
various methods of stiffening by the admixture of carbon or boron
fibers have been explored, as well as admixtures of particulates
such as montmorillonite clay.
A survey of cryogenic ices and slushes has been presented in
an earlier article by this author.4 For this paper it suffices to
note that hydrogen ice has a density of 70.6 g/l at -262o C, melts
at 20o K to become a liquid with density 70.8 g/l at -253o C, and
that slush is intermediate in density but has various advantages
over both solid and liquid.
For proposed antimatter propulsion29,30 it is suggested that
there be a significant excess of hydrogen to anti-hydrogen for
optimization. In such a case, the spacecraft would be constructed
of hydrogen ice as before, but with small very carefully suspended
and shielded units of anti-hydrogen, for which the
self-refrigeration concept is most definitely not appropriate.
Antimatter propulsion requires several breakthroughs.
Fission propulsion does not, and requires only ordinary hydrogen
as a propellant, heated by whatever fission reactions take place
in whatever reactor/engine. Fission power is not emphasized in
this paper. Fusion propulsion does require breakthroughs.31
Assuming the existence of adequate space-rated fusion reactors, we
must turn our attention from ordinary hydrogen ice to more unusual
materials.
2.2 Lithium or Boron in Hydrogen: Icy Isotopes
In one sense, ordinary hydrogen (protium) is the ideal
structure/fuel, as it is extremely cheap and has the lightest
molecular weight of any material exhaust. But the fusion reaction
attainable 20 with ordinary hydrogen fuses two protons to produce a
deuteron (deuterium nucleus), a positron (anti-electron), and a
neutrino, at an energy of 0.42 Mev (million electron volts). This
yields 2.0 x 1013 Joules per kilogram of fuel.
p + p -> D + e+ + v
But this is irrelevant, since the reaction involved is not
true nuclear fusion. As revealed by the emission of the neutrino,
this is a "weak force" reaction, rather than a "strong force"
reaction. Too much of the energy is carried away by the neutrino.
The reaction is too difficult to initiate. The total energy yield
is (relatively) low. And for little more effort, with more
sophisticated fuel, we can get better results.
If our hydrogen ice is made of equal proportions of protium
and deuterium, we can fuse the two to produce Helium-3 and a gamma
ray, with 5.49 Mev energy, corresponding to 1.75 x 1014 Joules per
kilogram of fuel.
p + D -> He3 + gamma
But this is not a good idea either. The gamma rays would be
emitted in all directions, and tend to fry the payload. We might
as well eliminate protium completely, and use either pure
deuterium ice or a deuterium/tritium mixture.
Pure deuterium ice would result in two different reactions,
yielding a combination of Helium-3, tritium, protons, and
neutrons.
D + D -> He3 + n 3.27 Mev (7.8 x 1013 J/kg)
D + D -> H3 + p 4.03 Mev (9.65 x 1013 J/kg)
Deuterium is easily obtainable in massive quantities, since
it makes up roughly 1 part in 6,000 of the hydrogen in water here
on Earth.23 Deuterium oxide, D2O, heavy water, costs from $0.06 to
$1/gram depending upon quantity and purity.23 The
deuterium-deuterium fusion reaction is moderately easy to
initiate, requiring a temperature in the 10 million degree range.
But the neutrons in the output are nasty. Since they are
uncharged, they tend to fly in all directions, uncontrollable by
electric or magnetic fields, frying and/or rendering the payload
radioactive. Nonetheless, this is the reaction and fuel used by
default throughout the remainder of this paper.
An energetic deuterium-tritium reaction seems at first to
have certain advantages. This is the most studied reaction today,
because of the low ignition temperature of roughly 10 million
degrees.
D + H3 -> He4 + n 17.6 Mev (3.37 x 1014 J/kg)
This is actually the easiest fusion reaction to ignite, and
may thus be the first used for terrestrial fusion power. But
tritium is quite radioactive, decaying in about a decade, and that
neutron is still trouble.
There are several interesting reactions involving Helium-3 in
the fuel, but we disregard them here for two reasons. First, it's
hard to obtain, although it might be extracted from the upper
centimeter of lunar regolith where it has accumulated from solar
wind. Second, the self-cooling approach described in my articles
for hydrogen doesn't work as well for helium isotopes, which have
to be cooled to below the background temperature of the universe.
Frozen helium is just too volatile.
This leaves us with several more exotic reactions. We
consider Lithium. Lithium occurs in nature21 with an abundance
ratio of 7.39% for the isotope Lithium-6 (Li6) to 92.61% for
Lithium-7 (Li7). Lithium melts at 180o C, and boils at 1,326o C.
If we built the spacecraft out of equal proportions of protium and
pure Lithium-6 isotope, we have:
p + Li6 -> He4 + He3 3.90 Mev (5.53 x 1013 J/kg)
We would be using hydrogen ice with lithium foil in the
self-refrigerating concentric structure, plus walls and girders of
lithium. Lithium is a soft metal, but at cryogenic temperatures
(and away from water) it is strong enough without brittleness to
suffice for structural purposes. Unfortunately, this is a
difficult reaction to ignite.
We get somewhat more bang for the buck if we use isotopically
pure Lithium-7, for a reaction yielding an electromagnetically
focusable stream of alpha particles.
p + Li7 -> He4 + He4 17.00 Mev (2.0 x 1014 J/kg)
Again, this is a hard reaction to ignite.
We can use deuterium ice and pure Lithium-6, again getting an
all-alpha output:
D + Li6 -> He4 + He4 22.30 Mev (2.67 x 1014 J/kg)
Or even consider protium plus Boron-11 for the so-called
Boron-fission reaction:
p + B11 -> He4 + He4 + He4 8.80 Mev (7.0 x 1013 J/kg)
But this is even less studied, and also extremely difficult
to ignite, requiring perhaps 1,000 times the ignition temperature
of Deuterium. Lithium or Boron fusion might be initiated by
incoming protons from interstellar space when rammed into at over
0.02 c, which might be useful for upper stages of a staged
interstellar spacecraft.28
If we use fibers of Boron-11 to stiffen deuterium or tritium
ice, it might be okay to let those boron fibers go right into the
rocket engine, vaporize, and partly engage in nuclear reactions.
The unreacted boron would reduce the energy yield somewhat, and
merely be expelled as part of the reaction mass.
There is a clever way to get the lithium mixed in with the
hydrogen. Lithium is very soluble in anhydrous ammonia (NH3 with
no water). The resulting solution is the lowest density liquid
known at room temperature, with a density of only 0.511 g/l.22
Regular ammonia, NH3, has a molecular weight of 17.03, a density of
0.7710 g/l, and melts at -77.7o C, while Trideutero ammonia,
ammonia-d3, ND3, has a molecular weight of 20.05 and melts at -74o
C.23 Lithium solutions in ammonia have metallic conductivities
above 9 Mole percent metal. There is a eutectic at 22 Mole
percent metal at 88o K., and at lower temperature is a stable solid
compound, perhaps Li(NH3)4.
We can mix up batches of Lithium-6 or Lithium-7 in ordinary
anhydrous ammonia, or Lithium-6 in fully deuterated anhydrous
ammonia, freeze the stuff in the concentric perforated
lithium-foil configuration, and build our spaceship out of that
lithiated ammonia ice. This does leave us with a certain amount of
useless nitrogen, which would contaminate the fusion reaction,
unless separated out and expelled as unreacted exhaust mass. But
lithiated anhydrous ammonia might be worth investigating as an
exotic chemical fuel for liquid oxygen combustion.
Where does this leave us? We don't have a clear idea of a
spacecraft fusion reactor that burns lithium or boron.31 So we may
have to bite the bullet on the neutron radiation problem and build
our spacecraft out of deuterium or mixed deuterium-tritium ice.
The rest of this paper makes that assumption. Nordley32 points out
"that as soon as the main reaction happens, the products become
available for side reactions. While the output of particles from
these side reactions may be several orders of magnitude below the
output of the main reaction, and thus not worthy of interest
regarding the kinematics, they will still be very significant
(especially the neutrons) to electronics and biological components
at the power levels needed for interstellar flight."
We note that Lithium can trap neutrons, heating up, and
transferring that heat to melt or slushify hydrogen ice. Future
considerations include analysis of the limits of neutron-hardened
payloads through redundancy, self-repair, or even nanotechnology.33
3.0 RELATIVISTIC KINEMATICS
Spacecraft constructed from cryogenic hydrogen ice can use
the same material for structure, shielding, coolant, and
fuel,2,3,4,5,6,7 but more importantly, from the kinematic viewpoint,
that means that very little of the spacecraft's mass is wasted as
non-productive non-payload.
This type of "autophage" (self-consuming) spacecraft achieves
an extremely low dead-weight fraction (fraction of non-payload
mass remaining after all fuel is expended), which is a critical
parameter for optimizing the performance of interstellar
spacecraft.8 At the same time, hydrogen is ideal in having a a
minimum molecular weight of exhaust material, and hence maximum
exhaust velocity.
As Spencer & Jaffe report,9 "the earliest studies of
relativistic rocket mechanics by Ackeret,12,13 Tsien,14 Bussard,15
and others made two implicit assumptions that severely limit
performance of the rockets considered. They assumed that
nuclear-energy rockets are limited to a single stage and that the
available energy corresponds to a fixed fraction of the final
vehicle mass. The latter assumption apparently arose from the
thought that spent nuclear fuel would be either retained on board
or dumped, rather than exhausted at high velocity. These
assumptions are neither necessary or desirable.
"More recently, interstellar travel has been considered by
Sanger16 and Stuhlinger.17 They realized that the limitation
regarding the amount of energy available being a function of the
propellant mass rather than the final mass was unnecessary;
however, they did not consider staging the vehicles as is done
with chemical rockets. They concluded, therefore, that
interstellar travel using nuclear reactions as an energy source
was impossible because of fundemental limitations on the amount of
energy available for rocket propulsion. In contradiction, the
analysis presented [by Spencer and Jaffe9] shows that nuclear
fission or fusion rockets can be considered for interstellar
travel."
The equations of Spencer and Jaffe have been used for the
relativistic kinematic calculations in this paper. These include
the correct relationship first given by Sanger 16 and Huth 18
between fraction of mass converted into energy (epsilon) and
exhaust velocity relative to vehicle (w), and between fraction of
mass converted into energy (epsilon) and specific impulse (I),
namely:
w/c = [epsilon(2-epsilon)]1/2
I = (c/g)[epsilon(2-epsilon)]1/2
For a one-stage vehicle, the burnout fraction (xi) is the
ratio of the rest mass of the vehicle at burnout to the rest mass
of fuel consumed:
xi = Mb / Mf
and the rest mass of fuel consumed is the sum of the rest mass of
fuel exhausted (Mex) and the rest mass of fuel converted to kinetic
energy
Mf = Mex + (epsilon)Mf
As Spencer & Jaffe pointed out, the performance of a
multi-staged interstellar spacecraft is very sensitive to the
dead-weight fraction (beta) and the overall payload fraction
(phi). In particular, for an n-stage vehicle, the final burnout
velocity of the payload (nth stage) in terms of over-all payload
fraction, deadweight fraction, and fraction of mass converted to
energy is
{Clyde: insert scanned in printout of nicely rendered equation
here}
[(1 + beta)/(beta + phi1/n)]^{2n[epsilon(2-epsilon)]1/2} - 1
un / c =
-------------------------------------------------------
[(1 + beta)/(beta + phi1/n)]^{2n[epsilon(2-epsilon)]1/2} + 1
and the over-all mass ratio is
delta = [(1 + beta)/(beta + phi1/n)]n
Then, if the payload fraction is 10-1 we have the following
relationship between dead-weight fraction (beta), number of
stages, and fraction of light velocity of payload:
Dead-weight Fraction Number of Stages Fraction of Light Velocity
(Beta) (n) (un / c)
____________________ ________________ ____________________
0.1 1 0.15
0.1 2 0.17
0.1 3 0.177
0.1 4 or 5 0.18
0.2 1 0.125
0.2 2 0.15
0.2 3 0.155
0.2 4 0.16
0.2 5 0.162
0.3 1 0.105
0.3 2 0.13
0.3 3 0.14
0.3 4 0.146
0.3 5 0.148
If the payload fraction is 10-3 we have the following
relationship between dead-weight fraction (beta), number of
stages, and fraction of light velocity of payload:
Dead-weight Fraction Number of Stages Fraction of Light Velocity
(Beta) (n) (un / c)
____________________ ________________ ____________________
0.1 1 0.20
0.1 2 0.37
0.1 3 0.44
0.1 4 0.46
0.1 5 0.47
0.2 1 0.16
0.2 2 0.30
0.2 3 0.37
0.2 4 0.41
0.2 5 0.44
0.3 1 0.14
0.3 2 0.26
0.3 3 0.32
0.3 4 0.36
0.3 5 0.38
If the payload fraction is 10-5 we have the following
relationship between dead-weight fraction (beta), number of
stages, and fraction of light velocity of payload:
Dead-weight Fraction Number of Stages Fraction of Light Velocity
(Beta) (n) (un / c)
____________________ ________________ ____________________
0.1 1 0.22
0.1 2 0.40
0.1 3 0.53
0.1 4 0.61
0.1 5 0.64
0.2 1 0.16
0.2 2 0.30
0.2 3 0.42
0.2 4 0.50
0.2 5 0.55
0.3 1 0.14
0.3 2 0.26
0.3 3 0.36
0.3 4 0.44
0.3 5 0.48
The assumption has been made in this paper that there is no
rocket-based deceleration of the payload at its destination. To
provide such deceleration, the mass ratio must be squared. To
decelerate at the destination, accelerate back to Earth, and
decelerate at the return would require raising the mass ratio to
the 4th power. But several proposals have been made20 (pp.116-7)
for interstellar spacecraft braking by solar sail, magnetic sail,34
or electrical deflection of interstellar plasma. It remains to be
seen whether any of these approaches are feasible at velocities
above 0.01 c.
3.1 Five-Stage Scenario: Multiple Instrument
Packages/Arrivals
Hartman35 in reviewing an earlier draft of this paper,
considered the time it would take for the limiting-case 5-stage,
10-5 payload fraction, 0.1 dead-weight fraction spacecraft. That
earlier (19 August 1994) draft was distributed as a pre-print at
Practical Robotic Interstellar Flight: Are We Ready?, 29 Aug-1 Sep
1994, New York University, New York City, and at ConAdian: The
52nd World Science Fiction Convention, 1 Sep-5 Sep 1994, Winnipeg,
Manitoba. In it, I had imprecisely claimed that the vehicle in
question would reach the Alpha Centauri system in "roughly 6
years."
As Hartman comments, "the lowest acceleration that will give
you a final velocity of 0.64 c by the end of the trip to Alpha
Centauri [assumed to be 4.1 light years] would be approximately
0.0485 gravities. That would require a constant acceleration for
the entire journey, and would take roughly 12.81 years [12 years,
294 days]. Any lower acceleration, and you would need more
distance (and time) to reach the proposed final velocity. With a
full one gravity acceleration the probe would reach 0.64 c in 0.62
years [0.622], while covering just under two-tenths of a light
year [0.199]. It would then coast for 3.9 light years [3.901],
thus taking about 6.7 years [6.717] for the trip."
He correctly observes that with low accelerations, little
structural strength is required, hence the plausibility of
hydrogen ice. "Will the probe's structure stand up to even 1/20
G? If not, the final velocity will be lower." The various
stiffening methods suggested for hydrogen ice may not be valid for
1 G, but are almost surely effective for 0.0485 G = 47.5 cm/sec2.
Hartman then elaborates on an aspect of my scenario which had
not been spelled out in the earlier draft. As he puts it, "all
five of the stages would reach Alpha Centauri in a reasonable
length of time. The fifth stage, if you use 0.0485 gravities,
would reach its goal in 12.81 years [accelerate full time, 4.1
light years], the fourth in 13.19 years [accelerate 4/5 time, 2.6
light years, and coast 1.5 light years], the third in 14.51 years
[accelerate 3/5 time, 1.48 light years, and coast 2.62 light
years], the second in 18.60 years [accelerate 2/5 time, 0.65 light
years, and coast 3.45 light years], and the first in 33.30 years
[accelerate 1/5 time, 0.165 light years, and coast 3.935 light
years].
"If higher accelerations are used, these times would be
compressed, ranging from 6.72 years to 32 years. If each stage
carried its own instrument package, the probe would return much
more data, and the additional packages would add little to the
massive lower four stages. Since the fifth stage would pass
through the target system at nearly two-thirds the speed of light,
it could take only a hasty peek at its goal. The following stages
could take longer looks, though only the first and perhaps the
second stages could benefit from directions influenced by the
fifth stage's information."
The following numbers, calculated by Hartman, apply to the
arrival after the nominal payload of four successive instrument
capsules. These figures assume no braking. A consensus reached
at Practical Robotic Interstellar Flight: Are We Ready? was that
payloads should be equivalent to a Hubble Space Telescope in order
to adequately image destination planets and to maintain an optical
communication link with Earth.
__________________________________________________ ________________
Stage Arrival Velocity Arrival Time Signal Return
5 0.640 c 12 years + 295 days 16 years + 331 days
4 0.512 c 13 years + 68 days 17 years + 105 days
3 0.384 c 14 years + 185 days 18 years + 222 days
2 0.256 c 18 years + 219 days 22 years + 256 days
1 0.128 c 33 years + 111 days 37 years + 148 days
__________________________________________________ ________________
4.0 FUTURE RESEARCH
This paper is a conceptual study, backed by quantitative
analysis. Future research is needed to develop the concept into
the systems design phase. The following are some of the important
considerations yet to be performed:
¥ Geometry: should the spacecraft be a "cluster of grapes"
configuration of spheres, or a more conventional cylindrical
configuration, still using the self-refrigerated hydrogen ice
concept?
¥ Attach/Detach: how are the spheres attached to each other,
and how are they detached to be used as fuel? If robotically,36,37
what is the deadweight fraction of that robotic mechanism, and is
it less than the tankage requirements for conventional liquid
fuel? Are robots chewed up and vaporized as reaction mass?
¥ Fuel Processing: how is hydrogen ice melted or slushified;
how separated from the metal concentric shields, stiffening fibers
or particulates, and insulating rods; how pumped or introduced
into the reaction chamber?
¥ Centroid: as spheres are plucked and moved, the
center-of-mass of the spacecraft shifts. How is attitude
corrected to maintain the proper thrust vector?
¥ Payload: should there be (one to five) centralized payloads
as such, or does a distributed array of superconducting avionics
embedded in multiple spheres suffice for operations at the
destination? If so, what science data can be captured and
returned?38
¥ Radiation: How much can payload be hardened against nuclear
engine neutrons and cosmic rays by redundancy, self repair, and
nanotechnology?33 I suspect that the optimum payload is the size
of a heavily shielded bacterium, able to build a useful
sensor/communication package from in situ material, but that is
outside the scope of this paper.
¥ Stages: how many stages should there be, given the
diminishing returns for additional stages in terms of coasting
velocity, at great expense in terms of mass ratio? The trade-off
should consider the multiple instrument package/arrival time
scenario of Section 3.1, above.
¥ Parameters: What are specific parameters of mass and thrust
for selected configurations of multi-stage fission and fusion
hydrogen ice spacecraft and specific stellar destinations?
¥ Destination: What should be the target star system for such
an intersetllar probe? I suggested in a separate presentation at
Practical Robotic Interstellar Flight: Are We Ready? the value of
fixing the date of arrival of probe transmissions at 2045 A.D.
(the Centenary of the United Nations) or 2076 A.D. (American
Tricentennial), so that a given destination and average velocity
fully determines the launch date, allowing scenarios to be more
easily compared.
¥ Ignition: can Lithium or Boron fusion be ignited by
incoming protons at above 0.02 c?28
¥ Braking: can the payload be decelerated at the destination
by solar sail, magnetic sail,34 or electrical deflection of
interstellar plasma?
¥ Hybrid: can this hydrogen ice concept be effectively
combined with other technologies, such as laser propulsion,39 solar
sails,40,41,42 ion propulsion, mass drivers, anti-matter43, pellet
streams (or streams of heavy ions such as, I suggest,
buckminsterfullerenes), and the like?
¥ Cost: what does such a spacecraft cost?
¥ Schedule: when are such spacecraft likely to be feasible;
what precursor missions are likely (i.e. Solar Gravitational Focal
Zone, Kuiper Belt, Oort Cloud); how does hydrogen ice spacecraft
development fit in with other aspects of space transportation
infrastructure?44
Many basic questions remain. The author hopes that the
"hydrogen ice spacecraft for robotic interstellar flight" concept
itself stimulates interesting answers.
5.0 SUMMARY & CONCLUSIONS
Spacecraft constructed from cryogenic hydrogen (or deuterium
and tritium) ice can use the same material for structure,
shielding, coolant, and fuel.2,3,4,5,6,7 This type of "autophage"
(self-consuming) spacecraft achieves an extremely low dead-weight
fraction (fraction of non-payload mass remaining after all fuel is
expended), which is a critical parameter for optimizing the
performance of interstellar spacecraft, especially multi-staged
spacecraft.9
To reduce the volatility of hydrogen ice, a particular
self-refrigerating structure invented by James B. Stephens of JPL
and quantified by James Salvail (U. Hawaii) and D. Hustvedt for
Earth orbit operations,24 was extended by this author to
interplanetary25,26,27 and interstellar applications. With
self-refrigeration, hydrogen ice lasts surprisingly long (1 meter
radius sphere at 1 AU lasts 12 years). Hydrogen ice by itself
(butter-soft) is imperfect as a structural element; various
methods of stiffening by the admixture of particulates or carbon
or boron fibers are proposed.
Ordinary hydrogen ice is an ideal fuel for fission and
anti-matter propulsion.29,30 Other cryogens are considered relevant
to fusion propulsion,20,31 including deuterium, tritium, Lithium-6,
Lithium-7, Boron-11, and a saturated solution of lithium in
anhydrous ammonia.21,22 Specific fusion reactions are discussed in
terms of fuel, radiation, energy, and ignition.
A quantitative analysis is presented of the relativistic
kinematics of multi-staged interstellar iceships. The relativistic
multi-stage equations of Spencer and Jaffe9 are utilized, and the
insights and errors of earlier authors noted.12,13,14,15,16,17,18,19
Tables are presented for fusion propulsion scenarios with
dead-weight fractions of 0.1, 0.2, and 0.3; payload fractions of
10-1, 10-3, and 10-5; and number of stages from 1 to 5; yielding
payload velocities of 0.15 to 0.64 c.
In the limiting case of a 5-stage deuterium ice fusion
spacecraft on a one-way mission with no deceleration at the
destination, a dead-weight fraction of 10-1 for each stage, and a
total payload fraction of 10-5, then the final burnout velocity of
the 5th stage is 0.64c, which at constant 0.0485 G acceleration
would reach Alpha Centauri in 12.81 years (with earlier stages
arriving with their own instrument packages at later dates), and
at 1 G acceleration would get a probe zipping through the Alpha
Centauri system in roughly 6.7 years.
This paper is a conceptual study, backed by quantitative
analysis. Future research is needed to develop the concept into
the systems design phase. There are some important considerations
yet to be performed, involving: Geometry, Attach/Detach,
Robotics,36,37 Fuel Processing, Centroid, Payload, Sensors,38
Radiation, Nanotechnology,33 Stages, Parameters, Destination,
Ignition,28 Braking,34 Hybridization (laser propulsion39, solar
sails40,41,42, antimatter43), Cost, and Schedule.44
Many basic questions remain. The author hopes that the
"hydrogen ice spacecraft for robotic interstellar flight" concept
itself stimulates a new set of interesting questions and
interesting answers.