E NASA NASA SP-8023 SPACE VEHICLE DESIGN CRITERIA f ENV! RON M E N T] LUNAR SURFACE MODELS MAY 1969 NATIONAL AERONAUTICS AND SPACE ADMINISTRATION FOREWORD NASA experience has indicated a need for uniform criteria for the design of space vehicles. ~ Accordingly, criteria are being developed in the following areas of technology: Environment Structures Guidance and Control Chemical Propulsion Individual components of this work will be issued as separate monographs as soon as they are completed. A list of all previously issued monographs in this series can be found on the last page of this document. These monographs are to be regarded as guides to design and not as NASA requirements, except as may specified in formal project specifications. It is expected, however, that the criteria sections of these documents, revised as experience may indicate to be desirable, ~ eventually will become uniform design requirements for NASA space vehicles. This monograph was prepared under the cognizance of the Marshall Space Flight Center. An ~ ad hoc committee on Lunar Surface Models, chaired by 0. H. Vaughan, Aerospace Environment Division, MSFC, was established to assist in the preparation and review of this monograph. The principal author was R. E. Hutton of TRW Systems; the program coordinators were M. T. Charak of the Office of Advanced Research and Technology, NASA and S. A. Mills of the Goddard Space Flight Center. The participation and contribution of the following ad hoc committee members are hereby acknowledged : S. Batterson NASA, Langley Research Center H. Benson NASA, Manned Spacecraft Center D. Gault NASA, Ames Research Center T. Gold Cornel1 University J. O'Keefe NASA, Goddard Space Flight Center G. Ulrich U. S. Geological Survey, Center of Astrogeoiogy L. Jaffe Jet Propulsion Laboratory, California Institute of Technology i Valuable contributions were also made by the following individuals: 0. Berg NASA, Goddard Space Flight Center N. Costes NASA, Marshall Space Flight Center J. Dragg NASA, Manned Spacecraft Center J. Harrison NASA, Marshall Space Flight Center B. Jones NASA, Marshall Space Flight Center H. Moore USGS, Branch of Astrogeology R. Pike USGS, Center of Astrogeology Comments concerning the technical content of these monographs will be welcomed by the National Aeronautics and Space Administration, Office of Advanced Research and Technology (Code RVA), Washington, D.C. 20546. May 1969 ii CONTENTS 1. INTRODUCTION ................................................ 1 .............................................. STATE OF THE ART 1 2.1 Physical Properties ........................................... 1 2.2 Morphologic Subdivisions ..................................... 1 2.3 Topography ................................................ 2 2.4 Block and Crater Frequencies .................................. 4 2.5 Soil Characteristics .......................................... 4 2.6 Bearing Strength ............................................ 5 2.7 Density ................................................... 6 2.8 Soil Layer Thickness ......................................... 7 2.9 Chemical Composition ........................................ 7 2.10 Seismic Velocities ........................................... 7 2.1 1 Thermal Properties .......................................... 8 2.12 Optical Properties ........................................... 9 2.13 Dielectric Constant .......................................... 10 2.14 Atmospheric Properties ....................................... 11 2.15 Gravitational Field ........................................... 11 2.16 Lunar Trafficability .......................................... 12 3 . CRITERIA ...................................................... 13 3.1 Physical Characteristics ....................................... 13 3.2 Terrain Properties 3.2.1 Mean Slope and Cumulative Frequency Distribution ......... 13 3.2.2 Surface Roughness .................................. 13 3.2.3 Topographic Features of Selected Regions ................ 13 .............................................. 3.3 Lunar Craters 14 .............................................. 3.4 Lunar Blocks 23 B!=ck ?r~pert,i.e.~. .................................. 23 a?.7A.11 3.4.2 Block Distributions in the Intercrater Region .............. 23 3.4.3 Block Distributions Around Craters ...................... 23 -- 3.4.4 Block Fields ........................................ 25 iii 3.5 Soil Characteristics .......................................... 27 3.5.1 Soil Parameters ..................................... 27 3.6 Thermal Properties .......................................... 30 3.6.1 Brightness Temperature ............................... 30 3.6.2 Brightness Temperature Directionality ...................3 2 3.6.3 Surface Thermal Properties ............................ 34 3.6.4 Thermal Radiation ................................... 34 3.7 Electrical Properties ......................................... 34 3.7.1 Dielectric Constant and Loss Tangent .................... 34 3.8 Optical Properties ........................................... 36 3.8.1 Normal Albedo ..................................... 36 3.8.2 Photometric Model .................................. 36 3.8.3 Polarization of Moonlight ............................. 36 3.9 Lunar Atmosphere .......................................... 37 REFERENCES ......................................................... 43 APPENDIX A . List of Symbols ............................................ 49 APPENDIX B . Short Table of Conversion Factors .............................. 51 APPENDIX C . Glossary .................................................. 53 NASA SPACE VEHICLE DESIGN CRITERIA MONOGRAPHS ISSUED TO DATE ....................................... 55 LUNAR SURFACE MODELS 1. INTRODUCTION Engineering models of the lunar surface are needed in mission planning and in the design of :anding siid cxploratio:: :.ehic!es xxl !~!nir bases. Mndels nf terrain and soil mechanical properties assist in the evaluation of vehicle landing performance, descent engine plume-surface interactions, and exploration vehicle performance and power requirements. Crater and block (rock) models aid in assessing hazardous landing conditions and obstacles encountered in typical traverse missions. Optical models help in establishing camera design parameters and in determining visual capabilities of astronauts. Dielectric models aid in radar system design. Chemical, bearing strength, density, and thermal models are used in design of surface and sub-surface base structures and surface vehicles. The lunar surface models presented in this monograph are based on 1968 state of the art; they upgrade and extend the earlier engineering models developed by Vaughan (ref. l), Vaughan and Castes*, and the criteria guidelines in reference 2. They are founded on a review and interpretation of available literature and lunar data as well as discussions with scientists familiar with data provided by the Ranger, Surveyor, and Orbiter programs, and the Russian Luna probes. In addition, these engineering models reflect, where possible, the consensus of the NASA Lunar Trafficability Model Working Group, composed of members of NASA centers and other government agencies working on lunar exploration programs. A design criteria monograph being prepared on charged particle radiation also applies to lunar missions. The meteoroid environment is also relevant and is presented in another monograph (NASA SP-8013). Therefore, these environments are not discussed in this monograph. 2. STATE OF THE ART 2.1 Physical Properties Many physical properties of the Moon have been known for years. The method of their determination and the values presented in this monograph are taken mainly from reference 3. These properties, presented in section 3.1, include the lunar radius, mass density, escape velocity, gravitational acceleration, rotation period, atmospheric density and pressure, and magnetic field strength. 2.2 Morphologic Subdivisions Two fundamental large-scale morphologic types of lunar terrain are clearly evident-Mare and Upland regions. Well-formed young craters are superimposed on both of these su~face types ax! constit~tea widely distrihi-1te.d third basic surface. *Vaughan, 0. H., Jr.; and Costes, N. C.: Lunar Environment: Design Criteria iviodeis I^ui Zx; ;II LiiiZ %if&= XzZ!it;' Studies, NASA Marshall Space Flight Center, Alabama, Nov. 1968 (unpublished manuscript). 1 The Mare surface is characterized by relatively gentle topography with low normal albedo and features, such as craters, ridges, rilles, domes, ray systems, and scarps. In contrast, the Uplands have higher albedo, and are rugged with complex superimposed craters. Besides “Mare” and “Upland,” this monograph uses the following more detailed terms; smooth Mare, rough Mare, hummocky Upland, and rough Upland. Since most lunar regions are composite, the morphologic term applied to any region describes the predominant type of terrain. Hence, a smooth Mare may contain subregions that are rougher than some subregions in a rough Mare. The topographies of lunar surfaces are characterized by craters of varous sizes and ages. Ideally, the surfaces can be grouped into two types*: (1) the young surface where the frequency distribution directly reflects the rate of crater production, and (2) the “steady state” surface which is the result of the combined effects of crater production and erosion-in filling produced by extensive cratering (crater saturation). Crater frequencies can be expressed approximately by equations of the form No = K D” where No is the cumulative number of craters per unit area greater than diameter D, and K and n are constants.The exponent, n, is about -3 for the young surface in which the craters are fresh and uneroded. For the “steady-state” surface (ranging from fresh, well-preserved craters to those so eroded and filled that they are barely discernible), the exponent, n, is about -2 and the coefficient K is lo-’. 2.3 Topography Rowan and McCauley (refs. 4 and 5) demonstrated with Earth-based photography that the median slope was related to the slope length** for both terrestrial and Mare topography (a linear relation on a log-log plot). The relationship thus obtained from Earth-based lunar observations predicted the mean slope which was later measured from Ranger 7 photographs (when the 0.75 km resolution was extrapolated to one meter). With Orbiter data, R. J. Pike*** extended the work of Rowan and McCauley and developed relations between the mean lunar slope and slope length for the smooth Mare, rough Mare, hummocky Upland, and rough Upland. *Moore, H. J., “Some Observations of the Lunar Trafficability Problem,” U. S. Geological Survey, Nov. 1968 (working paper). **The dope length is the incremental horizontal distance between two elevations over which the slope is to be determined. It is also referred to as sample cell length by Rowan and McCauley. u. ***Pike, R. J., “Preliminary Models of Slope Distributions on the Moon,” S. Geological Survey, Branch of Astrogeologic Studies, Oct. 29, 1968 (working paper). 2 i In addition, Pike's study of terrestrial slope distributions indicated identical cumulative distributions when normalized to the mean slope, regardless of the gentleness or steepness of the mean slope. By assuming that lunar slopes have the same characteristic distributions, Pike developed a basic distribution model using photoclinometry data obtained from 7 lunar regions read to 0.6 meter resolution, but most likely are valid only above 1 meter). (&it2 The slope distribution model presented herein, is a current estimate from a continuing investigation by Pike and others at the Center of Astrogeology, U. S. Geological Survey. Lunar topography studies are also being conducted by the Mapping Sciences Laboratory at the NASA Manned Spacecraft Center (MSC) in support of the Apollo program, primarily for the landing sites in the Mare regions. Cumulative slope distributions are presented* for slope lengths of about 1 and 10 meters for various locations in the Mare region. The data demonstrate that the slope distributions, for a single slope length, vary from site to site, even though, within the context of the morphological subdivisions, the region might be termed a smooth Mare region. Therefore, within a given morphologic region, a distribution exists for the mean lunar slope for any single slope length. The nominal lunar surface model presented in this monograph provides an estimate of the most likely value of the mean slope for a given slope length. Variations in the distribution of the average slope for a single base length can be inferred from data in reference 4 and unpublished MSC data (private communication). These MSC data consisted of about 50 lunar slope cumulative frequency distributions for Apollo landing site I1 P-8i n Sinus Medii. From the data the mean slope and standard deviation were computed to be 4.5" and 1.2', respectively for the lunar module base length of about 8.5 meters (distance between foot pads). These results were used in establishing the relation between slope standard deviation and mean slope. The United States Air Force Aeronautical Chart and Information Center also uses photometric techniques to determine lunar topography. Topographic charts included in reference 6 show 1 meter contour lines for Lunar Orbiter site I1 S-2. The lunar surface roughness models are described in terms of power spectral density (PSD) and were derived from data obtained from Pike (USGS) and Rozema (ref. 7). Similar data have been obtained by the NASA Manned Spacecraft Center although its interest has been concerned primarily with the smooth Mare regions in the Apollo belt. In reference 8, Jaeger and Schuring present power spectral density data for the Mare Cognitum. They also present a procedure that utilizes PSD data to determine the dynamic response of a vehicle moving over the lunar surface. According to Pike's data, the Mare regions contain both the smoothest and roughest regions on the Moon with the Upland roughness falling in between two extremes. Even though the Mare has rougher regions than the Upiands, the steepest slopcs are fmnd ir? the 1-Tpland *Anon.: "A Preliminary Analysis of Photometric/Computer Terrain Data for Lunar lratficabiiiry kiocieir," iviapyiig Sciences Laboratory, NASA Manned Spacecraft Center, Oct. 4,1968 (working paper). 3 regions. Table I summarizes the relations between the minimum, nominal, and maximum PSD models of lunar surface roughness presented in this monograph and the corresponding morphologic classifications used in references 1 and 4 and those adopted herein. TABLE I LUNAR SURFACE PSD MODELS AND MORPHOLOGIC CLASSIFICATIONS Morphologic Classification Lunar Surface PSD Models This Monograph Reference 1 Reference 4 Minimum smooth Mare dark regional smooth Mare Nominal rough Upland/ smooth regional Up1a nd hummocky Upland Mare ; smooth rayed Mare ~~ Maximum rough Mare rough rayed rough Mare Mare 2.4 Block and Crater Frequencies Most of the block (protuberance) and crater data models given in this monograph were derived from data furnished by H. J. Moore. These models also included results obtained by E. Shoemaker and E. Morris of USGS and R. Choate of JPL. Often the block counts by various investigators differed substantially, probably because different lunar regions and different sizes were used in making the counts. Block frequency data in this monograph reflect a compromise between the two block frequency curves in reference 9 (figs. 111-42 and IV-34). The workers mentioned earlier are continuing their block frequency investigations, and the final differences between their frequency distributions should be resolved in the near future. 2.5 Soil Characteristics Cameras on the Surveyor spacecraft with about 1 mm resolution (refs. 9 to 14) and Luna spacecraft with a resolution of several mm (ref. 15) have provided detailed information on the lunar surface material in both Mare and Upland regions. Surveyors 1 and 3 and Lunas 9 and 13 landed in a rough Mare region (Oceanus Procellarum, Western limb), Surveyor 5 landed in a smooth Mare region (Mare Tranquillitatis, Eastern limb), Surveyor 6 landed 4 between the rough and smooth Mare regions (Sinus Medii, middle region), and Surveyor 7 landed in the Uplands near Tycho. Data from both U. S. and U.S.S.R. spacecraft indicate the surface material to be a matrix of fine, partially cohesive particles less than 1 mm in diameter with a few rocks scattered in and on the matrix. Cherkasov et al. (ref. 16) concluded that at the Luna 13 landing site the lunar surface seems to be a layer of granular, -- ioose, w ~--I-a’--a -L~--G--yI-+I I G~L~c U IIIL-LAL,,I U1ru ny.n.ucliuct ino nf grains afid granules of porous mineral which are weakly interconnected at contact points. A terrestrial analog of this lunar material was described by the Russian investigators as a lightly-cemented sand with the addition of larger particles while Scott describes it as having properties of a slightly moist beach sand. In this monograph the surface material is simply called a “soil”. Other sources often call the surface material the regolith or epilith. 2.6 Bearing Strength The soil bearing strength, according to reference 14, varies rapidly in the first few mm of depth. For the first 1 mm of depth, the bearing strength is less than 0.1 N/cm2 (0.1 newtons/cm2), based on the imprints of small rolling fragments. From 1 to 2 mm the bearing-strength increases to 0.2 N/cm2, based on the imprint made by the alpha scattering experiment sensor head. Based on penetrations of the crushable blocks located on the underside of the Surveyor spacecraft truss frame, the bearing strength at a depth of 2 cm was estimated to be 1.8 N/cm2 . The analysis of the Surveyor 1 landing indicates the bearing strength to be between 4.2 and 5.5 N/cm2 at a depth of about 5 cm. The bearing capacity was also estimated from data obtained on Luna 13. This spacecraft (refs. 15 and 16) carried a conical shaped penetrometer (103” cone, maximum diameter of 35 mm) which was forced into the soil by the thrust force developed by a small solid fuel jet engine (thrust of 6.5 kg for 0.8 seconds). The bearing capacity is listed as 0.68 kg/ cm2 (or 6.67 N/cm2) at about a 4 cm depth, a little larger value than the estimates made from Surveyor data. In the same Russian references the soil cohesion is estimated to be 0.005 kg/cm2 (0.049 N/cm2) or essentially the same as the mean value estimated from Surveyor data. Reference 17 lists a value of 0.18 kg/cm3 (1.8 N/cm2/cm) for a parameter called the coefficient of proportionality between the intensity of load and the penetration depth. According to data obtained by Scott with the soil mechanics surface sampler (SMSS) on Surveyor 7 (ref. 14), the force exerted on the closed scoop was 27 N at a penetration depth of about 3 cm. With a closed scoop area of about 12.5 cm2 the ratio of the average pressure to the penetration depth is 0.72 N/cm2 /cm, roughly one-half the value estimated from Luna 13 data. Test method differences may explain the divergence in this value. The Surveyor 7 LLG^:_SLL W. .a s static whik the Luna 13 test war dynamic; also the penetrator sizes and shapes were different. Jaffe (ref. 18) presents a plot of Surveyor bearing capacity data against penetration depth for various bearing width to depth ratios. The width to depth ratios extended from 0.8 to 1I .Au and fi-oiil 5 to 16. Tjicse data appear to hzve .pp,rnximate!y a linear relation whose slope ranges from about 0.8 to 1.1 N/cm2 /cm. 5