Definitions

# Nuclear thermal rocket

In a nuclear thermal rocket a working fluid, usually hydrogen, is heated to a high temperature in a nuclear reactor, and then expands through a rocket nozzle to create thrust. The nuclear reactor's energy replaces the chemical energy of the reactive chemicals in a traditional rocket engine. Due to the higher energy density of the nuclear fuel compared to chemical ones, about 107 times, the resulting efficiency of the engine is at least twice as good as chemical engines even considering the weight of the reactor, and even higher for advanced designs.

A nuclear engine was considered for some time as a replacement for the J-2 used on the S-II and S-IVB stages on the Saturn V and Saturn I rockets. Originally "drop-in" replacements were considered for higher performance, but a larger replacement for the S-IVB stage was later studied for missions to Mars and other high-load profiles. Likewise the Soviets studied nuclear engines for their own moon rockets, notably upper stages of the N-1. However, neither design had progressed to the point where they were ready to test before the space race was ostensibly over.

To date, no American nuclear thermal rocket has flown, or even reached a stage of development where it could be. The Russian nuclear thermal rocket RD-0410 was flown in 1985.

## Theoretical designs

A nuclear thermal rocket can be categorized by the construction of its reactor, which can range from a relatively simple solid reactor up to a much more complicated but more efficient reactor with a gas core.

### Solid Core

The most traditional type uses a conventional (albeit light-weight) nuclear reactor running at high temperatures to heat the working fluid that is moving through the reactor core. This is known as the solid-core design, and is the simplest design to construct.

The solid-core has the downside that it can only be run at temperatures below the melting point of the materials used in the reactor core. Since the efficiency of a rocket engine is strongly related to the temperature of the working fluid, the solid-core design needs to be constructed of materials that remain strong at as high a temperature as possible. Even the most advanced materials melt at temperatures below that which the fuel can actually create, meaning that much of the potential energy of the reactions is lost. Usually, with hydrogen propellant the solid-core design is expected to deliver specific impulses (Isp) on the order of 800 to 900 seconds, about twice that of liquid hydrogen-oxygen designs such as the Space Shuttle main engine. Other propellants are sometimes proposed such as water or LOX; although they would provide reduced performance, their greater availability can reduce payload costs where the mission delta-v is not too high, for example within cislunar space or between Earth orbit and Martian orbit.

The weight of a complete nuclear reactor is so great that solid-core engines would be hard-pressed to achieve a thrust-to-weight ratio of 1:1, which would be needed to overcome the gravity of the Earth on launch. Nevertheless the overall weight of the engine and fuel for a given amount of total impulse is lower. This means that solid-core engines are only really useful for upper-stage uses where the vehicle is already in orbit, or close to it, or launching from a lower gravity planet, moon or minor planet where the required thrust is lower. To be a useful Earth launch engine, the system would have to be either much lighter, or provide even higher specific impulse. Both would, of course, be even better.

One way to increase the temperature, and thus the specific impulse, is to isolate the fuel elements so they no longer have to be rigid. This is the basis of the particle-bed reactor, also known as the fluidized-bed, dust-bed, or rotating-bed design. In this design the fuel is placed in a number of (typically spherical) elements which "float" inside the hydrogen working fluid. Spinning the entire engine forces the fuel elements out to walls that are being cooled by the hydrogen. This design increases the specific impulse to about 1000 seconds (9.8 kN·s/kg), allowing for thrust-to-weight ratios just over 1:1, although at the cost of increased complexity. Such a design could share design elements with a pebble-bed reactor, several of which are currently generating electricity.

### Liquid Core

Dramatically greater improvements can be had by mixing the nuclear fuel into the working fluid, and allowing the reaction to take place in the liquid mixture itself. This is the basis of the so-called liquid-core engine, which can operate at higher temperatures beyond the melting point of the nuclear fuel. In this case the maximum temperature is whatever the container wall (typically a neutron reflector of some sort) can handle, while actively cooled by the hydrogen. It is expected that the liquid-core design can deliver performance on the order of 1300 to 1500 seconds (12.8–14.8 kN·s/kg).

These engines are difficult to build however; the reaction time of the nuclear fuel is much higher than the heating time of the working fluid, meaning that some system must be used to trap the fuel inside the engine while still allowing the working fluid to easily exit through the nozzle. Most liquid-phase engines have focused on rotating the fuel/fluid mixture at very high speeds, forcing the fuel to the outside due to centrifugal force (uranium is heavier than hydrogen). In many ways the design mirrors the particle-bed design, although operating at even higher temperatures.

An alternative liquid-core design, the nuclear salt-water rocket has been proposed by Robert Zubrin. In this design, the working fluid is water, which serves as neutron moderator as well. The nuclear fuel is not retained, drastically simplifying the design. However, by its very design, the rocket would discharge massive quantities of extremely radioactive waste and could only be safely operated well outside the earth's atmosphere and perhaps even entirely outside earth's magnetosphere.

### Gas Core

The final classification is the gas-core engine. This is a modification to the liquid-core design which uses rapid circulation of the fluid to create a toroidal pocket of gaseous uranium fuel in the middle of the reactor, surrounded by hydrogen. In this case the fuel does not touch the reactor wall at all, so temperatures could reach several tens of thousands of degrees, which would allow specific impulses of 3000 to 5000 seconds (30 to 50 kN·s/kg). In this basic design, the "open cycle", the losses of nuclear fuel would be difficult to control, which has led to studies of the "closed cycle" or nuclear lightbulb engine, where the gaseous nuclear fuel is contained in a super-high-temperature quartz container, over which the hydrogen flows. The closed cycle engine actually has much more in common with the solid-core design, but this time limited by the critical temperature of quartz instead of the fuel stack. Although less efficient than the open-cycle design, the closed-cycle design is expected to deliver a rather respectable specific impulse of about 1500-2000 seconds (15–20 kN·s/kg).

## Practical testing

Although engineering studies of all of these designs were made, only the solid-core engine was ever built. Development of such engines started under the aegis of the Atomic Energy Commission in 1956 as Project Rover, with work on a suitable reactor starting at LANL. Two basic designs came from this project, Kiwi and NRX.

Kiwi was the first to be fired, starting in July 1959 with Kiwi 1. The reactor was not intended for flight, hence the naming of the rocket after a flightless bird. This was unlike later tests because the engine design could not really be used, the core was simply a stack of uncoated uranium oxide plates onto which the hydrogen was dumped. Nevertheless it generated 70 MW and produced an exhaust of 2683 K. Two additional tests of the basic concept, A' and A3, added coatings to the plates to test fuel rod concepts.

The Kiwi B series fully developed the fuel system, which consisted of the uranium fuel in the form of tiny uranium dioxide (UO2) spheres embedded in a low-boron graphite matrix, and then coated with niobium carbide. Nineteen holes ran the length of the bundles, and through these holes the liquid hydrogen flowed for cooling. A final change introduced during the Kiwi program changed the fuel to uranium carbide, which was run for the last time in 1964.

Using information developed from the Kiwi series, the Phoebus series developed much larger reactors. The first 1A test in June 1965 ran for over 10 minutes at 1090 MW, with an exhaust temperature of 2370 K. The B run in February 1967 improved this to 1500 MW for 30 minutes. The final 2A test in June 1968 ran for over 12 minutes at 4,000 MW, the most powerful nuclear reactor ever built. For contrast, the largest hydroelectric plant in the world, Itaipu, produces 12,600 MW, 25% of all the power used in Brazil.

A smaller version of Kiwi, the Peewee was also built. It was fired several times at 500 MW in order to test coatings made of zirconium carbide (instead of niobium carbide) but also increased the power density of the system. An unrelated water-cooled system known as NF-1 (for Nuclear Furnace) was used for future materials testing.

While Kiwi was being run, NASA joined the effort with their NERVA program (Nuclear Engine for Rocket Vehicle Applications). Unlike the AEC work, which was intended to study the reactor design itself, NERVA was aiming to produce a real engine that could be deployed on space missions. A 75,000 lbf (334 kN) thrust baseline design was considered for some time as the upper stages for the Saturn V, in place of the J-2s that were actually flown. Eugene F. Lally of the Jet Propulsion Laboratory had published proposals of manned Mars missions based on this technology in the early 1960s.

The design that eventually developed, known as NRX for short, started testing in September 1964. The final engine in this series was the EX, which was the first designed to be fired in a downward position (like a "real" rocket engine) and was fired twenty-eight times in March 1968. The series all generated 1100 MW, and many of the tests concluded only when the test-stand ran out of hydrogen fuel. EX produced the baseline 75,000 lbf (334 kN) thrust that NERVA required.

All of these designs also shared a number of problems that were never completely cured. The engines were also quite easy to break, and on many firings the vibrations inside the reactors cracked the fuel bundles and caused the reactors to break apart. This problem was largely solved by the end of the program, and related work at Argonne National Laboratory looked promising. However, while the graphite construction was indeed able to be heated to high temperatures, it likewise eroded quite heavily due to the hydrogen. The coatings never wholly solved this problem, and significant "losses" of fuel occurred on most firings. This problem did not look like it would be solved any time soon.

The NERVA/Rover project was eventually cancelled in 1972 with the general wind-down of NASA in the post-Apollo era. Without a manned mission to Mars, the need for a nuclear thermal rocket was unclear. To a lesser extent it was becoming clear that there could be intense public outcry against any attempt to use a nuclear engine.

Although the Kiwi/Phoebus/NERVA designs were the only to be tested in any substantial program, a number of other solid-core engines were also studied to some degree. The Small Nuclear Rocket Engine, or SNRE, was designed at the Los Alamos National Laboratory (LANL) for upper stage use, both on unmanned launchers as well as the Space Shuttle. It featured a split-nozzle that could be rotated to the side, allowing it to take up less room in the Shuttle cargo bay. The design provided 73 kN of thrust and operated at a specific impulse of 875 seconds (8.58 kN·s/kg), and it was planned to increase this to 975 with fairly basic upgrades. This allowed it to achieve a mass fraction of about 0.74, comparing with 0.86 for the SSME, one of the best conventional engines.

A related design that saw some work, but never made it to the prototype stage, was Dumbo. Dumbo was similar to Kiwi/NERVA in concept, but used more advanced construction techniques to lower the weight of the reactor. The Dumbo reactor consisted of several large tubes (more like barrels) which were in turn constructed of stacked plates of corrugated material. The corrugations were lined up so that the resulting stack had channels running from the inside to the outside. Some of these channels were filled with uranium fuel, others with a moderator, and some were left open as a gas channel. Hydrogen was pumped into the middle of the tube, and would be heated by the fuel as it travelled through the channels as it worked its way to the outside. The resulting system was lighter than a conventional design for any particular amount of fuel. The project developed some initial reactor designs and appeared to be feasible.

More recently an advanced engine design was studied under Project Timberwind, under the aegis of the Strategic Defence Initiative ("Star Wars"), which was later expanded into a larger design in the Space Thermal Nuclear Propulsion (STNP) program. Advances in high-temperature metals, computer modelling and nuclear engineering in general resulted in dramatically improved performance. Whereas the NERVA engine was projected to weigh about 6,803 kg, while the final STNP offered just over 1/3rd the thrust from an engine of only 1,650 kg, while further improving the Isp to 930 to 1000 seconds.

## Nuclear vs Chemical

Directly comparing the performance of a nuclear engine and a chemical one is not easy; the design of any rocket is a study in compromises and different ideas of what constitutes "better". In the outline below we will consider the NERVA-derived engine that was considered by NASA in the 1960s, comparing it with the S-IVB stage from the Saturn it was intended to replace.

For any given thrust, the amount of power that needs to be generated is defined by $P = T * V_e / 2$, where T is the thrust, and $V_e$ is the exhaust velocity. $V_e$ can be calculated from the specific impulse, $I_sp$, where $V_e = I_sp * g$, Using the J-2 on the S-IVB as a baseline design, we have P = 1014 kN * (414 s * 9.81 m/s2) / 2 = 2,060 MW. This is about the amount of power generated in a large nuclear reactor.

However, as outlined above, even the simple solid-core design provided a large increase in $I_sp$ to about 850 seconds. Using the formula above, we can calculate the amount of power that needs to be generated, at least given extremely efficient heat transfer: P = 1014kN * (850 * 9.81) / 2 = 4,227 MW. Note that it is the $I_sp$ improvement that demands the higher energy. Given inefficiencies in the heat transfer, the actual NERVA designs were planned to produce about 5 GW, which would make them the largest nuclear reactors in the world.

The fuel flow for any given thrust level can be found from $m = T / V_e$. For the J-2, this is m = 1014 kN / (414 * 9.81), or about 250 kg/s. For the NERVA replacement considered above, this would be 121 kg/s. Remember that the mass of hydrogen is much lower than the hydrogen/oxygen mix in the J-2, where only about 1/6th of the mass is hydrogen. Since liquid hydrogen has a density of about 70 kg/m³, this represents a flow of about 1,725 litres per second, about three times that of the J-2. This requires additional plumbing but is by no means a serious problem; the famed F-1 had flow rates on the order of 25,000 l/s.

Finally, one must consider the design of the stage as a whole. The S-IVB carried just over 300,000 litres of fuel, 229,000 litres of liquid hydrogen (17300 kg), and 72,700 litres of liquid oxygen (86 600 kg). The S-IVB uses a common bulkhead between the tanks, so removing it to produce a single larger tank would increase the total load only slightly, for argument's sake, perhaps 2,000 litres. Assuming this for the moment, this means the new hydrogen-only nuclear stage would carry about 231,000 litres in total (231 m³), or about 16,500 kg (36,350 lb). At 1,725 litres per second, this is a burn time of only 135 seconds, compared to about 500 in the original S-IBV (although some of this is at a lower power setting).

The total change in velocity, the so-called delta-V, can be found from the rocket equation, which is based on the starting and ending masses of the stage:

$Delta v = v_e ln frac \left\{m_0\right\} \left\{m_1\right\}$

Where $\left\{m_0\right\}$ is the initial mass with fuel, $\left\{m_1\right\}$ the final mass without it, and Ve is as above. The total empty mass of the J-2 powered S-IVB was 13,311 kg, of which about 1,600 kg was the J-2 engine. Removing the inter-tank bulkhead to improve hydrogen storage would likely lighten this somewhat, perhaps to 10,500 kg for the tankage alone. The baseline NERVA designs were about 15,000 lb, or 6,803 kg, making the total unfueled mass ($\left\{m_1\right\}$) of a "drop-in" S-IVB replacement around 17,300 kg. The lighter weight of the fuel more than makes up for the increase in engine weight; whereas the fueled mass ($\left\{m_0\right\}$) of the original S-IVB was 119,900 kg, for the nuclear-powered version this drops to only 33,800 kg.

Following the formula above, this means the J-2 powered version generates a $Delta v$ of (414sec * 9.81) ln (119,900 / 13,311), or 8,925 m/s. The nuclear-powered version assumed above would be (850 * 9.81) ln (33,800 / 17,300), or 5,585 m/s. This drop in overall performance is due largely to the much higher "burnout" weight of the engine, and to smaller burn time due to the less-dense fuel. As a drop-in replacement, then, the nuclear engine does not seem to offer any advantages.

However, this simple examination ignores several important issues. For one, the new stage weighs considerably less than the older one, which means that the lower stages below it will leave the new upper stage at a higher velocity. This alone will make up for much of the difference in performance. More importantly, the comparison assumes that the stage would otherwise remain the same design overall. This is a bad assumption; one generally makes the upper stages as large as they can be given the throw-weight of the stages below them. In this case one would not make a drop-in version of the S-IVB, but a larger stage who's overall weight was the same as the S-IVB.

Following that line of reasoning, we can envision a replacement S-IVB stage that weighs 119,900 kg fully fueled, which would require much larger tanks. Assuming that the tankage mass triples, we have a $\left\{m_1\right\}$ of 31,500 + 6,800 = 38,300 kg, and since we have fixed $\left\{m_0\right\}$ at 119,900 kg, we get $Delta v$ = (850 s * 9.81) ln (119,900 / 38,300), or 9,500 m/s. Thus, given the same mass as the original S-IVB, one can expect a moderate increase in overall performance using a nuclear engine. This stage would be about the same size as the S-II stage used on the Saturn.

Of course this increase in tankage might not be easy to arrange. NASA actually considered a new S-IVB replacement, the S-N, built to be as physically large as possible while still being able to be built in the VAB. It weighed only 10,429 kg empty and 53,694 kg fueled (suggesting that structural loading is the dominant factor in stage mass, not the tankage). The combination of lower weight and higher performance improved the payload of the Saturn V as a whole from 127,000 kg delivered to low earth orbit (LEO) to 155,000 kg.

It is also worth considering the improvement in stage performance using the more advanced engine from the STNP program. Using the same S-IVB baseline, which does make sense in this case due to the lower thrust, we have an unfueled weight of ($\left\{m_1\right\}$) of 10,500 + 1,650 = 12,150 kg, and a fueled mass ($\left\{m_0\right\}$) of 22,750 + 12,150 = 34,900 kg. Putting these numbers into the same formula we get a $Delta v$ of just over 10,000 m/s – remember, this is from the smaller S-IV-sized stage. Even with the lower thrust, the stage also has a power-to-weight ratio similar to the original S-IVB, 34,900 kg being pushed by ~350 kN, as opposed to 114,759 kg pushed by ~1,112 kN. The STNP-based S-IVB would indeed be a "drop-in replacement" for the original S-IVB, offering higher performance from much lower weight.

## Risks

There is an inherent possibility of atmospheric or orbital rocket failure which could result in a dispersal of radioactive material, and resulting fallout. Catastrophic failure, meaning the release of radioactive material into the environment, would be the result of a containment breach. A containment breach could be the result of an impact with orbital debris, material failure due to uncontrolled fission, material imperfections or fatigue and human design flaws. A release of radioactive material while in flight could disperse radioactive debris over the Earth in a wide and unpredictable area. The zone of contamination and its concentration would be dependent on prevailing weather conditions and orbital parameters at the time of re-entry. However given that oxide reactor elements are designed to withstand high temperatures (up to 3500 K) and high pressures (up to 200 atm normal operating pressures) it's highly unlikely a reactor's fuel elements would be reduced to powder and spread over a wide-area. More likely highly radioactive fuel elements would be dispersed intact over a much smaller area, and although individually quite lethal up-close, the overall hazard from the elements would be confined to near the launch site and would be much lower than the many open-air nuclear weapons tests of the 1950s.