# The Nuclear Rocket

Rocket science deserves its reputation as a subject that only geniuses dare study. Modern rockets are immensely complex systems that push the limits of aeronautics, chemistry, materials science, and engineering. But at the same time, the basic physics of rockets is simple enough for a college freshman to grasp. It does not take a rocket scientist to understand how a rocket works.

A rocket produces thrust by expelling matter at high velocities. It does not take a rocket scientist to recognize that the momentum of the rocket-fuel system is conserved. Therefore, if the fuel is expelled at a rate -dm/dt with speed vex, a corresponding recoil force F = -vexdm/dt acts back the rocket, accelerating it in a direction opposite the exhaust flow. Integrating Newton's Second Law over time, one finds a relation between the velocity boost and the mass loss:

Δv = vex log(m0/m)

Here m0 is the launch mass of the rocket (payload plus fuel), while m is the mass of the payload. The required boost Δv depends on the specific mission, and usually varies between 8–20 km/s. With such high boost velocities, the logarithm in Equation (1) does not bode well. For a fixed exhaust velocity and payload mass, the launch mass increases exponentially with Δv. It took a three-hundred foot Saturn rocket to send three astronauts to the moon and back; for a mission to Mars, the dimensions grow even more staggering. It does not take a rocket scientist to recognize that simply making bigger rockets will not get us to Mars.

MissionDurationΔv
Low-Earth OrbitVaries8 km/s
Moon Landing6 days12 km/s
Mars Mission2-3 years22 km/s
Table 1: Required boost velocities Δv for various space missions.

It is possible, of course, to increase the exhaust velocity, but with a conventional (chemical) rocket, this approach only goes so far. The chemical reaction between the fuel and oxidizer heats up the propellant, and the ensuing thermal energy is converted into kinetic energy of the exhaust. In an ideal rocket, the conversion efficiency is 100%, and the exhaust velocity is:

vex = (2E/m)1/2

where E/m is the energy density – the energy per unit mass released in the chemical reaction. Naturally, one wants to pick fuels that maximize the energy density; it turns out that hydrogen and oxygen are as good as you can get. This sets a limit to the exhaust velocity of vex < 4.5 km/s. This is not good news for deep-space explorers. With an exhaust velocity limited to 4.5 km/s, the launch mass of a moon rocket will be at least 15 times the size of its payload, and for a Mars rocket, the ratio is around 100:1. Missions to the outer planets are staggeringly more expensive.

The rocket equations stem from fundamental laws of physics – namely, energy and momentum conservation. No amount of hard work or ingenuity can circumvent them. It does not take a rocket scientist to recognize that deep space travel requires something beyond conventional chemical rockets.

## Nuclear Trumps Chemical

The obvious solution to the energy-density problem is to use nuclear power. Uranium has an energy density a million times greater than hydrogen fuel. This raises the maximum exhaust velocity to around 5,000 km/s. However, it so happens that converting fission products into thrust is not easy, and most practical nuclear rocket concepts have an exhaust velocities much smaller than the upper limit. Of these concepts, only one – the Nuclear Thermal Rocket – has ever been built and tested.

 Fig. 1: Schematic of a nuclear thermal rocket. Propellant enters through the turbopump on the right, is sent through passages in the reactor, and expelled out the nozzle. Credit: CommiM, Wikipedia [c].

The Nuclear Thermal Rocket consists of a high-temperature nuclear reactor with a series of thin channels for the propellant, as shown in Figure 1. The reactor is run as hot as practically possible, usually around 2500-2800 °K, just below the melting point of the fuel [9]. Hydrogen gas is used as a propellant because its low molecular mass enables it to be expelled at very high speeds. The propellant is sent through the channels and heated to the temperature of the reactor, and thereafter expelled through the rocket nozzle. Using the heat capacity of hydrogen, it is easy to compute the energy density of the fuel [a], and consequently the exhaust speed, which is plotted in Figure 2.

 Fig. 2: Plot of the maximum hydrogen exhaust speed as a function of reactor temperature [b].

For a reactor operating at 3000 °K, the propellant will be expelled at a speed of 10 km/s. This is far from the theoretical maximum of 5,000 km/s, but nevertheless is more than twice the exhaust speed of the best conventional rockets. Thanks to the logarithm in Equation (1), this doubling works substantial changes in the mass ratio of liftoff to payload mass; for a nuclear-powered lunar mission, the mass ratio is reduced from 15:1 to around 4:1, while for a Mars mission, it drops from 100:1 to 10:1. The impossible becomes possible.

There is another, simpler way to arrive at this factor of two. The velocity of the rocket propellant scales as vex ~ (T/m)1/2, where T is the propellant temperature and m is its molecular mass. In a chemical hydrogen-oxygen rocket, T ~ 6000 °K and m = 18 amu. For a nuclear rocket, the temperature is halved (T ~ 3000 °K), but the mass drops by a factor of nine (m = 2 amu), so the quotient increases by about a factor of four, doubling the exhaust speed.

## Engineering Considerations

### Temperature and Density

Rocket reactors differ from power plant reactors in two main respects: their temperature and their power density. In order to beat their chemical competitors, a nuclear rocket must operate at very high temperatures. At the same time, it must be extremely light and compact, so as not to weigh down the spacecraft it is launching. These requirements pose a unique set of challenges that the rocket scientist must address when designing the reactor.

 Fig. 3: Cross-sectional view of fuel elements for the experimental NERVA reactor. Credit: NASA [d].

Obviously, the reactor should be designed to run at the hottest temperature possible, i.e. just below the melting point of the fuel elements. The fuel of choice is typically highly enriched uranium carbide, a hard ceramic material that melts at 3100 °K, and the reactor itself is typically run at 2500–2800 °K. The fuel is dispersed within a matrix of graphite, chosen because it is one of the few moderators that can withstand the extreme temperatures. (Certain metallic carbides can also be used as a reactor material, although many are neutron-absorbing and thus necessitate that the rocket be run as a fast reactor [9].)

Graphite, however, has one major limitation: at the extreme temperatures involved, it is quickly corroded by the hydrogen propellant to produce hydrocarbons. This problem can be overcome (or at least mitigated) by lining the propellant channels with a thin layer of metallic carbide, NbC being used in test reactors in the 1960's [5]. The carbide slows, but does not stop, the corrosion, allowing test reactors to run for as long as 100 minutes [2].

Compactness mandates that the reactor run at a power density far above that of a power plant. During America's nuclear rocket program, the record average power density was set by the Pewee reactor (2.34 GW/m3) [2], and some more advanced reactor concepts work at upwards of 40 GW/m3 [8]. To maximize the power density, one uses highly enriched uranium fuel [6] and surrounds the reactor with a neutron reflector [8].

 Fig. 4: Reactor failure test KIWI-TNT. Credit: NASA [d].

While the rocket is designed to avoid radioactive leakage products, inevitably a small amount of radioactive waste will make it into the rocket's exhaust [6]. This, in addition to the fear of a Chernobyl-like rocket meltdown, has led many to believe that nuclear rockets should not be operated in the Earth's atmosphere. Even so, a reactor meltdown was simulated in the KIWI TNT test in 1965, and the radioactive fallout was not significant [5]. Moreover, the control rods can be fixed during launch, rendering the nuclear reactor safely subcritical even in the event or a launch abort [2].

Protecting the crew from radiation is as important as preventing a nuclear meltdown. Neutron shielding, which can weigh several tons, must be installed between the reactor and the crew, and the distance between the two should be maximized to take greatest advantage of the fact that radiation flux falls off with the square of the distance. Placing the fuel tanks between the crew and the rocket is a very effective way to shield the crew, since hydrogen makes an excellent neutron scatterer [8].

Paradoxically, a well-shielded nuclear rocket will on the whole decrease the crew's radiation exposure for long missions. This is because the nuclear rocket, with its larger exhaust velocity, can complete the journey more quickly. Space, not the reactor, is the primary radiation concern. As Table 2 demonstrates, the key to reducing radiation exposure is to limit mission time, which is one thing nuclear rockets are particularly well-suited to do [8].

Radiation Source Chemical Rocket (433 day) Nuclear Rocket (316 day)
Van Allen Belts2 rem2 rem
Mars Surface1 rem1 rem
Van Allen Belts2 rem2 rem
Solar Flares26 rem15 rem
Reactor0 rem5 rem
Total60 rem45 rem
Table 2: Radiation Exposure for two comparable mars missions with comparable liftoff mass and payload mass. The nuclear rocket reduces exposure by taking a shorter trip with a higher Δv. See Ref. [8].

## Project Rover

America's nuclear rocket program, Project Rover, was established in 1955 and ran for nearly two decades until its cancellation in 1972. Rover was operated from Los Alamos Scientific Laboratory (today LANL) under the direction of NASA [6]. Rover demonstrated that a nuclear rocket was indeed viable with 1960's technology, but for a variety of reasons, it was canceled and has been largely ignored since.

 Fig. 5: List of important reactor tests conducted during the Rover program [d]. See Ref. [3].

The first reactors built were the KIWI reactors: a series of non-flyable engines designed to test the physics of hydrogen-cooled reactor designs. KIWI-A operated at a modest 100 MW, and its successor KIWI-B ran at a ten times this power. However, a faulty design feature caused the reactor to vibrate uncontrollably and the device had to be reconfigured. Later tests, however, conclusively proved that nuclear rocketry could be feasible.

The NERVA reactor line built on the knowledge rained from KIWI, but was designed to be a fully functional rocket engine rather than a scientific prototype. The goal was a 1 MN thruster, but due to budget cuts in the late 1960's, it was scaled it down a 330 kN version. Tests began in 1964 and culminated in the 244 kN XE' engine tested just before the program's cancellation. In parallel with NERVA, Los Alamos continued to experiment on more advanced rocket prototypes, including PHOEBUS, which was intended to scale up KIWI; and Pewee, which focused on small, high-power-density engines with advanced fuel elements.

In 1961, noting Project Rover's rapid progress, NASA considered replacing the upper J-2 stage of the Saturn rocket with a nuclear engine [7]. Such an engine could reduce the mass of the stage by up to 30% [1]. However, instabilities in the early Kiwi engines caused serious concern that the nuclear technology was not yet viable, and in 1963 NASA chose to use a chemical upper stage instead, deferring indefinitely plans to test an in-flight nuclear rocket [6]. By the time NERVA had built a viable, flight-ready nuclear rocket, we had landed a man on the moon and the space race was over. In 1972, facing budget cuts in the wake of the Vietnam War, Project Rover came to an end.

QuantityRecordTestYear
Power4.1 GWPhoebus-2A1968
Thrust930 kNPhoebus-2A1968
vex8280 m/sPewee-11968
Specific Power0.43 MW/kgPhoebus-2A1968
Avg. Power Density2.34 GW/m3Pewee1968
Peak Power Density4.5 GW/m3NF-11972
Runtime109 minNF-11972
Repeatability28 restartsXE'1969
Table 4: Performance records set by the reactors tested during the Rover program. See Ref. [2].

While the NERVA program created a tested, flight-ready rocket engine with 1960's technology, it is has several limitations. For one, the exhaust velocity, while much greater than a chemical rocket, is far less than theoretically possible. In addition, the thrust-to-weight ratio (4:1) is marginal [8]. More advanced concepts have been considered to overcome NERVA's limitations, but none have been developed into a working model.

Two of the most promising solid-core alternatives are the Particle Bed reactor, designed for the Air Force's Space Nuclear Thermal Propulsion Program, and the CERMET reactor, also developed by the Air Force. The particle bed design contains the fuel in a dispersion of 1-mm particles cooled by a flow of hydrogen propellant. Due to the increased surface area, the reactor can operate at over 5 times the power density of NERVA, achieving a thrust-to-weight ratio of 20:1. The CERMET reactor, by contrast, looks much more like NERVA but operates as a fast reactor. Its chief advantage is robustness and longevity; since it does not require a graphite moderator, it does not suffer the corrosion problems that plague NERVA. It is believed that the CERMET engine could burn for as long as 40 hours. Such a reactor would be advantageous for a refuelable earth-to-moon "ferry" or a reusable Mars rocket [4, 8].

Liquid-core and gas-core nuclear reactors have been considered to raise the fuel temperature above 3000 °K and increase the propellant velocity beyond the 10 km/s limit for solid-core reactors. Such designs are not yet feasible with current technology and pose many unanswered physics and design questions, but offer the potential of dramatically reduced mission times and liftoff-to-payload mass ratios. One such concept, the Open Cycle Gas Core Reactor, is shown in the figure below.

 Fig. 6: Seceral advanced nuclear rocket concepts considered in a 1991 space exploration technology review. From Left to Right: Particle Bed Reactor, CERMET Fast Reactor, Open-Cycle Gas Core Reactor [d]. See Ref. [4].

## To Mars and Beyond

On April 15, President Obama outlined a new vision for manned deep-space exploration. By 2025, man is to set foot on a near-Earth asteroid for the first time in history, paving the way for a much longer Martian expedition in the mid-2030's. But will America put forward the resources needed to accomplish this extraordinary challenge? With conventional technology, such a mission would take at least two years and require tens if not hundreds of billions of dollars. The answer, consequently, is "no". This is not a lack of "vision"; it is an exercise in economy. Those billions could be better spent elsewhere.

Will nuclear propulsion change this? No one can be sure. The physics is sound. The technology is tested. Project Rover died with the space race, but if that race is ever rekindled, perhaps we will consider bringing it back.

© Ryan Hamerly. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

## Notes

[a] Strictly speaking, the exhaust velocity is limited by the specific enthalpy of the fuel, not the energy density. This comes from Bernoulli's Law, which states that along laminar flows, the quantity h + v2/2 is conserved. However, in a nuclear rocket, the fuel is heated at quasi-constant pressure, so the enthalpy increase equals the energy injected into the fuel by the reactor, and so energy conservation is not violated.

[b] Computed by taking vex = (2h)1/2, where the specific enthalpy h is obtained by integrating the constant-pressure heat capacity from zero to the desired temperature.

[c] Licensed under the GNU FDL 1.2

[d] Unless otherwise noted, NASA material is not copyrighted.

## References

[1] S. Borowski, R. Corban, M. McGuire, & E. Beke, "Nuclear Thermal Rocket / Vehicle Design Options for Future NASA Missions to the Moon and Mars", in Space Programs and Technologies Conference and Exhibit (Huntsville, AL, 21-23 Sep. 1993). ADS: 1995STIN...9611955B

[2] D. Buden, Acta Astronomica 18: 217-24 (1988). DOI:10.1016/j.physletb.2003.10.071

[3] J. S. Clark & T. J. Miller, "Nuclear Rocket Propulsion: NASA Plans and Progress – FY 1991", in Proceedings of the 26th Intersociety Energy Conversion Engineering Conference (Boston, MA, 4-9 Aug. 1991). ADS: 1991iece....1..391C

[4] J. S. Clark, P. McDaniel, S. Howe, I. Helms, & M. Stanley, Nuclear Thermal Propulsion Technology: Results of Interagency Panel in FY 1991 (unpublished). OSTI ID: 6151799

[5] L. C. Corrington, J. Spacecraft Rockets 6: 465-70 (1969). OSTI ID: 4768861

[6] J. L. Finseth, Overview of Rover Engine Tests: Final Report, 1991 (unpublished).

[7] P. G. Johnson, "Nuclear Rocket Applications", in Astronautics (December 1962).

[8] T. J. Lawrence, "Nuclear-Thermal-Rocket Propulsion Systems", in Nuclear Space Power and Propulsion Systems, ed. C. Bruno (2008).

[9] R. W. Spence, Science 160: 3831, 953-9 (1968). ADS: 1968Sci...160..953S