# Section 1.4 - Energy Sources

## Introduction

All space systems, indeed, all of civilization, require energy to function. This section discusses the sources of energy that can be used for propulsion, as tabulated in Part 2 of the book, and for other engineering purposes described in Part 3 and later. The general field of energy sources is vast, and that of energy for space applications is still very large, so here we will only provide an introduction and pointers to material for further study.

### Energy for Space Systems

By making a Matrix of energy sources vs propulsive forces, you can categorize all possible propulsion methods, and we do this at the start of Part 2 of the book. The law of conservation of energy states that energy can neither be created nor destroyed, merely transformed. So all energy for a project must come from a preexisting source. For a given project you can distinguish a proximate energy source, which is in the form consumed by the project, and an ultimate energy source, which traces the proximate source back through previous transformations to it's original form. For engineering purposes we are generally concerned with proximate sources.

For current space systems the energy is typically stored internally as chemical energy in the case of vehicles, or uses sunlight in the case of payloads. In the future, energy needs are likely to change, and so the sources of energy will also change. Permanent infrastructure projects, such as a large station with people aboard, generally need continuous sources of energy to operate. Devices like batteries become unwieldy to bridge the night part of Earth orbit or the two week Lunar night. Future projects may also need much greater power levels than now used. Thus the following headings attempt to include all possible energy sources, including many not yet used, but which may become useful in the future space projects. We list them all so that designers know the full range of possibilities, from which they can then select viable options for a given task. We specifically exclude sources such as human and animal power from consideration here, both due to their low power levels, and because living things are not subject to the same kind of design.

### Energy in General

A starting point for understanding energy sources in general, not just as they apply to space projects, is a National Academies book America's Energy Future, 2009. Other books available for free download from their site in the Energy and Conservation topic may be useful background. For more depth on the topic of energy, the Encyclopedia of Energy, Encyclopedia of Energy Engineering and Technology, and Macmillan Encyclopedia of Energy are good references. Those are expensive reference books, so library or other sources are recommended to get access. There are numerous engineering books on more specific aspects of energy systems.

Some of the concepts listed below are currently theoretical, so they are not well covered in books about current energy use or engineering. Information about them will mostly be found in research reports and scientific/technical papers.

## Mechanical Sources

This category includes energy stored by virtue of previous work, as in compressed gases, and that which exists by virtue of position (potential) and motion (kinetic). Objects in orbital motion have a combination of potential and kinetic energy.

#### A. Compressed Gas

The available energy stored in a pressure tank W can be found from

$W = p_B v_B \ln \frac{p_A}{p_B}$

where B represents the high pressure and A represents the low pressure, and p and v are pressure and volume respectively. Thus a 1 cubic meter tank with a high pressure of 20 MPa and a low pressure of 10 Mpa would provide 13.8 MJ of available energy. Compressed gas is a low density energy storage method. It is often used in vehicles for tasks like cold gas thrusters and pressurizing liquid fuel tanks. Its chief advantages are simplicity, requiring just a storage tank and a valve, and rapid release of the stored energy. When larger total amounts of energy are needed, a higher density but more complex system is often preferred.

#### B. Potential Energy

Potential energy is the ability of a system to do work by virtue of it's position. In space projects this is usually position relative to the gravity well of a massive object such as a planet. A simple hypothetical example is a stationary space elevator cable. While raising a cargo, electricity is converted to potential energy of height. When lowering a cargo, the potential energy can be extracted back to electricity. The formula for potential energy was given in the Physics section as

$U = -G \frac{m_1 M_2}{r}$

The difference in energy at two radii gives the amount of potential energy stored or released over the distance. For small changes in radius (height) relative to the distance r, the potential difference can be approximated by the gravitational force (weight) times height. On planetary surfaces, large amounts of available mass can be used to store potential energy. On Earth this is done with dams for hydroelectric power. On other bodies, a mountain and a pile of rocks can serve the same purpose. Transporting the rocks up and down the mountain can serve to store or release energy.

#### C. Kinetic Energy

Kinetic energy is that which an object possesses by virtue of it's motion. It is formula was given in the Physics section as

$KE = \tfrac{1}{2} mv^2 = F \cdot d$

where KE is the kinetic energy, m is the object's mass, and v is the velocity. It is also equal to an accelerating force times the distance it is applied. An object in orbit has both kinetic energy in it's orbital velocity and potential energy in it's altitude. In an elliptical orbit, it continuously exchanges altitude for velocity, thus potential and kinetic energy, but the combined total stays the same.

Rotating objects such as a space station or reaction flywheel have a form of kinetic energy in it's motion around an axis. Rotational energy is E(k) calculated by

• $E_k=\frac{1}{2} I \omega^2$

Where:

• $\omega$ is the Angular Velocity in units of radians/second, and
• $I$ is the Moment of Inertia of the mass about the center of rotation. The moment of inertia is the measure of resistance to Torque, or rotational force, applied on a spinning object. The higher the moment of inertia, the slower it will spin when a given force is applied. Moment of inertia depends on the distribution of mass in the rotating object. The farther out a given portion of the mass is, the larger the contribution. Formulas for many shapes are found in the List of Moments of Inertia. For complex shapes, the total moment can be found by dividing it into simpler parts and summing the individual moments. Some examples are:
• the moment of inertia for a solid cylinder is $I = \frac{1}{2} mr^2$,
• for a thin-walled empty cylinder is $I = m r^2$,
• and for a thick-walled empty cylinder is $I = \frac{1}{2} m({r_{external}}^2 + {r_{internal}}^2)$

Kinetic energy can be exchanged by gravitational forces, as in gravity assist maneuvers, or electromagnetic forces, as in many mechanical devices, for other forms of energy. Potential energy can also be exchanged for kinetic energy via the Oberth effect by expending propellant deep in a gravity well.

## Chemical Sources

Chemical energy comes from an arrangement of atoms in a higher energy state which is converted to a lower energy state by a chemical reaction, releasing the difference. Combustion is the most common way to release this energy, accounting for over 80% of total human energy use. Batteries are characterized by a reversible reaction, so that the same device can store and release energy multiple times.

#### D. Fuel-Atmosphere Combustion

The Earth's atmosphere contains 21% free Oxygen, which reacts with many other compounds to release energy. In the case of aircraft, a hydrocarbon fuel such as kerosine is reacted with the atmospheric oxygen. Since only the fuel is carried internally to the vehicle, the energy released, about 43 MJ/kg, is about three times as much as when both ingredients are carried internally, such as in a typical rocket. Free Oxygen in an atmosphere is unstable, and only exists on Earth because plants constantly replenish it. Therefore this source is not available on other bodies. The reverse option is available on a body such as Titan, which has a hydrocarbon atmosphere. In that case, Oxygen can be the carried ingredient, and burned with the surrounding atmosphere. For atmospheres which are mostly CO2 (Venus and Mars), which is an end product of combustion, or bodies with no atmosphere at all, this energy source is not available.

#### E. Fuel-Oxidizer Combustion

This is the energy source used in conventional rockets, where both fuel and oxidizer are supplied from internal sources. The highest energy combination in common use, Hydrogen/Oxygen, provides 15 MJ/kg of propellant. Although lower specific energy than Fuel-Atmosphere, it can operate in a vacuum, and liquid rocket engines have extraordinary power-to-mass ratios, enabling vertical launch. Combustion can also be used as a secondary power source in auxiliary power units. Because the rate of energy release is very high, combustion is more useful when high power levels are needed. Efficiencies are typically 30-50%, so other options are preferred when that is a more important factor.

#### F. Chemical Battery

In a battery, energy is stored in a reversible chemical reaction which uses electricity for input and output power. Examples of conventional batteries include Lead-Acid and Lithium-Ion. Depending on battery type, they can store 100-500 kJ/kg, considerably less than combustion. The ability to use the device multiple times can outweigh the lower energy density. A high performance "battery" for space use is a Hydrogen-Oxygen fuel cell to generate electricity, combined with an electrolysis unit to convert the resulting water back to Hydrogen and Oxygen. The energy density of this type can be in the range of 3-10 MJ/kg.

## Thermal Sources

Thermal sources supply energy in the form of more rapidly moving atoms, which we sense as heat, and transfer it by conduction, radiation, and convection. Where a temperature difference exists, some of the thermal energy can be converted to other forms.

#### G. Thermal Storage Bed

For locations like the Moon, which has a long night, solar power is not effective half the time. Therefore storing heat in a thermal storage rock bed during the daytime and extracting it at night to run a generator can provide continuous power. The rock bed is enclosed in a container, and gas transfers heat to a turbine for generation, and from a solar collector for storage. Since the rock can be obtained locally, the energy stored per mass of installed equipment is fairly high. Environment temperatures during the Lunar night are quite low, and this can be enhanced by thermal shields between a radiator and the ground. Thus the temperature difference between the storage and rejection temperature, and thus efficiency, can be fairly high.

Some bodies have relatively high interior temperatures. This can serve as a natural thermal source by drilling down to access the interior.

#### H. Concentrated Light

Particular tasks require heating, which can most easily be done in space by concentrating sunlight. Examples are heating of raw materials to extract volatiles, or maintaining temperature and growing ability in a Mars greenhouse. The concentration ratio determines the maximum blackbody temperature that can be reached, up to the temperature of the light source. In the case of the Sun, the limit is the Sun's surface temperature, 5,775K, less reflection losses and radiation losses from the object you are heating.

In particular, for propulsion, a reaction mass can be heated by concentrated Sun or artificial light. Since lighter molecules can be used than the exhaust of chemical reactions, higher performance can be reached. Lack of powerful enough lasers limits their use for propulsion at present.

## Electrical Sources

Electrons moving in a conductor, which we call electricity, is a very versatile energy source because it can be converted to other forms efficiently and moved about from place to place relatively easily. There are a number of ways to produce and distribute it.

#### I. Power Line

This option mostly applies to fixed locations rather than vehicles. If there is already electric power generation in place, or it can be reasonably added, a project can get energy by connecting to a transmission line. Ordinary transmission lines depend on either a vacuum gap, gas gap, or solid insulators to keep flowing currents from leaking to the surroundings or shorting. Resistance losses are found from the formula P = I2R, where P is power in Watts, I is current in Amperes, and R is resistance in Ohms. Voltage, V, in volts is also related by V = IR. So to reduce resistance losses for a given design with fixed resistance, you prefer to increase voltage to lower current. Higher voltages require more physical gaps or insulation, and step-down to the final use voltage, so the optimum design will depend on the details of a project.

#### J. Electric Generator

A generator converts mechanical energy to electricity using a dynamo or alternator. The mechanical energy can come from any of a number of sources. Most commonly on Earth it is from high pressure steam or falling water. In the case of steam, it is created by burning fossil fuel or a nuclear reactor, and recently, from solar concentrators. For space locations, lightweight thermal cycles such as Brayton can be considered.

#### K. Magnetic Storage

A superconducting or high inductance coil can store energy in a magnetic field. The amount is found from the formula E = 0.5LI2, where E is the stored energy in Joules, L is inductance in Henries, and I is current in Amperes. Storing energy in this way causes structural loads from the field back to the device, so the total amount is limited.

#### L. Semiconductors

Best research cell efficiency since 1975

Photovoltaics, as the name implies, converts light into electrical current. Conversion efficiency from sunlight of the best research cells using multiple layers has reached 44.0%, though more common terrestrial single layer cells are typically 20% or less. Thermophotovoltaics convert radiation from any hot object into electricity. Thermoelectrics convert a temperature difference into electricity. For space applications, pure efficiency is not the only significant measure. Variation with temperature, radiation exposure, and the mass to power output ratio are also important. Given the trend of past improvements, it is expected semiconductor devices will continue to improve, at least in the short term. The latest data should be checked for current performance.

• Anonymous "Conference Record of the Nineteenth IEEE Photovoltaic Specialists Conference- 1987", New Orleans, Louisiana, 4-8 May 1987.
• Anonymous "NASA Conference Publication 2475: Space Photovoltaic Research and Technology 1986: High Efficiency, Space Environment, and Array Technology", Cleveland, Ohio, 7-9 October 1986.
• Chubb, Donald L. "Combination Solar Photovoltaic Heat Engine Energy Converter", Journal of Propulsion and Power, v 3 no 4 pp 365-74, July-August 1987.

#### M. Solar-Driven Turbine/Generator

Since sunlight is abundant in space, concentrating it is one way to run a heat engine.

• Spielberg, J. I. "A Solar Powered Outer Space Helium Heat Engine", Appl. Phys. Commun. vol 4 no 4 pp 279-84, 1984-1985.

#### N. Microwave Antenna Array

Diode arrays can convert incoming microwaves to electric current at reasonably high efficiency.

## Beam Sources

Beam sources are highly directional, which means low entropy (randomness). This allows extracting work from them.

#### O. Sunlight

At planetary distances, sunlight is highly directional relative to a reflector, with a beam width of 1.25 degrees or less. This allows direct reflection as a propulsion method or for illumination, and concentration via lenses or mirrors. This item includes direct use of sunlight, while the items under electrical sources are for sunlight converted to electricity.

At larger distances, gravitational lensing of one star by another creates radial lines of concentrated light which may be intense enough to be useful.

#### P. Laser

A laser is an artificial light source which creates a coherent beam in one direction of a single wavelength. Because of the single wavelength, it can be coupled efficiently to an absorber, or a high reflectivity reflector for that specific wavelength. It can also be coupled to a photovoltaic device with high efficiency. As a propulsion source it can provide higher intensity light than natural sources like stars.

#### Q. Microwave

This covers direct use of the microwave beam, which N. Microwave Antenna Array converts it to electricity. A microwave beam can be converted directly to heat, or used to create photon pressure.

#### R. Neutral Particles

This is a collimated stream of high energy atoms to deliver energy from one place to another.

## Nuclear Sources

Natural decay of a radioactive isotope without attempting to affect the rate. While the decay may be natural, the isotope may have been previously created artificially.

• Lockwood, A.; Ewell, R.; Wood, C. "Advanced High Temperature Thermo-electrics for Space Power", Proceedings of the 16th Intersociety Energy Conversion Engineering Conference, v 2 pp 1985-1990, 1981.

#### T. Nuclear Fission

Intentional increased atomic fission caused by the arrangement and operation of a reactor.

• El Genk, M.S.; Hoover, M. D. "Space Nuclear Power Systems 1986: Proceedings of the Third Symposium", 1987.
• Sovie, Ronald J. "SP-100 Advanced Technology Program", NASA Technical Memorandum 89888, 1987.
• Bloomfield, Harvey S. "Small Space Reactor Power Systems for Unmanned Solar System Exploration Missions", NASA Technical Memorandum 100228, December 1987.
• Buden, D.; Trapp, T. J. "Space Nuclear Power Plant Technology Development Philosophy for a Ground Engineering Phase", Proceedings of the 20th Intersociety Energy Conversion Engineering Conference vol 1 pp 358-66, 1985.

#### U. Artificial Nuclear Fusion

Natural fusion occurs in stars, and the output has been addressed above under beamed power sources. This item is for artificial fusion sources. This has been achieved momentarily in nuclear bombs, but steady state operation has proved difficult. The most researched approach uses Tokamaks, which are donut shaped magnetic fields which contain a hot plasma. This approach has not yet produced a working device, although a prototype is under construction. It would be far too heavy a unit for a propulsion system. A number of alternate intermittent and steady state fusion devices are under varying levels of research, but all at much lower funding than the work invested in the Tokamak type devices. Some of those might yield a lightweight device.

All fusion reactions combine light atomic nuclei into heavier ones. Up to Iron-56 the binding energy of the heavier elements is lower than the lighter ones, so fusing them results in net energy output. What is required is to bring the positively charged nuclei close enough together against their electric repulsion for the nuclear forces to take over.

• Miley, G. H. et al "Advanced Fusion Power: A preliminary Assessment, final report 1986-1987". National Academy of Sciences report #AD-A185903, 1987.
• Eklund, P. M. "Quark-Catalyzed Fusion-Heated Rockets", AIAA paper number 82-1218 presented at AIAA/SAE/ASME 18th Joint Propulsion Conference, Cleveland, Ohio, 21-23 June 1982.

#### V. Muon-Catalyzed Fusion

Description: A beam of muons is directed at a deuterium/tritium mixture, where the muons catalyze mutiple fusion reactions. The heated gas powers an electric generator to power an ion or neutral particle beam thruster.

## Matter Conversion Sources

#### X. Antimatter

• Hora, H.; Loeb, H. W. "Efficient Production of Antihydrogen by Laser for Space Propulsion", Z. Flugwiss. Weltraumforsch., v. 10 no. 6 pp 393-400, November-December 1986.
• Forward, R. L., ed. "Mirror Matter Newsletter", self published, all volumes, contains extensive bibliography.

#### Y. Black Hole

Two forms of energy extraction are possible for black holes. The first is infall energy, generated as material in an accretion disk around the black hole heats by friction and emits energy. It is essentially converting potential energy into heat. Since the gravitational potential of a black hole is extreme, this can release a lot of energy. The second is Hawking radiation from hypothetical quantum black holes. This converts the mass of the black hole to emitted particles via quantum effects.