Engineering Halo: the Physics of Building a Ringworld Kent
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Bornemeier 1 Engineering Halo: The Physics Of Building A Ringworld A Thesis submitted for Albion College Honors Kent Bornemeier April 1, 2010 Albion College Bornemeier 2 Table Of Contents: I. Introduction and History of Ringworlds and Halo II. Mechanics a. Mass b. Orbit c. Rotation d. Materials III. Support a. Atmosphere Retention b. Power Generation c. Station-Keeping (RCS) d. Visiting Halo IV. Conclusion Bornemeier 3 Introduction and History of Ringworlds and Halo: In 2001, Microsoft published a computer game called Halo: Combat Evolved. The premise: a war between humans and aliens in the far future taking place on the megastructure known as Halo, a ring the size of a planet orbiting a gas giant.1 Halo, and other planetary or cosmic scale structures like Niven rings2, are usually given the title “megastructures,” referring to constructs greater than a million meters (a megameter) in size. At ten million meters in diameter, Halo easily qualifies. The idea of a ringworld is not new; some of the earliest space station concepts by pioneers at the start of the 20th century, like Wernher von Braun, proposed toroidal space stations that would rotate to generate centripetal force, which the astronauts aboard would feel as simulated gravity.3 The famous movie 2001: A Space Odyssey contained a space station built in exactly that fashion: two rotating rings mounted on an axle that simulated gravity for the occupants. In 1970, Larry Niven wrote his famous novel Ringworld. The structure it describes is a ring nearly a million miles wide with a radius comparable to that of the Earth’s orbit, called an Astronomical Unit. This ringworld was a cosmic-sized megastructure that was built in orbit around a star. Constructs like this provide their inhabitants with earth-like conditions of gravitation and atmosphere, as well as other terran features like mountains, oceans, and continents, but on a massive scale; Niven’s ringworld had a habitable surface area nearly three million Earths in size 2. Historically, architects have been proposing megastructures of sorts for centuries, with varied purposes. As the single largest artificial construct on Earth, the Great Wall of China is considered to be the earliest example of a megastructure (other structures like Bornemeier 4 the Pyramids, being less than a megameter in size, do not technically count as megastructures). In the 1960’s, a fresh wave of utopist megastructure designs surfaced, including British architect Ron Herron’s ‘Walking City’4. These early designs have never been built, remaining science fiction until such time as there is sufficient capital and technology to build them. The ringworlds in the videogame Halo are in fact planetary- scale structures similar to the orbitals used in the Culture novels by Iain M. Banks. 5 Two major reasons to build a ringworld are given by the Halo games and by Larry Niven. In Niven’s novels, the Ringworld is created with the intention of increasing the available land area for the builder civilization to use. Without superluminal technology, the Ring Engineers found their civilization growing beyond the capacity of the planets of their solar system, and so they built the Ringworld by using all the matter in their star system.2 In Halo, the planetary-scale ringworlds are called Fortress Worlds. They are used as massive laboratories and ultimately as weapons of mass destruction (via a radiation pulse generator that can create a lethal dose of radiation even at a range of 25,000 light years) for combating a parasitic alien life-form known as the Flood.1 Other possible uses range from something as simple as power generation (which will be discussed later) to massive construction and launching facilities for spacecraft. Although still well beyond the technical capabilities of modern civilization to construct, the Halo megastructures, through the games they’ve given their name to, inspire awe and incredulity at the very notion of such a large structure. The scientific knowledge to design one exists, and can be examined. This paper will explore the feasibility of a Halo-like megastructure using known physics and technology, assuming that the industrial capacity necessary to support such an endeavor existed. Bornemeier 5 Mechanics: The greatest challenge of building a ringworld lies in its physical properties: mass, volume, orbit, and composition to name a few. Structures the size of planets or larger would require massive expenditures of time and energy to fabricate, place, and stabilize in their orbits. In the case of a Halo, they would also need to be constructed in space, and then set rotating once finished – a process that would take even more energy. First we will explore the mass requirements of Halo, both how much material would be needed to construct it, as well as the energy requirements of lifting such material into orbit. Next will come a discussion of the orbital mechanics of Halo, then issues pertaining to its rotation and artificial gravity, and lastly, an analysis of the materials necessary for Halo’s construction. Mass: Constructing a ringworld is a sizable undertaking. Engineering, even on a planetary scale as in the Halo series, requires mass and industrial capacity beyond anything humanity has at its disposal. A simple physics analysis bears this out. A Halo megastructure, as seen in the game, is an annulus with an outer radius of 5,000 km, a width of 320 km, and a thickness of 22.3 km (see Figure 1), giving a total volume of 224 million cubic kilometers6. This entire space is devoted to all aspects of the station’s infrastructure: landmass (as seen on the inner surface of the ring), power generation, station keeping, the weapons system and laboratories that feature so Bornemeier 6 prominently in the games, and of course the physical superstructure that holds it all together. Fig. 1: Scale image of Halo showing relative radius, thickness, and width. 1 pixel = 22.3 km Halo is a massive space station designed to be useful and habitable beyond the ring’s inner surface. Several of the multiplayer maps lie deep within the structure, while many maps in both the multiplayer and campaign modes portray “bottomless” pits extending outward radially through the ring’s structure. These massive open areas are only part of a network of tunnels, corridors, and rooms that fill the structure, reducing its overall density.1 Bornemeier 7 “The Covenant did a thorough seismic scan. My analysis shows that Halo is honeycombed with deep tunnels, which circle the whole ring.” –A.I. Cortana in Halo: Combat Evolved As seen in the games, the Halo megastructures, though riddled with open space, contain many monolithic structures with thick walls, floors, and solid spaces. On the inner surface of the ring are also mountains and bodies of water. A conservative estimate of the physical space devoted to open volumes of air (habitable volume) would be half of the ring’s total size, though it could be larger or smaller depending on the needs of the builders. Assuming that only half of the annulus’ volume is made of solid structural material (say, structural steel), and the rest is sea-level pressure air, the density of the ring would be approximately 3900 kg/m3, nearly four times the density of water7. At 3900 kg/m3 and 223 million cubic kilometers volume, the Halo would weigh in at 8.73*1020 kg, just a little over 1% of the mass of Earth’s moon8. Given the assumptions made about the ring’s composition, of the total mass, 99.98% would be steel. Another possible construction material that would be much lighter is carbon. Carbon fiber is already used in composite materials for a variety of applications, and carbon nanotubes are predicted to be used for many different applications ranging from electronics to high-stress tensile structures like space elevators or cables. If carbon nanotubes (which will be discussed later) were used to build Halo instead of steel, the mass would be much less, 1.57*1020 kg, five and a half times less than a steel Halo. Bornemeier 8 To build Halo in or near Earth orbit, all the material needed would have to be lifted from the surface. For Halo, normal low-Earth orbit wouldn’t be high enough to begin construction. With a radius nearly as large as the Earth’s, a halo ringworld would need to be built in medium Earth orbit, at least 5,000 km above the surface (medium orbit is the range from 2,000 km to just inside geosynchronous orbit)9 to guard against accidents by making sure that, regardless of orientation, the entire ring is always far from a drag-inducing atmosphere or a planetary surface. For a unit mass, the energy required to lift it from the surface of the Earth into a stable orbit is proportional to the radius of that orbit. Calculated out, to place a unit mass into a circular orbit around the Earth at a distance of 3 Earth radii (2 Earth radii above the surface of the planet) takes nearly 52*106 joules of energy per kilogram. Multiplied times the mass of Halo, this yields a total energy of 4.53*1028 joules for a steel ring, and 8.14*1027 J for the carbon ring, figures roughly equivalent to 450 million and 81 million years worth of the U.S.’s total energy consumption in 200610, or just under two minutes worth solar energy production.11 Mining the asteroids is a possibility for gathering the raw materials to build Halo, but moving those materials to planetary orbit is even more costly than lifting them from Earth’s surface.