II-1

Effect of Environmental Parameters on Habitat Structural Weight and Cost

EDWARD BOCK, FRED LAMBROU, JR. and MICAEL SIMON

Space-settlement conceptual designs have previously been accomplished using "Earth-normal" physiological conditions. The purpose of this paper is to quantify the habitat weight and cost penalties associated with this conservative design approach. These penalties are identified by comparison of conservative Earth-normal designs with habitats designed to less than Earth-normal conditions. Physiological research areas are also recommended as a necessary prerequisite to realizing these potential weight and cost savings. Major habitat structural elements, that is, pressure shell and radiation shielding , for populations of 10², 10⁴, and 10⁶, are evaluated for effects of atmospheric pressure, psuedogravity level, radiation shielding thickness, and habitat configuration. Results show that broader habitable g-ranges, reduced atmospheric pressure, and detached radiation shielding all have a significant effect in reducing habitat costs. Also, a minimum cost per person is discovered for a habitat with a population of about 10⁵, and this cost is independent of habitat configuration.

INTRODUCTION

The design of space habitats is highly dependent on both the physiological conditions need to support life and psychological conditions conducive to enjoyable living. The physiological requirements for a breathable atmosphere, cosmic radiation protection, and psuedogravity have a direct effect on the structural weight and cost of the habitat. Psychological conditions also have an important, although less readily assessable, influence on weight and cost through variations in habitat configurations and interior design. This paper addresses only the physiological effects on habitat structural designs. The results obtained, however, should support subsequent livability analyses by supplying sensitivities for evaluating alternative habitat configurations and interior designs.

The minimum environmental requirements for short-duration life support in space are fairly well understood. Less well known are long-term effects under less than Earth-normal conditions. Conceptual space-settlement habitat designs proposed to date have eliminated this concern by use of the conservative design philosophy of Earth-normal conditions. The question which this paper address are: (1) How much does this design conservatism cost from a structural standpoint? (2) Which areas of physiological research into less than Earth-normal conditions offer the greatest potential decrease in habitat construction and operating costs? (3) Do the combined results of sensitivity studies performed during this investigation lead to a recommended habitat configuration that offers the best potential for satisfying physiological requirements at a minimum cost?

To address these questions, the following approach has been taken: First, the established range of human tolerance limits has been defined for those physiological conditions which directly affect habitat structural design. Second, these entire ranges, or portions thereof, were set as habitat design constraints as a function of habitat population and degree of ecological closure. Third, calculations were performed to determine the structural weight and cost associated with each discrete population size and its selected environmental conditions. These calculations were performed on the basis of habitable volume equivalence for four basic habitat configurations: sphere, cylinder with hemispherical ends, torus, and crystal palace.

Sufficient point designs were analyzed to permit graphical comparison of habitat structural weights and costs due to a broad range of environmental and population conditions. Those environmental parameters that then offered the greatest economic benefits when reduced to less than Earth-normal conditions (but within established human tolerance limits) were readily identified.

It should be emphasized that the work contained in this paper is not an analysis of a total habitat system; rather, it is limited to environmental and configuration sensitivity analyses of the habitat pressure shell and radiation shielding, plus considerations of habitat illumination and atmospheric composition. Except for their gross influence on the basic habitat structural design, such habitat subsystems as the following have not been evaluated or costed as part of this work: internal secondary structures (buildings); furnishings and personal effects; life-support equipment such as air conditioning, water supply, sewage treatment, etc.; photovoltaic power arrays and waste heat radiators; and spin alignment bearings, hub airlock, and docking facilities.

During performance of work at the 1977 Ames Summer Study relating to this paper, two study team leaders made significant contributions: Dr. Gerard O'Neill suggested the structural analysis approach used for comparing alternative habitat configurations, and provided an example derivation upon which the generation of structural formulas was based. Dr. John Billingham provided guidance on physiological conditions and was an excellent source for reference materials. Both Doctors O'Neill and Bellingham contributed to the selection of representative physiological design constraints for the three habitat populations investigated.

PHYSIOLOGICAL CONDITIONS

Human tolerance limits have been defined for physiological conditions that directly influence habitat structural design requirements. Those environmental parameters which directly affect the habitat structure include internal personal space and furnishings, atmospheric pressure, and gravitational acceleration. Other environmental features that can influence structural mass due to implementation options are radiation protection and illumination techniques. Additional features such as noise abatement or vibration control, which do not directly influence structural mass, have not been included in this analysis. (For a more complete general discussion of environmental parameters and habitat sensitivity philosophy, see ref. 1.)

Personal Space and Furnishings

Habitats must be designed to provide comfortable living, service, social, and recreational facilities. These needs can be analyzed in terms of area, volume, and internal mass requirements per person, as a function of population size, duration of stay, habitat remoteness, etc. Three population sizes (10², 10⁴ , and 10⁶) were selected for evaluation to encompass a broad range of habitat volumes. These populations span communities ranging from early space construction facilities to large, relatively self-sufficient settlements.

Volume and area requirements for "military-type" spacecraft and submersible vehicles have been established for relatively short durations (less than 12 months) (ref. 2). Use of these data for space settlements would be inappropriate, because these data apply to temporary assignments in which personnel return home when the tour of duty is completed. Although this same reasoning also applies to short-duration civilian habitats, a significant increase in volumetric allocation per person should be allowed. No real data are available for modern, long-duration (>1 year), remote civilian habitats, but information from the 1975 Ames Summer Study on Space Settlements (ref. 3) was used in conjunction with the existing short-duration data to provide the civilian volumetric requirement curves shown in figure 1.
The 10⁴ population design point is obtained directly from detailed analyses conducted during the 1975 Ames Summer Study on Space Settlements. The data point for a 10² population habitat was derived from the same source; table 1 summarizes the details pertaining to both configurations.

The location of these points on the duration abscissa in figure 1 was based on space manufacturing population buildup projections (refs. 4, 5). Early habitats with small populations will probably exchange personnel annually or biennially. Larger (10⁴) intermediate habitats are expected to receive Earth-trained personnel who will spend their productive years in space, but will return to Earth for retirement. Populations one or two orders of magnitude greater will probably spend their entire lives (vacations excepted) in the habitats. The transition point from an Earth-resupplied habitat to one that is mostly self-sufficient is expected to occur in the 10⁴ to 10⁵ population range, with substantial on-site food-production experiments performed somewhat earlier. The largest volume/person requirements curve in figure 1 reflects the additional volume needed for food production.

As mentioned previously, both volume and area requirements are important measures of habitat livability. When comparing alternative habitat configurations, however, only one of these measures of personal space can be used as the independent variable. Most previous efforts to define habitat configurations have imposed very strict limits on g-level variations (0.9 to 1.0 g), and have used area as the independent variable. For this comparison, wide g ranges will be studied (including zero g) which makes area a very poor criterion for comparison (essentially meaningless for zero g). All habitat population sizes and geometries have therefore been configured and analyzed on a volume equivalence basis, that is, a fixed volume per person for each habitat population, independent of habitat geometry.

Internal habitat mass per person is a measure of housing and furnishing, and of personal effects allocation. Unfortunately, little appropriate Earth data exist to aid in evaluating this parameter because (1) the cost of Earth-based housing materials, which comprise the largest percentage of personal habitat mass, is generally inversely proportional to their mass, that is, concrete and construction lumber, and (2) a large percentage of
habitat internal mass will be manufactured from "left over" lunar material, resulting in designs and material uses significantly different from their Earth functional counterparts. The best estimate of habitat internal mass available in current literature is found in the 1975 Ames Summer Study (ref. 3). Since the internal mass requirements should be relatively independent of total population size or volumetric allocation, fixed values for limited recycling (43,000 kg/person) and maximum recycling (53,000 kg/person) habitats were selected.

Pseudogravity and Rotation Rate

The physiological effect of long-term weightlessness is not fully understood. The Skylab 4 astronauts, who were weightless for 84 days, experienced progressive bone decalcification. It is unclear whether these losses stabilize for longer exposures. If they do not, then some level of artificial gravity will be required to prevent severe osteoporosis (ref. 1).
The only way to establish pseudogravity in a space habitat is by rotation. This rotation, however, can cause disorientation and motion sickness due to influence of the Coriolis effect on the vestibular system if the rate of rotation is too high. Because studies in rotating rooms on Earth have shown that most personnel adapt to rotation rates of 3 rpm (ref. 1), this rate will be chosen as the guideline for small, selective, 100-person habitats. For the adaptability and comfort of a general population habitat (10⁶), it is generally accepted that rates above 1 rpm should be avoided. Since the 10⁴ habitat will not be as selective as the earlier habitat but more selective than the 10⁶ habitat, it is reasonable to consider 2 rpm as its rotation rate.

Radiation and Shielding

Radiation poses a major problem in space-settlement development because of the constant presence of galactic (cosmic) rays. This type of low-level radiation is isotropic and consists of about 87 percent protons (low Z) and 13 percent heavier nuclei (high Z). "Z" is the charge on the particle, which determines its ionizing power or the quantity of chemical bonds broken by its passage through human tissue. The other source of space radiation, solar flares, is normally at an insignificantly low level, but can occasionally rise to extremely high levels for periods of a few hours or a few days (refs. 6-8).

The best protection against radiation is the use of passive shields. Active "plasma radiation shields" have also been proposed (ref. 3) but are currently speculative and require further substantiation. Figure 2 shows the galactic dose rate as a function of passive shielding thickness. Since nuclear interactions are the primary attenuation mechanism, secondary emission products are a major concern. These secondary products consist of four main types: cascade protons, cascade neutrons, evaporation protons, and evaporation neutrons. Of these four, only the cascade products are significant since the effects of evaporation products are approximately two orders of magnitude smaller than those of the primary protons (ref. 6).

Current U.S. standards for whole-body radiation are 5 rem/yr for radiation workers and 0.5 rem/yr for the general population. Since the inhabitants of the early habitats (100 and 10,000 people) will be selected adult groups with short to intermediate stay times (1 to 30 yr), we can consider them to be radiation workers and design the shielding for 5 rem/yr. To achieve this protection from galactic radiation, 280-g/cm² shielding is required.

The problem of solar flares, however, must still be addressed. Figure 3 shows the total radiation dose as a function of shield thickness for the proton component of an anomalously large flare approximating the intensity of the August 1972 flare. The secondary products are included in this calculation, but the dose from alpha particles is ignored. The alpha flux, however, is less than 20 percent of the primary rem dose (ref. 9). Thus, 280-g/cm² shielding would attenuate the radiation well below the current U.S. standard for a single emergency exposure of 25 rem. However, on 23 February 1956, the largest flare on record took place. It has been estimated that during this flare people shielded by approximately 500 g/cm² would have received 25 rem (ref. 10). Fortunately, a flare of this magnitude occurs only once in 20 years. Thus, since people will only live in the 100-person habitat for about 1 year, there would be little need for any additional protection. However, because of the longer duration of the 10,000-person habitat, a flare shelter with an additional 220 g/cm2 of shielding will be necessary.
The 10⁶-person habitat has an unselected general population. Thus the radiation level must not exceed 0.5 rem/yr. To achieve this, shielding of 550 g/cm² is required. Not only does this protect against galactic radiation, but it also attenuates the radiation of the largest solar flare to below the maximum permissible for a single emergency exposure. A shelter still might be desirable, however, to protect young children and pregnant women.

Atmosphere

In considering the structural design of a habitat, the total atmospheric pressure is important since it is one of the most significant loads. The lowest pressure will result when the atmosphere contains pure oxygen at a partial pressure similar to that in Earth's atmosphere. Figure 4 shows the pure oxygen atmospheric pressure required for human lungs to physiologically achieve an equivalent Earth altitude. To obtain an Earth sea-level equivalent, 25.3 kPa of pure oxygen is required. This can probably be reduced to 20.0 kPa for the early 100 person habitat since the personnel will be highly selected and could reasonably be expected to function normally in an atmosphere equivalent to 2400 in (8000 ft) above sea level. The inhabitants of the intermediate 10,000-person habitat would also be selected, but to less stringent criteria, so they could operate at an equivalent 1200-m (4000-ft) level or 22.5 kPa pure oxygen.

The desire to operate at such low pressures might be tempered, however, by the fact that sound does not travel well at low pressure (refs. 11, 12). For instance, the Skylab astronauts, who lived in a total pressure of 34.4 kPa (0.33 atm) said that the limit of a loud speaking voice was about 5 in. This often left them hoarse (refs. 11). Another possible problem with low pressures is diminished effectiveness of the cough mechanism (refs. 12, 13).

For these reasons, and to reduce fire danger, it is desirable to increase the total pressure by adding a relatively inert gas. Considerable experience has been obtained with nitrogen, Earth's atmosphere diluent, and helium. Although nitrogen is our natural atmospheric diluent, it has one disadvantage: under fast decompression, nitrogen bubbles are released, causing the bends. The best alternative inert gas, helium, reduces man's susceptibility to the bends. Helium also inhibits atelectasis, the tendency for lung collapse, better than nitrogen, but since both helium and nitrogen are superior to pure oxygen, this difference becomes insignificant (refs. 13, 14). Because helium is much less dense than nitrogen its use could lead to significant reductions in transportation cost. Its major disadvantage is severe voice distortion.

The most important function of a diluent gas is to reduce fire danger. Fire hazards in O₂-rich environments have been studied extensively. It has been demonstrated that the burning rate of filter paper in 0.2 atm of pure oxygen is approximately twice that in 1.0 atm of 21 percent O₂ + 79 percent N₂ (ref. 15). Furthermore, many conventional flame-proofed materials burn readily in 30 percent to 40 percent O₂ (ref. 16). Helium diluent is not as effective in reducing the burning rate as is nitrogen (refs. 14, 16). The major factor in overall fire safety, however, is not to control the burning rate but to prevent ignition (ref. 17). As the percentage Of O₂ in the atmosphere increases, the minimum pressure required for ignition decreases dramatically.
Figure 5 shows the components of oxygen-nitrogen mixtures that are physiologically equivalent to sea-level air as a function of total pressure. To reduce the total pressure to 0.5 atm, the O₂ partial pressure must be increased to 50 percent. The trade-off between decreased total pressure and increased fire danger must be fully considered before final selection of a space habitat atmosphere is made.

Illumination

The most important component of man's sensory apparatus is his visual system. This makes it particularly important for space-settlement inhabitants to have proper lighting in their work, rest, and living areas. One of the largest habitability problems aboard Skylab was the lack of proper illumination. In fact, the lighting was so poor the astronauts were unable to read a book (ref. 11).

The amount of lighting required depends on the specific task being performed. Table 2 presents illumination requirements for the 10,000-person habitat.

As shown the maximum power required is 929.7 W/person for living and work areas and 11,210W/person for agricultural areas. These numbers were calculated assuming that the lights are on constantly. A more useful number can be obtained by calculating the percentage of time a particular area will be used, that is, when lights are on. Conservative estimates for these requirements are: 556.7 W/person for living and work areas and 5692 W/person for agricultural areas - a total illumination requirement of 6248 W/person.

These values are conservatively high. The values were converted from lumens to watts by assuming a luminous efficacy of 50 lumen/W. Furthermore, the light reflected from walls, ceilings, and furnishings, which can have a significant effect on illumination intensity, was ignored. These surfaces become secondary sources of illumination, thus lowering the primary light-source intensity requirement (refs. 18, 19).

Studies have shown that the best light for reducing eye fatigue in industrial work is diffused or reflected. Reflected light depends on the properties of the work area surface. Reflection from a matte surface is diffuse while that from a polished surface is specular. Mirrorlike surfaces tend to glare, which greatly increases eye fatigue. Furthermore, the overall color climate of the habitat can have great physiological and psychological effect (ref. 19). Thus, the detailed design of the habitat must consider these factors.

DESIGN CONSTRAINTS SUMMARY

The tolerable environmental range for satisfying basic human physiological needs has now been established. This range was constrained on the basis of total habitat population. Early construction facilities with small populations will be inhabited by carefully selected crew members and their mission durations limited by reasonable exchange periods. As the population and size of habitats increase, environmental conditions should be changed toward Earth normal, so increased livability and comfort permit extended stay times. This trend is important since personnel selection criteria will be progressively relaxed, and transportation costs for frequent large population exchanges will be excessive.

Table 3 summarizes the physiological design constraints selected for the three habitat populations investigated.

These populations represent the full growth range from early construction shacks for space manufacturing to large "ecologically closed" settlements for unselected space immigrants.

Rotation rates for providing pseudogravity decrease from a maximum 3 rpm for a small carefully selected crew to a rotation rate <1 rpm for a more general population. Similarly, radiation worker dosages of 5 rem/yr are constraints for the 10² and 10⁴ habitats, while general population dosage limits of 0.5 rem/yr are used for the largest habitat.

A range of three atmospheric pressures has been selected for comparative purposes. Full and approximately half sea-level pressures are the maximum and intermediate selections for all three populations. The minimum pressure is a 100-percent oxygen physiological equivalent to the partial pressure of oxygen at 2400 in (8000 ft), 1200 in (4000 ft), and sea level on Earth for populations of 10², 10⁴, and 10⁶, respectively.

All habitats are limited to a maximum g level of 1.0; minimum g levels ranging from 0 to 0.7 are used as design constraints . These minimum g levels, combined with volumetric requirements, serve to define the habitat geometry for each of the four configurations investigated. The appearance of these volumetrically equivalent geometries varies as a function of how close the spherical configuration approaches the g_max limit at the maximum allowable rotation rate, as shown in figure 6. The example on the left depicts a sphere where the radius required to obtain the specified habitable volume is not close to the g_max limit. For this case an equivalent cylinder does not exist, the equivalent torus has a circular cross section, and the crystal palace has multiple layers. Habitable volume for the torus and crystal palace configuration is equal to their respective total volumes.

The example on the right in figure 6 shows a sphere for which the radius required to meet volumetric requirements would result in g levels exceeding g_max if the sphere were to rotate at the maximum allowable rate. To satisfy all design constraints, the radius is increased and the rotation rate decreased until the habitable volume just fits within the g_max/g_min limits. For this case, an equivalent cylinder rotating at the maximum rate does exist, as well as toroidal design with cylindrical walls. The equivalent crystal palace has fewer layers (only one layer is depicted) to remain within the g limits.

The appearance of an "equivalent" torus with cylindrical inner and outer walls imposes one additional design constraint. To prevent the inside cylindrical wall from buckling because of atmospheric-pressure-imposed compressive stresses, the "gravity load" on this surface can be made equal to or greater than the pressure load. This can be accomplished by suspending the entire internal mass from the interior wall and/or adding attached radiation shielding. An alternative approach provides compressive load-carrying capability by structurally stiffening the interior wall.

Radiation shielding is required on all habitats to protect the population from cosmic rays and solar flares. A choice exists, however, as to how this shielding is integrated with the structural shell. Direct attachment is undesirable because centrifugal loading added by the rotating shielding has a major influence on the structural shell thickness (and mass) requirements. The alternative is to mount the shielding outside the structural shell so that it either remains stationary, or counter rotates at a reduced angular velocity to obtain a net zero angular momentum for the entire habitat. This requires that alignment/positioning devices (i.e., mechanical bearings) be used to maintain a positive separation distance between the shell and shielding. To permit structural comparison of these two alternatives, both attached and detached shielding options were investigated.

SENSITIVITY ANALYSES

Both mass and cost sensitivity analyses were conducted for selected habitat elements. The structural mass sensitivities are presented first, followed by cost sensitivities for structural configurations (pressure shell and radiation shielding), atmospheric composition, and illumination implementation. All cost estimates were based on common ground rules which assumed use of lunar materials, unless the required elements were unavailable in lunar feedstock, in which case these materials were obtained from Earth. Asteroidal resources were not considered. Mass estimates were obtained by performing structural analyses of habitat pressure shell and radiation shielding configurations as a function of population, atmospheric pressure, minimum g level, and shielding integration techniques.

Structural Analyses

As the initial step of the habitat structural design trade, geometries were determined for the sphere, cylinder with hemispherical ends (when applicable), torus, and crystal palace on an equivalent habitable volume basis. The geometric relationships used are summarized in figure 7. Dimensions and important geometric parameters for the 65 shapes included in this analysis are listed in table.4. These characteristics were obtained by applying the design constraints identified in table 3.

Each of these habitat shapes was investigated for structural effects caused by the full range of established design constraints. Membrane stress-analysis techniques were used for the spherical, cylindrical, and toroidal monolithic geometries. For the modular crystal palace, element techniques based on O'Neill's work were used (ref. 20). The membrane analysis was accomplished by resolving all shell loads (atmospheric pressure, skin inertial, internal furnishings inertial, and attached shielding inertial) into combined normal and tangential distributed loads. This enabled the required structural material thickness to be determined by the relationships:

where

Derivation of these equations is illustrated by the example for the spherical shell skin inertial loading due to centrifugal force depicted in figure 8.
The inertial force of the skin is

Therefore,

Components for internal furnishings inertia and attached radiation shielding inertia are similarly derived. These components are grouped and added together, substituted into the appropriate formula, and the resulting expression extensively manipulated to obtain the final equations listed in figure 9.

The crystal palace equations, also shown in figure 9, were obtained from O'Neill's work (ref. 20) by setting h = r and incorporating the effects of skin inertial loading. Cable mass was calculated by neglecting the additional cable cross section needed to support its own inertia (this assumption results in underestimated cable mass for larger habitats). Attached radiation shielding was not considered for the crystal palace configuration. Employment of these crystal palace formulas presupposes that the minor radius r is much smaller than the major radius R. To remain within this constraint, a maximum minor radius of 10 m was selected. The crystal palace "r" radii shown in table 4 are obtained by selecting suitable integer values for the number of modules and solving for the required habitable volume.

Results of these structural shell analyses are presented in figures 10 through 17. Figures 10 through 13 show habitat structural shell mass as a function of minimum g level for fixed populations and atmospheric pressure.

• Figure 10.
• Figure 11.
• Figure 12.
• Figure 13.

• Figure 14.
• Figure 15.
• Figure 16.
• Figure 17.

The following general trends were obtained from data generated:

• At lower populations, the structural mass of spherical habitats is more sensitive to gmin than are other configurations (fig. 10).Attached shielding results in a substantial structural shell weight penalty.
• The structural penalty per person for attached shielding increases with population (habitat size).
• For larger habitats (figs. 12 and 13), the curves for toroids with attached and unattached radiation shielding bracket the "spherical habitat with unattached shielding" curve. This is important since the "torus with separate shielding" structural mass has been derived by neglecting the compressive loading condition of the inner cylindrical wall. Correction of this condition will shift this curve (increase the mass) closer to the spherical habitat curve.

Referring now to figures 14, 15, 16 and 17 :

• Habitat structural mass increases linearly in proportion to internal pressures.
• With a broad habitable g range (0.25 to 1.0), habitat pressure sensitivity is independent of configuration for larger populations.
  
• For larger habitats with a constrained g range (0.70 to 1.0), pressure sensitivity is configuration-related, with the crystal palace showing the least sensitivity due to "fixed" cable mass.

Shielding masses for each of the habitats were obtained via the equations in figure 18 for the following alternatives:

1. Sphere or cylinder - Shielding can either be attached or detached for all cases, and surrounds the structural shell.
2. Torus - Circular cross-section toroids can have either attached or detached shielding. Torii with cylindrical walls also have an attached/detached option, but must either have sufficient shielding on the inner wall to equalize the internal pressure, or additional shell structure must be incorporated to sustain these compressive loads. All shielding configurations investigated were toroidal and surrounded the structural shell.
3. Crystal palace - Only detached shielding was evaluated for the crystal palace. Since the crystal palace employs cables to react centrifugal loads, cylindrical rather than toroidal shielding was used.

All attached shielding was assumed to be immediately adjacent to the structural shell. Detached shielding was separated by 1.5 m. Owing to the increased area of separated shielding, its mass ranges from about 0.2 to 4 percent more than that for attached shielding. The following general shielding mass trends were obtained from separated shielding data shown in figures 19, 20, 21 and 22.

• Shielding mass sensitivity increases as the habitable g range is constrained (g_min =>1)
• Spheres exhibit greater sensitivity to shielding mass at lower populations than do other configurations.
• The shielding mass is two to three orders of magnitude greater than habitat structural mass for small habitats (10² population), but is only one order of magnitude greater for large habitats (10⁶ population).

Cost Comparison Ground Rules and Assumptions

The assessment of alternative habitat design concepts can best be accomplished by cost comparison. Our analysis shows considerable cost differences owing to overall habitat material requirements, and between terrestrial supplies and the various products manufactured in space from lunar material. Habitat cost comparison has been conducted by assuming that all habitat atmospheric oxygen, pressure shell structure, and radiation shielding are derived from lunar resources. It was also assumed that other items such as lighting fixtures are required in sufficient quantity so that they can be economically manufactured from lunar materials. The only materials or products imported from Earth are those which are either unavailable in lunar resources, or which because of complicated manufacturing operations requiring expensive facilities coupled with relatively small quantity requirements can be more economically obtained from Earth. Since the sensitivity studies in this analysis were conducted at a major subsystem rather than a component level, no complicated Earth products of this sort were included. The special ground rules and assumptions used for costing of lunar and Earth habitat construction materials are as follows:

1. Space processing and fabrication costs are obtained from data generated for the 11-year space manufacturing buildup period for the construction of solar power satellites from lunar resources (ref. 5). This information was used in lieu of equilibrium data because it was obtained by more rigorous methods and is better documented. This approach is conservative for comparison with Earth imports because space manufacturing equilibrium costs should be somewhat lower.
2. Space processing and fabrication costs are based on the conversion of 1737 ktons of lunar material into useful products. A total of 5745 man-years and $6.45 billion are expended to perform this conversion, that is, personnel cost (including transportation and all support), equals $1.123 million/man-year.
3. Material processing costs and fabrication costs constitute 25 and 75 percent of this total expenditure, respectively (R.Williams, personal communication, 1977).
4. Costs for each major space-manufactured product obtained from lunar material are shown in table 5. The constituents of lunar material shown reflect some lunar beneficiation prior to delivery to the space manufacturing facility (SMF). The processing and fabrication factors reflect the relative difficulty of manufacturing that particular product (R. Williams, personal communication, 1977).
5. Transportation costs from Earth to the SMF were derived for equilibrium conditions using third-generation launch vehicles. This approach is purposefully optimistic so that cost comparisons with space-manufactured products will be more conservative.
6. A single-stage to orbit vehicle delivers payload in low Earth orbit (LEO) at $47.06/kg, and a heavy mass-driver reaction engine provides LEO to SMF transfer at $10.16/kg, for a total transportation cost of $57.22/kg Q. Engel, Dept. of Systems Engineering, Univ. of Illinois at Chicago, personal communication). For most items, this transportation cost will be an order of magnitude above the Earth purchase price, which has therefore been neglected.

Habitat structural elements included in this comparison are the pressure shell and radiation shielding. Windows for illumination are evaluated later. in this paper. Internal furnishings were not included because their allocated mass per person was assumed to be equal for all populations within each of the two habitat classes. The smaller habitat class, 10² and 10⁴ populations without agriculture, used 43,000 kg/person internal furnishings. The larger class, 10⁴ and 10⁶ populations with agriculture, all used 53,000 kg/person.

To provide better cost sensitivities for the larger-class habitats, the radiation shielding thickness for the 10⁴ population configurations with agriculture was increased from 1.08 to 2.04 m. In addition, spherical habitats with 10⁵ and 10⁷ populations and shielding 2.04 m thick were also included in an attempt to establish the habitat size for minimum cost per person. A geometric definition of these added habitats is included in table 4.

The cost comparison performed assumes that all materials needed for the structural shell and radiation shield are obtained from processed lunar soil. The shell is assumed to be aluminum with a working stress of 218,000 kPa at a cost of $7.05/kg, and the shielding, molded industrial slag at $0.21/kg from table 5. If a significant percentage of shell alloying elements must be imported from Earth to meet the assumed working stress, then the shell costs must be increased accordingly.

All cost comparisons shown in figures 23, 24, 25, 26, 27 and 28, are for habitats with unattached shielding and an intermediate atmospheric pressure of 51.7 kPa. Unattached shielding and intermediate atmospheric pressure were both previously shown to result in reduced structural shell material requirements. Figure 23 shows the cost per person of the shell and shielding structural components for spherical habitats as a function of habitat size (population) and minimum g level. The shaded bands show the cost range from g_min = 0 to g_min= 0.7. It is interesting to note that the shielding cost exceeds shell cost up to a population of about 10⁵ for larger populations the reverse is true. Similar results were obtained for toroidal and crystal palace habitats.

Figures 24, 25, 26 and 27, show cost as a function of habitat size (population) for various habitat configurations at fixed minimum g values. The smaller-class habitats (radiation shielding thickness = 1.08 m) are characterized by a very wide configuration cost spread at 10² population, narrowing to $20,000/person difference at 10⁴ population for all values Of gmin. For the larger-class habitats (radiation shielding thickness = 2.04 m), the minimum cost per person always occurs between populations of 10⁵ and 10⁶ except for the special case of zero-g spheres, where the cost per person continues to decrease as population increases. The data for zero-g spherical habitats can be obtained by summing the left hand curves of Figure 23, . For most values of minimum g, toroidal habitats show a significant cost advantage ($10,000 to $20,000/person) over spherical and crystal palace habitats. It must be noted, however, that both toroidal and crystal palace habitat configurations require additional hub structures, which have not been included in this analysis. These hub features include cargo vehicle docking provisions, personnel access structure, and shielding alignment support structure, all of which are inherently provided by a spherical geometry. Also, as noted previously, the geometric constraints employed for this comparison result in toroids with cylindrical sections. With unattached shielding, these inner toroidal habitat cylindrical walls are compressively loaded. The additional structure required to prevent buckling was not included in the "detached shielding" structural weights used.

Large class habitat costs as a function of minimum g level are shown in figure 28. All geometries and populations exhibit lower cost per person for reduced minimum g.

Habitat Atmosphere Cost Comparison

The combination of habitat configuration, atmospheric pressure, and atmospheric composition have a significant effect on the total habitat atmospheric mass and its acquisition cost per person. Toroidal and crystal palace habitats are efficient from an atmospheric volume standpoint, and spherical and cylindrical habitats are inefficient since their total pressurized volumes exceed the habitable volumetric requirements of their populations.

Possible habitat atmospheric compositions of oxygen and diluent were previously established as a function of total pressure and population (see figs. 4 and 5 and table 3). The oxygen for the habitat atmosphere will be recovered during lunar material processing at the space manufacturing facility. Since it is produced in large quantities at the habitat construction site, the cost of oxygen is a reasonable $1 .02/kg

Possible inert atmospheric constituents include nitrogen or helium. During early space-settlement efforts, these diluents will probably be imported from Earth, with a delivery cost of $57.22/kg. Since the cost of atmospheric inerts is 56 times that of an equal quantity of oxygen, their use for large habitats will either be limited or a nonterrestrial source will be developed. Some scientists have suggested that volatiles may exist in frozen form at the lunar poles, but a more probable source is asteroidal material. It has been estimated that up to 0.3 percent of the mass of carbonaceous chondrite asteroids could be nitrogen (ref. 21). If nitrogen can be recovered from a convenient extraterrestrial source, its cost should be approximately equal to that of oxygen.

Figure 29 shows atmospheric cost sensitivity assuming that either nitrogen N₂ or helium (He) diluents are imported from Earth. The cost of an O₂/He atmosphere is significantly lower than an equivalent O₂/N₂ atmosphere since, at equal pressure, nitrogen is 7 times more dense, and is therefore equivalently more expensive to transport. All the curves in figure 29 are for habitats with total volume equal to habitable volume. Spheres and cylinders usually have total volumes greater than the habitable volume as shown in the right-hand column of table 4. For example, a large spherical habitat (10⁶ population), with a 51.7-kPa atmosphere of O₂N₂ and minimum pseudogravity one-half Earth-normal, will have a volume 1.5 times greater than shown, or a cost revision from $36,600 (shown in fig. 29 ) to $56,300/person.

The primary conclusion reached from this cost comparison is that if a significant percentage (>20 percent) of a settlement atmosphere is imported from Earth, then the cost of these diluents may be a major contributor to total habitat cost.

Habitat Illumination Cost Comparison

The interior of a space habitat can be illuminated by either artificial fights powered by photovoltaic cells, or by natural sunlight admitted through windows. This study evaluated the costs of these alternative lighting methods for one representative habitat configuration. Since the natural illumination choice is probably reasonable only for larger habitats, the 10,000-person spherical habitat was selected for this evaluation. This sensitivity analysis was performed only, for photovoltaic versus natural illumination independent of habitat configuration and population variations. Further work should consider possible configuration and population effects.

Artificial lighting- Recent solar photovoltaic array estimates use a specific power generation factor of 138 W/kg (ref. 22). To account for power transmission, conditioning, and control equipment, an efficiency of 90 percent was assumed for an effective array output of 124 W/kg. Photovoltaic array cost was based on space manufactured components of 30 percent silicon and glass and 70 percent aluminum and other metals. The cost for light bulbs and fixtures was estimated using a specific weight of 0.03 kg/W of rated fixture output. Space-manufactured components were selected over Earth imports owing to the estimated acquisition cost ratio of 1/6. Table 6 displays the weights and costs for the various illumination system components. These calculations were based on the power requirements obtained from table 2. Weighted values were used for array sizing and maximum values for distribution fixtures. The use of maximum power requirements for fixtures reflects the difficulty in moving them as lighting needs vary. As indicated, the cost of illuminating the agricultural area is an order of magnitude higher than that for the living area. Of particular interest is the overwhelming influence of distribution costs, which account for 88 percent of the total artificial lighting cost. If Earth-imported fixtures had been assumed, the distribution cost would have exceeded $200 M, instead of the $33.73 M used.

Natural illumination - The corresponding analysis for determining weight and cost of illuminating with natural sunlight is more difficult because of the many implementation options available. To reduce weight and the possibility of meteorite damage, it is desirable to minimize the window area. This can be done by concentrating the sunlight before it enters the habitat, but the concentration is limited by the 800-K softening temperature of window glass. It was assumed that the maximum window temperature should be less than 600 K (337^o C). To maintain this temperature, the absorptivity of the glass must be balanced by its conductivity. The energy admitted to the habitat is also a function of window absorptivity; specifically (refs. 23, 24):

Only sunlight in the visible waveband is useful for habitat illumination. This constitutes 38 percent of the total solar radiation (fig. 30). Admitting energy outside this band into the habitat results in many penalties, including the requirement for larger windows and increased internal thermal control capacity. It is therefore desirable to use concentration mirrors that selectively reflect sunlight in the visible spectrum into the habitat for illumination. The degree of allowable concentration is influenced by glass thermal limits and absorptivity, which are functions of glass thickness. The thickness of the window is determined by structural requirements. Based on terrestrial manufacturing experience, the practical window weight limit is about 1 ton. A weight of 0.5 ton per window was selected or volume = Ad = 0.2 m³, where the glass density is 2450 gm³ . This equation is solved simultaneously with the structural equation for a pressure-loaded square plate with simply supported edges:

The solution resulted in a window 5.65 cm thick with an area of 3.5 m².The transmissibility of 5.65-cm-thick glass is 0.84 in the visible wavelengths (ref. 25). Since the sum of reflectivity, absorptivity, and transmissibility must equal 1, an absorptivity of 0.16 may be conservatively assumed.
The total energy transmitted through the windows by selective mirrors is therefore 36.5 kW/m². This is equivalent to a solar visible energy concentration factor of 70. Window areas, weights, and costs are delineated in table 6.

Illumination requirements were again obtained
from table 2 with the following assumptions. Since distribution in living areas may be cumbersome, twice the maximum energy/person allocation was used. Agricultural areas are relatively open and a simple swiveling mirror can control light, so the weighted power requirement was used.

The mirror estimates shown in table 6 were derived assuming 90 percent efficiency, a total concentration plus distribution factor of 80, and aluminum mirrors and support structure weighing 0.20 kg/m².

There are several ways to provide radiation protection for habitat windows: one alternative employs very thick glass windows that supply all the shielding 'necessary; this is undesirable, however, since the thickness must be 1.02 or 1.92 in to meet the 5.0 or 0.5 rem/yr dose rate requirements, respectively. This increases the total absorptivity, and these windows weigh and cost more than 20 times those that are only 5.65 cm thick. Another approach is to use shielding constructed from lunar slag in a chevron configuration to protect thin windows. Comparable thicknesses are still needed but material costs are 67 times lower and manufacturing requirements are greatly simplified. Chevron construction requires about twice the amount of normal shielding, but as shown in table 6, the cost remains below that for thin-glass windows.

The results of the preceding discussion and a comparison of total costs in table 6 lead to several conclusions:

1. If natural illumination is used, it should be concentrated with selective mirrors before it is transmitted into the habitat.
2. Thick glass windows that supply radiation protection are expensive and impractical, table 6. Natural illumination should be used for agricultural areas since its cost is 1/6 that of artificial lighting.
3. Natural illumination should also be considered for living/working areas unless distribution becomes awkward or expensive.

CONCLUSIONS

The introduction to this paper posed three questions to be addressed and, it is hoped, answered by these habitat structural/cost sensitivity analyses. Sufficient habitat options have been evaluated to obtain a quantitative answer to the initial question: How much do "Earth-normal" physiological conditions cost when applied to a space habitat structural design? Obviously, many "less than Earth-normal" design options are possible, but a representative example should be illustrative.

The data in table 7 compare 10⁶ population habitats having identical habitable volumes (2000 m³/person), internal furnishings (53,000 kg/person), and radiation protection (0.5 rem/yr). The variables noted in the table are limited to habitat configuration, atmospheric pressure, atmospheric composition, and the range of pseudogravity in the habitable volume.

The total costs obtained offer some interesting comparisons between conservative and reduced cost designs, as well as for alternative configurations. As shown, when only habitat structure, shielding, and atmosphere are compared, the conservative to reduced cost design ratio is 7.5, 4.8, and 3.5 for spherical, toroidal, and crystal palace habitats, respectively. The answer to the first question is that design costs associated with Earth-normal conservatism are at least significant and may, in fact, be excessive. Also, table 7 cost data shows that the cost dispersion for conservative designs varies by more than a factor of 2.2 due to configuration differences, but the dispersion for reduced cost designs varies by only 1.4. This reduction in configuration sensitivity demonstrated by the lower cost habitat designs is due primarily to the reduced effect of their atmospheric costs.

The second question asks which "less than Earth-normal" physiological conditions offer the greatest habitat cost savings. Minimum g-level constraints and atmospheric pressure have strongly synergistic effects on structural shell design requirements and costs. The selected habitable g range significantly affects the overall structural shell geometry as demonstrated in table 4, while pressure affects the structural shell thickness. When evaluated independently, these influences are of the same magnitude. The structural mass difference for a 10⁶ population spherical habitat is 4.7X10⁶ tons for a gmin range from 0.7 to 0.25. This difference is due to geometry effects; it is not caused by a change in rotation rate, which varies only between 0.9 and 1.0 rpm. Similarly, the mass difference over the 76 kPa atmospheric pressure range is 8.IX10⁶ tons and 3.7XI0⁶ tons for gmin values of 0.7 and 0.25, respectively. Similar results are obtained for toroidal and crystal palace habitat geometries. Shielding mass and its resultant cost at a fixed population and radiation requirement are influenced solely by habitat geometry, which is a function of minimum g-level. The relative importance of structural shell and radiation shielding costs is also a function of habitat population. Below 10⁵ inhabitants, shielding costs are higher, but above 10⁶ inhabitants, structural shell are dominant.

The quantity of atmosphere diluent imported from Earth has the largest potential influence on habitat cost. The mass which must be imported depends on excess habitat volume, total atmospheric pressure, and the inert gas selected. These factors combined produce a cost factor of 40 for the spherical habitat example given in table 7.

Illumination alternatives also exhibit substantial habitat cost effects. The use of unselected/unconcentrated natural solar lighting results in window plus extra shielding costs similar in magnitude to those for the basic habitat structure. The costs for this technique are two orders of magnitude higher than for a selected/concentrated natural illumination system.

The third question, regarding identification of a recommended habitat configuration, has not been fully resolved by the limited analyses conducted during this investigation. Each habitat shape offers benefits for certain applications, and configuration selection may well depend on design considerations outside the scope of this study. These considerations include implementation of life-support functions, power supply, waste heat dissipation, shielding alignment, docking functions, and illumination for each of the habitat configurations.

Although an overall best habitat configuration has not been recommended, some interesting configuration comparisons can be made:

1. Torus - Offers the lowest habitat basic structural cost (pressure shell and detached radiation shielding) for almost all combinations of population and g_min. It is also volumetrically efficient and contains only as much atmosphere as required. Unfortunately, several parts of the torus structure were not included in this analysis: spokes, hub, shielding alignment, and additional stiffening needed in compressively loaded cylindrical sections. Also the distribution of illumination in a torus appears cumbersome. These factors will combine to increase the basic torus structural cost so that its cost per person approaches that for spherical habitats.

2. Crystal Palace - Has attributes and disadvantages similar to the torus. Its basic structural cost always exceeds that for the torus and is less than that for spheres when g_min exceeds 0.5. It is atmospherically efficient but has illumination distribution difficulties and requires unestimated spoke and hub structures. The crystal palace cylindrical radiation shielding, which contributes to its high basic structural cost, also offers several potential advantages. Its flat ends provide structure for spin axis alignment, and also radiation protection for the unpressurized volume within the crystal palace's inner structural wall. If additional facilities for space manufacturing were placed within this volume, they would be provided free radiation protection.

3. Sphere - Has a basic structural cost which exceeds that of the torus and crystal palace over most of the population and g_min ranges. It also exhibits an inefficient volume ratio, which results in high atmosphere costs. Its advantages include straightforward illumination distribution and no need for separate hub or shielding alignment structure. The sphere's excess pressurized and shielded volume could become advantageous by locating space manufacturing facilities in this region.

One important discovery about habitat configurations was made during this work: based on habitat basic structural cost, the cost per person has a minimum for habitats in the 10⁵ to 10⁶ population range. Even more interesting is the fact that this minimum is independent of habitat configuration; spheres, toroids, and crystal palaces all had minimum costs in this population range. This minimum is obviously dependent on the ground rules and scope of this investigation, but an equivalent minimum should also exist for revised ground rules and for more extensive habitat subsystem considerations.

RECOMMENDATIONS

Physiological research should be concentrated in those areas where less than Earth-normal conditions offer the greatest savings in habitat cost. Based on the work conducted during these sensitivity analyses, recommended research falls into two categories: (1) that necessary to validate our assumptions and (2) that highlighted by our results. Our assumptions included allowable habitat rotation rates for pseudogravity, and the use of a broad range of habitable g levels. Since higher angular velocities and broad habitable g ranges result in smaller, less massive, and lower cost habitats, it is very important that we fully understand the long-term physiological effects of these conditions. Specifically, the following research is needed:

• Rotation rates: The angular velocities used for this study were based on work performed in a 1g (Earth surface) environment. Initial human adaptation, long-duration habitability effects, and transition effects between rotating and nonrotating enclosures must be obtained in a reduced g environment.
• g-level variations: As inhabitants move radially within a settlement with a broad habitable-g band (0.25 -> 1 g), they will be subjected to continuous or stepped g-level variations. This effect, with special emphasis on human adaptation and transition, must be investigated.
• Low-g tolerance: More knowledge is required on long-duration physiological effects of low- and zero-g habitation. Experimental data are limited to those obtained during the 84-day Skylab mission.

The results of our sensitivity analyses indicate that the combined influence of atmospheric pressure and composition have potentially the most significant effect on habitat cost. Therefore the following research is recommended:

• Low atmospheric pressure: Perform extended duration and adaptability testing for O₂/N₂ mixtures at less than sea-level pressure. Evaluate speech transmission effects in addition to respiratory effects.
• Low-density diluent: Conduct tests similar to those above for O₂/He atmospheres at less than sea-level pressure.

As repeatedly pointed out in the preceding text, this habitat sensitivity investigation was limited to the basic habitat structure (pressure shell and radiation shielding) plus some considerations of atmospheric composition and habitat illumination. It is recommended that additional habitat sensitivity studies be performed to expand this work. The following sensitivity investigations should be accomplished to pin a better understanding of certain habitat design conditions and subsystem options on overall habitat mass and cost.

• Influence of secondary structures, such as spokes, hub, shielding alignment, and additional stiffening in compressively loaded sections, on overall habitat structural mass and cost comparisons.
• A detailed look at habitat illumination sensitivity for various configurations. Illumination implementation appears to be fairly important and should be treated in much greater depth than was possible in this paper.
• The effect of fixed personnel area requirements on habit structural weight and cost. (The work described in this paper assumed a fixed volumetric requirement.)
• Habitat heat rejection sensitivity as a function of habitat shape and radiation shielding design.
  
• Evaluation of life support function integration in various habitat configurations. These functions include air circulation and conditioning, power, water and sewer services.

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Curator: Al Globus If you find any errors on this page contact Al Globus.

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