Nuclear Thermal Propulsion Using a Particle-Bed Reactor

1
Nuclear Thermal Propulsion using a Particle-Bed Reactor
Benjamin Bauldree1
Graduate Student in Aerospace Engineering, Auburn University, AL
Using nuclear energy as a means of propulsion with regards to space flight has long been a
topic of discussion. Nuclear fission produces large amounts of energy, far greater than that
produced by typical chemical propellants such as liquid oxygen and RP-1. The idea of a nuclear
thermal propulsion system consists of transferring thermal energy from the nuclear material to a
propellant of some flavor via a nuclear reactor, vaporizing the propellant into a high-pressure gas
which is then expanded through a nozzle. The particle-bed reactor (PBR) offers the highest
performance compared with other solid-core reactors. The PBR consists of fuel elements, typically
spherical, that are surrounded by layers of moderator blocks. The propellant flows directly over
the fuel elements before passing into a channel and exiting through the nozzle. The direct heat
transfer from the fuel particles to the propellant increases the temperature of the gas entering the
nozzle and ultimately the performance of the system. The PBR has undergone preliminary system
design work with promising results, but due to lack of funding, no physical specimen has ever been
assembled and tested.
Nomenclature
A = atomic mass number
c = speed of light (m/s2
)
cp = specific heat of propellant (J/kg-K)
c* = characteristic exhaust velocity (m/s)
dx = distance traveled by neutron
Hcore = height of the reactore core (cm)
hv = enthalpy of vaporization (J/kg)
i = interaction type (scattering, fission,
absorption)
mcore = mass of the core (kg)
mp = mass of the proton (kg)
me = mass of the electron (kg)
mn = mass of the neutron (kg)
matom = actual mass of the atom (kg)
mprop = mass flow rate of propellant through the
reactor (kg/s)
n = concentration of atoms in material
(atoms/cm3
)
P = probability of interaction i
Pcore = reactor power generated (W)
Pw = specific reactor power (W-s/kg)
R = universal gas constant (m2
kg s-2
K-1
mol-1
)
Rcore = radius of the reactor core (cm)
T = propellant temperature (K)
T0 = chamber temperature (K)
T1 = propellant temperature entering the reactor
(K)
T2 = propellant temperature exiting the reactor
(K)
Vcore = volume of reactor core (cm3
)
Z = atomic number
Δ = mass defect (kg)
γ = specific heat ratio
ρcore = density of the reactor core (kg/m3
)
Σ = macroscopic cross-section for isotope j of
interaction i (cm-1
)
σ = microscopic cross-section for isotope j of
interaction i (cm2
), as a function of energy (E, in eV)
I. Introduction
HE age of rocketry dawned in the early twentieth
century with Wernher Von Braun and his V-2
rocket, the first successful, long range ballistic missile.
[1] With his success came the next footsteps in human
exploaration and the technology to reach beyond the
realm of Earth and into the heavens for which all of
1
Graduate Student, Aerospace Engineering, Davis Hall, Office 313.
human history had long dreamed of. Larger and more
grand rockets followed the V-2, such as the Mercury
Redstones and then the Saturn family. Despite putting
men on the moon with the awe-inspiring Saturn V and
its many ground-breaking achievements, the
technology to extend human reach beyond that of the
T

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moon and possibly outside of this solar system has
remained elusive, even to this day.
Nuclear energy, however, has provided a possible
solution to this problem. In a nuclear rocket, the
energy released from the controlled fission of a “fuel”
such as uranium can be used to thermally excite a
propellant; whereas in chemical propulsion, the
propellant releases energy through combustion
typically with some thermal source. The efficiencies
of these two systems provides the nuclear system the
key advantage. A comparison of each system (Fig. 1)
can be made using specific impulse, where the higher
the specific impulse of the system, the more efficient
it typically is. To increase the specific impulse, the
propellant must exit with either a higher exit
temperature or a lower propellant molecular mass.
The nuclear thermal system allows the use of
propellants with extremely low molecular masses; in
fact, the system can use the propellant of lowest
molecular mass: hydrogen. Extremely high exit
velocities can be achieved without the limitation of
combustion properties of the propellant. The only
requirement is that the temperature of the fuel (the
radioactive material) does not reach its melting point.
[2]
The nuclear thermal propulsion system consists of
many different concepts, most of them revolving
around the design of the reactor and its fuel. The most
famous nuclear system by most regards is the Nuclear
Engine for Rocket Vehicle Applications (NERVA).
The NERVA program consisted of the most extensive
nuclear rocket development and demonstration in
history, achieving twenty-eight succesfull full-power
tests and even meeting certification requirements for a
human mission to Mars before the end of the program
in 1972. The NERVA reactor, called NRX (Nuclear
Reactor Experimental) consisted of graphite fuel
elements impregnated with pyrolyic graphite uranium
carbine particles. [3] The fuel particles provided the
heat source while the graphite matrix provided the
structural support and stability, which can be seen in
Fig. 2. Rotary drums made of boron plates were used
to control the fission process by rotating in toward the
core or out toward the perimeter to absorb neutron
production. This reactor design suffered limitations,
though, one being the temperature of the fuel rods.
Because of the thermal gradient between the coolant
channels and the fuel rods, increases in the coolant
(propellant in this case) temperature would raise the
core temperature beyond the allowable constraints.
Overall, the NERVA design demonstrated a thrust-to-
weight ratio of ~5:1 and a specific impulse of 825
seconds. [2]
In 1987, nearly a decade after the NERVA
program ended, the Space Nuclear Thermal
Propulsion (SNTP) program started with the goals to
achieve a specific impulse of 1000 seconds, with a
thrust-to-weight ratio of 25:1 to 35:1 for engines
producing thrust between 20,000-80,000 pounds. The
design concept focused on the particle bed reactor
(PBR), conceived by Dr. James Powell of Brookhaven
National Laboratory in the late 1970s. [4] The PBR
core consisted of a number of small fuel particle
spheres suspended along the inner diameter of a
cylindrical assembly of hexagonal moderator blocks,
shown in Fig. 3. The spheres consisted of a uranium-
carbine fuel coated with layers of graphite with an
outer layer of zirconium hydride, while the moderator
block had a combination of beryllium and lithium
hydride.[4]
Figure 1. Performance Comparison of Various
Propulsion Systems. Solid-core fission rockets
have greater specific impulse than chemical
rockets while maintaining similar thrust-to-weight
ratios. [2]
Figure 2. NERVA Fuel Element. The NRX fuel
elements made with graphite uranium carbine
particles embedded in a graphite matrix for
support. [2]

3
The hydrogen propellant flowed through an inlet
channel in the moderator before penetrating the outer
edge of the cylindrical fuel element (called the cold
frit). The propellant directly cooled the particulate
fuel spheres before passing through the hot frit (the
inner diameter surface separating the particle bed from
the inner hollow region of the structure) where the
propellant, now a hot gas, would exit towards the
nozzle. By directly cooling the fuel elements, this
reactor design was capable of achieving much higher
temperatures, over 3000 K, as opposed to the NERVA
which was limited to 2650 K. [2] This design also
decreased overall system weight drastically from the
NERVA design by using the small fuel particles as
opposed to fuel rods. This made the PBR much more
ideal for launch vehicle upper stages. The overall
performance improvements compared to chemical
propulsion systems were dramatic, with payload mass
capabilities increased nearly two-to-four times what
current configuartions allowed. [4]
II. Nuclear Physics
A. Nuclear Fission
The subdivision of an atomic nucleus, such as that
of uranium or plutonium, is defined as nuclear fission.
The splitting of an atom can be induced by exciting the
nucleus to an energy equal to or greater than its fission
barrier or through excitation of the nucleus by the
bombardment of particle(s), typically nucleons
(protons or neutrons). [5]
Before beginning the fission process, consider the
forces that hold an atom together. The neutrons and
protons are held together by the strong nuclear force.
The electrons maintain their orbit around the nucleus
due to Coulomb forces, the electromagnetic force that
causes like charges to repel and opposite charges to
attract. [2]
Fission begins once a nucleon, typically a neutron,
breaks through the electron cloud and imparts energy
(between 0.25 eV to 10 MeV) upon the nucleus. The
additional neutron exerts enough energy on the
nucleus to cause it to split into two charged fragments.
These fragments separate to a distrance greater than
the range of the nuclear force, leaving Coulomb forces
to be the dominant force. This causes the fragments to
experience a large Coulomb repulsive force pushing
them further apart. The fragements will experience
velocity increases as they repel off other atoms, while
also exerting kinetic energy onto neighboring atoms
causing additional nuclei to split, eventually creating a
chain reaction effect of nuclei splitting. [2]
The division of the nucleus of an atom results in
the release of large amounts of energy. This energy
comes from the mass defect within the original
nucleus. The mass defect is the difference between the
actual mass of the nucleus and the sum of the masses
of the nucleons that make up the nucleus. In fact, the
sum of the masses of the nucleons is always greater
than the total mass for the nucleus for heavy atoms.
The mass defect can be calculated using the equation
below:
The mass defect is then converted into energy using
Einstein’s equation:
where c is the speed of light. The energy conversion
yields the total binding energy of the nucleus. The
release of the binding energy through fission causes
the average temperature of the radioactive material, or
fuel, to increase due to the collision and iteractions of
neutrons with other atoms and fragments. This
increase in temperature is the cornerstone for many of
the worlds nuclear devices and applications including
nuclear plants, military vessels, and, of course, the
nuclear thermal propulsion system. [2]
B. Reactor Control
After the fission process has started, control
mechanisms regulate the fission reactions to insure
criticality of the system. When the number of neutrons
being produced is constant (the rate of change of
neutron production is equal to zero), the reactor is said
to be in a critical state. If the criticality is not
controlled, radioactive fallout (beta and gamma rays
along with fission products) can increase to dangerous
levels and cause the fuel elements to melt. There are
two primary methods used for fission control:
moderators and control rods (drums). [2]
For a thermal nuclear reactive, fission is caused by
neutrons with energies at or below 1 MeV. The typical
Δ = [Z(mp + me )+ (A − Z)mn ]− matom
E = Δc2
Figure 3. Cross Sectional Views of the Fuel
Particle (left) and Fuel Element (right). The fuel
particles consisted of a uranium carbide core
surrounded by graphite with a zirconium carbine
exterior surface for protection against high heat.
[2]

4
fission process, however, produces neutrons with
energies much higher than 1 MeV (up to ~10 MeV).
In fact, for a uranium-235 atom, most neutrons
produced from fission fall within 1-5 MeV, as shown
in Fig. 4. Moderators help to slow down the neutrons
to correct operating levels. The moderator is made of
a low atomic mass material (beryllium, lithium
hydride, graphite) and envelops the radioactive fuel
creating a control blanket. [2]
Control rods assist in slowing down the fission
reaction by acting as “poisons”. Where moderators
assist in decreasing the kinetic energy of the neutrons
after the fission reaction, control rods can stop the
reaction altogether. The control rods are usually made
from boron, which has a high nuclear cross section,
and are dispersed symmetrically around the core to
insure that neutron absorbtion is adequate for fission
control. By controlling the fission process in such a
manner, the control rods can increase or decrease the
power level of the reactor simply by either being
removed or rotated outoff or away from the reactor for
an increase in power or by being inserted or rotated
into or towards the reactor for a decrease in power. For
the rotation method, a single control road would have
one side made of boron with the otherside my of a
reflective material such as beryllium. [2]
1. Nuclear Cross Sections
The nuclear cross section can be used to describe
the probability of a neutron interacting with the
nucleus of some material. Neutrons can interact with
a nucleus in one of three ways:
1) Scattering: the neutron impacts the nucleus,
transferring some or all of its kinetic energy,
before rebounding off in a different direction.
2) Absorption: the neutron can be absorbed into
the nucleus
3) Fission: the neutron has a sufficient kinetic
energy to split the nucleus
The nuclear cross section of a material can help
determine the probability of which interaction will
happen. The interaction concept depicted in Fig. 4.
The probability of the interaction of a neutron with a
nucleus can be described mathematically in terms of
the energy of the nucleus, in the following manner:
The relations above show that a probability of
interaction exists for all neutrons, with dependence
related to the target nucleus size and the energy of the
fissioned neutrons. A difference is made between
microscopic area and macroscopic area due to the
inability to precisely define the area of an atom. The
microscopic cross-section simply defines an “effective
area” that the neucleus will have the greatest
possibility of being located, whereas the macroscopic
is a relation to the probability of a neutron
encountering the nucleus of a material after traveling
some defined distance through it. [2]
C. Thermal Hydraulics
As the fission process begins heating up the fuel
particles, propellant flows through the moderator and
over the particles. The goal here is to transfer as much
heat from the fuel particles to the propellant as
possible. This achieves two goals:
1) As the cryogenic liquid hydrogen flows over
the particles, it extracts the heat from the
particles, maintaining a safe level within the
reactor to avoid melting the exterior shell as
well as the radioactive material.
Pi = nj
σi
j
(E)dx = (E)i
j
∑ dx
Figure 4. Neutron Energy from Fissioned U-
235. Most fissioned neutrons have energy leves
between 1 and 5 MeV. Moderators assist in
slowing down the neutrons for usability in a
thermal reactor. [2]
Figure 5. Neutron Cross Section. The neutron
cross section analogy is best represented by
imagining a slab of volume dAdx with some
neutron bombardment impacting its surface. [2]

5
2) The heat transfer from the fuel to the
propellant causes vaporization. The gas then
expands rapidly upon entering the gas flow
chamber and then exits the nozzle at a high
exit velocity.
It should be noted from the above points that in order
to insure the nuclear fuel particles do not reach their
melting point, a minimum heat transfer must be
achieved. Therefore, one key limiting factor in a
nuclear thermal propulsion device is what amount of
thermal energy can be transferred from the fuel
particles to the propellant, which is largely dependent
on the material used in the fuel element shell and the
moderator material, the surface area available for the
propellant to make contact with, and the flow rate of
the propellant through the moderator.
III. Particle-bed Reactor System Design
Designing a nuclear thermal rocket is simpler than
designing a liquid rocket in many aspects. Because
there is no combustion occurring within a nuclear
rocket, one does not need to concern themselves with
the many factors that must be considered in a liquid
propulsion system. The nuclear thermal rocket simply
heats the propellant from storage temperature to the
maximum chamber temperature, which ultimately
depends on the maximum temperature allowable by
the fuel and materials.
The key preliminary steps to designing a functional
nuclear thermal propulsion system are as follows:
1) Determine the gaseous properties in order
to choose the appropriate propellant.
2) Choose the expansion ratio that will
provide the level of Isp required for the
mission.
3) Calculate the propellant flow rate given
the Isp and required thrust level
4) Determine the required reactor power
needed to heat the propellant to the
necessary temperature to achieve the
required characteristic velocity.
5) Determine system pressure levels,
specifically pressure drops through the
core.
6) Calculate the reactor and core size.
While the above steps are not all-inclusive, they touch
on the major functional points of a nuclear thermal
propulsive device. The following will provide more
detail on particular steps. [2]
A. Gaseous Properties
The characteristic velocity for the system depends
soley upon the propellant molecular weight and
chamber temperature. The common choices for
propellants are listed below:
1) Hydorgen (H2) – 2.016 grams/mole
2) Methane (CH4) – 16.043 grams/mole
3) Carbon dioxide (CO2) – 44.01 grams/mole
4) Water (H2O) – 18.015 grams/mole
The specific heat ratio can be determined from the
molecular weight and specific heat of the propellant.
Figure 6 shows the specific heat distrubtion for a
temperature range of 300-3500K. [2]
The characteristic velocity for the various propellants
can be calculated using the specific heat ratio for each
with the equation below.
Taking the specific heat values as calculated before
gives a characteristic velocity trend as shown in Fig.
7. The data for the four common gases shows why
using a low molecular weight propellant offers the best
possibility for an increased Isp for a nuclear thermal
rocket. By having a reactor at a high thermal
temperature with a low molecular weight propellant,
the system can produce very high exit velocities and
ultimately increase the specific impulse greatly above
what is achieveable by chemical propulsion rockets.
[2]
c* =
γ RT0
γ
2
γ +1
⎛
⎝⎜
⎞
⎠⎟
γ +1
2 γ −1( )
Figure 6. Cp as a Function of Temperature for
Various Gases. The specific heat values for the
common nuclear thermal propulsion system
propellants. Hydrogen has a much greater
specific heat compared to the others.

6
B. Required Reactor Power
A simplified version of the first law of
thermodynamics can provide the required reactor
power in order to increase the temperature of a fluid
(in a liquid state) to some temperature given a
specified mass flow rate. The equation to calculate
core power is given below:
In Space Propulsion Analysis and Design, the authors
provide a useful chart showing the correlation between
desired temperature of the propellant and specific
reactor power. This chart is provided in Fig. 8. It
should be noted that hydrogen requires the most
specific power to increase its thermal energy;
however, because of the high specific impulse it
generates, the mass flow rate is lower than compared
to the other propellants, required less reactor power
overall. [2]
C. Reactor Sizing
Using all the information discussed so far, a
simplified assessment of the reactor size can be
calculated. Typical reactor sizing depends on the type
of reactor under analysis, but generally requires a
detailed examination of thermal hydraulics, control
rod effects, Doppler feedback, and many other factors.
A lumped-parameter approach is typically used for
simplification purposes by assuming the reactor to be
homogenous (no variation in power distribution and
performance through the core). However, for the
particle-bed reactor, this generalization does not hold
true due to the disperision of fuel particles within the
system.
Instead, for this discussion, a parametrix analysis
of Fig. 9 below can be done to determine reactor
sizing. Figure 9 was developed by Ronald W. Humble
and coauthors for Space Propulsion Analysis and
Design and is based off a Los Alamos National
Laboratory (LANL) code derived empirically from a
Los Alamos particle-bed reactor. Using the calculated
reactor power from previous discussions, one can
simply use the graph to determine the radius and
height required for the core. The curve equations for
replication of the graph are provided in the appendix.
Pcore = !mprop hv + cp dT
T1
T2
∫( )= !mpropP
Figure 7. Characteristic Velocity as a function
of temperature. Hydrogen, having the lowest
molecular weight and highest specific heat, has the
highest characteristic velocity.
Figure 8. Reactor Power Required for a Given
Propellant Temperature. Given a required
propellant temperature, the required specific
reactor power can be determined from which the
necessary reactor power for a given mass flow rate
can be calculated. [2]

7
In the case where two solutions are possible for a given
reactor power, the best solution is typically the core
with the smallest radius, which minimizes the required
radiation shield size. [2]
Once the reactor size has been determined, the
mass of the core can be calculated. To calculate the
mass of the core, the overall core density is multiplied
by the core volume. Although this method is not
precise, the results are generally close, within 90%.
The reason for the inaccuracy is based on the nature of
the particle-bed reactor. The PBR has very complex
geometries such as fuel particle size, distance between
the fuel particles, and the makeup of the material. [2]
For calculation purposes, the core is considered to
be cylindrical; in relation to PBR fuel particles, this is
applicable for if the particles were packed into a
cylindrical container (which is basically the overall
design of the reactor itself). The volume of the core
can be calculated using the equation below:
The mass of the core can then be calculated using the
core density, which for a PBR is typically ~1,600
kg/m3
. [2]
This mass calculation provides the total mass for the
entire reactor, including plumbing, moderators,
control rods, and other components, except for the
propellant tank. Figure 10 shows a comparision of
reactore core mass of a particle-bed reactor compared
to two other nuclear thermal propulsion systems:
NERVA and CERMET. The PBR is approximately
five to six times less in mass then the NERVA. This
is because the NERVA uses a fuel rod configuration.
The power density is much less than the PBR which
requires more hardware to increase the temperature of
the propellant. Comparably, the PBR is two to four
times less in mass than the CERMET, except for
powers below 1000 MW, where mass differences are
below ~100 kg. The figure also shows the differences
in the number of fuel elements chosen for the PBR
system. The three element configurations (7, 19, and
37) are restrictive to a certain range of power output
by the reactor. The 37 fuel element configuration can
operate in the greatest range of powers, from ~600-
2000 MW. [2]
IV. Analysis of the SNTP Program
The Space Nuclear Thermal Propulsion Program,
started in 1987, was a follow-up to the NERVA
program which ended over a decade before. The
SNTP’s goals were to:
1) Verify the feasibility of a particle-bed
reactor as a propulsion source for an
upper stage launch vehicle
2) Perform ground demonstration tests of
the PBR design
3) Launch a PBR nuclear thermal stage
using an Atlas IIas launch vehicle
The program partially completed the second phase of
the program (ground demonstration) before being
terminated in January 1994. [4]
During the program, many significant
advancments in terms of nuclear thermal propulsion
were accomplished, including:
1) Identified missions that were enabled or
enhanced based on SNTP performance
Vcore = πRcore
2
Hcore
mcore = ρcoreVcore
Figure 9. Reactor Core Sizing. The radius and
height of a core can be determined based on the
required reactor power for the system, as well as
the number of fuel elements required for the
system, based on criticality constraints. [2]
Figure 10. Reactor Mass Comparison. The
particle-bed reactor outperforms all other nuclear
thermal propulsion systems except at low power
outputs, where the CERMET has the lower mass.
[2]

8
2) An engine was designed with a specific
impulse of 930 seconds and a thrust-to-
weight ratio of 20:1
The original performance goal for the program was to
have an egine that could achieve a specific impulse of
1000 s with a thrust-to-weight ratio ranging from 25:1
to 35:1 (88-355 kN); however, additional safety
criteria and a desire for a system that could be restarted
multiple times caused the decrease in performance to
just 20:1, which still outperformed the NERVA by
four times. [4]
A. Sizing the SNTP System
The SNTP program developed a preliminary
engine design by selecting the following initial
properties: thrust of 178 kN (Isp = 930 s) with a reactor
power of 1000 MW that used liquid hydrogen as the
propellant. All engine designs also made us of a thirty-
seven fuel element configuration to take advantage of
the larger operating power range. An engine of this
design would have the following properties:
Comparison of these calculations to the actual engine
are within a few percent difference. The final iteration
of the “LV03” engine had a total core assembly mass
of 475 kg. Figure 11 provides a schematic of the side
profile of the engine. [4]
The overall mass of the system came in to 910 kg,
including reactivity controls, nozzle assembly, and
instrumentation. The final thrust-to-weight ratio was
21:1. [4]
B. Reactor System
The reactor system for the SNTP engine had the
following requirements:
A trade study was performed between a bleed cycle
system and a partial-flow expander cycle system. This
greatly affected the materials that would be used for
the construction of the propulsion system as a whole.
The trade study results are provided below. [4]
1. Fuel Particles and Elements
One of the major efforts of the SNTP program was
to develop a fuel particle that woulc withstand the high
temperatures produced in a particle-bed reactor
system. The particle would need to operate in the
range of 3100-3500 K in order to produce an exhaust
gas temperature of ~3000 K. The program ended up
zeroing on a mixed-carbide nuclear fuel particle that
could withstand temperatures up to 3200 K. However,
before the end of the program, it was discovered the
Table 1. Preliminary Design Configuration
for SNTP Engine
Properties Design
Mass flow rate 19.5 kg/s
Radius of Core 40 cm
Height of Core 62 cm
Volume of Core 311,646 cm3
Mass of Core 499 kg
Figure 11. SNTP Engine “LV03”. [4]
Table 2. SNTP Reactor Requirements
Power 1000 MW
Outlet Temperature 3000 K
Outlet Pressure 6.89 MPa
Firing Time 600 sec
Table 3. Design Characteristics based on the
Type of Cycle.
Bleed Cycle
Partial Flow
Expander
Cycle
Reactor
Power (MW)
1000 1000
Engine
Thrust (kN)
184 185
Isp (s) 930 935
Reactor:
Reflector Beryllium Beryllium
Moderator Be/Li-7H Be/Li-7H
Turbine:
Material
Carbon-
Carbon
Titanium
Inlet Press
(MPa)
5.8 15.7
Inlet Temp
(K)
2750 375
Nozzle:
Material
Filament
Wound C-C
Filament
Wound C-C
Exit Area
Ratio
100 100

9
Soviet Union, under the Nuclear Rocket Engine
(NRE) program had developed a mixed-carbide fuel
capable of 3500 K. The SNTP team was unable to
reproduce this before the program was terminated. [4]
The fuel elements consisted of hot and cold frits
that contained the nuclear particles and controlled the
flow of liquid hydrogen over the fuel bed. The
moderator “moderated” the production of neutorns to
maintain structural integrity of the reactor and to avoid
overheating. The cold frits were made out of stainless
steel while the hot frits were made of a combination of
graphite and nurobium-carbide. During test, fractures
were found in the hot frit, which under a post-test
analysis, were found to be due to large temperature
gradients within the moderator causing by a movement
of fuel particles. The cold frit also suffered
deformations to the maximum extent. [4]
C. Mission Applications
The SNTP program performed mission design
analysis for a nuclear propulsion system using the
particle-bed reactor and showed that the PBR offered
great improvements over current capabilities for
second stage, chemically propelled systems. Payload
improvements varied from 1.5 to 4 times greater than
conventional systems. The program also showed
greater financial savings by utilizing the PBR design.
The higher payload capabilities meant smaller first
stages could be used to deliver payloads to orbits that
would conventionally require much larger systems. [4]
The program looked at a multitude of launch
systems and developed variations of each based on
sub-orbital ignition and orbital ignition. The vehilces
of primary focus were based the Atlas IIE for
suborbital insertion, Titan for orbital ignitions, and
Minutemen for intercontinental ballistic applications.
Figure 12 shows an overview off all different
configurations along with payload capabilities for
each. [4]
V. Conclusion
Nuclear thermal propulsion has great advantages
over conventional, chemically based propulsion
systems. Nuclear thermal designs allow for greater
efficiencies in terms of specific impulse, as well as
simpler overall vehicle configuartions. The nuclear
propulsion system also have the ability of sustaining
large thrust-to-weight ratios, ranging from 5:1 – 35:1,
making them viable as full-stage propulsion systems
and not just for orbital transfers. The high efficiencies
and thrust-to-weight ratios attest that the system can
satisfy most mission requirements, while also
decreasing mission lengths substantially, sometimes
by half.
The past half-century has proven the viability of a
nuclear thermal propulsion system, from the NERVA
program in the 60s and 70s, to the SNTP program at
the end of the 20th
century. And of the nuclear
propulsion systems, the PBR has exhibited
performance characteristics do not have to be
sacrificed in order to achieve significant efficiency
increases. The SNTP program is a testament to this,
showing that the PBR system can increase the
capabilities of human-space flight reliably, with higher
performance than any other system, while still
maintaining strict safety guidelines and cost effective
methods.
In order for human exploration to move beyond the
moon and into deeper areas of our solar system, and
even possibliy beyond, nuclear thermal propulsion
technology must be considered a critical component of
the next phase of launch vehicle development.
Figure 12. SNTP Upper Stage Applications. [4]

10
Appendix
Curve fits for replication of the particle-bed reactor dimension (specifically, the radius and height) based on the
number of fuel elements to be used in the reactor. These equations are curve first for the Los Alamos design code, as
presented in Fig. 9.
For 7 Elements:
For 19 Elements:
For 37 Elements:
Rcore = 9.0958(10)−10
Pcore
4
−1.3261(10)−6
Pcore
3
+ 7.1665(10)−4
Pcore
2
− 0.1735Pcore + 47.625
Hcore = −0.000283Pcore
2
+ 0.5203Pcore + 26.06
Rcore = −2.655(10)−12
Pcore
5
+ 8.846(10)−9
Pcore
4
−1.1703(10)−5
Pcore
3
+ 7.427(10)−3
Pcore
2
− 2.2955Pcore + 313.34
Hcore = −4.027(10)−5
Pcore
2
+ 0.1427Pcore +17.9883
Rcore = 4.905(10)−11
Pcore
4
− 2.881(10)−7
Pcore
3
+ 6.2522(10)−4
Pcore
2
− 0.5992Pcore + 252.28
Hcore = −6.502(10)−6
Pcore
2
+ 0.05009Pcore +18.335

11
References
[1] K. Grinter, "A Brief History of Rocketry," [Online]. Available: http://www-pao.ksc.nasa.gov/history/rocket-
history.htm. [Accessed 1 May 2016].
[2] R. W. Humble, G. N. Henry and W. J. Larson, Space Propulsion Analysis and Design, McGraw-Hill, 1995.
[3] W. H. Robbins and H. B. Finger, "An Historical Perspective of the NERVA Nuclear Rocket Engine
Technology Program," NASA, Cleveland, 1991.
[4] R. A. Haslett, "Space Nuclear Thermal Propulsion Program," Grumman Aerospace Corporation, Bethpage,
1995.
[5] E. P. Steinberg, "Nuclear Fission," Encyclopædia Britannica, [Online]. Available:
http://www.britannica.com/science/nuclear-fission. [Accessed 2 May 2016].

Nuclear Thermal Propulsion Using a Particle-Bed Reactor

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