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 Box 1035 ❖ Fort Worth ❖ Texas 76101 www.lunarcc.org 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.