Papers on the Lunar Settlement
Engineering 8 : Launch Vehicles
mass of each stage is 10% the fuel mass, 0. Introduction This paper since the larger lower stages will be accompanies number 03-01 on the more structurally efficient but must bear logistics of space access. It is intended the load of the upper stages. to present technical analysis of relevant concepts, specifically the expendable If the required velocity increment for multistage rocket for direct ascent, the direct ascent, without an intermediate single-stage reusable terrestrial orbiter, orbit, is taken as the sum of the escape two-stage reusable and partially reusable velocities of Terra and Luna, 13.6 km/s, configurations, the lunar rocket, and the the necessary mass ratio with exhaust space gun. At this early date, however, velocity 4.0 km/s is 30. This sets the nothing more than approximations and maximum delivered mass at 33 t, and general considerations can be furnished. indicates that several steps are required. While specific numerical values are As a little calculation will show, the indicated in certain places, it must be overall efficiency of a step rocket is understood clearly that few of these have improved by using low mass-ratios in any validity ; they are presented in order the lower steps. We may select a to indicate trends of expected behaviour. tristage configuration, with step mass ratios of 2, 3, and 5. 1. Expendable Rocket For the expendable rocket to be useful, it must The mass of the first step, then, is 550 t, be very large. Two factors are at work of which 500 t is fuel ; the second, 330 t, here : first, ceteris paribus , the larger with 300 t fuel ; and the third is the the rocket, the larger the useful mass lunar-landing stage, 120 t with 96 t fuel. fraction ; second, expendable rockets If the first two steps are the same normally permit only infrequent diameter, the third may be built as a launches, so each one must deliver the nose-cone ; its usable load should be largest possible payload. increased by designing the structure for recycling, since it will not be reused. The detailed description of such a rocket requires analysis of technology and Of course, 4.0 km/s is the vacuum usage, but the rocket capabilities are exhaust velocity, and the rocket must liable to have an effect on the payload launch from within the terrestrial just as the payload affects the rocket, so atmosphere. To account for this, the it is not improper to begin here with a effective exhaust velocity may be broad outline. reduced 20% for the first stage only, and the second and third considered as A few arbitrary choices and rough operating in vacuo. The mass ratio of 2 estimates are necessary inputs to the with 4.0 km/s becomes 2.4 for 3.2 km/s design process. Let us propose a launch and the same final velocity, and the mass mass of one thousand tonnes, or one of the first stage increases about 40%. third that of the Saturn V . Further, The recalculated launch mass is suppose that the propellants are liquid approximately 1250 t. oxygen and liquid hydrogen, that the engines realize an effective exhaust A better mass-ratio could be achieved velocity of 4000 m/s, and that the dead with fluorine as oxidizer, less because it
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is possible to produce an expendable is more energetic than oxygen than rocket capable of reaching terrestrial because of the reduced proportion of orbit in a single stage, but such a thing hydrogen, as the hydrogen tank is a would be of little value, having less major contributor to the dry mass. payload capacity than a comparable step Fluorine, however, is not a well- rocket and no more availability. The developed rocket propellant. There are reduction in complexity is substantially no operational fluorine-hydrogen rocket offset by the loss of redundancy from engines, and the time needed to develop not being able to substitute a them is probably too long for near-term malfunctioning stage. The single stage use. There is a substantial cost for the concept is probably only useful for a substance, and the cloud of hydrofluoric reusable craft, which can carry numerous acid emitted by the rocket would be small payloads over its lifespan. No toxic, and probably deleterious to the such craft yet exists, although a small- spaceport physical plant. scale prototype, the McDonnell-Douglas DC-X, has been built. The difficulty of employing even the hydrogen-oxygen combination, which is Using oxygen and hydrogen as far better established now than in 1962, propellants, and aiming for a low orbit is considerable. The largest available with a velocity of 8.0 km/s, the required hydrogen-burning engines are in the 2.5 mass ratio is 7.4 with the vacuum MN class, and the rocket contemplated exhaust velocity, and 12.2 with the 20% would require 4 to 8 such in order to lift reduced exhaust velocity. The truth lies at all. The M-1, hydrogen equivalent to somewhere between these two figures, the 7.5 MN class kerosene-fuel F-1 since the rocket is moving upward, and engine of Saturn V , seems called for. thus increasing its exhaust velocity, all Alternative design approaches are the time that it is burning. possible, of course, such as the use of strap-on boosters, preferably recoverable. Two observations may be made on this mathematical basis. The first is that the The expendable launcher is very much a single-stage orbiter requires a high known quantity. Once a design altitude launch, with reduced approach is identified, the path from atmospheric pressure, in order to design, through subsystem testing and perform decently. Quito will make a assembly, to use is relatively clear. It is good home port for such craft. true that modern expendable rockets have design and proving cycles Secondly, only a very large single-stage measured in decades, but this is typical vehicle is viable. For the hydrogen- of aerospace projects today, and may be oxygen propellant combination, with said to have more to do with industry exhaust velocity reduced by 10% to structure than with practical 3600 m/s, intermediate between altitude requirements. Saturn V , the largest and sea level, the mass ratio is 9.22. rocket ever put into service, was Such a rocket, having a launch mass of delivered in less than 5 years by a team 100 t, would deliver 10.8 t to orbit. The of experienced rocket men. S-IVB rocket stage of the 1960s, which was not sufficiently rugged to survive 2. Single Stage Reusable Rocket It reentry or be reused, had a dead mass
fraction of about 1/10. If superior appear from this that an advantage is to materials and design were to replicate be gained by the use of denser fuel. this figure for the rocket contemplated, its payload to orbit would be perhaps The use of fluorine with hydrogen is 800 kg. Without practical experience, it called for in this connexion if any, but is not clear whether this figure can be added to the usual drawbacks are the considered representative, but such a wearing out of the tanks and engines, vehicle would be little more than an and danger to the service crew. The expensive toy. only quarter from which relief may obviously be looked for is sheer bulk. A A brief investigation may be made of the 1000 t vehicle with the same use of a denser fuel than hydrogen. The characteristics as the 100 t hydrogen fraction of mass required for the fuel model described above would deliver a tanks would decrease, but the required payload of 8 t to orbit, and could be mass ratio would increase. The economically successful if it had a following analysis assumes that the sufficiently brief turn-around cycle. vehicle is the frustum, altitude 2 r, of a With increasing size, also, the square- right circular cone of altitude 3 r, a cube law operates to improve the compact shape of the sort typically used structural and payload mass fractions. in such designs. The non-fuel mass is Applying the analysis used above to treated as distributed uniformly over the compare fuels to the 1000 t hydrogen surface in the form of a titanium skin, vehicle, the areal density is 106 kg/m 2, nominal density 4510 kg/m 3. The or 2.36 cm equivalent. It rather appears thicker this fictitious layer is, the easier that the most successful spaceship will the problem of inclosing the required be the largest, and in this respect, it is volume, and the more mass available for very like the airship. other purposes. In any case, it appears that the single- At approximately the proportions used in stage rocket presents problems which are the US Space Shuttle, the bulk specific not clearly understood. The operational gravity of the hydrogen-oxygen principles of the Luna Project suggest combination is 0.37. The fuel mass of a that the appropriate response is to try it. vehicle with a gross liftoff mass of 100 t It is unlikely that the first prototype, will be 89.2 t, occupying a volume of even if it achieves orbit, will carry a 241 m 3, and requiring a surface area of payload capable of supporting early 220 m 2. The remaining mass being 10.8 Project activities, and the design cycle to t, the skin areal density is 49.3 kg/m 2, develop from zero a model capable of which is equivalent to a thickness of such support is probably more than five 1.09 cm of titanium. For methane, with a years. Since the sustaining phase will vacuum effective exhaust velocity of probably occupy at least three years after 2950 m/s, again reduced 10% to 2660 the landing of the first party, the m/s, the mass ratio is 20.4. At a bulk development of reusable concepts to specific gravity of 0.75, the 100 t vehicle become operational in this period, taking has a volume of 127 m 3 and a surface over from expendable launchers, must be area of 144 m 2. With a remaining mass pursued. of 4.91 t, the areal density is 34.2 kg/m 2, or 0.759 cm equivalent. It does not 3. Reusable Combinations Rather
than design a single vehicle to meet all over the single-stage system. the challenges involved in going from ground to orbit, it may prove easier to 4. The Booster Let us examine, as divide the functions among separate an example of such adaptable hardware, vehicles. This can take various forms, the North American B-70 Valkyrie including the balloon-rocket hypersonic bombing aeroplane. This combination or “Rockoon”, and groups remains, after forty-five years, one of the of winged rockets. The discussion largest and highest-performing aircraft below addresses the case in which two ever constructed. In terms of speed, stages are used, the lower being purely altitude, and lift, it appears well adapted an aircraft. to serve as the booster component of an operational prototype two-stage-to-orbit As seen in the discussion of the single- combination. stage orbital rocket, the principal problems are the large velocity Performance figures for the B-70 vary increment required, and the impairment somewhat. Two developmental units of the rocket effective exhaust velocity were built, both different, and a third by atmospheric pressure. If the rocket vehicle which was to have been the can be carried near the limit of the prototype of the production model was sensible atmosphere before launching, scrapped on the ways when the project the second problem is dealt with, and if was cancelled. In round figures, the the carrier can impart velocity as well as takeoff mass was 250 t, 110 t being altitude, the first can be ameliorated. An disposable lift (mostly fuel), the engine additional advantage of high-altitude thrust was 800 kN, and the maximum launch is that it can be more nearly speed achieved was 920 m/s at 22 000 m horizontal, in the direction of the altitude. intended orbit, than a ground launch. Some improvement may be possible to These gains come at the cost of greatly the design. Since the second prototype increased complexity for the overall XB-70 was destroyed in a crash, only the system, due to the necessity of building, lower-performing first unit now exists, maintaining, and operating the radically and it is a museum piece. Even if it different vehicles, separately and as a were to be had, the kind of inspection unit. If the restriction of functions in the and renovation necessary to make it individual units reduces the difficulty of ready for flight, not to speak of the the development process more than the modifications required for carrying an need for interoperability increases the upper stage, could well prove more difficulty, the development of the two- difficult and time-consuming (if not stage system is justified. Two important expensive) than building a new example cases appear. First, if several different of the third model from the original upper stages can be used with the same plans. It is not unreasonable to suppose booster, versatility can be increased over that some design alterations could be developing an entirely new launch made to better suit the aircraft for its system for each function. Second, if new role. existing hardware can be adapted, the two-stage system may have an Structural hard points and other facilities advantage in development cycle time for carrying and launching the upper
stage are a necessary addition. Control respect to booster speed. For the 100 t systems could be replaced with more upper stage, the results are 16.9 t, 17.4 t, modern equivalents, and the volume and 18.3 t, the least favourable of which intended for the bomb bays may prove is handily superior to the most useful as top-up tanks for the rocket’s favourable 60 t case. Considering that cryogenic fuel, some of which will boil the larger rocket can be expected to have away during the ascent to the launch the larger payload mass fraction, it point. In general, however, the appears desirable to concentrate on important modifications will be in the increasing payload capacity. area of propulsion, with the intent of increasing thrust, or reducing vehicle With a fixed lift-to-drag ratio, aircraft mass, or both. load capacity can be improved either by reducing mass or increasing thrust. A brief tradeoff analysis may be Turbojet thrust-to-mass ratios have attempted, to examine the effects of improved considerably since the B-70 increased speed as against increased load was designed, but it is not clear that capacity in the booster. Three velocities modern units will maintain their are taken : 900 m/s, representing performance at Mach number 3 and realized performance of the B-70 ; 1000 above, even with the assistance of m/s, representing a reasonable variable intake nozzles. More radical improvement with increased thrust ; and modifications, such as employing 1200 m/s, representing an extreme methane rather than kerosene for fuel, probably beyond the achievable belong properly to the design of a performance. It may be supposed that purpose-built booster stage. In the event the airframe design is valid only out to that an engine were found having the about Mach number 3.5. Two same size and mass as the original, the conditions of loading are examined : an question of powerplant configuration upper stage of 60 t, representing would depend on high-speed thrust. reasonable performance with a light fuel Four engines having a unit thrust of 200 load, recognizing that the booster need kN at low speeds, for example, but only make a dash to its maximum speed considerably less at Mach 3, could be and altitude and then return to base ; installed on an “over and under” basis. and an upper stage of 100 t, requiring High speed power would be provided by some combination of increased thrust ramjets, which are lightweight but and lightening of the aircraft. The target generate no thrust at rest, in the parameter is on-orbit mass. remaining two bays.
Mass ratios for a final velocity of 8.0 Further tradeoffs are possible, since km/s, assuming a hydrogen engine with supersonic aircraft are unlike subsonic vacuum performance at the launch aircraft in requiring full power at speed altitude, are : for 900 m/s launch, 5.90 ; rather than only at takeoff, and for 1000 m/s launch, 5.76 ; for 1200 m/s considering that a spaceplane will not be launch, 5.47. For the 60 t upper stage, expected to operate except from the corresponding final masses are 10.2 t, specially-prepared facilities. A turbojet 10.4 t, and 11.0 t. This, of course, is complement of less than 800 kN might false precision, but it represents clearly be installed in tandem with ramjets, and the scale of performance variation with the additional impetus needed to lift off
supplied by a catapult. deserves further examination. Experience with the A-12 /D-21 This process can, however, only be taken combination shows that hypersonic so far. The combination of pure ramjet separation of “piggyback” aircraft is engines with catapult launch would possible, although demanding apparently require accelerating the considerable care, and that the parasite aircraft to above Mach number 1 at may be rather large without producing ground level, presenting considerable excessive drag or aerodynamic aerodynamic challenges even at a high- interference in supersonic flight. altitude launch site. Somewhat better, if top-up tanks were built into the booster, The lifting body has an advantage in would be firing the orbiter rocket for structural mass fraction over a winged takeoff thrust, especially if its exhaust aircraft, and its density empty would be were channeled through an ejector to quite low, reducing the problems of draw air into the ramjets. In either case, atmospheric heating on reentry. A however, the booster would be unable to titanium-alloy airframe could probably fly back from a remote landing site such be employed with minimal heat as might be reached in an aborted launch, shielding. If hydrogen fuel were used, a and there is no other way to transport single engine in the 1.5 MN thrust class, such an enormous thing intact. such as the J-2 type, could supply the required thrust for launch masses at least The best approach appears to be to begin up to 100 t. with a minimal modifications. The aircraft can be flown alone and with a Versatility is above alleged to be an dummy upper stage, to gain experience, advantage of the two-stage spacecraft. It before the use of a live upper stage is is worth examining some possibilities attempted. Based on experience with presented by modifications of the upper this baseline booster, a model with stage. The figures given above for the further modifications can afterward be minimum launch speed are 10.2 t final built and proven. Since the base design mass for the 60 t orbiter, and 16.9 t for already exists, it should be possible to the 100 t model. Assuming that the dry begin flying within three years of mass is 1/8 of the total launch mass in committing to the configuration, and if it both cases (somewhat more than for a proves viable a second-generation shuttlecock-shaped vehicle), the possible configuration should be possible within useful loads are 2.7 t and 4.4 t three additional years, in time to support respectively. the continuing settlement phase. The above estimates are extremely crude, 5. The Orbiter The above has but suggest that even the smaller craft taken the upper stage as given, without could carry a man, in a pressurized examining its design, and assuming a compartment with life support for a minimal effect on the high-speed reasonable period, and maneuvering fuel aerodynamics of the booster. The broad, to make a controlled reentry. This flat back of the B-70 delta wing appears performance would suffice for suitable for hosting a flat-bottomed demonstration and training purposes. parasite rocket, such as a lifting body of The larger might carry more than one the FDL-5 design, but the matter man, and some payload as well, perhaps
in the form of additional maneuvering booster aircraft. fuel. If the same basic designs were used for unmanned craft, a smaller factor The development programme will be of safety would be allowable, and the eased by the interchangeability of upper useful load could be correspondingly stages, and the fact that both stages can increased. Considering the probably fly to a landing. If several are built, increased difficulty and danger of air- even with a single booster, modifications launching an unpiloted vehicle, the 60 t can be made without withdrawing the model may not be worth bothering with. whole system. Flight tests and pilot The payload of close to 5 t possible with training might be conducted by dropping the 100 t type, on the other hand, seems an empty airframe, or a flyable mockup, large enough to justify the effort, given from a large subsonic transport, and by the frequent launches possible with a launching from the ground (perhaps with reusable system. a partial fuel load) if sufficiently strong landing gear is provided. Since the The same type of analysis may be major danger is a collision following a applied to these vehicles as was done botched air launch, supersonic above for the single-stage orbiter. experience before mating the Approximating the lifting body as a components is a necessity. As with the regular tetrahedron, and using figures for single-stage solution, reusability allows hydrogen and oxygen as before, the development to proceed by incremental required volumes for 49.8 and 83.1 t are steps in the course of operations with 135 and 226 m 3 respectively, and the working ships. Since the Project cannot corresponding surface areas 217 and 306 remain dependent upon expendable m2. The remaining masses of 10.2 and launch vehicles, even if they are required 16.9 t give areal densities of 45.7 and for the initial phase, the development of 55.4 kg/m 2, equivalent to 1.0 or 1.2 cm both approaches is indicated, in order to titanium. As with the single-stage insure that one will work. orbiter concept, the advantage of smaller structural mass fraction using a denser 6. Partial Reusability The fuel is swamped by the increase in mass booster aircraft of the two-stage reusable ratio, 11.1 using methane and oxygen combination might be used in another with a vacuum effective exhaust velocity way. If a reusable rocket benefits from of 2950 m/s. For the 100 t rocket stage, an improved mass ratio when launched the volume is 122 m 3, the area 203 m 2, from high altitude and high speed, an the remaining mass 9.0 t, the areal expendable rocket will also benefit. density 44.5 kg/m 2, and the equivalent titanium thickness 0.99 cm. The usefulness of combining an expendable upper stage with a reusable All of these figures are comparable to lower stage is a matter of availability. the single-stage figures, indicating that The same payload can be lifted to orbit the two concepts are equally viable. The using a significantly smaller rocket, or criteria of choice appear to be time and conversely the same rocket can lift a capability. It is expected that the two- larger payload, if it is launched from the stage solution will be developed more air. The question is whether this fact rapidly than the single-stage, but will will permit substantially more payload to remain limited by the capacity of the be orbited per unit time than ground
launch, such as by permitting the use of velocity ; half that velocity gives a readily-available expendable rockets range less than one tenth the beyond their rated performance, or circumference. Accordingly, the rocket allowing the use of simpler (perhaps will be designed to reach orbit and make solid-fuel) units having less efficiency a soft landing. This will enable one-way but more convenience. The present U.S. payload delivery anywhere on Luna, or Space Shuttle is partially-reusable, but two-way travel within a reasonably large (in effect) discards the bottom stage zone. As the zero-altitude circular rather than the top stage, and so does not velocity is 1680 m/s, the total velocity of present a model for the concept mooted. the rocket is 3360 m/s. This is less than The topic deserves consideration, as a the exhaust velocity attainable with concept which could begin delivering oxygen-hydrogen fuel, and such a rocket payloads to Luna as soon as the booster would require a mass ratio of only 2.32. is proven, but nothing definite can The fuel actually to be used, however, presently be said. will have a poorer performance.
7. Lunar Rocket The purpose of 8. Performance Estimate Among the rocket fabricated from lunar conventional rocket fuels and oxidizers, materials is twofold. First, it serves as a only aluminum and oxygen are plentiful mode of lunar global transportation. in the lunar environment. These two Second, when launched by the space gun, substances do not form a conventional it is used for maneuvering in lunar and propellant combination. Aluminum is terrestrial orbits. Its characteristics are normally encountered in solid rockets, as defined largely by the first purpose and a dispersed phase in an organic binder, by the requirement that, since it will be accompanied by perchlorate oxidizer, fabricated in large quantities, it should while oxygen is typically used as a not use any scarce materials. liquid and paired with a liquid fuel.
A transportation mechanism can be It does not appear practicable either to characterized broadly by load and range. feed a liquid-fuel motor with molten If the lunar rocket is to be useful, it aluminum, or to encapsulate oxygen in should at least be capable of carrying a solid aluminum. Accordingly, the rocket man, with supplies for several days and will be of the hybrid type, using a solid various tools, or a significant cargo. As fuel grain with a separate oxidizer. This a round figure, a suitable payload might type of engine has the advantage over be 1 t. Since Luna is an airless body, the pure solid that it can be throttled and rocket braking must be provided, and the restarted, although not controlled so total velocity increment is equal to twice finely as the liquid-fuel motor. the velocity required for the trajectory. To go, brake, return, and brake again The principal difficulty presented by would require a velocity of four times aluminum as a rocket fuel is that the the initial. product of combustion is a refractory solid, having a tendency to adhere to the The question of range becomes parent surface. The resulting problems important. A rocket intended to travel help to give shape to the final design. one quarter of a planet’s circumference requires about nine-tenths of orbital First, a solid product of combustion does
not expand and escape from the nozzle. power than before. As long as the mass Thus, left to itself, such a burning is not sufficiently porous to allow the process will not produce any momentum rocket gasses to escape through the walls, transfer. Second, if the product remains inclosing the grain with a case may be at the surface, no new fuel area is avoided, improving the structural mass exposed, and the reaction is rapidly fraction. extinguished. Therefore, it seems reasonable that the rocket should operate The result of these measures should be with a substantial excess of oxygen. that the oxidation of the metal surface This will absorb some of the reaction will cause melting and even local boiling heat and serve as a working fluid ; it immediately below the surface, shedding should also help to erode away the oxide the oxide into the oxygen stream, and from the metal surface, in the form of exposing new surface area to minute particles (hopefully!) which will combustion. The bulk of the rocket, join the exhaust stream, participating in meanwhile, will retain its integrity. momentum transfer while not choking Firing the rocket will probably require the combustion process. squibs of thermite, and to allow restarting these might be mounted in a It appears necessary to reduce the mechanism like a revolver barrel, at the thermal conductivity of the fuel grain. end of the oxygen fuel line. A thermite Unlike common solid propellants, squib would be rotated into place and massive pure aluminum is highly fired, and the oxygen then turned on to conductive, and if the loss of heat blow the burning material into the thrust through the combustion surface were not chamber, spattering it on the walls and sufficient to extinguish the reaction, igniting the propellant charge. there would be a danger of bodily melting and sloughing, with consequent This is no more than a conceptual design, failure of the rocket. but with sufficient assumptions a simple thermodynamic analysis can be Two approaches may be identified. The performed to evaluate feasibility. The first is to reduce the thermal conductivity fuel is chosen to be an alloy of ten of the bulk metal, by alloying it with weight percent calcium in aluminum, some other flammable metal. It is a burned with a fifty percent stochiometric property of alloys that a small admixture excess of oxygen. The fuel is taken as in even of one highly-conductive metal into the solid phase, the oxidizer as gas, and another drastically reduces the thermal the products of combustion as solid. As conductivity. Also, alloys tend to have the grain is a metal, having inherent lower melting points than the parent structural strength, and the exhaust is metals. Calcium and magnesium are vacuum, some liberty is available in the fairly common in lunar rock and might selection of chamber pressure and be used. Secondly, if the grain is made expansion ratio. For convenience, the not from solid metal, but from a grain geometry is supposed to be a consolidation of small particles, such as constant-area type, although constant sintered powder with moderate thrust could be maintained by throttling compaction, heat transfer between the oxygen supply. individual particles is impeded, and the whole mass has a much higher insulating The chamber pressure is selected to be
2.0 MPa, and the expansion ratio 20. transferred out of the solid. At a lower The solid products of combustion are equilibrium temperature, more heat assumed to occupy zero volume, and to would be present in the gas phase, and be intimately mixed with the excess thus available for propulsion. Other oxygen gas, being expelled through the propellant compositions must also be nozzle. The momentum transfer is investigated. The burning of a series of accordingly the same as if the excess test motors is clearly called for, in order oxygen had been heated indirectly, but to observe the actual behaviour of the the exhaust velocity is less by a factor of device. 5.4. 9. Space Gun Under lunar conditions, A thermodynamic analysis proceeds as with low escape velocity and no sensible follows. The oxygen is introduced into atmosphere, the possibility arises of the chamber by pumps, in the liquid state treating space-launch payloads as and at chamber pressure. Heat from the projectiles, accelerating them by external reaction vaporizes the oxygen, and the means near ground level. This is the stochiometric quantity immediately purpose of the so-called space gun. combines with the fuel metal. Heat is then transferred from the products of Obviously, a gun in the strict terrestrial combustion to the excess oxygen until an sense is not what is required. Something equilibrium temperature is reached. The capable of launching relatively large mixture of oxygen and combustion objects at relatively gentle accelerations products then expands isentropically is called for, if the device is to be used through the nozzle. for manufactured goods or a fortiori men. Electromagnetic machines of various The overall exhaust velocity calculated types have been proposed. by this method is approximately 800 m/s. This is a very poor figure, requiring a The “rail gun” requires the projectile to mass ratio of 67 for the velocity desired. be suspended in a magnetic field and The reliability of this figure, however, is conduct an electric current in the normal also extraordinarily poor due to the very direction, and is limited by several approximate methods used to derive it, factors, including destruction of the to the fact that the calculated chamber electrical contacts. A type of “coil gun,” temperature is over 8000 K, a condition referred to as a mass driver, is under which chemical equilibrium must incorporated in the O’Neill colony be considered, and to the fact that proposals for the purpose of delivering transfer of heat from the solid phase to lunar payloads to cislunar space. This the gas phase during expansion was not machine consists of a long line of considered. toroidal electromagnets, each of which is triggered to conduct a pulse of current The physics of the problem suggest that by switches keyed to the passage of a a much larger excess of oxygen is “bucket” in which the payload is carried. desirable, both because of the decrease This bucket is fitted with strong in average molecular weight of the permanent magnets, and must be braked exhaust, and because at the high to a stop at the end of the gun. chamber temperature quoted only 12% of the combustion energy can be A second type of coil gun relies on
polyphase alternating current. The coils laid out horizontally. A vertical gun are wound in such a manner as to set up located anywhere near 50° N would a traveling magnetic wave within the have its muzzle pointed well out of the tube which they form. The result is that ecliptic plane. An oblique shaft directed a conductive body placed at the muzzle at Terra would not be radial, and would is, by self-induction of currents in the send its projectiles somewhere else. The skin, held firmly at the centre of the bore proper obliquity for putting packages and moved toward the other end. The into terrestrial orbit, or trajectories velocity of the body asymptotically around Terra for other destinations, approaches the phase velocity of the could be determined, but appears traveling wave, with an acceleration unuseful. dependent principally on its mass and surface electrical properties. The energy Most uses would require some rocket efficiency of this type of gun can be power on the projectile, and this once improved by switching circuitry which granted, a horizontal gun has advantages. feeds energy only to coils near the Firstly, by varying the excess velocity, a projectile, but its operation does not variety of hyperbolic trajectories is require such. If the projectiles are available. The combination of a slight sufficiently uniform, the coil spacing can initial velocity deficiency and properly be increased toward the muzzle end in timed rocket thrust will allow access to accordance with the velocity profile, escape trajectories not directly available. improving the acceleration without Again, the horizontal gun allows placing requiring higher power frequencies. the projectile into lunar orbit with a small apoapsis rocket. The resulting All of these so-called guns are special orbit would be of high inclination, but cases of the electric motor, and with any this does not appear to be a disadvantage. kind of competent design should be able It would allow access to a large fraction to achieve a conversion efficiency of of the lunar surface without plane electrical to kinetic energy of 50%. On changes, and increase the achievable this assumption, a gun expelling its variety of transfer orbits. projectile at lunar escape velocity, 2380 m/s, will require an energy input of 5.7 Lunar orbit is essentially at infinity as MJ/kg. For a projectile of 5 t mass, far as Terra is concerned, and the energy accelerated at 200 m/s 2, which even the required for a plane change at infinity is most delicate manufactured goods zero. Accordingly, a terrestrial orbit of should be able to withstand, this any desired inclination can be reached translates to a power of 2.4 GW for 12 s. from an equatorial lunar orbit. The With the same mass, but a lower advantage of a high-inclination lunar acceleration of 50 m/s 2, suitable for men, orbit is that, by performing the lunar 560 MW is required for 48 s. escape maneuver at a carefully selected moment, any inclination of terrestrial Even the higher-acceleration gun orbit can be reached by firing the rocket requires a bore length of 14 km, and along the line of flight. To reach non- although the excavation of very deep equatorial terrestrial orbit from shafts has been mooted in connexion equatorial lunar orbit would require with the construction of Luna City, it either firing at an angle to the line of seems reasonable that the gun should be flight, or a second burn after the escape
maneuver to perform the plane change. The same applies, mutatis mutandis , to high-inclination escape trajectories.
Accordingly, the horizontal gun, laid out along a parallel of latitude, appears perfectly suitable. In practice, a slight elevation of the muzzle may be required in order to avoid striking the terrain, but this will result in only minor operational changes. As lunar development increases, it may prove economical to construct additional guns, at other azimuths, for point-to-point transportation, although the controls problem of catching a projectile in a gun muzzle appears sufficiently difficult that rocket braking will still be required.
A. Conclusion The choice of space-launch techniques and vehicles must necessarily have a major effect on the execution of the Luna Project. Options have been described, and briefly discussed, but none of the approaches discussed represents an available, off- the-shelf product. Without sufficient data to make definite choices, the only possible recommendation is that study of all alternatives be pursued at least to the point that some selection can be made. It is recognized that some combination of choices may be superior to the exclusive use of one.
revision 0 submitted for comment by publius 2007-213