The Basics of Nuclear Rocketry

A nuclear reaction typically releases ten million times the energy of a chemical reaction. Thus, it would seem that the weight of the fuel necessary for a nuclear rocket to deliver a certain payload would be significantly less than the weight of the fuel a chemical rocket would need to heave the same weight the same distance. So, a larger fraction of a nuclear rocket's total weight—including the weights of the rocket engine(s), the airframe, the fuel, and the payload—could go into the payload weight.

However, the following components significantly increase the nuclear rocket's total weight: a nuclear-thermal rocket's reactor vessel, reactor core (excluding the fuel), radiation shielding, liquid-hydrogen tanks, and hydrogen-circulation equipment. As a result, a nuclear-thermal rocket can deliver only approximately twice the payload weight of a chemical rocket. Even so, early atomic weapons were so heavy that the theoretical increased "throw weight" of nuclear rockets managed to spark the United States Air Force's interest in them.

No More "Gravity Assists"

An additional advantage of a nuclear-thermal rocket is that it could travel directly between planets, without gravity assists (also known as slingshot effects), at least twice as fast as a chemical rocket could, cutting the transit time between planets. For example, a trip to Saturn using chemical rockets would take seven years—nuclear rockets could make the same trip in as little as three years. Although gravity assists (Fig. 1) conserve fuel during interplanetary missions, such assists make the trips much longer—a trip to Mars could take more than one year, for example.

An artist's conception of JIMO

Fig. 1. In this simplified schematic, a spacecraft moves at speed v while a planet moves at speed U. As the spacecraft moves closer to the planet, it moves at speed U+v, relative to the planet's surface, because the planet is moving in the opposite direction. Because the planet is moving at speed U, the total velocity of the spacecraft will consist of the velocity of the moving planet plus the velocity of the spacecraft relative to the planet. Thus, the velocity of the spacecraft would be U+(U+v), or 2U+v.

The higher speed results from the fact that the exhaust velocity for a nuclear-thermal rocket is about twice that for a chemical rocket. The exhaust velocity, Ve , is the speed with which the propellant gas leaves the rocket nozzle.

A gas-propelled rocket's ultimate speed and its exhaust velocity are related by the following ideal rocket equation:

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where ∆V is the rocket's maximum change in velocity—produced by acceleration during lift-off, changes in direction during mid-course corrections, or braking at the rocket's destination (no other external forces act). The other variables in this equation are mi, the rocket's initial weight, including the propellant; and mf, the rocket's final weight, when the "fuel tank" is empty. Rocket performance is often given in terms of the specific impulse, Isp, rather than Ve. However, the two terms are simply related as follows: Ve=Isp g, where g is the acceleration of gravity at the Earth's surface.

For example, to escape Earth's gravitational pull (the minimum requirement for traveling from the Earth to space, such as going to the moon or another planet), a rocket's velocity must go from zero at Earth's surface to at least 7 miles per second—the "escape velocity." If Ve is too small, ∆V will be less than the escape velocity, and the rocket will merely go into orbit around the Earth or fall back.

This argument applies to a single rocket stage. If the payload is going to another world aboard a chemical rocket, several stages must be used to obtain a ∆V for the final stage that exceeds the escape velocity, largely because the maximum value of Ve for a chemical rocket is typically only about 4 km/s (2.5 miles per second). A solid-core nuclear-thermal rocket will have a maximum Ve of about 8 km/s (5 miles per second).

The rocket equation also says that higher values of ∆V are possible when the fuel comprises a larger fraction of the rocket's total initial weight. For example, only 1.6 percent of the lift-off weight of an Apollo Saturn V rocket went all the way to the moon. Most of the lift-off weight was in fuel.

Chemical vs. Nuclear: It's About the Gas

Note that Ve is proportional to (T/M)1/2, where M is the molecular weight of the propellant gas and T is the temperature (in Kelvin) of the gas after it is heated—by the nuclear reactions in the core of a nuclear-thermal-rocket's reactor or by the chemical reactions in a chemical rocket's engine—but before the gas enters the rocket nozzle. This relation shows that a nuclear-thermal rocket has the highest exhaust velocity when a propellant gas with the lowest-possible molecular weight is heated in the core of a reactor operating at the highest-possible temperature. Hydrogen has the lowest molecular weight of any gas (2 atomic mass units) and is, therefore, the ideal propellant gas when heated by either chemical or nuclear reactions.

With a chemical rocket, one is stuck with the propellant gases produced and heated by a chemical reaction. For example, the space-shuttle boosters (Fig. 2) burn a mixture of hydrogen and oxygen to produce a propellant gas of hot water vapor. The gaseous product of this chemical reaction has one of the lowest molecular weights (18 atomic mass units) and the highest temperatures—and therefore one of the highest exhaust velocities—of any of the chemical reactions used to propel rockets. The molecular weight of water vapor is considerably higher—nine times higher—than the molecular weight of hydrogen.

Shuttle launch photo

Fig. 2. During the first two minutes of powered flight, NASA's space shuttle relies on a pair of huge solid rocket boosters. Together, these boosters provide approximately 83% of liftoff thrust for the space shuttle.

However, the propellant gas for a nuclear-thermal rocket can be freely chosen, because in this case, a chemical reaction does not produce or heat a gas. The propellant gas flows through the core from a storage tank; the nuclear reactions from the reactor core heat the propellant gas.

The temperature of the gas heated in a solid-core reactor is unlikely to exceed the temperature of the gas produced and heated by a chemical reaction. Burning a mixture of hydrogen and oxygen produces water vapor at a temperature of 5,555 K (9,540°F), twice the maximum temperature in a solid-core reactor (2,750 K or 4,490°F). But water vapor's molecular weight is eight times that of molecular hydrogen (2). The nuclear-thermal rocket's advantage is that one can choose the best-possible propellant gas—hydrogen—to obtain an exhaust velocity about twice that possible with a chemical rocket, according to the above relation for Ve.

The gas temperature that can be reached in a solid-core reactor is limited by chemical reactions at the absolute extreme by the melting points of the core's materials. As mentioned in "Nuclear Rockets: To Mars and Beyond" on page 16, Project Rover reactors had solid cores. But fission reactions can also take place in molten or gaseous cores (modes of operation that have been studied), especially for rocket propulsion, although these rockets were never tested at full scale. Nominal core temperatures for solid, molten, and gaseous cores are 2,750 K (4,490°F), 5,250 K (8,990°F), and 21,000 K (37,340°F), respectively. The much higher temperatures of molten and gaseous cores would produce higher exhaust velocities than are possible with solid cores.

In addition to its potential effects on a solid-core reactor's structural integrity, the core temperature can also affect the form of the propellant gas. When heated in a solid-core reactor, hydrogen molecules remain molecules. But at about 5,000 K (8,540°F), slightly below the predicted temperature of a molten core, hydrogen molecules thermally dissociate almost completely into hydrogen atoms. Moreover, atomic hydrogen thermally dissociates into plasma (a mixture of positively charged hydrogen ions and negatively charged electrons) at the temperature predicted for a gaseous core.

Other Nuclear-Rocket Schemes

Another promising scheme for nuclear space propulsion is to use heat produced by a fission reactor to produce electricity. Electricity is produced by using a thermoelectric element or a heat engine to drive an electrical generator, as is done in nuclear power plants. The electricity is then used to accelerate ions to high speeds. In this case, the ions are the propellant gas. This scheme, called nuclear-electric propulsion (Fig. 3), can reach much higher exhaust velocities than are possible with nuclear-thermal propulsion, but at much lower thrust.

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Fig. 3. This artist's conception shows a spacecraft powered by nuclear-electric propulsion. Similar to nuclear-thermal propulsion, this form of propulsion does not heat the fuel to accelerate it. Instead, it ionizes the fuel and then sends it through an electric field to propel the spacecraft at extremely high velocities.

Other nuclear-rocket schemes studied over the years include propelling a rocket with a succession of atom-bomb explosions or with nuclear fusion. Matter-antimatter reactions were considered, although a method to produce significant amounts of the second half of the fuel—the antimatter—needs development. These rockets could have much higher thrusts and specific impulses than those of nuclear-thermal rockets. To date, however, researchers have only built and tested nuclear-thermal-propulsion engines.

-Octavio Ramos Jr.

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