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Home , Atmosphere of the Moon, Peak of eternal light

DOCUMENT document title/ titre du document

UNAR OBILITY TUDY

UNAR NVIRONMENT

AND

YSTEM EQUIREMENTS

prepared by/préparé par Paolo Massioni – Stefano Nebuloni reference/réference issue/édition 1 revision/révision 0 date of issue/date d’édition 9/9/2005 status/état Document type/type de document Technical Note Distribution/distribution

a

ESTEC LunarEnvironmentAndSystemRe Keplerlaan 1 - 2201 AZ Noordwijk - The Netherlands quirements.doc Tel. (31) 71 5656565 - Fax (31) 71 5656040 Lunar Mobility Study s issue 1 revision 0 -

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T ABLE O F C ONTENTS

REFERENCES ...... 1

1 INTRODUCTION ...... 3 1.1 Purpose of this document...... 3 1.2 Overall properties of the ...... 3 1.3 List of abbreviations...... 4

2 LUNAR ENVIRONMENT FEATURES...... 5 2.1 ...... 5 2.2 Illumination conditions and thermal characteristics of the surface...... 5 2.2.1 Light and temperature on surface...... 5 2.2.2 Polar environment ...... 6 2.3 Topography and terrain properties...... 8 2.3.1 Craters ...... 9 2.3.2 Apollo Landing Sites ...... 11 2.3.3 Polar topography...... 11 2.4 Soil characteristics...... 12 2.4.1 Granulometric composition...... 12 2.4.2 Bulk density and void ratio ...... 13 2.4.3 Compressibility and shear strength...... 13 2.4.4 Allowable bearing capacity...... 15 2.4.5 trafficability ...... 15 2.5 Dust effects...... 16 2.6 Radiation ...... 17

3 SYSTEM REQUIREMENTS ...... 18 3.1 Launch requirements...... 18 3.2 Landing requirements ...... 18 3.3 Thermal requirements ...... 18 3.4 Power requirements...... 19 3.5 Dust countermeasures ...... 19 3.6 Mobility Requirements ...... 19 3.6.1 Lunar terrain features ...... 19 3.6.2 System requirements ...... 21

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REFERENCES

RD1. Heiken, D. Vaniman, B.M. French Lunar Sourcebook, a User’s Guide to the Moon, Cambridge University Press 1991.

RD2. The Moon, Nationmaster Encyclopaedia http://www.nationmaster.com/encyclopedia/Moon

RD3. Lunar Surface Models SP-8023, NASA

RD4. Euromoon Mission Feasibility Study Report – ESA http://ids2.esa.int:81/ATTACHEMENTS/A117179/esa-cr-2847.pdf

RD5. E.A.Kozlova Temperature mode in cold traps on the Moon – Sternberg State Astronomical Institute, Moscow. http://www.planetary.brown.edu/planetary/international/Micro_38_Abs/ms049.pdf

RD6. Ben Bussey, Paul Spudis Extreme Lighting Conditions at the Lunar Poles – Johns Hopkins University http://www.spaceagepub.com/pdfs/Bussey.pdf

RD7. - DSPSE http://www.cmf.nrl.navy.mil/clementine/

RD8. Michiel Kruijff (Delta-Utec) Peaks of eternal light on the : how they were found and what they look like http://www.delta-utec.com/papers/ESTECMoonPaperFinal2.pdf

RD9. D.B.J. Bussey, M.S. Robinson, K. Fristad Permanent at the - Lunar and Planetary Science XXXV (2004) http://www.lpi.usra.edu/meetings/lpsc2004/pdf/1387.pdf

RD10. Apollo Lunar surface Journal. http://www.hq.nasa.gov/office/pao/History/alsj/

RD11. T.J.Stubbs, R.R.Vondrak and W.M.Farrell, A dynamic fountain model for lunar dust. – NASA Goddard Space Flight Center, Greenbelt, MD 20771. http://www.lpi.usra.edu/meetings/lpsc2005/pdf/1899.pdf

RD12. The Effects of Lunar Dust on EVA Systems During the Apollo Missions

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http://gltrs.grc.nasa.gov/reports/2005/TM-2005-213610.pdf

RD13. EuroMoon 2000 - A Plan for a European Lunar South Pole Expedition http://esapub.esrin.esa.it/br/br122/br122lan.htm

RD14. Gwendolyn D. Bart, H. J. Melosh Ejected boulders: implication for secondary craters and the age dating of surfaces – Univ. of Arizona, Tucson. http://gwen.barnesos.net/LPLmainpage/publications/2022.pdf

RD15. Dimitrios Apostolopoulos Systematic Configuration of Robotic Locomotion – Carnegie Mellon University

RD16. V. Gromov Physical and mechanical properties of lunar soil http://selena.sai.msu.ru/Symposium/phmp-ls.pdf

RD17. UW-MADISON http://fti.neep.wisc.edu/neep602/LEC22/NEAL/neal.html

RD18. Lunar Exploration Study - CDF

RD19. Human Spaceflight Vision (HSV) – CDF Study Report (CDF 23(A), January 2004)

RD20. NASA DART experiment http://powerweb.grc.nasa.gov/pvsee/publications/wcpec2/dart.html

RD21.] rover chassis evaluation tools – Survey report method and tools for rover locomotion evaluation, Contraves Space/DLR/EPFL.

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1 INTRODUCTION

1.1 Purpose of this document The aim of this document is to collect and analyse all the peculiar features of the lunar environment. These statements have to be considered for designing any device that is going to operate on the surface of the Moon.

This document has been written within the Lunar Mobility Study, so it is focused on the issues related to the functionality and survival abilities of a mobility system, with a special attention to lunar poles.

1.2 Overall properties of the Moon The Moon is the only of . It is in a synchronous rotation with Earth, which means that one side of the Moon (the "near side") is permanently turned towards Earth. The other side, the "far side", mostly cannot be seen from Earth, except for small portions near the limb which can be seen occasionally due to effects. Most of the far side was completely unknown until the era of space probes. This synchronous rotation is a result of torque having slowed down the Moon's rotation in its early history, a process known as . The far side is sometimes called the "dark side". In this case "dark" means "unknown and hidden" and not "lacking light"; in fact the far side receives (on average) as much sunlight as the near side, but at opposite times. are cut off from direct radio communication with the Earth when on the . Orbital and physical characteristics are shown in the tables below.

Orbital characteristics Physical characteristics Semi-major axis 384400 km Equatorial 3476.2 km Eccentricity 0.0554 diameter Perigee 363104 km Polar diameter 3472.0 km Apogee 405696 km 3.793×107 km2 Surface area Revolution (0.074 ) 27 d 7 h 43.2 min period Mass 7.347×1022 kg 29 d 12 h 44.0 Mean density 3.34 g/cm3 Synodic period min Equatorial 1.622 m/s2 Average orbital gravity 1.022 km/s speed 2.38 km/s Inclination to Rotation period 27 d 7 h 43.2 min 5.145° ecliptic (to 1.5424° Table 1: orbital characteristics [RD1.][RD2.]. ecliptic) Albedo 0.12

Table 2: physical characteristics [RD1.][RD2.].

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1.3 List of abbreviations GCR Galactic Cosmic Radiation HAB Habitation module HSV Human Spaceflight Vision IM Independent Mobility LEV Lunar Excursion Module MFP Mean Free Path RD Reference Document TBC To be confirmed TBD To be defined UT Utility Truck

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2 LUNAR ENVIRONMENT FEATURES The Moon is an alien world, completely different from the Earth.

The main features of the lunar environment that have to be considered in a mobility system design can be sorted as follows:

• Atmosphere • Illumination conditions and thermal characteristics of the surface • Topography and terrain properties (craters, slopes and rocks distribution) • Soil characteristics and trafficability • Dust () effects • Radiation.

2.1 Atmosphere The lunar atmosphere is very tenuous, the gas concentration on the surface varies from 2 × 105 molecules/cm3 during the lunar night to 104 molecules/cm3 during the day. It has been estimated that the total mass of the native lunar atmosphere is about 104 kg, and each Apollo mission has released on the surface about the same amount of exhaust gas [RD1. p. 40].

Atmospheric characteristics Atmospheric pressure 3×10-10 Pa 25% 25% 23% 20% Ammonia trace Table 3: the [RD2.].

2.2 Illumination conditions and thermal characteristics of the surface

2.2.1 LIGHT AND TEMPERATURE ON SURFACE The Moon rotates around its axis in about 28 days. The equatorial regions thus get 14 days of sunlight and 14 days of darkness. The axis tilt of the Moon is 1.5424° with respect to the ecliptic, so the effect of seasons is very limited. The absence of a significant atmosphere makes the temperature change abruptly from day to night, with only conduction and irradiation as means of heat flow.

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Shadowed Front Back Typical Other polar Limb polar equatorial equatorial mid- areas equatorial craters (near side) (far side) latitudes Average 40 K (?) 220 K (?) 254 K 256 K 255 K 220÷255 K temperature Monthly ? ±10 K (?) ±140 K ±140 K ±140 K ±110 K range Table 4: estimated lunar surface temperatures [RD1. p. 36]. The absence of atmosphere results also in no light diffusion, making the objects which are not reached by solar light almost invisible. The albedo of the surface is 0.12, so object that are not reached by direct illumination are visible thanks to the light scattered from the surface. The solar irradiance on the surface varies during the (because of the different distance from the sun); it varies from 1360 W/m2 (, near side) to 1374 W/m2 (, far side), making the far side at the local noon a bit hotter than the near side. During the night, the temperature of the deeper layers of the soil is usually higher, for example it is about 40 K higher at 35 cm of depth.

2.2.2 POLAR ENVIRONMENT The lighting conditions on the lunar poles are peculiar due to the small axis tilt with respect to the ecliptic. The sunrays at the poles are always almost tangent to the surface, with sun elevation ranging from +1.5° to –1.5°. This peculiar situation creates two kinds of geographical features, the “cold traps” and the “peaks of eternal light”.

The cold traps are bottoms of crater that never get sunlight because of the shadows generated by the crater rims. These places are colder than any other place on the surface of the Moon, and their temperature (around 40 K) has small excursions (Figure 1) and anyway it is always below 100 K. The cold traps might hold precious frozen volatiles (for example, ), which could become useful in case of human settlement.

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Figure 1: the distribution the temperatures inside a crater located at 85, 1 N.; the maximal and average temperatures are shown [RD5.].

Figure 2: location of cold traps on lunar south pole [RD6.].

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The peaks of eternal light are theoretical places that are always hit by sunlight. True peaks of eternal light could be only an infinitesimally small location, on the very top of a mountain, but good approximations of this situation have been found both on the south and north poles. The Clementine [RD7.] mission has provided almost all the data for discovering such places [RD8.] [RD9.].

On the south pole, several places have been detected where there is sunlight for almost the 70% of the time of a lunar day during winter. Moreover, two areas near the rim of a crater () are illuminated for the 98% of the time.

On the north pole, the rim of the crater has been found to be constantly lit during the summer, being a good candidate for a .

A peak of eternal light is an attractive place for locating a lunar base, for the following reasons: • the continuous (or almost continuous) illumination will ensure continuous power supply via solar panels • the long 14-day night is avoided, allowing more operations to be done • the temperature excursion is expected to be more acceptable than in equatorial regions • easy shielding from solar radiation can be obtained thanks to terrain features (e.g. small craters) • a cold trap containing ice could be near.

For what concerns the temperature on a hypothetical peak of eternal light, only speculation is possible. [RD1.] proposes 220±10 K that could drop down below 200 K during the short periods of absence of illumination, while a similar result (223±10 K ) is given by [RD9.]; [RD8.] and [RD4.] suggest 260±10 K instead.

2.3 Topography and terrain properties The Moon has a great variety of terrains and geological structures, generated by both meteoroid impacts and volcanism. The lunar surface can be sorted into two main categories, the maria and the highlands. The maria are flat, darker (albedo ≈ 0.095) and low areas, all located on the near side, which are believed to have been originated by the filling of ancient impact basins with basaltic lava. The highlands are brighter (albedo ≈ 0.15) and they host a greater number of superimposed craters. The amount of cratering is usually an indication of the age of a geological surface: the more craters, the older the surface, because if the surface is young there has not been time for many craters to form. Thus, the Earth has a relatively young surface because it has few craters. This is because the Earth is geologically active, with plate tectonics and erosion having obliterated most craters from an earlier epoch: in contrast the completely cratered surface of the Moon is much older. Different parts of the surface of the Moon exhibit different amounts of cratering and therefore are of different ages: the maria are younger than the highlands, because they have fewer craters [RD3.][RD1.]. The oldest surfaces in the are characterized by maximal cratering density. This means that one cannot increase the density of craters because there are so many craters that, on

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average, any new crater that is formed by a meteor impact will obliterate a previous crater, leaving the total number unchanged. Some regions of the moon exhibit near maximal cratering density, indicating that they are very old. The lunar ranges from 60 km of thickness on the near side to 100 km on the far side. The whole surface of the Moon is covered by a thin sand called “regolith”. The regolith thickness varies from 3 to 5 m in the maria to 10 to 20 m in the highlands.

2.3.1 CRATERS The craters on the surface are the results of high-velocity asteroid impacts. They can be sorted in 3 categories [RD1.], on their diameter (D) and appearance:

• Simple crater (D < 15÷20 km), bowl-shaped • Complex craters (15÷20 km < D < 140÷175 km), with central peaks • Basins (D > 140÷175 km), with terraces and inner rings.

Crater frequency [RD3.] can be described by the formula: N = KDn Where N is the cumulative number of craters greater than D (km) per unit area (km2) and K and n are constants (Table 5). The formula is reliable for D > 1 km.

Land type K n Young (maria) 0.1 -3 Old (highlands) 0.1 -2 Table 5: approximate values of K and n. A detailed analysis of the images has allowed the description of different geometrical characteristics of lunar impact craters by equations of the form: Y = aDn where y is a given characteristic (e.g. depth, rim height) and a and b are constants [RD1. p. 66]. This formula can be used for correlating (Table 6), for example, the diameter of a crater with the slopes inside it, under the hypothesis of a bowl shape:

crater diameter [km] rim height [km] depth [km] max slope [°] 0.01 0.00034 0.00187 47.7 0.05 0.00173 0.00951 48.4 0.1 0.00349 0.01915 48.7 0.5 0.01783 0.09732 49.5 1 0.036 0.196 49.8 5 0.184 0.996 50.5 10 0.372 2.006 50.9 Table 6: average properties of simple craters; the max slope can be overestimated. Bigger craters are not bowl-shaped and such hypotheses cannot be made for them.

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Usually on the rims of a crater there is a layer of debris ejected during the impact. The maximum diameter (d) of the ejecta boulders can be described by the same formula [RD1. p. 72]: n dmax = aD where a and b are constants. The following table (Table 7) shows the relationship between the size of a crater and the maximum size of the rocks on the rim:

max ejecta crater size (km) boulder size (m) 0.01 0.48 0.05 1.38 0.2 3.45 0.5 6.32 1 9.99 5 28.90 10 45.66 50 132.09 100 208.72 Table 7: maximum size of boulders on crater rims. There is not much information on the global size-frequency distribution of boulders near the craters, due to the lack of high-detail images of the surface. [RD14.] reports the results of the analysis of a photo from the Lunar Orbiter III mission, where the distribution is described with the equation: log(Nb) = k log(d) + c where Nb is the cumulative number of boulders of size greater than d found, and the constant k = – 4 (Figure 3).

Figure 3: boulder frequency vs boulder size, for a crater of 145 m of diameter.

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The boulders are located at a distance from the crater center that ranges from 1.2 to 2.4 of the crater radius. The applicability of the results to other parts of the Moon is questionable, but the –4 slope seems to be of general value (even outside the Moon) for small (simple) craters, as it depends on the physics of the impacts that generate the crater itself.

2.3.2 APOLLO LANDING SITES The lunar terrains that have been explored by Apollo missions can be sorted in the following categories [RD1.]:

• Maria (Apollo 11, 12) Flat terrain, with small craters ranging from 50 to 250 m of diameters, with no sharp edge. Boulders and mounds of up to 5 m size where found outside the craters. • Ejecta ridges () They are located at the side of craters, and they are filled with the fragments produced in the impact. Boulders of 1 to 16 m found. The terrain is almost flat, with craters ranging from 10 to 100 m of diameter, with maximum slopes of 15°. • Highlands (Apollo 16) Both hilly and plain terrains are found, slopes at the sides of the mountains range from 18° to 40°. Both types of terrain are heavily cratered, the walls of the crater have slopes up to 40° covered with loose regolith and boulders (the boulders prevented the lunar roving vehicle to cross a crater rim). • Basin margins (Apollo 15, 17) The two landing sites were at the boundary of a mare and a highland. The slopes found were up to 30°, with massive boulders (10 m) on the edges of the maria.

2.3.3 POLAR TOPOGRAPHY The poles are very little known, the only accurate data available on them come from the Clementine probe. As no lander has ever reached the poles, there are no data available on the slopes and boulders on the surface. Anyway, the average situation on the poles can be assimilated to a generic highland [RD13.]. Table 8 summarizes the situation that can be expected on a polar landing site like a peak of eternal light on a 20-km crater rim:

Maximum slope 25° Boulder size on landing site 1 m Maximum boulder size (at some kilometres from 72 m landing site) Table 8: properties of a polar landing site. Another reference [RD15.] supplies a general description of a typical lunar highland, which should suit for a polar area as well. The data are adapted from [RD1.], and they are shown in Table 9:

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Boulder size: < 50 cm Boulder distribution: 4 / 100 m2 Craters Size: diameter < 3 m, depth < 0.2 m type 1 Distribution: 10 / 100 m2 Craters Size: diameter < 5 m, depth < 0.4 m type 2 Distribution: 1 / 200 m2 Nominal slope: 20° Maximum slope: 40° Table 9: characterization of a lunar highland [RD15.]. The data shown above are only attempt to imagine a typical situation that could be met on a polar site. Actually, there are no sufficient data or images about the lunar poles, and only speculation is possible. If some manned mission will actually land on a lunar pole, a campaign of probes for terrain photography and altimetry sensing will be necessary for safely preparing the mission and choosing a proper landing site (as it happened for the Apollo missions).

2.4 Soil characteristics The knowledge of the physical and mechanical properties of the soil is of fundamental importance for the development of a mobility system. The study of the physical and mechanical properties of lunar soil had been started before the first flights to the Moon were realized, by analyzing data coming from radio-telescopic investigation of the lunar surface as well as on studies of terrestrial soils and artificial materials with the same optical, thermal, and electrical characteristics as the lunar soil. Those data served as the basis for designing unmanned lunar spacecraft. The landing of unmanned spacecraft on the surface of the Moon provided much more detailed information about the properties of lunar soil, especially with the study of the soil samples delivered to Earth [RD16.].

Blanketed atop the Moon's crust is a dusty outer rock layer called regolith. Regolith is a layer of loose, heterogeneous material covering solid rocks, mostly composed of extremely fine debris. Both the crust and regolith are unevenly distributed over the entire Moon. The crust ranges from 60 km on the near side to 100 km on the far side. The regolith varies from 3 to 5 meters in the maria to 10 to 20 meters in the highlands [RD2.].

The soil features can be sorted into 3 main characteristics:

1. granulometric composition 2. bulk density and void ration 3. compressibility and shear strength.

2.4.1 GRANULOMETRIC COMPOSITION One of the main soil characteristics that govern its physical and mechanical properties is the granulometric composition (size and shape of the particles). The particle-size distributions detected in the samples returned to Earth are relatively uniform, even though they were taken from different

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regions of the lunar surface. The average particle size detected from Apollo missions runs from 0.051 mm to 0.153 mm. The samples, for the most part, consist of small mineral particles that differ in shape. The particles easily stick to each other to form separate clods and aggregates. In its granulometric composition, lunar soil resembles dusty sand.

2.4.2 BULK DENSITY AND VOID RATIO The main factor that determines the physical characteristics of a lunar soil sample is the degree of packing, as estimated by the void ratio (ratio of void volume to solid volume). In Table 10, the bulk density, void ratio and relative deformation for soil samples delivered by Apollo missions are listed.

Lunar soil sample Bulk density, g/cm3 Void ratio Density of grains for Condition of soil Loose Compact Loose Compact void ratio, g/cm3 Apollo 11 1.36 1.8 1.21 0.67 3.01 Apollo 12 1.15 1.93 0.89 1.55 2.26 0.87 2.9 Apollo 14 0.87 1.51 2.37 0.94 2.93 Apollo 15 1.1 1.89 1.94 0.71 3.24 Apollo 16 1.115 1.793 1.69 0.67 3 Apollo 20 1.040 1.798 1.88 0.67 3 Table 10: bulk density and void ratio [RD16.]. The estimates of average bulk density of the lunar soil in the intercrater areas of the lunar surface are reported in Table 11.

Average bulk density, g/cm3 Depth range, cm 1.5 0 - 15 1.58 0 - 30 1.66 0 - 60 1.74 30 - 60 1.9 300 Table 11: average bulk density of the lunar soil in the intercrater areas [RD16.].

2.4.3 COMPRESSIBILITY AND SHEAR STRENGTH Compressibility and shear strength parameters of the lunar soil samples were measured under different packing conditions, thus permitting the determination of general trends and relations of the physical and mechanical properties. Average values of the physical and mechanical properties of the lunar soil samples when compressed under static pressure are given in Table 12.

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Soil parameter Void ratio > 1.3 1.3 - 1.0 1.0 - 0.9 < 0.9 Coefficient of compressibility, (1/MPa) > 40 20 8 < 3 Cohesion, (kPa) < 1 1 - 1.5 1.5 - 2.5 > 2.5 Angle of internal friction, (deg) < 10 10 - 15 15 - 20 > 20 Table 12: average compressibility and shear strength parameters of delivered soil samples [RD16.]. The physical and mechanical properties of lunar soil samples returned from different regions of the Moon are rather similar; the main factor that control the lunar soil packing process is particle sliding and tighter compression of soil particles and aggregates. The shear strength of the soil is well described by the Mohr-Coulomb formula. The parameter of shear strength depends considerably upon the degree of soil packing. The angle of internal friction and the cohesion coefficient increase with more packed soil. The physical and mechanical properties of lunar soil obtained in situ by Apollo astronauts are summarized in Table 13.

Void ratio Soil parameters >1.3 1.3-1.0 1.0-0.9 0.9-0.8 <0.8 Bearing capacity, kPa <7 7-25 25-36 36-55 >55 Cohesion, kPa <1.3 1.3-2.2 2.2-2.7 2.7-3.4 >3.4 Angle of internal friction, <10 10-18 18-22 22-27 >27 (deg) Isolated On edge of In areas of bumps and fresh craters On shallow depth Typical locations on the small beds with small elements of Inter- crater of re-worked Lunar surface of fine- dimensions; very eroded areas soil; stone-like grained on steep craters formations, material slopes isolated stones Table 13: the in situ physical and mechanical properties of lunar soil [RD16.]. Lunar soil with bearing capacity of 25-55 kPa is the most widespread (60%): these locations are characteristics of intercrater areas; bearing capacity of less than 25 kPa can be observed on the rims of crater formation and on slopes steeper than 10 degrees. Typical values of lunar soil cohesion and friction angle are given in Table 14.

Depth range, cm Cohesion, kPa Friction Angle Void Ratio Average Range Average Range 0-15 0,52 0,44-0,62 42 41-43 1,07+0,07 0-30 0,90 0,74-1,1 46 44-47 0,96+0,07 30-60 3,0 2,4-3,8 54 52-55 0,78+0,07 Table 14: typical values of lunar soil cohesion and friction angle [RD16.].

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2.4.4 ALLOWABLE BEARING CAPACITY Any load posed on the surface of the Moon will experience a sinkage due to soil compression and displacement. The sinkage can be estimated by the equation [RD1.]: sinkage = q/k where q is the contact pressure and k is a constant. Acceptable values for k are 8 kPa/cm as average value to 2 kPa/cm for a safer value. The formula can be reversed choosing a maximum sinkage (e.g., 1 cm), and deriving the maximum ground pressure (allowable bearing capacity): allowable bearing capacity = k sinkage.

2.4.5 LUNAR SOIL TRAFFICABILITY Trafficability is defined as the capacity of a soil to support a vehicle and to provide sufficient traction for movement. From the experience of the Apollo and Lunokhod missions it is now clear that almost any wheeled vehicle will perform satisfactorily on the lunar surface, if the ground contact pressure is no greater than 7÷10 kPa [RD1.].

The energy consumed by a wheeled vehicle operating on the lunar surface will depend on three components: soil compaction, surface roughness and elevation changes. The contribution due to soil compaction can be estimated from Bekker equations: 1 ⎛ W ⎞ n Z = ⎜ ⎟ ⎝ Ak ⎠ sL ⎛ K ⎛ − ⎞⎞ H = (Ac +W tan φ )⎜1− ⎜1− e K ⎟⎟ b b ⎜ ⎜ ⎟⎟ ⎝ sL ⎝ ⎠⎠

⎛ bk ⎞ n+1 Rc = ⎜ ⎟z ⎝ n +1⎠ where Z is the wheel sinkage (cm), W is the wheel load (N), A is the wheel footprint area (cm2), n 2 is the exponent of soil deformation, cb is the coefficient of soil-wheel cohesion (N/cm ), L is the wheel chord length of ground contact (cm), b is the wheel width of ground contact (cm), K is the coefficient of soil slip (cm), s is the wheel slip (dimensionless), φb is the soil friction angle and k is the soil consistency (N/cmn+2), defined as: k = kc/b + kφ n+1 being kc the cohesive modulus of soil deformation (N/cm ) and kφ the frictional modulus of soil deformation (N/cmn+2). The values of the parameters for the lunar soil are shown in Table 15.

kc kφ n cb φb K 0.14 N/cm2 0.82 N/cm3 1 0.017 N/cm2 35° 1.8 cm Table 15: trafficability soil parameters. The µ adhesion coefficient between a metallic wheel and a rock can be estimated as 0.3÷0.5.

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2.5 Dust effects A layer of a fine, gritty powder, mainly constituted by regolith, covers the surface of the Moon. For the Apollo astronauts and their equipment the dust was defined a problem. The lunar regolith has grain-size characteristics similar to sand, with mean grain sizes mostly between 45 to 100 µm. It was discovered that sunlight was scattered at the terminators giving rise to "horizon glow" above the lunar surface; this was observed from the dark side of the Moon during and sunrise by both surface landers and astronauts in orbit. Subsequent investigations have shown that sunlight was most likely scattered by electrostatically charged dust grains originating from surface. It seems to be possible that a sub-micron dust grain can reach altitudes around 100 km over the lunar surface [RD10.][RD11.]. Mission documents from the six Apollo missions have been studied in order to catalogue the effects of lunar dust on Extra Vehicular Activity systems. It was found that the effects of lunar dust could be sorted into 9 categories [RD12.]:

1) vision obscuration (few problems with photography, reported on the vision camera) 2) false instruments readings 3) dust coating and contamination 4) loss of traction (the adhering to the surface of the tractive element caused loss of traction) 5) clogging of mechanisms 6) abrasion 7) thermal control problems 8) seal failures 9) inhalation and irritation.

Most of these effects have to be taken into consideration for the development of a mobility system. The vision obscuration effect might affect the guidance system capabilities so it is necessary to find a way of protecting vision sensors from dust raised by the vehicle while moving; the positioning of the cameras is equally an important issue: for instance, a camera standing high over the surface may allow a better dust avoidance.

Clogging of mechanism, abrasion and seal failures effects may be a serious problem for long stays on the lunar surface: articulate systems or mechanisms that have a hinged-like devices could be particularly affected by this problem. An elevate protection would be required for those systems.

One other fundamental problem is related to the coverage of thermal control surfaces: the dust adheres electrostatically to any surface which comes in contact with it, and coating changes the radiating and absorbing properties, causing the thermal control system not working properly. Fine coating of dust obscures solar panels as well, thus reducing gradually the available power. Tests have been performed in order to know the effects of dust on thermal control surfaces; it was found that radiator performance is degraded primarily by increasing in absorption in UV and visible regions, which raises the temperature of the radiator. Different strategies have also been studied to remove dust by radiator surfaces, like brushing, electrostatic curtain, vibrating surface or gas jets. None of these methods were found to be perfectly working; eventually, primarily due to its lower weight, the mechanical bristle brush was chosen to fly.

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2.6 Radiation The radiation environment of the moon is harsh. The lunar surface is exposed to the continuous flux of galactic cosmic radiation (GCR) and to infrequent periods of intense solar energetic particle activity. The GCR flux is between 1 and 2.5 particles per square cm per second, depending on solar activity. It consists of about 90% protons, 9% helium nuclei, and 1% heavier nuclei. GCR dose is difficult to shield; approximately 5 to 10 m of lunar soil reduces the GCR dose to terrestrial levels. Particle fluxes on the lunar surface are about 1/2 of their intensity in free space because of the presence of the Moon itself so they are blocked below the horizon. The absence of an atmosphere and a magnetosphere as well also means that there is no overhead protection from space radiation. The consequences of the radiation exposure are of primary importance for solar panels and on-board processor units degradation effects: a correct sizing and opportune shields are thus required in order to avoid malfunctioning of the system.

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3 SYSTEM REQUIREMENTS After the survey of the lunar environment, it is finally possible to derive the requirements for the mobility system. Some requirement (e.g., thermal) are strict and cannot be object of changes, but others (e.g. max slope) can be object of trade-off, and they will be marked in the text as “to be confirmed” (TBC). The first class of requirements is common for any mobility system choice (either utility truck or independent mobility), while the second, which is related to mobility, depend on the scenario of the mission as well. Different mobility requirements have been thus chosen for the Utility Truck and for the Independent Mobility.

3.1 Launch requirements The Mobility System shall be compatible with the launcher environment (volume, loads, acoustic frequencies, thermal). Table 16 shows the structural requirements for launch [RD18.]:

First lateral frequency: 9 Hz First axial frequency: 27 Hz Fairing diameter: 4.5 m Highest longitudinal steady state 4.55 g acceleration: Highest lateral steady state 0.25 g acceleration: Table 16: launch requirements (Ariane 5). (to be confirmed).

3.2 Landing requirements The Mobility System shall be compatible with the shocks at landing, to be defined.

3.3 Thermal requirements The temperature on a peak of eternal light is quite uncertain, anyway a range between 190 and 270 K can be assumed. The sizing cases can be defined as in Table 17:

Surface temperature: 190 K Cold case: Solar irradiance: 0 W/m2 Surface temperature: 270 K Solar irradiance: 1370 W/m2 Hot case: Albedo: 0.15 Earth irradiance: negligible (TBC) Table 17: cold and hot case. For the bottom of a cold trap (if the system is required to go there, in addition):

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Very cold case Surface temperature: 40 K (cold trap): Solar irradiance: 0 W/m2 Table 18: cold traps. The dust coverage of surfaces will change their thermal properties; this effect has to be considered especially for radiators (a 11% dust coverage will double the solar absorptance of a radiator).

3.4 Power requirements The Mobility System shall be self-powered. The worst lighting condition in a peak of eternal light can be assumed as a 35-hours of per lunar day [RD19.] (to be confirmed). As the availability of the light depends much on the local shading and topography, some margins should be taken in considering the total irradiance available, for example reducing it to half its nominal value (685 W/m2). If the system is to operate on a cold trap, longer eclipse times shall be considered. The solar arrays (if any) shall be placed as high from ground as possible, both to reach better light conditions and to avoid contact with the dust. Solar panels degradation may be assumed as 0.3 % per operational (earth) day due to dust coverage [RD20.], assuming the same value that has been measured for the Mars Pathfinder probe. The usual panel degradation due to use and radiation has to be considered as well.

3.5 Dust countermeasures All mechanism shall be sealed. The number of gears and exposed mechanism should be minimised [RD15.]. A system can be introduced for cleaning surfaces (panels, radiators).

3.6 Mobility Requirements

3.6.1 LUNAR TERRAIN FEATURES The analysis of the terrain features lead in section 2.3 is not of much use, unless some assumptions are made. The cumulative number of rocks outside a crater of diameter D is described by: log(Nb) = – 4 log(d) + c if Nb is set as 1, then d is the biggest rock (dmax), that is described by the relation: n dmax = aD thus c can be derived for each class of craters (as a function of the diameter): c = 4 log(dmax). [RD14.] reports that the boulders have a Gaussian distribution outside the crater, with most of them located between 1.2 and 2.4 radii from the centre. In the hypothesis of the 95 % of boulders located in this area, and 2.5 % equally distributed inside the crater, the number of cumulative rocks per unit area on the crater rim can be derived (Figure 4, Table 19).

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4 1 .10

3 1 .10

100

smpb()x, 20

10

1 cumulative number / square kilometre

0.1 0.5 1 1.5 2 x Boulder diameter Figure 4: boulders distribution on the rim of a 20 km diameter crater.

Boulders in a 100 m x 100 m square Boulder size Number 0.5 m ÷ 0.6 m 170 0.6 m ÷ 0.7 m 75 0.7 m ÷ 0.8 m 36 0.8 m ÷ 0.9 m 20 0.9 m ÷ 1.0 m 11 1.0 m ÷ 1.1 m 6 1.1 m ÷ 1.2 m 4 1.2 m ÷ 1.3 m 3 1.3 m ÷ 1.4 m 2 1.4 m ÷ 1.5 m 1 1.5 m ÷ 2 m 1 > 2 m 1 Total area covered: 141 m2 / 10000 m2 = 1.4 % Table 19: boulders on a 100 m x 100 m square of terrain. The applicability of the above assumptions is questionable, but this is helpful to provide an example of the rock distribution on a landing site. The results are consistent with what is reported in [RD21.].

The mean free path (MFP) can be computed with the formula [RD21.]:

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S ∞∞1 1− Dρ(D)dD − D 2 ρ(D)dD 2 ∫∫dd002 MFP = ∞∞ S ρ(d)dD + Dρ(D)dD ∫∫dd 00 where S is a characteristic dimension of the vehicle, d0 is the size of the biggest rock which can be overcome and ρ(D) is the density probability of finding a rock of size D in the unit area. For the problem considered, S can either be the diagonal of the vehicle (it can be assumed as 10 m, with reference to [RD19.]) or the minimum steering radius, if bigger. The MFP can be computed for different values of S as a function of minimal rock size considered as non-crossable (Figure 5).

3 1 .10 588.908

100 [m] h MFP2()20, d, 10 10 MFP2()20, d, 20 ean Free Pat M

1

0.15 0.1 0.5 1 1.5 2 0.2 d 2 maximum size of crossable boulder [m] Figure 5: mean free path, with respect to rocks. Red line: S = 10 m, blue line: S = 20 m. For what concerns the crater distribution, the same situation illustrated in Table 9 can be assumed. A small number of craters of size of the same order of magnitude of the vehicle will not influence significantly the MFP. The MFP can be used for deriving the basic terrainability and manoeuvrability requirements, with the criterium that the MFP must be at least one order of magnitude bigger than the characteristic length S. This means that a 10 m vehicle with a steering radius of 10 m shall have a MFP of 100 m, thus it shall be able to cross rocks of 1.2 m size. Otherwise, a vehicle of 20 m of steering radius (like a rolling system) shall have a MFP of 200 m, and so it shall be able to cross rocks as big as 1.7 m (see Figure 5).

3.6.2 SYSTEM REQUIREMENTS The mobility system requirements are derived from the tasks that are necessary to complete the mission, and from the information available on the environment. Some requirements are not strictly derivable from the information, so there has been put a choice between a stronger and a weaker requirement. The stronger requirement is more suitable to a Utility Truck, while the weaker

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to an Independent Mobility, which is supposed to be a simpler system. Table 20 shows the requirements of the mobility system, including the ability of unloading the habitat module (if applicable)

Performance Requirement HAB mass (for UT): 7400 kg Cargo mass LEV mass (for “moving lander” systems): 12400 kg (without ascent module) Diameter: 4,5 m HAB size Height: 2,3 m LEV center of mass height: 5.7 m (without ascent Center of mass: module) HAB center of mass height: 8 m Average speed: Speed • 1 km/h (TBC, mandatory) • 10 km/h (desirable) • 1 km (IM), 2 km (UT) (mandatory) Range • 10 km (UT, desirable) Trafficability in lunar soil Maximum contact pressure: 7 kPa Maximum negotiable Maximum negotiable step: 1.7 m Terrainability over discrete step: 1.2 m Minimum body terrain features (steps, rocks) Minimum body clearance: 1.7 m (if clearance: 1.2 m applicable) Minimum turning radius: 10 m Minimum turning Manoeuvrability Point turning abilities radius: 20 m desirable. Maximum uphill slope: 30° (TBC) Maximum downhill slope: 30° (TBC) Maximum crosshill slope: 30° (TBC) Slope climbing Static stability: 40° (TBC) (the static stability of the LEV without ascent module is 38°, it is considered enough for IM) Terrainability over combined Maximum negotiable step on a 15° slope: (TBD) terrain Table 20: mobility system requirements. The speed basic requirement is a minimal value that could be assumed for the “basic” mission only, which is achieving the mobility of a habitat module for moving it from the landing site to the assembly site. The desirable average speed is based on the assumption that the vehicle could be used as well for the astronauts’ locomotion, and so its average speed shall be greater than the walking speed of a human.

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The range basic requirement is as well the minimal value for the basic mission. A utility truck used for transport of humans would require longer ranges.