ADVANCED PROPULSION SYSTEMS
10.1 GETTING THERE QUICKLY
In the last chapter we considered the Hohmann transfer orbit as a means of traveling from Earth to Mars or another planet. It was an energy-efficient method of getting there from here, but it had one big disadvantage: it took a long time. This was because the planets had to be in the right relative positions when the rocket was launched, and also because when the rocket was launched it became a planet in effect: a satellite of the Sun, acted on only by the force of gravity (except for short times when changing orbits). A trip to Mars took about 0.7 years, and trips to the outer planets took much longer. Everything is governed by Kepler’s third law.
The reason it took so long is that the times when the spacecraft was accelerated by its engines were relatively short. For a minimum-energy, Hohmann-type orbit, the spacecraft is in free-fall orbit around the Sun except when making (brief) Δv maneuvers. However, if we want to travel to Mars over the weekend and be back in time to watch My Favorite Martian reruns on Monday night, we need spacecraft that are capable of acceleration for very large stretches of time, meaning they will need to expend a lot of energy. It is pretty easy to see that conventional rockets simply won’t work for this particular job.
10.2 WHY CHEMICAL PROPULSION WON’T WORK
Let’s take a hypothetical spacecraft that can accelerate continuously at 1 g so that we feel our normal weight along the voyage. The three questions we want to look at are:
1. How long will it take?
2. What is the greatest speed we reach along the voyage?
3. How much fuel will we need for a 10,000 kg payload?
We’ll use the final question as a criterion to evaluate the promise of different types of propulsion systems.
The average distance of Mars from the Sun is 1.52 AU, that is, 1.52 times the average distance of Earth from the Sun. Therefore, at closest approach, Mars is 0.52 AU from Earth, or (about) 7.5×1010 m, that is, 75 million km, or about 40 million miles. The acceleration of gravity is about 10 m/s2; I’ll assume that the ship accelerates halfway, then flips around and decelerates the other half. We don’t want to zoom by Mars at high speed, after all this effort.
We start with a formula from freshman physics:
That is, at constant acceleration the distance a body travels (d) is equal to one-half the acceleration (a) multiplied by the voyage time (t), squared. I’m assuming that the spaceship isn’t moving when the trip starts. Inverting this,
One interesting thing about this equation: because the spacecraft is continuously accelerating on the way out (that is, traveling faster and faster all the time), going four times the distance takes only twice the time. From this, the time it takes to go halfway to Mars (remember, we are accelerating halfway and decelerating the other half) is
The total transit time is t = 2t1/2 = 2 days. In more useful units, if we wish to go a distance of d AU at an acceleration of 1 g, the time it will take is
So, if we can accelerate at 1 g, the Solar System is ours!
The maximum velocity on our trip to Mars is at the midpoint and is given by
As fast as this is, it is only about 0.2% of the speed of light. To achieve this velocity for a 10,000 kg payload with chemical rockets (i.e., a typical exhaust velocity of about 3,000 m/s), we need a mass ratio of approximately e287 ≈ 10124, which is clearly impossible. This is a physical impossibility, not merely a practical one, as there is not enough mass in the universe to achieve this.
10.3 THE MOST FAMOUS FORMULA IN PHYSICS
Chemical rockets rely on chemical potential energy for propulsion. Chemical energy is the energy released when you rearrange molecules to form other molecules—in other words, the energy released when atoms in some sort of compound change their relative positions with each other. This places an intrinsic limit on the amount of energy that can be released by a chemical reaction, as it is due to the electrical potential energy between different atoms.
This is a limiting factor because atoms, although teensy on a human scale, are pretty far apart in the microworld. We can do a rough estimate of the electrostatic potential energy in a kilogram of matter by thinking about two adjacent atoms. Typically, atoms are separated by about 10−9 m in a solid or liquid. Let’s approximate this with the idea that the atoms are represented by two charges separated by a distance r about equal to the average interatomic spacing. This will underestimate the energy, but not by a whole lot:
Here, k = 9×109 Jm/Coul2, e = 1.6×10−19 Coul, and r =10−9 m. This gives about 2×10−19 as the approximate potential energy between a pair of atoms. Since there are about 1026 atoms per kilogram of a solid, this implies about 2×107 J/kg (i.e., 20 MJ/kg) available in the form of chemical energy. This value is pretty good for a crude estimate: gasoline, for example, liberates about 80 MJ/kg when combusted.
However, there is a lot more energy in matter; indeed, matter is a form of energy. This is what Einstein’s famous formula,
states: there is an energy equivalent in matter to its mass (M) multiplied by the speed of light squared (c2). In other words, 1 kg is equivalent to 9×1016 J—90 million billion J, or about a billion times the energy present in chemical reactions. If we could somehow liberate even a small fraction of the energy present, we would not only have a working space drive but could also solve all of Earth’s energy problems, essentially forever (but more on that later.) But how?
10.4 ADVANCED PROPULSION IDEAS
10.4.1 Nuclear Energy Propulsion Systems
The idea for nuclear propulsion of spacecraft dates back to at least 1945, as Richard Feynman documents in his book “Surely You’re Joking, Mr. Feynman!”:
During the war, at Los Alamos, there was a very nice fella in charge of the patent office for the government, named Captain Smith. Smith sent around a notice to everybody that said something like, “We in the patent office would like to patent every idea you have for the United States government, for which you are working now [concerning nuclear energy].… Just come to my office and tell me the idea.”
… I say to him, “That note you sent around: That’s kind of crazy to have us come in and tell you every idea.… There are so many ideas about nuclear energy that are so perfectly obvious, that I’d be here all day telling you stuff.”
“LIKE WHAT?”
“Nothin’ to it!” I say. “Example: nuclear reactor … under water … water goes in … steam goes out the other side … Pshshshsht—it’s a submarine. Or: nuclear reactor … air comes rushing in the front … heated up by nuclear reaction … out the back it goes … Boom! Through the air—it’s an airplane. Or: nuclear reactor … you have hydrogen go through the thing … Zoom!—It’s a rocket. Or: nuclear reactor … only instead of using ordinary uranium, you use enriched uranium with beryllium oxide at high temperature to make it more efficient.… It’s an electrical power plant. There’s a million ideas!” I said, as I went out the door. [84]
Atomic energy is very attractive as an energy source for spacecraft propulsion because of the enormously high specific energy (energy/per kilogram of fuel) compared to chemical fuels. There are two types of nuclear reactions: fission and fusion. In fission, the capture of a neutron (n) causes large, unstable nuclei to fall apart, while in fusion reactions, energy is generated by the fusing together of lighter nuclei into heavier ones.
I’m going to digress for a moment on the structure of the atom and the atomic nucleus. Atoms are mostly empty space. An atom is electrically neutral, but all of the negative charge is on the outside: the electron shells that make chemistry possible extend out to a distance of about 0.1 nm, or 10−10 m, from the center of the atom. All of the positive charge, in the form of protons, is at the center of the atom; for each electron in a neutral atom there is one proton as well. The protons are confined to a space that is about 10−15 m in radius, or 1/100,000 of the extent of the electron shells. Because like charges repel each other, something must act to “glue” the nucleus together. This glue is the neutron. For every proton, there is at least one neutron in the nucleus that provides a force (called the “strong nuclear force”) that keeps the protons from exploding outward. Neutrons are neutral (i.e., they carry no charge) and are about the same mass as the proton, which is about 1,800 times heavier than the electron.
The total electrostatic potential energy of the nucleus is very much larger than the electrostatic potential energy between a pair of atoms—about 100,000 to 1,000,000 times bigger because of the size factor involved. The energy liberated from the nucleus is still pretty small compared to the ultimate amount of energy stored in matter, but is large compared to the chemical energy.
Currently, all commercial nuclear reactors work through the fission of heavier elements into lighter ones. As elements become heavier and heavier (i.e., having more and more protons and neutrons in the nucleus), they become unstable and the largest ones can fall apart spontaneously. This process liberates energy: by fissioning into two nuclei, one large nucleus moves about half the protons far away from the other half.
10.4.2 Fission Reactions
In each process, the energy released can be calculated by the difference in mass between the end products and the initial nuclei. A typical fission reaction used in reactors is [246, pp. 1198–1199]:
(keep in mind that 1 MeV = 1.6 × 10−13 J).
Because an extra neutron is generated by the fission process, the process can be self-sustaining if enough 235U is present; this amount is called a critical mass. Nuclear reactors use an amount very slightly over criticality to generate energy in a controlled way, whereas nuclear bombs suddenly throw together two or more very slightly subcritical masses so that the chain reaction is fast, resulting in a huge, short burst of energy. Both types of reactions have been proposed for propulsion systems.
The energy density of the fission of 1 kg of 235U can be calculated from the molar mass (235 g/mol) of this isotope:
However, in a reactor, only about 3.5% of the uranium is enriched into 235U; most is in the form of 238U, which is less reactive, meaning that the energy density drops to about 3×1012 J/kg. This is still about 105 times greater than the specific energy available from chemical reactions.
Most work on nuclear propulsion systems for spacecraft are in drives that use a nuclear reactor to heat hydrogen gas as an exhaust fuel. Hydrogen is used because, as the smallest atom, it achieves the highest exhaust velocity for a given amount of energy dumped into it. For reasons discussed below, the exhaust velocity is limited to about 8,500 m/s, or roughly twice the maximum achievable by chemical fuels.
Work on nuclear spacecraft engines was stopped by the Nuclear Test Ban treaties of the 1970s. Up until 1972, NASA was working on a series of nuclear rocket engines dubbed the NERVA, or Nuclear Engine for Rocket Vehicle Applications series. Interest in them has revived because of a series of initiatives started during the second Bush administration and carried on by the Obama administration to have manned missions to the Moon and Mars. Nuclear rockets could potentially shorten the time to Mars to under 100 days by allowing a Δv for the initial orbital maneuver greater than 34 km/s.
Both NERVA and the Orion concept have several advantages over chemical propellants. One is that they tend to work better for larger payloads (meaning they can be designed to give higher thrust and impulse). There is a minimum size at which nuclear reactors can be built, but scaling them up is comparably less difficult. There are, of course, obvious disadvantages of using nuclear fuel, but they tend to be overstated.
Robert Heinlein’s novel Rocket Ship Galileo is about a group of Boy Scouts and their nuclear physicist mentor who build a spacecraft and go to the Moon, defeat a group of Nazi astronauts while there, and return triumphantly home. It is the first science fiction novel I know of to use the idea of a nuclear reactor to heat up and eject propellant, even though this predated the NERVA program by 20-odd years [109]. However, this idea hasn’t caught on as much as other propulsion ideas in the science fiction literature, principally because of the limitations of conventional nuclear reactors.
The NERVA program was initiated by NASA in the 1960s to build a nuclear-powered spacecraft for a planned manned mission to Mars (scheduled to take place around 1970). A small nuclear reactor was designed as a power source for the spacecraft; the reactor heated liquid hydrogen to a temperature of 2,200 K and expelled it through a nozzle to generate thrust. The initial design showed some promise: the exhaust velocity was u ≈ 8,600 m/s, which is nearly twice the best value obtainable from rocket fuels. It also had a relatively high thrust of 73 kN. The NERVA propulsion system was also proposed as a potential engine for the Space Shuttle but was killed by post-detente cuts in NASA’s budget and a general distrust of nuclear power in the 1970s.
The biggest issue with this type of propulsion system is that although a lot of energy is liberated in nuclear processes, it isn’t obvious how to use it. The limitations imposed on fission reactor spacecraft have more to do with materials science than with energy usage: for one thing, the energy liberation rate is limited by the melting point of the material one makes the reactor from (ultimately, the uranium alloy used as fuel). Also, the neutrons that are produced embrittle the spacecraft engine, which places limits on the energy generation rate. Finally, the method simply heats the reaction mass (the hydrogen fuel), which may not be the best way to use all of this energy. There should be a better way, a more clever design, that uses all the energy directly. NERVA represents an incremental advantage over chemical rockets because it is a relatively conservative design. The design of the propulsion system for the Orion project, however, represents a real departure from most rocket concepts.
10.5 OLD “BANG-BANG”: THE ORION DRIVE
The most interesting nuclear propulsion system was invented by the mathematician Stanislaw Ulam and C. J. Everett and developed by physicists Freeman Dyson and Ted Taylor in the 1950s [41] [75, pp. 22–24] [240, chap. 7] It is no longer taken seriously by anyone except science fiction writers; however, it does represent thinking big. The idea was to build a spacecraft with a big, highly shielded plate at the back and blow up a nuclear bomb behind it to push the ship forward. I swear to God I am not making this up. This was referred to euphemistically by NASA as a “nuclear pulse drive” [210]. Dyson, currently a fellow at the Institute for Advanced Study at Princeton University, thought it could be done safely, and ran a pilot program to study it. The full story is related in the books The Curve of Binding Energy, The Canoe and the Starship, and Project Orion [75][164]. Dyson is a firm believer in thinking big in science; we will examine the idea of a “Dyson sphere” (another science fiction fave) later on in this book. His idea to make Orion work was to use a sequence of small nuclear bombs to give a more or less uniform acceleration to the ship. One thing to note here: I realize that at this point I’ve discussed only nuclear fission (the power source of atomic bombs), whereas Orion would be using specially made hydrogen bombs.
This idea has proved incredibly popular in the science fiction community. I’ve read two novels that use the idea, S.M. Stirling’s The Stone Dogs [228] and Larry Niven and Jerry Pournelle’s Footfall [187]. The Stone Dogs is set in an alternate–history present/future in which the world is divided between the United States and its allies and the Domination of the Draka, a highly advanced technological slave-owning society based in South Africa. Stirling assumes that because of the rivalry between the two, certain forms of military technology (especially developments in space) are accelerated relative to our own world. By the 1960s, nuclear pulse drives have been developed and are later used to put colonies on the Moon and settle the asteroid belt.
In one of their patented cast-of-thousands novels, Larry Niven and Jerry Pournelle in Footfall present an Earth being invaded by aliens resembling miniature elephants. The aliens use a Bussard ramjet for propulsion, which I discuss in the next chapter. The humans in the story, led by a team of science fiction writers and fans, institute a crash program to build an Orion-type spacecraft to combat the aliens. There are many others examples of the genre. Science fiction writers (and readers) like space travel and things that go bang; combining them is almost irresistable.
The energy released by a Hiroshima-sized nuclear bomb is about 1013 J. If this could be converted to kinetic energy, it would get our canonical 10,000 kg payload moving at a speed of about 50 km/s. Unfortunately, the energy is liberated in a few microseconds, meaning that everyone would be crushed to jelly from the high acceleration. Also, a payload as small as 10,000 kg is unrealistic for a manned vehicle. In reality, the initial studies were of payloads ranging in mass from 10 tons to about 400 tons, with mass ratios of about 10. They relied on small nuclear devices blown up at a rate of roughly one per second and an effective exhaust velocity of about 20,000 m/s, or about seven times what we’ve assumed for chemical propellants [9]. It’s pretty clear that if such a system could be made to work, then one could send fast rockets to the far corners of the Solar System, if not to the stars. You would need to launch the rocket from orbit, as the radioactive fallout is not something you want in your back yard. Three major technical issues have to be overcome in designing a spacecraft using nuclear bombs: shielding the passengers from the radiation produced in blowing up a nuclear bomb every second or so behind them; keeping the average thrust low enough so that people wouldn’t be smashed to jelly by the high acceleration; and designing a system to throw a nuclear bomb behind the ship once a second and detonate it there—a difficult design problem. According to George Dyson, the Orion team consulted the Coca-Cola Company on the bomb delivery system for the spacecraft [75, pp. 177–178]. A final problem is that getting Congress (or any agency) to fund such a program is improbable, to say the very least. This is what eventually killed the program. It is fun to think about, though; a lot of sweet design problems stem from trying to figure out how to launch spacecraft with nuclear bombs. A few are listed on the book website.
The preliminary studies for Orion were for ships traveling to the Moon or on conventional Hohmann orbits to Mars; the pulse drives were to be turned on for only a few minutes during the two Δv boosts, and the total trip time was 450 days. However, Dyson and Taylor were ambitious: they wanted ships that could accelerate continuously, and it is clear that this is what they expected the Orion project to eventually deliver.
In overall design, the main part of the ship rests on top of a “pusher plate” that serves both as radiation shielding and as something for the bomb to push against. A bomb is dropped behind the plate and blown up. The pusher is attached to the rest of the ship by an arrangement of springs and mass dampers that smooths out the inherently jerky nature of the acceleration.
The overall (theoretical) performance is very impressive. The specific impulse is very high (Isp ≈103 s, or u ≈ 104 m/s or higher). This means that for typical Δv corrections of 1–10 km/s, the ratio of fuel mass to payload mass is of order one. As one might expect, thrust is also high.
One thing unique to Orion is that there is no way to make a small spacecraft using this concept because of the difficulty of making low-yield nuclear bombs. The first design (for a Mars mission) called for a 4,000-ton (4×106 kg) spacecraft using 0.1 kT yield bombs specifically designed for the project. By comparison, the lunar landers for the Apollo missions massed about 14,000 kg. Several thousand of these bombs would be detonated during the round-trip mission. Because of the high impulse, one can also use faster orbits than the minimum-energy Hohmann transfer.
The development of Orion came to a halt in the early 1960s when priority was given to the Apollo program, which used more standard chemical propulsion systems to reach the Moon. However, Orion is the only feasible high-impulse, high-thrust propulsion system studied in detail to date.
10.6 PROSPECTS FOR INTERPLANETARY TRAVEL
There are definite advantages to using nuclear propulsion; the effective exhaust velocities range from twice to about five to ten times what one can get by using traditional chemical propellants. They really are the only way one could envision large-scale manned interplanetary travel, in that they could cut the travel time between Earth and the other planets in the Solar System by about an order of magnitude. If one could use Orion to accelerate a spacecraft at 1 g indefinitely, one could cut the time by a factor of 100 or so.
However, the nearest stars are thousands of times more distant than the farthest planets in the Solar System. To get to the stars we need even more energy than even Orion can provide, but for this saga, we take up the story again in the next chapter.