Lunar Terrain and Traverse Data

for

Lunar Roving Vehicle Design Study

W. J . Moore R. J. Pike G. E, Ulrich

0

March 1.9, 1969

Section A -- Traverse profile for a hypothetical Lunar Roving Vehicle Mission (U lrich)

Section B -- Lunar Surface Geometry (Pike) J Section C -- Crater frequencies and morphologies (Moore)

Section D -- Distribution of blocks on the lunar surface (Moore)

Section E -- Increased travel distance due to craters and other

obstacles on the Moon (Moore)

This report is preliminary and has not been edited or reviewed for conformity with U.S . Geological Survey standards and nomenclature. Prepared by the Geological Survey for the National Aeronautics and Space Administration Section A

Traverse Profile for a 'ilypothetical Lunar Roving Vehicle Mission

G. E. Ulrich Section A Y)

TREIwKSL' PROFILE FOR A lIYPOTHETICA7, LUNAR ROVING VET-IZCLE MISSION

Introduction

This report summarizes the preliminary results of on-going studies in the Terrain Analysis, Trafficability, Crater Studies, and Advanced

Systems Traverse Research Projects of the U.S. Geological Survey under

NASA Contracts W-12,388 and R-09-020-041, The information included herein has been prepared under the auspices of kke ~ci&nce'andTraver'se Planning

Panel for the Lunar Roving Vehicle Study Management Team. It is intended to provide a base line LRV traverse plan from the best currently available supporting data on lunar terrain character istics and geologic interpretations both of which will critically affect the use and application of roving vehicle concepts in Post-ApoELo lunar exploration. a

It should be made clear that thi.s is a preliminary effort and subseqrlent , revisions should be expected.

Procedure

The traverse profile proposed here is intended to be representative of a wide range of scientific mission objectives and lunar terrain types for an unmanned LRV mission having a map-distance range of 1000 krrl and a one-year duration. It is not derived from any single area of the

Moon but rather it is an assortment of selected sites of scientific interest and terrain types for which data were already available or could be readily obtained for this study. The traverse presents the variety of terrains and sites to be expected in the course of a number of LRV traverses. The geographic locations from wirich the data are

obtained are not cited except where acknowledgmex~t for the work by

h other than the author must be made.

This first: section of the report attempts to place the hypothetical traverse in a ge,ological context and in a logical

sequence of traverse segiwnts alternating with relevant sites of major

scientific interest (Table 1). The budgeting of time, distance, and vehicle velocity is dependent on the combined effects of slopes, craters,

and bloclcs based on analyses by 1-I. J. Moore and R. J. Pike of measurable

lqnar data for. broad terrain categories as set forth in the sections-

following in this report. The primary sources of inforination on the

lunar surface to date are the published and unpublj-shed results from

the Ranger, Surveyor, Lunar Orbiter, and Apollo 8 missions. The

importance of topographic definition of the lunar surface on both large

and small scales has become increasingly evident with the growing demands

for definitive mission plans and mobility concept studies (Ulrich, 1968) ,

The primary methods of obtaining such data for this report have been

photogramlme try, photoclinometry and shadow measurements.

There are limitations in the accuracy of quantitative data

gleaned from spacecraft photography when using photogrammetric, photo-

clinometric and other measureri~ent techniques. Thus, the data listed

here should be considered a current best estimate which will require

revis ion as more in£ormat ion is obtained. Primary Assumptions

In addition to the constraints imposed by Lunar terrain and trafficability estimates, certain basic assumptions concerning LRV traverse concepts nust be made orz which to base the mission profile. The fol.lorving assumptions have been generally agreed upon by the Science and Traverse Planning Panel for purposes of the present study:

1. The mission duration is one year, consisting of approximately

4000 hours of lunar daylight. Effective mission operation will continue around the clock throughout each lunar day, except for 112

s " I P day at each end when sun elevation is less than 7".

2. The mission profile is for an LRV in the unmanned mode, deployed from a Lunar Payload Module (LPM) at the traverse origin. The LRV will rendezvous with a manned mission at its term$-nus to deliver samples for return to earth and to provide mobility for one or two astronauts for up to 120 hours of 3-hour sorties, each up to 30 km long. An example of a 3-day manned mission profile is given by Karlstrom,

McCauley, and Swann (1968) and'a comparison of the gross time allotments for the manned and unmanned missions is shown in Figure 1.

3. The unmanned LRV traverse is 1000 km in map distance consisting of about 50% mare and 50% upland terrain.

4. The traverse is further divided into four ge'neral terrain type s for which preliminary data are available: smooth mare, rough mare, hummocky upland, and rough upland. Data are also available for large fresh craters such as Tycho, Aristarchus, and Copernicus and are included, on a preliminary basis, for this terrain category. 5. Average velocities of the LRV, on the basis of map distance

attainable for the several terrain categories are estimated as follows

and in Table 2 :

Smooth mare 1.7 kph

Rough mare 1.5 kpfi

Hummocky upland 1.8 kph

Rough upland 0 -5kph

Large fresh crater 0.3 kph

These velocities are considered reasonable for the LRV operating in

-. a ~ontinuousmgde. To the extent e that they turn out to be pessimistic,

they may also be reasonable for the step mode of operation as well.

6. Frequency of stopc required to update geographic position and to

evaluate hazards and landmarks in areas to be crossed:

Mare--every 0.5 km (total of 1000 stops)

Upland--every 50 m (total of 10,000 stops)

Time for a single, routine LRV stop-and-go including communication

delay is estimated to be 40 seconds.

7 . Time for shut -down or warm-up procedures be£ore and af ter lunar night,

and use of time and power during lunar night is not determined here.

The half day periods when sun is 0.7' above horizon may satisfy the

first item.

8. ~ciknti.ficinvestigations are to include the following basic group

of experiments selected by the Science and Traverse Planning Panel as

generally applicable to all unmanned LRV traverses:

a. Facsimile camera system with the option of small field

magnification and stereo capability (in addition to

the navigation TV, stabilized to operate continuously on moving vehicle; both cameras have 360' scan capability.

b. Samplers for rock core (or fragment) and particulate materials

c. Sample storage for 400 samples, under 1.12 lb. each

d . X-ray diffractometer/spectrometer, incl-uding sample preparation

and introduction .

e. Gravimeter, cleployable/retvievable

f . Magnetomtter, continuous reading (if applicable)

g. ~hreedeployable Remote Geophysical Monit ~rs(passive seismic)

Additional experiments may be added for special application on particular missions. The LRV and its various appendages will provide engineering experiments in soils mechanics that are not charged to

science.

9. Scientific operations with respect to time consumption are divided

into two categories (Figure 2) :

(a) Major Science sites (Table 1) each of which is allotted

50 hours for local maneuvering and traversing operations

(40%), camera scanning for science and general purposes (20%),

sample coll-ection (20 saniples at 15 minutes each) , preparation,

insertion, and storage/discarcl (12 min. each) , sample analysis

(20 min. each) , and 20 gravimeter stations (12 min. each) .

(b) Routine station stops at an average map distance of 0.5 km

enroute between major science sites; 360" camera scan (5-10 min.),

collection of .grab samples (10-15 min.) , and a gravity measure-

ment (10-12 min.) comprising 1/2 hour at each station for a

total of 2000 stations. Analysis of sample is performed

while enroute, and one in every ten coll~ctedis retained. 10. The LRV must avoid mature, young, and fresh craters which are

two meters across and larger and blocks which are one meter

across and larger. The width of the vehicle for purposes of

obstacle calculations is two meters.

A-Q Manrred Manned Automated 3-Day 3 -Day 1-Year LRV & IJti"U LRV Only LRV 0

Figure 1.--Comparison of gross time allotment in manned and automated mission concepts. (Manned mission allotments modified after Karlstrom,

McCauley , and Swann (1968) ) ' UNNANNED LKV 1000 K1\IZ TRAVERSE Hours-- ljear ----I P on2 L -----..w traverse traverse tiliw -7 --.----cL..-." . Driving I -- I Routine ~ t ando ~Cart~ -*--.-----*---"----- .------

-..--..------Hazard continzenc ies- ---- Navigation ------."------Routine sampling and geophysics I (1/2-km interval) I Major science sites (21)

MAJOR SCIENCE SITE Hours at kite *- % of site tisne --*------a ' I 'available-I---L___

Maneuvering for vantage points, hazard appraisal and avoidance, sample collection, and local geophysical investigations. (Magnetome try, if applicable, should record continuously while vehicle is operating)

Sample collection 20--Keep 10

preparation, pre instruments,and'storage(~~'-- discard) Diffractometry and spectrometry

Gravimetry--20 stations

Figure 2.--Gross budget of time consumption on overall LRV traverse and at individual major science sites. 8 Table 1,--,Major Science Sites Sequence in Terrain Type 1000-krn Traverse --.or equivalenr I. Vol-canic sites V-1 Lava flow front and top with linear 2 rough mare depressions V-2 Mare ridge witlz terrace 5 rough mare V-3 Caldera or pit crater rough mare- rough upland V-4 Low lava clo~ne rough mare V-5 Crater-top dame (or steep-sided dome) humnzocky - r oug1.1 up 1and V-6 Maar crater (or chain crater) rough upland V-7 Dark halo craters and associated rille rough mare- hummocky upland V-8 Trans ient phenomenon/ thermal anomaly smooth- rougl.1 mare b .

11. =act cr-ater sft~ 1-1 Crater with secondary impacts & blocks rough mare 1-2 Secondary field of small blocky craters rough mare and concentric craters in regional ray- covered area 1-3 Large fresh crater rim large crater 1-4 Normal & inverted stratigraphic large crater succession in wall and rim 1-5 "Ponded" plains on crater rim or wall rough mare 1-6 Floor-wall contact near concentric rille large crater 1-7 Central peaks with block fields and large crater bouldcr tracks

111. ~ectonic/masswasting sites T-1 Smooth regolith at traverse origin smooth mare T-2 Mare-upland contact and talus slopes 6 smooth rnare- rough up land T-3 Straight rille with fault scarp 7 rough -hurnmocl~y upland T-4 Debris flow 13 large crater T-5 Mare rille concentric with basin rim 15 rough mare- rough upland T-6 Sinuous rille with levees 19 rough mare- rough upland Table 2.--Distance, Velocj-ty, atld Tirrle Constraints derived from Sections B, C, and D

Fresh Large

Distance anLVeloc ity - Crater a %increase over map distance due to: 1. Slopes crossed, s 2. Slopes too steep, Lts 3. Craters, L C 4. Blocks, L 5. locks an8 craters, L~t-~ 6. Total % increase,l T 7. Ground distance travel per unit map distance " 8. Avg. hap velocity (kph) 9. Ground vc loc ity (kph)

Time Hours per km traverse increment (map distance)

-Summation exclusive of Science Sites 19. Distance

21. Time rkquircd, hrs. 22. % of total time 23, % of total distance

+

remotely controlled on the lunar surface clearly places severe require-

* ments on the earth-based control and data handling facility. These

requirements silould become more clearly defined as the LRV design

study progresses. The evolution of a conceptual design for the mission

operat ions center which meets both engineering and scientific needs

- should parallel that of the LRV.

The hypothetical lunar traverse presented in the following pages

is intended partly to illustrate some of the routine demands which will be

made on the miss'ion operation center and pn the &scientificdat~ facility

associated with it. Among these are requirements for personnel such as

investigators, data handlers, prime vehicle controllers, and operators

of remotely controlled scientific instruments. Obvious problems are

expected from the simultaneous operation of several vehicle- and instrumented

components, the co~nmunications time-lags, the power consumpti.on allowable

P on the vehicle, and the heavy demands from both the scientific and

engineering areas on the use of available computers for real-time data

handling, decision making, and issuing of commands to. the vehicle. In

order to operate on a 24-hour basis, four full teams of investigators,

data handlers, controllers, and operators will probably be necessary.

A1.l observational data will require real-time interpretative geologic

commentary that can be quickly stored and retrieved along with the visual

image, as a substitute for observations by an observcr aboard the vehicle.

Several geophysicists will be required to interpret gravimetry and

magnetometry as it is received and plotted; in addit,i.on active seismic data from manned missions wi 11 require real-time analysis. Geo- chemists will have to evaluate the textural and analytical data on samples collected in order to select the best working geologic models or hypotheses and as a guide to future sampl.ing. A navigator will be continually responsible for the vehicle 's geographic posit ion as well as its elevation, and it will be his job periodically to update the vehicle's navigation system.

Operators or computer-controlled commands with earth &errides will be required for all of the following functions, some of them simultaneously, determined mainly by the scientific mission objectives :

6. a. TV pan and tilt and 360" scan

b. Facsimile camera pan and tilt, 360' scan, and close up of

rock and "soil1' samples

c. Sampling of lunar materials

d . Sample preparation and insertion into analytical instruments

e. Storage, retrieval, and discarding of selected samples

f . Deployment, leveling, reading, and retrieval of gravimeter

g. Ranging to artificial or selected natural reflectors or hazards

h . Driving the vehicle: starting, accelerating, decelerating,

stopping, backing, and turning

Displays in the science data facility based simply on the vehicle- mounted science package described above for the unmanned rendezvous mission should include a't least four XY plots driven by telemetry as received from the vehicle: (1) geographic position and heeding of the vehicle on a controlled photographic or photogeologic base map, (2) gravimeter readings with capability of contouring, profiling, and

solving 3-point problems for regional gradient, (3) magnetometer data

in both X1 and profile form as required, and (4) elevrr~ionprofile of

vehicle position continuously along traverse. In addition geochemical

displays will be needed to show sample locations, classification, and

position in storage unit, tabulated results of elemental and mineralogical

- co~npositionswith textural characteristics, and off-line ,plotter

displays for comparison of any combination of geochemical data.

These basic requirements are only a first cut on the projected

needs of a science data facility . Terr~strial expfriqent s co~lbiningthese t * and other concepts should permit more precise statements of organizational-

and hardware requirements for the 'data facility. Hypothe tical Traverse--- Missioll------.----.--- Prof i-le The remainder of this section presents the chronological sequence

of missio~lsegments in which detailed investigations at individual

major science sites (Table 1) are linked together by routine traverse

sections across uniform types of lunar terrain. Each science site

consists of a brief description of scientific objectives, the allotment

of time at the site, and the types of terrain and hazards anticipated.

Where data is availableJ maps and profiles are provided as examples

of real lunar features. The tabulated terrain characteristics are also

given for each site. D t * I *, . . The traverse segments between science sites are presented as data

sheets, and when each terrain typevins visited for the first time a

representative sample of topographic profile is also provided.

Table 3 is a summary of the schedule and cumulative increase of

distance, time, and geologic sampling for the entire traverse. For

engineering studies and comparative analyses, calculations for any

length of traverse and any combination of terrain types and science

sites can easily be made by cutting out or rearranging portions of the

traverse.

The sequence of science sites, lunar nights, and deployment of

Remote Geophysical Monitors in relation to traverse distance and

cumulative number of earth days is illustrated in Figure 3. This

sequence is based on the traverse presented in the following pages,

one of many possible combinations that would be equally logical and

-feasible from a scientific point of view.

O r:C) a 4J cn -1-1 Tb

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Q) k 3 bO .rl Cli Definitions of terrain symbols used in Table 2 ard in data compilations for each segment of the traverse profile, partly modified from Sectio~lsB and E.

Map distance Distance in km obtained by direct measuremeilt between two points on a map.

Ground distance True distance in kln on the surface betweer~two points which accounts for the statistical irregularities in the surface requiring deviation from a straight, horizontal path.

Map velocity The map distance divided by the estimated hours required to traverse between two points. .

Ground velocity The truespeed in kn~per hour required to traverse the ground distance so as to achieve the predicted map velocity.

Percentage of map distance which must be added to get ground distance Ls due to traversing slopes, perpendicular to strike of slope and not allowing for curvature.

Percentage of map distance which must be added to get ground distance Lts , due to slopes too steep to egot ti ate. . .

Percentage of map distance which must be added to get ground distance LC circumventing craters of mature and younger morphology, 2 m to 2 km in diameter.

Percentage of map di.stance wllich must be added to get ground distance L~ circumventing blocks and boulders, 1 to 30 m in diameter.

Percentage of map distance which must be added to get ground distance L~+~ due to circumvention of craters and boulders.

Total ground distance increase as percentage of map distance due to L~ the combined effect of slopes, blocks, and craters.

Number of craters per km' of ground distance that must be circumvented N~ (2 m - 2 km in diameter) .

Number of blocks per km of ground distance that must be circumvented N~ (I m - 30 m in diameter).

Number of craters and blocks per km of ground distance that must be N ~ + ~ circumvented. 2 PSD Power spectral density in meters per cycle per meter; given for frequencies of 0.05 and 0.5 cycles per meter.

Abs. mean slope---absolute arithmetic mean slope'

Alg . std . deviati.on---algebraic standard deviation REFERENCES

~arl-stroiu,T. N. V., McCauley, J. F., and Swann, G. A., 1968, Pre-

liminary lunar exploration plan of the Marius Hills region

of the Moon: U .S . Geol-. Survey opfn-f ile report, 42 p. Middlehurst, B. M., and Burley, J. M., 1966, Chronological iistine of

Lunar Events : NASA TM X-55470, 39 p.

~'~onigle,J. W., and Schleichcr, D. L., Preliminary geologic map of

thc!'Plato Quadrangle of the Moon: LAC 12, in preparation.

Shoemaker, E. M., Batson, R. M., Holt, H. E., Morris, E. C.,

Rennilson, J. J., and Whitaker, E.A., 1968, Television

Observations from Surveyor 3 : Jour . of Geophysical Research,

v. 73, no. 12, p. 3989-4043.

Shoemaker, E. M., Batson, R. M., Holt, H. E., Morris, E. C.,

Rennilson, J. J., and Whitaker, E. A,, 1968, Television Observa ti.ons from Surveyor VII -in Surveyor VII , A Preliniinary Report, NASA SP-173, p. 13-81.

Ulrich, G. E., 1968, Advanced Systems Traverse Research Project Report

(With a Section of Problems for geologic investigations of the

. Orientale Region of the Moon by R. S . Saunders) : U .S . Geol. . - Survey open-file report, 59 p.

Wu, S. C., 1969, Photogrammetry of Apollo 8 Photography, Part I of

Apollo 8 Mission, Preliminary Scientific Report: 25 p.

S itc T-1 Smoot'l~regolith sur Eacc Terrain type: Smooth Mare

.( Ls 0.2 % l.m kOnl 501n *- - -

Abs. llcatz Slope . St: V-1 Lava flow front and top with linear depressions

Terrain Type or equival.ent: rough mare

Objectives : Cornposit ion and history of lava flow and surrounding plains. Origin of linear depressions : lava tubes, surf ace flow channel^,^ grabens, or other. Estimated Time (hours)

Maneuveri-rig us i.ng TV camera for vantage points, hazard appraisal and avoidance, sample collection and geophysics traverses on top of flow and off of flow 200 n~ beyond front. Linear depressions and flow front slopes are special hazards.

FacsirniLe camera for site study and sample . collection,.

Collection of 20 samples; away from flow, on flow top, at foot of flow front , and from blocks and outcrops where present.

Sample preparation, analysis, and selection of 10 for return (to be performed concoinittant with other tasks when power permits)

10 gravimeter readings on flow top and 10 off of flow. Comncnce on outcrop if possible. Site V-1 Lava flow front and top with linear depressions Terrain: rough mare

Site: 1-1 Crater with secondary impacts and blocks

Terrain Type or equivalelzt-: rough mare

Objectives: to examine blocky ejecta and geophysical evidence of stratigraphy beneath the crater rim and origin of various types of secondary craters NOTE: Lj-ghtirzg angle wlil.1 be critical. to color and textural interpretat ion of Estimated Time (Izours) ax~gular blocks

Operation ------pv" Maneuvering using TV camera for vantage points, hazard apprai.sa1 and avoidance, sample collection, and geophysics profiles . Blocks are primary hazards. Secondary craters 'may be assymetric in shape and contain large boul.ders or blocks.

Facsimile c,anlera for site study and sample collection,

Collection of 20 samples from blocks, rim materials, ancl surrounding p 1ains

Sample preparation, analysis, and select ion of 10 for return

20 gravimeter readings from rim outward spaced 5 meters apart. Site 1-1 Fresh craters

Dia 107m 10 Rim height 2.2rn 100m.1Slo~o30" -1- 0 Relief 13 rn

0 200 4OOm Max slope >30° Max relief IOOm

Shadow measurements (Moore) v.7 1--- I _, . - -- .. -- . - ---- ._ .. . ."I ----- , * _ _ _ __..__ . , __ _,__^__-___._ _ __ _ ._------. I-. ------_ ._._._- - _ _ _ __ .- -_ -_ . _..___ -___._.______^l.__l._ -- - Site: 1-2 Secondary field oC small blocky craters and co~lcentl-jecraters in regional ray-covered area

Terrai.11 Type or equi-valcrzt: rough mare

Objectives : to dekcrminc variety sf composition in bedrock arzd the extent to whicf-r depth of over-burden controls the dis~ribukionof blocky craters; also the origin of concentric craters Estimated Time (hours) Segment of original 1000-km traverse: 100-150 hn

Terrain type: Rough. Mare I.( U m3 LARGE BL-OCKS FFiOM kL/AhIR ORG/TEN LIZ, HI54 PWOTOGEAPtI 1 0 5 IOm x SMALL, BLOCKS FROM SURVEYOfllLz' PICTURES 0 OUTLINE OF CRATER mrn, SOLID WHERE DISTINCT DASHED WHERE INDEF1INi7E

(Modified from Shoemaker, et al, 1968)

Concentric (double) crater

' Shadow measurements (Moore)

Site 1-2 Secondary field 'of snial-1 blocky craters and concentric craters in regional ray-covered area.

Site: Vs-2 Mare ridge with terrace

Terrain Type or- eclui.valer~t: rough mare

Objcctives : to axialyze the poss iblc rneclzanisins by which mare ridges are emplaced and - the nature of post-emplacement: processes Estilnated Time (hours)

r) Qpcra t ion ------*-we ------"-"----- Maneuvering along ridge-mare contact, along terrace, and across ridge. LocalZy stcep, possibly unstable slopes are primary hazards.

Facsimile camera scanning and sample selection.

Follection of 20 samples from bl-ocks and soil on ridge top, on terrace surface, and along ' ridge-mare contact

Sample preparation,analysis, and selektion of 10 for return

20 gravimeter stations across ridge if terrain correctiol~sare feasible; otherwise take readings at least 500 m away from ridge.

B, L. 0. IIX (Langley Worki-ng Paper) A 6 '"""L terrace L"LLL"~II.IL..~~--- 0 500 I000 ISOOm Sfgnient of original 1000-km traverse: 200-300 km

Cumulative time to date: * 979 hrs, f-iurarnoc ky Upland

Apollo 8 farsi.de, photograrnmctry (Wu, 1969) Site: T-2 Mare-uplands contact and talus slopes

Terrain Type or equivalent : sinooih mare-roug11 upland

Objectives : Comljauative study of composi-tion and geologic processes in adjacent mare and upla~zcl areas 4

Estimated Time (hours)

Operat ion -----,"-----..-^I- V-^-wLL- ID-- "..-I-.---"~~~lll-~~-^~ ------.

Marzeuverj-ng along base of uplalzd slopes for sampling and possible access route up onto upland. Loose talus slopes and abundant blocks are primary hazards,

Facsimile camera for scanning and detailed . . textuiral analysis of fresh blocks aryl boulders .

TV and Facsimile camera for landniark study and navigation

Collectiotl of 20 samples from mare & up]-and (or from blocks at foot of talus slopes)

Sample prepararion, analysis, and selection of 10 for return

20 gravimeter stati.ons, probably on mare Site 1-2 ItAarc - uplands c&ontc?ct

Apollo 8 farside, pho~ogra~~metry(Wu, 1.969)

Terrain type: Smooth Mare - Rough Upland

TZI LS Oe2 - 1.7 % -~--1 -lorn -5On1

T l 0 -5.7% Abs Mean Slope 2,9-11.0' 2,O-7.7' 1.4-5.2' t s .

0.21.- 2 Alg. Std. deviation 3.6 - 13.7 2.'5 - 9.6 1.7 6.5 N~ -

15.5 - 38.9 Abs. Fiean Curvature 0.6 2.0 1.0 - 2.7 0.8 3.8 N~ - -

17.5 - 39.1 Alg.Stc1.devi.ation 0.8-"-3.1 1.3-3.4 0.9-3.4 'B+C

0.04 - 0.4 % Nax Min I

5.0 - 15.7 % PS@O .05 @,=20m) : 0,25 - 0,50 0,045 - 0.200 Lc 13 80 x low4 1.2 I~o-~ 5.5 - 15.7 % PSWO .5 Cr\iz2m) : - - 4 L~f~ 12.9 - 15.9 % L~

------.--+-- Segment of original 1000-kin traverse: 300-350 km

Terrain type: Rough Mare u

Ls 0 elk % Im 10m 5Om w w

1, .m U Abs a Mean Slope 5*3O 3 *8O 2 .so ts

2 Alg. S td . deviation 6*6 4.7 3.1 . . .

39 E kbs'. Mean Curvature s 8 -9 1.3 N~ 4.1

' 4IeX Nn-tc . Alg . Std. deviation 1,3 1,8 5 .O 0.4. % L~ Max. ._____YMin . 16.9 "/, &c. PS@S ,OS V\=20n1) : 1.OQ 0 i4.20

* . 17.5 % - PS@0 -5 &2m) : 0.0035 * 0.0003 ~ ~ - : t - ~

i L~ 17,9 %

------I------*--- _11__.--1---1___^__.

Map dist:ance , th is segment : 50

Ground distance, this segment: . .5g km

'Jvg. hap vSlocityi . 1,5 qkph . , . . .* .

Ground vc loc lty : 1.77 kph . . Driving time: 34 hrs

Routine science each 0,s hl: 50 hrs

' Other operat ions : 32 hrs

Total time, thts segment: 116 hrs

&

- Cuntulative grouncl distance to'date: 507 krn

Cuxlulative time to date: 1145 hrs -

A -27

Shadow rneasuren~ents (Moore:)

Site T-3 Straigllt rille with fault scarps

Terrain type: Rough-EIumocky lJpland

Abs. Mean Slope 8,2 ll.OO 5.8 7.7O 3.9 5,z0 I~ts 0 - 5.7 % - -- -

Alg. Std. deviation 10~0'-* 13.7 9.6 N~ 2 7.2 - 4.8 - 6.5

15.5 - 39.3 Abs. Mean Curvature 0.8 - 2.0 2.4 - 2.7 1.5 - 3.8

17.5 - 41.3 Alg. Std. deviation le2 3 .I 2.9 - 3.1 1.9 - 3.4 N~fc

0 *4% L~ . Max. . pin.

5.0 - 22.4 %. [email protected] C?\=20nr): 0.34 - 0.50 - 0.075 - 0.2.00 PSWO .S fiz2rn} : - 211 - 80 x low4 0.13 - 4 x low4 LB-E 5.5 -*23.1 %

LT 12.9 - 24.1 % - .

Site: 1-3 Large fresh. crater rirn

Terrain Type or equival.ent: rough uplaud

.Objectives: to exa~i~inechanges in composition of surface ~uaterialsand nature of geophysical gradients radial kra a large fresh crater m C\ rn ,-I hl m Ti'. *I 4 l-i ';3

crl $4 (,J kc) 4-J -9 am 2 Li .rjU ii ;; cj? .. ha3 ij OJ $4 c 25 2 U 4 rJ P 3 .& r(c 5 SO 0 5 *& ZiG g 3 m 0 2 ci ti a :3 & E-l r: .. -64m 071 k 43 fi

9i-l 0 V3 w L . 0 . V photogra~~fi~etry

Site 1-3 --"--- -

Sites 1-3 and 1-4 Large fresh crater rim and wall

proba blc bcdroclc 8

ins j -q,000

L. 0. V, photogrammetry

.5 lkrn 1 B ----,- ---- Site 1-5 'i~ondodt'plainson crater wail terrain

Terrain: rough mare Site: 1-6 Floo~~-waI.Lcontact near concentric rilles

Terrain Type or equi.val.e~lt: laree crai:elr

Objccti-ves: to examsl~leref-atioil of crater floor to wall and of concentric ri1l.e to each of trwsey wl-letllcs processes are priraa-rily st-ructt~ralor volcanic L';COO!.;r crater wall. 2000- - crater floor 2(3OQ 7'- 0 P -- ---.--.-- d o

0 10 20 ' 304(n L -l-..--%---..-..A ---.- ..-- A

Apollo .8 farside, photogrammetry (iqu, 1969) - --- i

Segment of original 1000-km traverse: 450-500

Terrain type: Fresh Large Crater -.

Rough upland

,Hap distance, this segment : 45 krn

Ground distance, this segment: 59 km

. .. ** 'Avg . map vel6ci.ty: - * ..o.j kph ......

Ground velocity : 0.39 , kph . . . - . s 4 .

Driving time: ' 151 hrs

Routine science each 0.5 la: 45 hrs

Other operat i.oizs : 48 hrs

Total time, this segment: 244 6 hrs

' 6th lunar night* @ 1872 hrs for 3G0-hr period. Cumulative ground di.skance to 'date: 712 Icm

- Cumulative time to date: 1940 hrs

. in

Site: T-4- Debris flow Site T-4 Debris flow ' Torfain : large crater

Site: V-3 Caldera or pit crater P A Explosion (and col-lapse?) calders B

*-" .-../'-----

Shadow measurernellts (Moore)

e

Site V-3 Caldera and pit crater Terrain: Rough mare-rough upland

f?ough Uplands

Max. overall slopes 19-22° Shadow measurements (Moore)

, Apollo'8 farsi.de, photogrammetry (Wu, 1969) -

Rille 50Ori1

0- 0

0 I 2 3 4 krn L-."L--"--L -*---- L---l

Shadow measurements (Moore) ,

Site T-5 Mare rille concentric with basin rim.

Terrain Type or equivalent : nouell 1nay-e 10th lunar night @ 3120 hrs for 360-hr period

- ~umulat-ive-ground'distance to date: 1119 km

Cuntulative time to date: 31.57 hrs - b

Site V-4 Low Lava dome Site: V-5 Craher-top dome (or steep-sidrd domc)

Terrain Type or equivalent : t~~~~~~l~-c~..~~~@

.Objectives: to investi.gat:c evidence for volcanism ai:d magmat j-c clif Ecrcntiation in dome-=forlilirzg processes Site V-5 Crater-top dome (or steep-slclcd dome)

lOOOrn Shacloiq measurements (Moore) ---~------..--

5

L. 0 I V photogrammetry

Terrain ?1~11~110~ky-.r\oughUpland

7;s 1.0 '- 1.7 % . a"-km --IOrn ---5Om

Abs . Mcan Slope =ts 0 - 5.7% 8.2 - ll.OO 5.8 - 7.7O 3.9 - 5.2' P 2 liig. Std. deviation - 7.2-9.6 4.8-6.5-

NC 15.5 - 39.3 Abs. Mean Curvature 0.8 - 2.0 2.4 - 2.7 . 1.5 - 3.8 v

17.5 - 41.3 Alg.Std.deviation 102_3.1 . 2.9 - 3.1 1.9 - 3.4

0.4 % . Fax= gin.

=c 5.0 -. 22.4 % PSSO ,OS &=t:20rn) : 0.34 - 0.50 0.075 - 0.200 p, 5.5-23.1% PSm0.5 *2m) : 21 - 80 x 10-4 0.13, - 4 x l.~-~ B+C

12.9 - 24.1 % L~ Sep,mc.nL of origi-nal 1000-k~utzravcrsc:: 800--850

Terrain type: Smooth Marf

.) Es 0,z % lm --10111 ----501n

- -s Abs. Mean Slope Lts 2.9' 2 .OO 1 e4O

0 ,2 Alga Std. deviation 3,6 2.5 1,7

N~ ** 38,9 Abs. Mean Curvature 0*6 1.0 0,8

39.1 ' N~-b-~ Alge Std. deviation Q .8 1,3 0,9

l[J 0.04% . B Max. -__ UUIXPlirx. 15J % Lc PSW0 -05 (7\=-2 Om) : 0.25 O.Oti.5

15.7 % PS@O .5 &22171) : 0 .OOL3 L13-k~ 0 .00012 . * -. - I P

' 15.9% L~ .

__ll_p-P--_lll---"------.--I------

Map di-stance , th is segment : 50' k111

Ground d istance , this segment : 58 km . . .

Avg. map velocity: '. 1.7 kph -

Ground velocity: 1.97 kph

Driving time: 30 hrs

Rqutine science each 0.5 km: 50 hrs

Other operat ions : _ 30 hrs

Total time, this segiilent: 110 hrs

~umulati6c distance to'date: 1187 knl

Cumulative time to date: 3317 hrs

A-66

0 500 lO0Om L,-,, k---- 1 Shadow mcasureinents (Moore)

Site V-6 Maar or chain crater .Ground distance, this segment: ' 58 krn

. Avg . 'map Gel-ocity: 1,7 kp1-i . %. Ground velocity: 1.97 kph

Driving time: 30 hrs

Rotatine science each 0.5 km: 50 hrs

Other operat ions : 30 Irrs

Total time, this segment: 110 hrs

11th lunar night. @ 3432 for 360-hr period

Cumulative ground distance to .date: 1250 kin

Cumulative time to date: 1 3477 hrs

A-69 Sit:c: T--6 Sinuous rille

Terraill Type or eqrlivalent : Roi1gZ1 mare S].ope map and shadow measureinent s (Moore)

Site T-6 Sj-nttous rille with levees Segi~ieiltof original 1000--1:nltraverse: 900.,,950km

, C7kerrni-n type: Rstl.gh Uplaucl

---Im

Abs . $lean Sf-ope ' El. .OO

ALg. Std. deviation 313 -7 9,G

Site V-7 Dczrk halo craters and associated lrillo

Ranger LX, shadow nleasuremelnts

Terrain Type or equivalent : ~~oot.l~-to--rouglima-ce

Objf ctiv~s: TO investi-gate source of tl~ecmalarronaly ailcl, if possj.hlc, area of active vol.caxii.sm; to rcndez-vor~switl.1 rnallned mission ancT dclivei.- l-wnar Mop n~odificdoftcr prclirnirlciry ~colcgymap, LAC-I2 (Sclzleicher & M 'Gonigle Fransicnt phorromana fco:i'i fb9lcldichurs.i. cnd Burley (I":6)

Site V-8 Transient phenomena/thcrmal anomaly

' T i : Smnoth-to--rougl~mare .d Section B

* Lunar Surfac.e Geometry Introduction- -dat:a _Y___I_.--*.-- -I.------"-.... ---

This sectioi~provides numerical descriptive information on lunar surface roii$hness cor~tributeclby the geometry o£ the terrain, without regard for specific features such as craters or blocks. The data were obtained througli photoclino~netry, the method of deriving s lope informat ion from the brightness distributio~i of ~nonoscopiclunar iirlages by calibrated techniques (Van Diggelen 1951, Watson 1968) . Data sources arc high resoliitj.on imagery (elfrctive resolution one n~cter)from I,unar orbiter spacecraft (Missi-ons 11, 1x1, and V) and selected terrestrial telescopic photographs (effective resoluti.on 0.75 km).

The photoclinometric method affords a means of gathering large quantities of data in a relatively short timc, once the necessary instrumentation and coiuputer software have been assenlhled . Thus, it has some advantage over the niore laborious shadow measureinents . As current ly developed, the photoclinometric method for reducing spacecraft imagery is suited more to the smoother lunar terrains, the mare, than to the rougher, upland arcas (I,a~itbiottc and Taylor, 1.967) . One meter resolut ion data for the lunar uplands are comparatively nieagcr and are less reliable than rnare data. Hence, consLderablc reliance has been placed upon the b .75 km data, originall-y reduced by Rowan and McCauley (1966) .

8' This information has been extrapolated into the resolution range most relevant to vehicle mobility problems. Photogra~nm~tricterrain data, best obtaincid from ApoLl-o 8 nrtd

Lunar Orbi trr V rnediurn rcsol~~tionimagcs, are not yet avai-lable in

suFficient ciuant i ty . Addit ionally, photogcanirnetr ic reductioi~of the

Orbiter and Apollo 8 imagery docs not yield the one meter resolution of wl~ichthe photoclinometkic mcthod is capable, and wlii-ch is thcPnlost useful. scale for tlle prescni: sirudy. The available lunar slope data have been supplemented and e~il~nncedby a sl.ope distl-ihution~model.of a type previously employed in studies of terrestrial surface roughness conditions.

The most critical question, "How reliable are tl~e11 igb resolut-.iou *. pl-~otocli.nornetrj-cdata," has yet to be answered satisfactori-ly,

particularly for the rougher lunar areas. When avail abl-c, such an evaluation will be made available to users of the informaki-on contained in this section. At most, the prescilt terrain nlodcls and data should

rcqui-re but a s in~plerecalibration,

Classif kcation of Lunar Terrain ----."------.------_I

Heterogeneity of the ~oon'ssurface cl~aractcrvirtually prccludes a complete numerical descriptioi~of all. types of terrain that might be encountered by a lunar roving vellicle. The only meaningful alternative is a sanipling of representative lunar terrain types or

classes. Such a sampling may be as generalized or as inclusive as time and the availabi'lity of large scale tcxrrain data permit. These two

constraints thus far have limited the nunlhcr of lunar t-crrnir~class~i:

to four: smooth and rough mare and humnlocky and rougl? upland. Thcse

four terrain cl-asses are the princi.pl.e divisions used by Rowan and

McCauley (1.966) . Table 1 shows the topographic ieatures typically

includc:d in each category. As iucrc~nsiilgda tn allow, this brcakdo~~~l

will be expanded to a six-.part classificat-ion (Table 2). It is anti-

cipated that each of tiiesc six classes eventually wili be suhdividcil,

yielding perhaps as many as two clozen differei~tterrain types.

Selection' of Dcscript ive ~o~bora~hicParnmoters AM------e-...--.------.".-- --.--.------~-,- ----L?-.- .-, ----,,,.. "---,--&",,

The thrce parameters chosen to describe the ~oon'slarge scale

- surface geomet.ry were select-ed 011 the following consiclera+tions (3.)

app1icnti.011 to prof i lc data, the on3.y Format in wlliicl~ photoc:linometric

data can be obtaincd reliab1.y; (2) ability to express surface roug2:ncss

rather than other, interesting, 1mt lesh; ,apyropri.akc terrain ,

characteristics; (3) ease of interpretat ion and application to problems

of vehicle mobili ty ; (4) ability to characterize surface roughness at

any desired base lcngt'l.~pertinent to vcthic3.e traf ficability problems.

The three parameters are powcr spectral density, slope angle, and angle

of sl-ope curvature. The varied expression and prcsentati-on of each of

9 tlzese measures for t:he four gross lunar terrain types is disc:ussed

at length below,

Power Spectral Density ------..-.-...-"#.-

This p~lrarlletcrexpresses the relief frequency content of a terrain

profile as a time series, and is used principall-y to evaluate the

dyrlaniic response of a vehicle to different types of terrain (Jacger

and Schuring, 1966, Rozerna, 1968). Like slope curvature, it is a

measure of relative Lerrain rougliness, and can bz somewhat imdcpcndcnt

of absolute slope angle and regional. slopes. The measure is expressed 2 as a full logarithmic graph of power spectral density, in meters /

cycle/~neter, against frequency, in cycles/nleter.

Fig~irc!s 1-6 present the inost rr:crrrt. powel: spectral dc~rsitycurves

available for the Moo11 . Tiley are a substantial. impvovemcnt over

previous curves (Pikc 1368) . Two curves, represej-itrii~groughest and

smoothcst terrain corlcliti.ons wCLlit11j~1 each of the fo~lrmain Zuliar terrai.n

types, are shown iri each di-agraln. The upper. curve in Figure 5 i.n an

educated liypot.11esi.s only. Figure 6 sliows thc mnxi~num roughness range of

the entire Moon. Whilc all curvcs prcscated here arc subject to

revision or replacement by sti 1-1 more representative curvcs, Figures 1-6

probably include most of the roughness condi-tions prcxsent on the Moon.

Power spectral dcnsi-ty iunctions of terrestrial terrains easily . B bra'ctcet t.l~eentire range of 1.unar curves presented here. Figure 7

shows curves for three freshly formed rough terrains, a lava flow

surface, a bloclcy nuclear crater excavated in basalt, and a volcanic

fissure vent. T11ese tevrai-ns would be traff icablc only with the greatest difficul-tp, if at all. Thesc curves are displacecl well above the roughcst

lunar curve yct obtained. Thus, most lunar terrains are appreciably

smoother than these exceedingly rougli terrestrial samples and should be

traversable with relative security by a roving vehicle.

The frequency range nlost applicable to velliclc dynamics lies

between 0.05 and 0.5 cycles/meter. bixpressed more simply, this means

that topographic features having base lengths between two and twenty meter-shjve tk ,g;tat:cst effect upon vehicle dynamics. Table 3 gives the

powcr spectral density values of tliese two critical frequencies for

the four lunar terrain classes. Maxiniciiii and n~ininlunlvalues, as deter- mined by the bounding power spectral dclisity curves in Figures 1-6,

are given for each terrain type,

Ranges 01 Power SpclctraX Densit:y (YSD) Values for

Four Gross Lunar Terrain Typcs at Two Frequencies

2 Terrain Type PSD in mctevs /cycLe/rncter

Srilootli mare

Rough mare

Hu~~m~ockyuplarid

Rough upl.and

ALI terrains Sl-ope Anole ------<&*:-- M~asuringthe departure of topography from the l-iorizontal, slope

angle i-s an absolute irxdex of terrain rougiii~css. Slope angles measured

along a profile may bc expressed either as absolute values or as

algebraic valucs , whc:re s l.opes facing, for exa:iipl.e, east , are dcs ignated

positive, and t17e west -facing slopes negative.

On the Moon, algel~raicslope-frequency distributions typic:ally approach, bu.t never quite achieve, the gzussian configuratj.or+. Thus,

the usual central tendency and dispersion statistics (mean, mode, median,

standard deviation, variance, skewness, and kurtosis) can be applied, albeit with caution, to algebraically cxprcssed lunar slope samples: llowever, the applicability of all oi these statisiics to vellicle mobility problems has not been established, so lunar slopes customarily are expressed as absolute values.

Absolute value slope frequency distributions on tllc Moon are skewed strongly toward low slope angles and only the mean, median, and niodal slopes should be extracted ironi ti-~esedistributions. If all lunar

slope data were available along any desired azimuth, then algebraic

slopes would furnish usefu 1 informat ion on slope sysrm~etry . However,

lunar photocl-inometric data can only be obtained along the phase plane, which does not change sufficieintly among the five I,i~narOrbiter miss ions to prov~clctlne required var j-at j-on in azirnut-51.

With cornpanat ively 1-ittle to be gained from us%ng algebraic * slopes, the slope angle data gathered for the present study are ex- pressed mostly in absolute val.ues. Three aspects of slope angle are presented here : (I) mean absolute slope, (2) algebraic standard deviation, and (3) absolute slope freqiiency distribution. Each of these three pararnetcvs is given 101: s10l)e base leng~hsoi one, ten, and

fifty meters for eacli o2 tiic four classes of lunar terrains listed in

Table 1,

Scarcity of r~prcscntativeLarge-scale slope data for all Lour

lunar terrain classes has necessitated e~~rapolationof small scale photocl~ir~omeiricdata and the dcriva~ionof statistical nlodels of slope distributions. Tile pliotoelinometric niethod , designed expressly for tlrr relatively smooth and level mare, is not readily applicable to stecper and rougher upl31-d terrain (Taylor and Lamhiotte, 1367) . Few slope distributions have been successfully obtained for the upland terraills . . ailthe base length of one meter. o ow ever, prcdictivc: models have been formulated for the upl-aids using one meter 1:esolution spacecraft: data from mare sites together wi.rh the 0.75 k111 resolutio~iterrestrial data for both uplands and marc. Derivation of these models is treated

in Pike (1968) aild in the appenciix to this section, and need not- be disctlssecl fz~rtherhere.

Tablcs 4-8 and Figures 8-11 prcse~ltslope information for the four lunar terrain t:ypcs at one, ten, and fiiky meter base lenglhs.

Most oi these data are straightforward; their cal.culation is discussed

in the appc:ndix. Tablcs 6-8 show only tentative l00t11 pcrccntil e slope values, which are not shown by the curves in Figures 8-11. Maxi- mum slope values, which co~mnonly are not accurat:ely measured by the photoclinometric mcthod in any but the smoothest arcas, vary also according t,o the number of slope angles inspected in a particul-ar sampl-e, and are not readily predicted.

E- 1.6 Table 4

Mean VaLties o? Absol-ute Slope at Three Base 1,engtils for Four Gross Lu13ar Terrain Types

Average Lowest H j-gliest Range of .Terrain Type Mean Mean Mean Mean S lope Slope S lopes

Base Lc~igtlzis oix rncter

Smoot11 mar e 2.9' leZO 4 *0° 2 ,Go

Rotrgh mare

~du,ghupland *

Base Length is ten i11ctex-s

Smootli marc 2 .O 1,O 2,8 1.8

fXtrrilmockyupland 5.8 3,6 7.0 3.4

Rough upland 7.7 6.2 11. .O 4.8

Ease Length is fifty rneter~s

Srnoot-XPmare 1.4. 0.7 L9

Rough mare 2.5 1..7 3.7

Hu~moclcyupland 3 .9 2 4.7

Rough. upland 5.2 LC .l 7 ,3 Table 5

Mcan Values of Algebraic Standard Deviation of Slope

Angle for Four Gross Lunar Terrain Typcs

* ------".-----.l---.------ll-Ll--.-YW*-" .--.ml.III.^I---- vd-l~.--X^Y.-~~---.---~." ------*--- "*-- Average Lowe s t Higlzcst Range of Terrain Type Standard Si.andarc1 Standard Standard Deviation Deviatiorz Deviat iorr Devj,ations

Base Length is One Meter

Smooth mare 3.6' . 1..5O e, , 85.O? . 3 35°

Ro~~gl-1mare ' 6.6 4.4 9.7 5.3

Flrxmmocky upland 10 ,2 5.8 12.4 6.6

Rough upland 13.7 10 .O 18,6 8.6

Basc Lei-~gthis Ten Meters

PI I---"- --- Y_--I_~~--~-~-.--~-~I-l_.-~" m^_---~-----p---*p-..-~-~~ll

Smooth mare 2.5 1.3 3.5 2.2

Rough mare 4,7

IIunurlaclcy up1.a nd 7 .2

RougF~ tlpl.anc1 9,6

------. " - - " " . - - - * *

Basc Length is Fifty Meters

------=---.------.".- -*------**" ----~ -wr.- m-**---*" --*--.b-**-----.--d- -*"----" -----?---,% "-. ------*-

Smootli marc 1.7 0.9 2.4 1.5

Korzgh marc 3.1 2 ,1- 4 .6 2.5

Rou gll up1and 6.5 Table G

PYcdici-ed Di-stribut ions oL Orie Mc t:cs: Slopes for Four Lunar Terraii-t Types bJftose Mean Sl-ope Values are ICnawn or Estimated

Meall Slope VaXucts 2,g0 5.3" 8.2O 11. .OO

Mode 1. S1noottl Rough %N %sfMeara mare upland S lope Table 7

Predicted Distributionr; of Ten Meter Slopes for Four Lunar Terrain Typcs Whose Mean Slope Val~~esare Knowrl or Estimated

Mean Slope 'values

Moclel. Smootl-I Rough Ht~mmocky Rouglz "/,N % of Mc3a1-1. mare mare upland , ma re Slope li'redi-ctedDi-st-1-i-butions of Fi fty Meter Slopes fnl- ]Tour Lunar Terrain Types Wh.ose Mcan Slope Va1ucs are Known or Estil-izated

Meal? Slope Val.wcs 1. JiO 2,5O 3 .go 5.2" * Moclc 1- Smooth Ro~~gh. Hurmnocky Rough %N %ofMeal~ mar e marc up1. and upland S 1.opc

f U I*.IL D s:id The s l ope i111oriiiat ion preceili-cad here suggesls th at the gt:ncral

terrain gcometry will not pose a serious traffi.cabi1i.t~hazard in

average smooth and rough mare areas. Special mare features, including

rilles, domes, and fresh craters will have to be considered as specific

hazards where encount.cred. The uplaiid areas, however-, can be expected

" to be totally in7passal~J.e in places, due to thc general. terrain

gcoiiie try alone. l:emciiihering tllat thc upland s 1-opc frequcn cy curves in

Figures 1.0 and 11 are 30121y averages, it is a virtual certainty t.llat

some of tlie rougher upl.anc1 areas wil.1. be excecciii~gl.yhazqrdous to a

lunar roving vehicle. Of course, such areas stil.1 rnilr;lit- provc to be

traf.Eica'6le if thg vehicle was carefully routed around the most - dangerous slopes.

An additional terrain typc, large Xresh craters (over 15 km in rim

diameter) , including clesireable scientific sites such as Aristarchus ,

Tycllo, ai~dCopernicus, may well. be even i~iorchazardous than any of the

four basic terrains discussed prcviously . Preliminary photograzmi~etric

profjles (Wu 1969, and unpuljl.ishcd data) of Lcesl~, Large craters both

in the mare artcl in the! upl.ands, indicate. tllal: Long and stccp slopes at,

and even exceeding, 30 to 4.0 degrees may be conmon in these areas.

Data wi4.l be made ava-ilablc pencling evaluatiorr. of tlze precision, .

Angle of Slope Curvnturc ---.-,"-__l_^." -.-- - I"...---^I.- --"* ---

*Like power spectral density, slope curvature is a measure of

relative, rather than absolute, surface roughness . Curvature anglc as * used in the present study and defined j-n Figure 12 is considerably less

complScatcc1 than t11a"ioJ: Scllloss (1965) . The statistical properties of slope curvature as derincd hcre are not yet well known. Algebraic curvnlurc, Prequcrrcy cl j st-I-Tbut:'LC)LZS on the Moon arc not strollgl y slcewc!d, ai~d,lilte slope allgl cl, approach normalit-y . While the mean absolute val-tre OF sl-ope curvatt-rre us~iallycorrelates posi~ivclywitlr mean absolute v9lue of Ll~eslope angle, the degree oL corresporrdence varics for different terrains. The parameter, calculated at several base lengtl~s, is complcixentary to slope angle and power spectral density, ancl perhaps somew1,at repet itive of the latter, although this redundancy has yet to be demonstrated.

Insufficient in formati.on on the properties oT slopc curvature * * angl e prec'l.uc1es use of gc!neual.ized pr.ecli.ctivc modc,ls simi-lar to tliose cornputed for s lopc angle, above. Insi-eac-l, four specific lunar samples were selected Co reprcscnt eaclz of the foz~r-major terrain types. Tables

9 and 10 present curvat-ure absolutc means and a1gehrai.c standard devi.ations at base lengt1.1~of one, five, tell, and fifty nzeters. Figures

13 and I4 are curvature angle frequency curves for ~llefour terrain types at a base length of five meters.

Again, the lack of additional lunar and terlcestrial curvat:ure informat ion parecZudes mz1.c.27. compal: ison of the presen"rl..t~nar sites wi t:h other areas . I'iowevex _., the data do point up some i.ntercs)iirig va~^ia*Cio~~s among the four lunar samples, At a base length of five meters, mean curvature values and the frequency curves display a systcniatic increase in curvature fronz smooth mare to rough up]-and. At: base 1engt:lls o;f: otie and Ej-Pty meters, Iiowever, the progression is not as regular. The variation of curvature with base length 1i.Ztewise shows both systc~r~atic Hcan Slope Curvatux-e of Four Gross Innar Terrain Types

At- Four Base. Leng1:l.r~

Terrain Type Values o.E Mean Slope Curvature 1 ' in ~r~kecs'of 'Arc '

0n.e Five Ten Fifty meter meters meters meters

I-'--.-- - .". . -- ..-.---.I- .- _...." ..-. "" l_l_...ll ,- .. --... I."l~__."_i.llX ___l..l-l---_... I"^ .-^."")-. .." "?ll.-I.....-I ^._..-...-..---

Smooth mare % Rough mare

Rough upland Table 10

Al-gebraic S tancliird IJeviation of Angle of Curvature

Of Four Gross Lunar Tr?rrai~rTypes at Four Base Lengths

Value of Algebratc St:a~~daudDeviation irz degrees,of arc ~

One F i.ve Ten S?ifty meter meters meters meters

Smooth maxc 0.8 1.3 1,3 0.9

IIumlmochy upland 1.2.

Rough upland 3.1.

progressioiis and mudi less ordcr1.y changes, depending upon the terrain type. Such i-rregularitics can readily be interpl-etecl in tcrnis of the varying geoiuorpl~icdevcl opiient of tire four sa~ilpl-eareas . Al.l-ii1-al1 the curvature angles shows1 in Figures 13 and 1.4 do not appcar to be large enougl, to sevcrely impede tlic mobility of a lunar roving vehicle.

s, When available, curvature data for analagous te~restrrialterrains will be furnished for compari.son with the luiinc sair~plesgiven here.

Surface Geometry and Traverse Distancc ."..-Y.^L-- "------.il---"lll---w---.M

Irrcgularitics of the 1.unau terrain tq:i.ll material 1.y; if but slightly, increase the map distarrce of any projecteci vellj-cular traverse.

P ' While avoidance ox small steep craters, block fields, steep-"walled rilles, ancl other hazarcls wil.1 contrj-bute most to suclz an irzcreased distance, the overall surface geometry has some affect as ti-ell. The figures in Tahl-e 11 were obtaii~edby colrlpuiring sccants of 111cdria11 slope values of seven slope angle classes for eacl: of tlle one-meter slope frecluerzcy curves in l'ijirjres 8-11. Percentage increase figures for large, fresh craters were estimated fl-onl photogra.mmetr-jc prof i.lcs of tire craters Copernictzs ancl Tycho (trizpub1islrc.d data) . ProbabIc Coli1.x-il~uttpl~of Topograpliic Slope. to Increase

P of Actr~allJIU Travel Di.stamce over PZan-l-Ecd Map Distal-~ce

As a FuncL i.on of Lunar Type

Average percentage of c-fistancc I Terrain Typo adck:$I to rnap cZLS~~~I~CCby ~:OIIO- graphic sl opc (data at one meter base 1c11gtl1)

StnootE~mare

Rough upland

Fresh Craters over 1.5krxi diameter R.IIPERI?NCIISS

Jaeger, R. M., and Schuring, D. J., 1.966, Spectrum anal-ysi-s of terrain

of mare cogl-iituiii: Jour . ~eopllysicalResearch, p. 2023-2028.

Lamhiotte, J. J., and Taylor, G. R., 1967, A photolnetric technique for

deriving slopes from Lu-nar Orbiter pl~oCography: Conference on

use of Space Systouit; for Planetary Geology and Geophysics, Boston,

McCaul-ey, J . F., 1964, Tcrrui.~?analysis of the 1.unar cq~latorial.belt:: I * . - ' U.S. Geol. Survcy open-file rcporl:, 44 11.

Pike, R. J., 1961, The Order of Valley Depth -in The Monadnock: Jour. of the Clarke University Geographical Soc., Worcester, Mass.,

v. 35, no. 2, p, 12-1-9.

Pikc, R. 3 ., 1968, Prel-iminary rnoclels for the prcclictiotl of slope angle

on tlie lunar surface: Unpub l islied U .S . Geol.. Survey workiiig paper,

8 P*

Rowan, L. C., and McCauley, 3. li., 1966, Lunar terrain analysis -in

Lunar Orbiter--Image ailal-ysis studies report: U .S . Geo1. Survey

Rozema, Wesley, 1968, The use of spectral analysis iu describi.ng lunar

surface roughness : IT .S . Geol-. Survcy interagency Report, 34 p.

Schloss, M., 1965, Quantifying terrain roughness of lunar and planetary

surfaces: AIAA Paper 65-389, 7 p. Van Diggclcn, Jollannes , 1951, A photometric jnvestigat+jon of the stagc3s

oL the ltcight-s of the ranges of hills in the ~l~aaciaof the moon:

Bull.. Astr. Tnst. Netl~erlnnds,v. II, no. 423, p. 283-289.

Watson, Ken~?el:li, 1968, Photocli.nometry from spacecraft images : U. S .

Geol, Survey Prof, Paper 599-B, JO p.

Wood, W. F1.', 1.961, Ranger, of unobstructed gl-ound-t o-ground visihili ty :

---in Proceed ings of tl~cSyrnpos i-trm on. the enzvirorrrnerztal. factors

influencing optimum operation of ordnance material, September 27-

30, 1-960, San Antonio, Texas, p, 17-29.

Wood, W. P., Soderberg, P . G., and Pjke, R. J ., A prclimi~~arymodel of t d -. t most-severe contour flying: U.S . ;\fi~iy Quater.~nastcr~esckrc~i and

Engineering Co~mandReport AE-$4, 33 p.

Wu, Slrermair S . C., 1969, Photogrammctry of ApoZlo 8 Photography, Part 1

of ApoLlo 8 Mission, Pre1.j-minary Scientifi.~Report: 25 p. , (Appendix to Section B)

PRETJLP/IINARY MODELS FOE TSIE PREDICTION

OF SLOPJI ANGLE ON T11E WNAR SURJ?2CE

by

RicElard J. Pike

Flagstaff, Arizona U.S. Geological Survey March 17, 1969 Astrogeologtc Studies Mcan slope anp,l-c values ;or four l-tiilr-r terrain types -----_II--I__-" ------X__I_wI------a_^^-l_l------.w I.--

McCau Ley (I 9bL;) and llowail and McCa~~lcy(1966) in previous photo-

clinometric st~~dicsof lunar surface gcos~iztry, ol~taii~edabundant slope

data at.. a rcsolutinn of 0.75 kiil anti grcaicr. One rcsulk o.L their work

(the curve tE.l'% oi-I Fjgure 1) , depicts median slope against sl-ope lengi-hs

for an "averngc 1"unar rfiare, " c0111prisi.ng botll S~IOO~~CTand rougher narc

types. The slopc of this curve, almost exactly -0.25, is very well

detel-i~inedby tl~e Four points. ROW^^ and McCriuley also calculated

median lunar slope for 53 different lunar localities, and dividtd t:he f n . 8 samples into four gross terrain uhits, >i3ootil Mare, Rougher re,

Ihn~rnoclcyUpl.antl, ancl Rough Up]-and . Iiy averaging rncclians oL sr,mples in

each category, we obtain poi-ut-s 15, 6, D, and 1':. Point- A, the average

for all, marc sampl.es, demonstrates the validl'.t.y of the curve kTXY%,

derived ear 1 ier by PllcCaulcy.

AVXlIAGE ME113:PiN SI_,OPE ERRAIN TYPE at 0.75 kin ii 1,

Smootli liar c We let ililc: four ~CII'II~Si-11 tlic above table dcfi!rc four ctarves

dcsrribj_x?;: ttzc rclair ionsliip hc irirccxl median stope ~ncislopc Icngt-h .

we set tlrc. EOLIY ctirves pars-ill el to that for thr: zli7crage mare, assunning

it is LikcLy that+ the median slope:slope lengi;th rr~latrior~sllipunder-

goes a similar rate of clrangc with varying slo~rlsScngtli, regarcllc!ss

of the terrain type. Since tl~esccurvc.s are constzucted from so fc:~

data, we have orixitteci conf idcnce inter-vals, ta11ic"l b7~u1.d be meaningless here. 4.

The four ctti'ves are describecl by tlre f olIot.~i;'g s simple power

expressions :

xukirll"E-?14 -- - *------0.25 Smooth Mare SmedZ 2.9 111,

0.2.5 Smed =5.4 1>1, 0.25 EJunxn~oclcy Up 13-11~~1 smedZ 8.1 UI,

0.25 Rough Upland Smed =lO,CDT,

' Where is median slope $ med' in ciegx-e-cs, al-kc1 DL is slope length in meters.

Altliough Figure I givcs iiscful inf oriiiat 'on concerning t:hc lt117a~:

surf3cc, thc imdirii~is not an especially powerful statisii-cal parn- meter. Roirali and i.fcC:+uley (1.966) also conputed iileaii slopc values for

their 53 lunar terrain snr~plesat 0.75 krn resolution. Using techniques

sirnil-ar to ,those by wiiich the prcvious set of curves was produced, we derive four curves dcpi cling tile relationshil~ betweell mean lunar slope

and slol~elengtli, Figure 2. Tile mean slopes at 0.75 krn resolution,

F, G, H, and I, are listed below for thc four gross terrain types:

AV~~UGEI$F;IT.~AN SLOPjS TE17&ATN TYPE (at 0.75 krn DL)

S~loothmarc

Rough mare

Husmocky Up1and

Rough Upland

----

~gain,these data were averaged fr:oln Rowan and McCaulcy (1966). ~t is

assumed that tlrc slopes of tlre cui-vcs are similar, and for most of their

length, do not depart sigr-iificantl-y from tllc value of -0.25 used for

the median slope curves of Figarc 1. Conficienre in this choice

increases so~i~ewhatupon calcul atiiig the incan sl-ope of samples at base

lengths snialler than 0.75 kn. Point J is located oil a hurn~~~oclcymaterial

near the craier Arislarciius. The slope l.cngtlr is 12.0 meters, and the

terrain appears to br older, pre--mare topography hcst classified as

Elumi~ocl:y U;)l;;nd. Poiiit li, is tire flooi- of tlie cralei- Pi-olenlaeus,

at2 upJar~dplains unit raiil~r15-kc tin avc~rag~lmarc surface. Point 1,

is a sample From the ror~g,ilc:rup lxr-rcls *

Figure 3 shoi:.; tirat the linear niodel is less satisfactory at base

lengths ui~dcr10 ~:cti?cs. Poi lit M is thc averagc of 10 smooth mare slope

1 means, arjcl point N the average of 19 rorrgh rnare means. These data are at. 0.6 n resolutio~l. Since the vertical distance between points M and N is idci~ticalto that bctwcen C and F on Figure 2 it is likely

that tile two upland cui-ves also follow belox 10 m base 1-engths, thc

It is to be e~nplrasizecl that the curves in Figure 3 are for average -*-

lunar terrains within each of tlze Tour gross morphologic categctries.

It is likely, therefoz-e, that specific lunar terrain samples wi14 be both ro-uglii'r and smoother than the idealizecl cases depicted here.

Ranges of mcan s1opc values were determined using the data of

Rcr~~ar-lanc"cCaul.ey (1966----their Table 4 and Figure 13) and tEte 0.6 m resolutiois spacecraft data generat cd by the Lnngley -11 photacLino~l~etric prograrrz. Consiclerable overlay:, is present, and is to bc exyectccl in a classificati.on as elementary as that: availiable atr. this time.

'She four average mean slop^: slope lengt-11 curves (Figure 3) for base lengtl-1s over 10 meters are described by t:he fallowing simple power iu~ictions :

Rough ntarc: .

Kux:rtmo clty up fL anal

Rougl.1 up1-ancl

-- Where S is mean slope in degrees, and

DL is slope leiigtll in rnctcrs

Lunar slaGpc frequency distribution model ------".--" --A---* -" -----*" Previous experience with terrestrial slope distributions by

W. F. Wood (1961, 1962) and the writer (1961) has shown that, given

a sufficiently large number of cases (50 -< N -C100) all disiributions can bc "normalized!' to yield nearly identical pcrc~ntage-of-mean slopc

frqquency curves, regardless of how steep or gentlc tile average sl-opes might be. The resulting model percentage-frequency curve can be used

to predict slope-2requcncy distributions for any k ype of terrain for which the mean slope value can bc derived.

This technique has been extended to lunar slupc distribut i.ons in this preliiliinary investigation . Figure 4 is the niodcl curve derived

from. existing photoclino~~~ctricslope-frequency distributions at 0.6 m resoluti-on. Thirty-,two slope-frequelicy distribuiioi-is, aggl-egatin:, . 171.025 individual slope' values, were plotLed for different lunar

localities (most ly mare) . Each cumulative-frc(1~1cncycurve was then

converted into a percentage-frequency curve: curnulatjvc % of cases js

plotted on vertical axis, and % of mean slope angle is p1ot:ted on t-he

@

horizoiltal axis (ariihmetic coorclinatcs) . While al.1 these curves

differ slightly fro111 one anotliel-, they are remarkably s iuiilar in

overall configuration. Percentages of mean slope werc read fro111 each

curve at 11 coiivcnicnt intecvals.Thcse values were averaged at each of

the 11 interval-s of % N, ail$ the averages plotted as Fi-gure 4, the

# prelilninary lunar slope distribution model.. This curve is virtually iclenti.cal (r - 0.997) to a similar curve derived for terrestrial $1-ope

distributions (Table 1). At this stage, no attempt has been made

to clemonstrate tlzc correspo~zctenceof the rnodel lunar curve with the

curves From whi.cll it was computed . I'rcvious experri-encc with f a . . 1 I * # terrestrial distributions suggests that corrclati.on is exceedingly good

(probably AbOO.953) for the l~lnardata.

This li.kel i-hood of high correl atiorr of model. with indj.vidua1

curves suggests that the inodel. curve can be usccl far prediction of real.

lunar slope--frccjuency di.stribrztions when. the mean slope value is known

(or can b.,-j-i~ferredstatistically) . Fi-gurcs 2 aiicl 3 provides estimates

of mean slope for fc~rgross 3.unar terrain units, smooth mare, ~:ougher

mare, tlumnlocky upland, arid rough upland, at any desi-recl level of

general-ization. These est imates can he used in conjunctj-on with Fi-gure

4 to compzte probable sl.opc-frequency cliskribution!; For any of the four

terrain types at any sl-ope length. Tables 6 through 8 in the text are

nolnograplls by wl~icln tl~iscan be accompli.shec1. Val.ucs of % mean slope

have been ccjnvcrtcd back to real slope valucs siniply by multiplying

the model % msan slope valucs by all of the mean slope values listed

across the top of flie tab]-c, Sl.c)pe distributions presented in Tables

6, 7, 8, and Figures 8, 9, 10, and 11. in the text \rere computed from

B - 44 Table 1-

Comparisol-~of lunar arrci tcruestri-al. slope dist.l-ibut ion rnodel_s

Model Percentages of Mcan Slope Angle

Fi~nar-slop^? Angle Terrestrial Slope Angle pcrcemtagc _L --.-.-"._-__.%"",,,-kW*,~U___Cn*.*e-*im- ----.---* "-"- -,----.--- of cases (in degrees 01arc at ftangerzi: of valley side ("/,I a constant: base length sl spcs con-iprisilzg linear of about Oe6rn-1..0m scgnlents between major from photoclinornctry slopc reversals; variable of Lunar 03-biter- 2, 11, basc length; data from 1x1, and V irnagc.ry) acri-al. photos of scale 1:20,000) Total N is 1.71.,025 . 0 . Tcatal N j-s 2876

Correlation cocff icient , r, for above data (omif-ting 100th pc.srcelzti.le.) is 0.99774. mean slope values at one, ten, and iifty nieter slope lci~gtllsread from Figure 3 of the appendix ( a f in lie tcxi:) .

Figure 4 shows t11aL departures of tlic conskl-j.tuent curves iro~n the average, or modcl, percentage-of-mean slope curvc increases markedly over the 30tl1 percenlri1.e of N . Analysis of percentage-of - mean slope values for the 95 th, 98th, and lOOti1 pclrcentiles confivliis that: tile dispersion increases sharply with percentile, and that prediction of the l0Oell percentage-of-mean slope froin the model is poor. Analysis shor.is also that the percentage of mean slope at tlie

100th percc:ntile of N depends strongly upon ti~cnwnber oT slope valuc!s *. included in tllc shii~ple. Thtls, the 1.0O~h pcrcentilc slope values i-n Figures 8-11 01 the text are only test estiinait>s, relying in park upon terresirial slope data. Efforts will be made to provide b~ttcr estimates of the 100th percentil-e valtrcs .

Like all. theoretical models, the lunar slope distri-bution cul-vc

(I?igure 4) and the predictive noinographs (Tables 6, 7, 8 in tcxt) must - bc treated with so~necauti.oi~. Visual exarninai ion of high--resolution I,t~nar

Orbit.cr imagery suggests tha t many terrains which appear exceed ing1.y rough at lower resolutions are in fact cluitcl siilooill at slope lengths on the order of a metcr. Conversely, other terrain types (crater' floors, etc.) which appear s~nootliat 1.o~resolution arc quite rough at higher resdlut ion and smal ler slope lengths. Ho~wevcr, tl,~nlodel derived here should constittite a useful basic froin ~r.lriclito proc~cc?in the deterryi natjon of lunar surface roughness from absolute sl-oipe angle data. Sections C, D, and E

Section C--Crater Fr,equencies and llurpl-~.ol.og%es

Section D--Distribution of 131ocks on the Lunar Surface

Section E--Increased Travel Distance Due to Craters and *. , -. f 8 Other Obstacles on the Moon

H. J. Moore Grater irec~uciicicisand morphologies

by 11, J, Moore

f nt:raclvc t 0x3 _*rrOr- "I- err--^_\. IIVIIII

This section has hecn prepared in response to a request for an

appraisal ol trafficability of the lunar surface for Lunar Roving

Vehicles. In the rcpori: nluch of thz data present-ecl should help to

form an integrated modcl of tllc lunar surface. Such an il2tegrated

model has not tcci~formed at. this time, however. An integraccd model

for thc lunar su-rInrc can be forn~edby combi.uing data on tile frcqucncy

. . distributions 'of crai.crs of variouz niorphologj-c:; wit11 thc data on

crater r11orphologj.c~and frr~~uencydistributions of blocks in and

around craters (see Sc~ctionD). 11ai:n in the section do pcr~nil:an

evaluat:ion of ~;9;gnj2$_50]~!:1,2~$0~72-to LP exp:.ctc!d froun crater frequencies.

In so far as data permit, thcy are considered in terms of rough

(wcskern) ii~ariu,siilooth (eastern) maria, and upland::. This is done by

considering (1) frcqucncy distributions of craters, and (2) morphologies

Crater freqrrencies *marnrm- r--- -s. D"" v,m-UI rr-am.d*un)u-l*e; -U

Thc topo8raphie.s of lunar surfaces are characterized by craters of various sizes with varj.ous states of preservation. Ideally, the surfaces can bc grouped into two types : (1) th2 young surface wIiere the frequency distribution directly reflects the rate of cratcr production and (2).thc

"steady-state" surface which i.s the rcslxlt of the combined effects of of cratcr productioi~and crosj.one-infillj2g prociuccd by extei~sivecrat-crjng

(Moore, 1964). Crater Ercquencjes can be approximat ely exprcsscd by

eqzra.tia~aso.f thc L'orrra:

whcrc: N is thc. cumulative frequci~cyof cratcrs,

k is a colastant ,

D is the crater diameter,

n is an exponent,

For the young surface n is near -3 and for the "steady-statefr surface

n is near -2. A mature surface would be described by two equations d I r . t I where 11 - -2 wor~ld apply to the smaller: size craters and n = -3 would apply to thc size craters,' The equation for the "steady-state"

surface:

wIiexg! : N i-s the cwiiulative number of craters per square meter, %? D is the diameter of the craters in meters,

applies to all cratcrs less than a ccrtair~size on a surface which has

reached that state and the "steady-state" attains fur thc smaller craters

first and extends to larger and larger craters with time. The

rnorphologics of craters for the two idealized surfaces differ. Craters

on the young surfac.e are typically, but not entirely, fresh and uneroded.

For the "steady--statcf9surfacc, crat.ers range from fresh, we1.l prcscrved

craters to thosc so eroded and filled that they are barcly discernibl-e.

As nature would havc it, lunar surfaces are typically a mixture of the two types of sz~rfacesor ~21~~x1ILIO~C GOIII~~CX~CICRUSC of variasns cvc,:nts,

Some freclucncy disisr.li?:ul",ions are showzn j.u f:ig~tre@-I wZj~:rk3: t17c CCCIT~IX~:~

for Bangc-rs VLI, V.iSI, and 1.X ('.CrasJc, 1966) rcl>re:;cnt the "steady si:atcn

frecpancy dis,;tr193~"iie,1.1, The COUI~~S:for -"i.:l. Y--6 and XIT P-12 tll-ere taker1

fram Lw~ar0s:b:i.t.e~ scnrcening reports (Screening Group, l967a, 19672>) az7.d

ctrrrertt data suggcsts thcy may be IOCZ~by a factor near 2. Their form

is correct, howc-ver, Iwn spite of complications, a fev ggeneral.izatj,om

can be made : (1) the "stead y-stai:c" freqzzcncy distribution' describes

all surfaces for craters a few meters across and less (Shoemaker ct al,

1966, 1967a., 1967b, 19683, 1968h), most lnavc surfaces for craters 40 to

100 ineters across and less, arid for some s~a.~face,r?,suclz as the f bodr of .

Al.pl~onsus,for craters a. few kiloiiletcrs across and less (Trask, 1966),

(2) 1.ocall.y frequency distril~utionsmay be signi.ficnntlp less than the

"steady-state" distribution such as on stecp slopcs, (3) iliost mare and

terra have the same frequency of cl"at:erti i.n the 10 to 50 meter rangc?,

except on steep sl.opcs, (&) rough marc has a signi.ficci.nt frequency (10-5 2 craters/i~~eter) of subdued craters 80-400 rnetcrs across wl~ilcthosc of -6 2 the sama size in the srnootll maria are 1css (4~1.0 craters /meter ), and

(5) for inare craters larger than 1 Ian th.e slope of thz frccjuency distri- bution curve is steep (n .= -3),

Recent data ha.ve sl~ownthat the form of Frccjirczrrcy distrj-butions of

fresh appearing craters are similar to tbost for thc "ste;~ily-stat:el'

(Moore and Trask, unpublished data), Crater frcqucncics of fresh craters made by 5 different obsc.:rvcrs using Lunar Orhitcr photographs (2i.g. C-2) indicate t1za.t the frequency d3st-n.ibutior-aof such cz:ate-fl.s can bc dcseribcd Crater dictm-rifcr [meters)

G4

N L 1111Y2 (39

*- 6 -5 wl-1c:x-e : 1c ranged fro:ii 2.1 x 10 to 2.0 x 10 fur tlic various obscrverr;.

Althoug1-1. tlic ol~xervcrr;did liot sex-cc on thc definition of a frcsll crater,

they did aguec on the form of the ecluailion for tlli?ir distui-butiolx. Thcir work was douc? as parL 01 studl.cs desip,i-ted to estimate the thf.ckness of

the lunar epi.li.th. Eq~ietion(3) is also in agreement: with earlier daf:a

on f xesll (eui~iorphj.~)cratel-s s how^^ i-n Ranger l3hotut:l:aphs (l:ras?c, 1.960) .

Eqnakions 2 and 3 are important ingredients for. this s-eatibl~sirxce

they imply "stcady-sstatc" frequency distributions exist ntjf: 0111-y for all

cratcrs but: al-so for craters with givcn morphologies. Frequency distrie-

b~tionsof cratcrs of various morpholoeius can be estimated by co11~bi115ng

the foregoing data in cynat:i.ons 2 and 3 wit:h a theory which posi:ula.tcs

that cratcc life*-timi.; are proportional to t:lleir original depi-b and hcrlcc

diameter (Moore, 1964). In the theory, craters ranging, from fresh

craters to those so erodcd and fi1l.ed that they are barely discernible

leads to equation 2. If crater 1.ife-times (t) are proportional to theie diarnetcrs according t u :

where: D i.r; i.n meters, tha~tlxe variations of frequency of morpliologics

for each size can be esti-mated. For craters whosf relicf has been reduced by a factor of 1/2 or less:

For those with 3/4 or more of their original relief preserved: and for tllosc with 31/32 of tlieir urjg:inul. relief or inorc:

These disi:ril~ui:jons arr shown in figure C-3 where crai-cr rnorpbol.ogj-cs

have Lecn ~mmcd. Fresli craters have 31/32 or more of their ori.ginal

1 Young cratccs have betwwn 31/32 and 3/4 ox their origillal. relie-f, Matltrre craters have between 3/4 and l/2 of their okiginnl. relief. 01~1craters have 1/2 t:o almost: none of thcir ori.ei~~alrelief.

It can be seen from iignre 3 that 1/2 of the craters of a given size are. old," 1/4 of thcin mature, and 1/4 of the young to fresil.

The forcgoillg f requci~ciesdi s tributuions can be generali.xed as

follotas (see also fig, C-4) :

A, Rough mare:

B, Smooth mare:

------1/ Crater:; near 80--400meters on ~~~ariaare largely subducd in morphology bud their walls are often bboeky.

E Heavily cratcred surfaccs

F. All crati?Yi; 011. "steady state" surfaces (fresh, young, mature, al~dold crntcrs):

-el -2 N=10 D *

G. All craters on "steady stateti surfaccs that are fresh: -93 -2 N = 3,1 x 10 D

H. All cratcrs 01-1 "steady state" surfaces chat are fresh al-d young:

-a2 -2 N - 2.5 x 1-0 D I. All craters on "steady statc" surfaces that arc fresh, yciung, and mature:

where : N is the cuniulativc freqilency of craters/meter 2

I) is crater diantc&er ira meters,

Before going to a description of crater morphologies, it is important to realize that the area covcred by cratcrs between equal logarithniic intervals is the same when the frequency dist:ribution is of the ~OST~II:

\ N = m-2 (1) Thus cratcrs Letwecn 100 and 200 meters can occupy as much area as those between 10 and 20 mctars,

As mentioned previously, craters bf a givcn size can be classed into four types: (1) fresh, (2) yourig, (3) mnturc, and (4) old. Fresh cratcrs are. identified on the basis of their ~jcctavyl~ichare cl~actcrized by tllc prcscncc oL bl.ocl::: arid secondary impact c.tSate~-sand, vJ1lc.n i.bcy

are slnal.1, by rzys and br-L.ght h;ll..o:;, Pforpholngics and cjccta af tllrsc

fresh. cratcus vary wi-i-11 size especially iu th? maria i~herclayering

prodrrccs pz'onoaficeeb e.CCects on tl~crater slzapes (Qua-icle slid Okjr:rbeclc,

19633, Swh size cfEccts arc? less pronoimced in more uniform materials or wl~entl-lc cxaier dcpth is either smaller than or much 1.argelr than the tf.~ichl@ssof the upper layer, For crater diarnctcrs that are less tiaalz

3.8 - 4.2 times the thickness oJC the laycr, thsia: shape i's unaffected by the Iayer, Plat floored cxaters are prc~ducedW~IC~the dj.amcter of the crater 5s between. 3,8 4,2 and 8 -* 3.0 ti.mes tlx t-,l-rj.ckazessof tfle layer. Conccni:r2 c strract~zrrsare produV@ld for' ' larie daat-ers,'

Altho~agJ7t'2~er~are fax-EC local variata'orxs of thick~~cssof thc soil-

1-ilte layer (epilith) on the 1i1a1-c?; rough mare bas a thjnner regol.it:h than. sinooth marc, Few data arc avni1nbl.c for the uplands so the presence of an epi.l.i.th w-i.3-1 he neglected, The median thiclaess for a rough lrtarc of 3 - 4 meters was obtaincd for Lunar Orbiter site TIT P-12 (Qua:i-dc. % and Oberlicck, 1468) and 6 - 9 meters for I1 P-8 (Sinus Medii), a qrlasi- rough mare, 1x1 contrast Trask and Wilson (personal. corm,) both obtain a niedrian tlzickness riear 5 meters far 11 P-8 (Sinus Mcdii). "Seat: of the pants" cstirnates irxclicate a median tlxi-ckness OF 5 - 6 meters for

11: 1'-5 (a smooth maxe), For this report, a median thickness of 3 rneters will bc used Tor rough mare and G for smooth (castern) mare, Small fresl~cratcrs in ro~rghma3:c tllclle have diameters up to about 12 metcrs across alnd tllose of smooth nt3l:e have dia111~tersu13 to about 24 meters,

Studies of missile impact craters (Moore, unpublislicd data) and labouatory impact- CT:~ZI:L?IPS in s;xncl (GZLI.~~:,Q~~~;i-i~i.ii?,OLc.ebeck and Ifooi-c, lS)G7), sl~ow that dept-Ti-t.o~~di.orncl-c~-rnI:ios of sue11 c.ra.t:crs arc uz~ar3./4 LO l/4.4 ELII~ rim height t.o di;iiii~t.er rnti-ns are 6 /SO0 to 2.2 /101). $foupl~ologicsof

lunar era tcrs , Snla 1.1. craters an tl:c 1-zrnar szrr Pact wizicIr rcprescllig: tl~c botrndary between yozrng and rrtat:tnrc craters have tl~cirrelief reducc:rt tc)

3/4, yielding deyl:h-.to-diaactcr-ratios betwccu l/5.3 and 1/5.9, and rim heights bet:ween 1.6/100 to 4.5/100. The houndairy between mat-ure and old sznaII crat-ers are rcprcscntcd by craters with dcl>@h=-t~-~dia~riet~r ratios of 1/8,8 to 1/8 wlii.le rim height di.a;:;te~: ratios are 0.8/100 to . - 3 000. This r~orphologj.calscheme'j s su~~~rnnrizedin figure C-5.

Fresh cralcrr; on aroug1-i. mare between 12 and 70 meters across are f 1a.ttcn.ed arzrl may 1-a.a-v~conce.azt~:ic structures witlxizr the craters.

VariaLj-ons in. cletails of tlie crater:; are marked, but: several. examples af such craters are sli~asirrli.rz figures C-6 and Cw.7, A sonzcwl~atf latttened crater 13,2 meters across wit.h a dept11 to diar1zet:e.s ratio of 1/4,9 is shown i.n fi.gu?:e C-6 alo3.1~wit11 a 72 mrtcr crater tslzicl-1 is bot:kz flatkencd

(dept:h/clia~ozt:cr = 1/6,5) and has conccntrJ c strz~ctzlrcs, Thc sI~a.pi..oof these craters ancl rnosl: subseqrzcnt oncs wcrc obtainecl using shadcm tech33.icjucs an6 cnlax-gcd ca 36x) 1,unaz.- 0rl)i.te-r photogra pll,.; with scales near 0.45 mm/in. Rim heights were usually esi:irnatctl using rim height-#to- diametcr ratias of 2,2/100. Craters ~neasnrringnear 200 rncters across

(fig. C-7) on rough mare with depth-to-di.ni-nter ratios near 1/6.2 normally have wcll developed internal concentric structures,

Figure C-7 includes a profile of a crater near 130 meters across -- - I- - to .-.- I D 4.4 4

-- h r 3- ....-G--.- D t00 100

Young Crafcrs

Mat uro Cralo~s

Figure C-7

C15 aid a depth to diaiiietcil ~:ai.:i.oxiear I,/1.3. I-. Its depL~rf-todialili2~t~;3rratio

coupl.ed with the assn~ilpi::i.or~hat the cr;~,t,crwas or;"g;.na 3- ly liliet,lir.

E~.CCCXB~~~I~~~.~:,.~Ifla) 1:nk:t:cl.: c:i:a.L'c.:r szrl;ges"l:s it is old ci:a.;l:cr b.ill: 11,ear tile

boundary betrqcru matui-c! and old crnt~er:: of t6i.s si.zee I)cptll to i-J-jaIileyr

ratios of larger fresh cr:a,t:ers 500 meters across (f:{-ge ~.-g)nlay be

larger (15 2) tlmn those oT thc snial lcr crat-cl-s and i I-lternal. s i.l:ur tunes

arc, common,

For srncil l c8ratem on smoo Lh mom. the li~orpIlo l ogiral schcnie above would apply to crakcrs with diaiiicter:; up to 24 meters across; because of

the grcatcr thickucsc oT the epilith (taken as G mctcrs). In zddition,

Inrgcr (24-70 111) crntcr pl-ofilcis Tor slnootb mare diifcr froiii those go£

the ro~igllmare in that concentric structt~icsdo not appcnr until tllc

cralcrs are hrgc-r, F:igzsr'e 6-9 shc~~sa 30 meter an6 1.37 xcter cra8:er

from site I:TP P-9B. The depth. to din~neterratio of the stnal ler crater

obtained from sl~adoiustudies of 36x e~~largerneiltsof Orbiter photograpiis

is ncar 1-/5.0 while that of the larger frcsh crater is i1ca-i- 1/7.f~.

Concentric structures are wcalcly de~cl-oped on tlrc floor of thc smzall.cr

crater and wcll dcvclopcd on the larger cra"ie7-, Fresh craters nca:t- LOO

to 150 meters across in si-tcs 1x1 Pw.6 and 1x1 1'-5A have cleptl) to diainetcr ratios of L/8,2 to l/7.5 and the floors arc flattrned to doxnical (figs.

C-EO and C-TI),

Fresh craters for the uplands will be assumed to have dcpth to diai11et:er ratios near l./Li.f~ Tor a3-I sizes to several hundred mctcrs. Some justification for unifopn crater shapes in the ttplnnds i.s foulld for .one upland crater which was 236 meters across (fig. C-12) and was estimated

by sllnduwi; to be 50 rficf:c:;:s dccp yi-elding a clcpilh--to~=diari~kc!te~-rair.io of

l/4,7 w1iicl-k is r~casrt:he L/4 to 1/4A ~"atioof small. craters.

Estini:ll:c?s of relic?" i'or yotu~g,trraturc, and old craters Cox botll

marc and up1af~dcraters :in tlxe 20 to 500 ~:~etexclass can bc estimated

using the proccdurcs out lined Tol* the snml l cratclrr; but si.artil~gwith

the exariiples givcr?.above? fox the J argc crat-crs. Sone exairtp1es of

young, rn:aLurc, and o1.d eratcrs in the %00-~400meter sizcs a-cc given in.

figures C-13, C--1.4,Ca*15 where the original crabers are taken to E-eavc;

depth-~dinmetevratios near 1/5.2. The young crater (fig. C-13) was

measured using shadow f ecliniques , whi.cl~yi.cl cls a depl:h-to-di.ailzikc~rratio I = t . I I of 1/6.l and a rim height-diameter ratio near 1.3/100. The mature

crater in figure C-wl4 has, a. clepth.tcs diameter of 1/7,7 am.d thc rim is

guessed to be 0.8/100 or less. Surveyor 111 landed in an old crater

(fig, C-15) which has a depth to diameter ratio of 1/18 (Shoernalccr et

al-, 1966b); tile rim hci.ght-diamrter ratio is very small alld probably

less tkrm 0,63/3.00,

Moore, H, J,, 1964, Dc~~sityof slilall craters 011 the Itmar su;:facc: U,S,

ckol. Survcy Astro2cologi.c Studies Arm, Prog. Rept., hug. 25, 1962

Gault, 11. E., Qunidc, W. L., OLr--rbcck, V. R., and Mooue, 1 J, 1966,

Luna 9 photographs: cvidence for a fragmental surface 1.ayer: Science,

v, 153, no, 3739, p. 985-9238,

- Quaidc, We T;,, and Oberbee:k, V, R, , 1968, TI-~icltnessdeterminatioxzs of

the lunar surface layer from lunar impact craters: Jour. Geophys.

Res,, v, 73, no, 16, p, 5247-5270,

I Screenixie Groi~p,196ia, Preliminary geplogic e~aluatipnand bpollo

landing analysis of areas pilotographed by Lunar Orbiter 11, Langley

Working Paper, LATJP 363, 113 p.

1967b, Prcliiuinnry geologic eva1uati.011 and Apollo landing

analysis of areas photographed by Lunar Orbiter 111, Langlcy Workirg

Paper, LMP 407, 128 p, * Shoeinaker et al., 1966, Lunar surface topography and geology: Surveyor I,

U__--_*--- 1961a, Tel~visionobs~rvationsfrom Surveypr 1x1; Surveyor 111 a preliminary report, NASA SP-146, 159 p.

-w-*--w-* 1967b, Television observations from Survcyor V: Surveyor V, A

preliminary report, NASA SP-163, 161 p,

----- 1968a, Television observations from Surveyor VI: Surveyor n,

A preliminary report, NASA ST-166, 165 g, I

------1968b, Televi.sioli obser-vations from Surveyor VII: Surveyor- V11, A prelirniiialry report, NASA, SF-173, 303 p. Z'raslc, H, J,) 3.966, Size and spati.al. c'lis"i:-bution of craters estiri~af:c.d

froin the Ranger phoiogxaphs: Kaijgcr V11 and IX, part 1%. Expcri-

mcnters ' Analyses aiid intexpretations, Jet: Propulsion Laboratory

Tech, Rcpart no, 32-800, p, 252-264, Section D

I)ri.stribui:ion of ~IOG~CSor1 the lt~?~arsurface

by H, J, 11oore

Inlzrocluct ion YII.r*-zrPr-m-^w-a-~m.-m WU

Although blocks large enough to corrstjtutc hazards to lunar rovil~g vehicles are generally rare, they are found loceLly in concei~tratioxls

1.arge enough to seriously affect th2 succcss of a mission. Such concen-

trations of blocks are found in and ncound frcsh craters, on the

interiors of large subdued craters, in isolated block fields not

related to craters, rille walls and other steep slopes and scarps.

Examples .of block ircquex-cies for thcse features will bc discussed ]>elow

along with thosc for average marc.

It should be pointed out before proceeding that much work needs to

be done in intxrpreting block frequencies in terms of vehicle mobility

and that soille of the interpretations below may be optimistic.

Fre~uen c ~i~r&b~-~i._onof bJa_o~,Z~~~~c.d~+~g~~ ___YF

Like crater morphology, the frequency of blocks around fresh cratcrs

varies with locale. Craters with abundant blocks characterize rough mare

and contrast rnarlicdly with craters on surooth mare. Quasi-rough mare,

such as Sinus Medii, may have craters with block frequencies be~ween

those of the rough and smooth mare. Insufficient data for the uplands

are available, but current data suggest block frequencies around the

craters are between those of the rough and smooth maria and large concen-

trations of blocks are found around sinall craters at the apices of upland

hills. Thus 1-arge frequencies of blocks should be cxpected to occur around frcsh craters in my terrain,

During tlic I ii. was also shown. that. tllc frcqi~c~~ciesof blocks

per urtit area usua11y decriin:;r witli clist.aixcc froin the crater. The photo-

grapi~icii~ingcsof thr: ejccta and craters werc divided into rings of

crater radii From rile center to the riiil (o-sr), from tile ri.m to one crater radius bcyond the rim (r=-2r),and so forth to a ring at one and one-half to two diniiicLcrs (4r-5x1 in. order to er:timcii:e tllc out,wnrd changes. 'Uhc resales of sucll changes are listed and shown in figures and tables which

foJJow,

Roush mare. --Block frcquei-1ci.c~around crakcrs arc not only a function -=?am- #--- - __j___i

oil locale and distancc irvm the rirn but also sizc. Such chariges arc. cl.carly i.ll.usl:ratcd by ~:o-ugbtnam craters, The near-rim flank, of thc

30 mctcr crater east of Surveyor I (Elliot Morris arid We J. Moore, unpubl. data) has blocks up to 0.64 meters on the rim (fig. D-l and Tab1.e D-1).

Thc rim and flanks are not particularly rough and less than 1/2 pcrcmt of the area. is covercd by blo::hs large enough (SS .5ni) to be collsidered hazardous (fig. D-1 and Table D-la). In contrast, counts on 36x enlarge- ments of Lunar Orbiter photographs of a larger crater about 72.3 meters across show that frequcilcics of bloclcs larger than 1.2 meters on its near -3 2 rim (r-2r) reach 6.0 x 10 blocks/m~tcr and higher; and 2.8 percent

of the area is covercd by such bloclcs (figs. D-2a, D-2b, and Table D--IIa,

D-~XS_b). AltI~ougIcomparisons between the two cormts are dif f icul.$: because of resolution diffcrcnccs, it is clear that the 72.3 meter crater

is blocki-cr and more hazardous to roving vehi.cles.

Although block frcquencics normally incrensc with size, t:ilis is not Figure D-l Table D-aIa

Surveyor 1 30 meter crater 2 Curnulati-ve: f rccpency f.n bl.nclrs /incta?x

BlocIc si?~mi-ers r -3 2r --as- ->."*--. -<, -> *."am ?s*.,*>---r- *gm -- - w-.m,wrdl.--*- m ,. 0,6/1- 4.7 lom3

CumuLa,ti.ve freqvrency of blocks /meter 2

Block diameter crater ejecta (meters) 0-4 r - 2r 2r - 3r 3r - 4 1: 4r - 5r r - 5.r ----'a *-*-* ------v.-'--e -C*---- * --m---ip-acr kF-*-.m*----v" w*----*~we*m--~~.w- evml,-lu-mrmrr a ----- . *..-a..r..Qnxg-all(T,w>

-I/ Sun angle 20.65', ta7.1 - 0.376.

ZIP P-E2A 11 193 7% ,3 meter crater

Cul:l'Gl citi.vil .~%'C~UCIIV 131.(31:!~~/I~':cLI(?~'G2

Table I)-ITb

Fraction of 'area covered by blocks larger t1a.a~size x d iarxcter crater ejecta (rnctcrs) O-r r 2r 2r - 3r 3r - Ltz: 4a- - 5r r - 5r always true, Tal)lc 3)-11-, ro]~resc~~h:ssrzc12 a c~c'l."ir WI-~~?~\.J"Cit can he scexl that. tIac blocfc frc.qs~c-i.ici@sIxo~rt.x to %rarc less t-hrjiu tl-nosc? of the snell-er 72,3 r-ireter cr;~b,c.r in Tat~lc17-*Lla,

Ilowe-vcv 1rj.i-h coil tirlui~igil~crcacein size, the general tcindei-icy Eor i~~crenseof b1.0~1~frcsjtiexacj.~?~ becomes clear, For craters near 200 mc\t:ers across (figs. D+-3n, 1)-312, and Tnbles D-IITa, I)-I:L7b) near rim (r-2r) -3 freqircncies o:E blocks larger t:knn l,06 meters reach L7,3 x 1-0 blocks/ 2 meter and about 4.1 pcrceltt of tllc area is covered by such blocks. The crater in figures D-3a. and D*03b is on a quasi-rough Innre (Sinus Medii),

Frequc.mci.es of blocks larger than 2@/1meters around larger cra.tcrs near. -3 2 300 and 500 rnetcrs across are a.s high as 2.9 x 10 bloclcs/rnctcr alld d beiaeen 5 and 6 percent of the area is covered by such blocks (figs. D-4a,

D-4b, D-5a, D-5b, and Tables D-IVn, D-IVb, &I-Vn, and D-Vb). The counts for these two lal-gc cratcrs wcrc obtained on 14x enlargements so that the counts stop ak about 2 rnctcrs but attempts to conr~tthe s~m?.,lesbloclis suggest tlleir frequency incrcascs rapidly to 1 meter with a slope of -3 about -3 on the frequency curves. Thus frequencies near 20 x 10 blocks/ 2 meter fol: blocks larger than 1 mctler s1loul.d be expeet:ed and about

10 percent of the area should be covercd by slaclr blocks.

S~ncwehmare,--The low fsecjucncics of blocks arourrd craters on smooth --v-----m- mare contrast sharply with the high frqucncies of tllnse on the rough mare, Thc diffcrencc is so marked that it: is difficult to find fresh craters with bl-ocks around them, cspcc-ially for craters near 70-100 meters across and less. For the smooth mare (figs. D-6n, D-6b, D-7 , D-8a, and

D-8b, and Tables D-VZa, D-VLb, D-VXZ-a, D-VLIb, and D-VIIIa, and D-VIIIb), 1-Qp 7 I-{--95 Dia 202ri-1 Sun clncle i9.6Q Tun 0.260 Block diameter (rnctcrs)

Figure D-3b Table D-lI.J:a

IT1 P-7 13. 95 202 mekpnr d-iarncicr er;il-.cair

Block cl inrrzc t er c 1: at*e 1: ejccta (rncte~..s) o == r .w: 2r 2r - 3r 3r - 4r 4x7 51: r - 5-x: - P O m-a-=l-l%*-----'-*- -I-=--"* - w--*-vm+. ?"*" -u-- a * *err *- -- ar-al^-r-rr>---mx*w -7 -*d--~~-"~~~"~-~7-'---*- --L%--%----*------

8,52 mv ms , ."I- .)-Y .mi .m - es Sm

4,2G 0.052~10~~aa w Oe0045x10-3 0*02S~10-3 0 .015~10-~

Fraction af area covered by bloclcs larger than size x

ICQ

Figure D-4.b r-4 r-l f PI I I0 Block diamc~lcr(meters) Dl5 8 Block dianrcltcr (meters)

Figure Dae5b RlocIc. diameter cyaper ejects. (mete.3:~) em xP r 2r 2r 3r 3-g 4r 4.r -. 5r r - 5r .Il.'*~C*~~=n~nr-~"mW*-"~5"*n*~rrsinu?... *,".->~r-.xnir.*"m"" "~~L*L,#r~"-~..~~"L-a~~~",.~-a.".~.=-m~w~L~*~~"--~~*~w~. - '-.*"*' ,*-&--M~>-B%*W,W.-*--~% "*

Fraction of area covexed by blocks larger tlzartn size x 1-4-52 Dia 152 rn SU~UYICJ?C17.44' .." . fan --0.3/4

Block diamcf-er(meters) Figure D-Ga

' nlR Black dicarnefer ( ri3ztcrs) ctiamci:cr crai:er eject-a

(meters) o -- r r - %r 2r N- 3%: 3r - 4r 4a" - 5r r -, Sr

Fraction of area covered by blocks larger than size x diameter crater ejecta. (meters) Q-T: 4 - 21: 2r - 3r 3r 4r 4r -. 5r r - 5r Block dicamebar (me?ctds) TabI..& Da-VZT a

Fra~tionof area covercd by bloclcs Lar~erkllail size x

divameter crater eject:a (meters) 0-r r -. 2x4 2r - 3r 3r - 4r 4r - 5r r 5r Block diurncter (n~eteers)

3423 Bloc kg cliam~f~r( n7ef CPS) Table D-Ella

Fra.ction of area covered by blocks larger than. size x 6 ' Block diamet.e-r crater - ejecta (meters) Q-T r - 2r 2r - 3r 3r - 4r 4r - 5r r - 5r crnkerr rear 130 mci-crs across Ilrrvi! fxcqucricics 01 blocks cliich reach 2 2 x bloclir;/incl-cr- For ~.i.~cslarger than 1.1. meter and only ahout-.

0.3 pc~cciilof l.hc art23 is covcred by such bloclcs, T11r:sc co~icciitrations

are lcs:; t.lr?n tbosri Tor siliii:Li?~and. c*vc!n cinall.i..~-crat-ecs 0x7 ro11~11rna.rc.

Low bl ocic Lrc\qiiciicics arciu~ld2 craters iir sll~oot:h inare part1.y

keflect:; tii;. tljick epilitil which is largcr in tl~csmooth than in the

rough.innre, Tlrzsc low Llocli frecjuencies could arise from other factors

as well, sucl~dil.icrcnccs in fracturing of the rocks.

ypl aild, -- block freqi~c*ncicsfor one lxunlmocky upla~xdcrater 200 meters D- V*lll ts-

across were obirairrcd because onl-y one 3Gx cnlargemcnt of Lunar Orbiter '

photograph of such a cratcr was riyailnble for thc count. The frcquenc:ics

obtained show, hoiccvcr, that signiricani. numbers of blocks can occur around uplnnd crrrters. Thc frcquncics ol blocks larger than oilc? r~ter -3 2 TC:IC~~3.7 x 10 bl~clis/n?et~rlarg~rthan one meter, and arc interiliedi.ute betwecn thosf of the rough and smooi-.ll maria. Inspecti-onof other crat:ers of coiliparahle size on standard prints of Lunar Orbiter p11oi:ograr)Rs show

that blocks occur: around other upland craters near 200 meters across and

smaller. Some Orbiter pllotograpl!~ show smnLL craters near 40 meters across at tllc apices of upland hills may have a profusi-on of blocks around them. The frcquenciec axid data for tl~cupland crater arc shown in Ta.bles DI:Xa, D-=I::Xb, ancl figures D-9a, and D-9b.

, . Interiors of large craters ~v--ra"-"-F_-__%U-*.----v-< - j_--C--w,. *.N___w_i

As mentioned in tho Section C, both rough and smooth marc have large subdued craters measuring near 80 to 400 mcters across with frequencies Tjl .L .L .- p 3 /-I -- 1 2 5 DIa 23:tGnl Sun cngje 17v3a Tun = O.3I Block diu~nci-or( ~ie'rers) BLocli: diameter cxater ejecta (meters) oL.-2.- -.. 2,r 2x: - 3r 31c 4.r 4.r - 5r Y' - ST

*- il~~rrwixnn-~-~'*a~**~~~"-*~".%.,~....."*~.- -=--* m--.. "* 151.%7m-" - ",1-" >~~,s..,~-wL~*. =.-

Table 39.-IXb

.Fractlcsn of area co-verecl l~y blocfcs L;IT~~.Y:than size x of bl.ocks 01.1 intex i.0~\gal 1s that arc2 l-a,l:gc eno.tigh to consi.(jer ~_-l~t~~,~

potenti.a.l, h,zzards to 1uno.i- x:ov?ng vch:iclcs. Fo1r.r such crayrr; are

considered here. One is used to E;~QFJthat it may be possible to enter

such crai.crs with planijed traverses but unplanricd t:ra-gi:rses result.

i~n,dj,cf;astcr,

One crnLcr in, smooth mnl'e mt?ns~~l::irig about: 351 mcLr:rs across was

found to have concentrations 0.2 blocks 01%its riiu, walls, and floolr

- coi~~pal*aI~lcto klie conccntzrat ion arorrnd some. blocky craters in rougll

marc. The results arc shown in Tablo I)--X. Ilcre ngajn the blocks were

counted in sectors using 36x enlargements of Lunar Orbiter photogray~lls

on which bl.ocks and protuberances. dowl-1 to one meto: an@ less Can be ' #

h a rnanncr similar to sxLicill.cr cratexrs, these large cratc'cs sflow

morphological. gradations (see Table UmXT, and II~QXII)and rnay be quit:e

srnoo~hand free of blocks (Table D-XII). Normally the frequency of

blocks on crater walls are higilcr than thosc 0x3 the floor.

91 he215 meter cratsr (fig, Dm-9) was selected to il.lustratn,what thr:

difference bctb~eel~a planncd traverse and a rar~dolntraverse mielxi: be.

This crater, which docs not appear to fit into the murphological schcillc

described previously, has a depth to diamster ratio near 1./5.3, i.s

rimlcss, aild blocks are absent on the Xlaltks. Thc upper crater walls

are bl-ocky arrd stccip slopcis arise from this. Us:i.ng shadow techni.cli~es

on a 36x cnl;icgen~:ntsof the Lunar 0rb:iter l;hokographs, it was found tiiat

near-vertical slopcs with local relieis of 3 to 4 meters are present.

One route (upper profile fig. D-9) would surely bc di.sasteroun for a

roving vehicle because of xlurilcrous blocks with relicfs of 3 metcrs and 2 Cumu l t.1i-i-v~Lapecluenccty of bloclic fznr~tcr

Block diameter Floor Lower,wal.l Upper wall Rim (meters) Q=?L-'2 %r-- 3f4r 3/4r - r r - 514.8" o - 5f4r

-*------s------**"-"A-~-*-.----- I*--I--*--+Xe--ilLCIIY'-- 8 -I --.%-I"*.---a-.,m--v*-- - -Tsli-m*X-r**-I-- --i- * n---*-*IIIw-.-II.- "---" ---.-

Tab1-e I)-XI 1

Crat-cr Wall Crater rim r mr*na-n"a M, 4 r 3: X 2. - 3 Figure D-9 marc, A sccond .j-orctc: (l.ljwc2.1: prof :i.l.e f i.8. Dm9) was free of 1~l.ucksand

wou1.d p."-~:n;:i..i: access for a roving v~i:li.c:k,

One bJ.ock fis:ld (I,ur-rarc Orl-,i.tc?r 2rnrac II 26, s-ite ITS P-2) was cormi:ed

bccausc oC t11c avaj. l ability 02 35x enla~-geriicnt-:; of Lun3.r brbi ter photo-

graphs. For the bloclc fiel-d a strip 46.87 nietcrs by 656.2 metccs was

divided into 14 scjilarcs and cuunirecl. The resul.t:s (see l:??ble D-XIIT) show

I 1argc vacintio~lsas thc fjeLd is hpproa5licd. l:ocajly,' there Arc no

l~azardsand locally coilcentrations of bl ockc measu~:ing between 9.44 and -3 2 1,123 meters rca,c!~2,7,0x 10 bloelrs /rnd:cr . This exceeds the concet3-

Talus slopes do not pl:csc;nt thc 3.argc concentrations of blocks sccn

in the block fi-eld above, TWO counts 042 150 x 750 meter and 150 x 900 P meter strips dorvn the wa1l.s of a rille in the Marir~sILills using 36x

Lunar Orbiter V photographs yield coiiiparnble rcsults. Here, as in the

block field, parts of the strips are relatively free of blocks. This

occurs a.f- both the f lat bench at tkc top of the ri 1l.e and on the floor

of thc rille. Tlrr 1.ar.gesr:concentra,t:ion of blocks are found on the uppoc

slopes of the r?lle. Surp~:isingly, it was found that blockfi and pro'iubei--

axnces less than 2,Q meters could be d$\rt~fttedand rracasured on enLarg~~it~kx~!lts

of Lunar 0~13it:er V plzotogra~~l~~.The TC*.SUJ.~:S of the counts arc sElown in

Tables 11.-XTV a.nd D-YLV ,

a r-l r-l *r4 F-:

m 1 M Q 8 r-4 Q 36 r-l X cO V"\ 0 4 cO 0 0 0 c\I

Va 1 ley .tsI?i:re cuiriu lai -i"v;: f-rc:rpwnxcies of 117 cxkg ~OWJ-Ito 3 il:e rcacl-lcs 2 2.1 x hloc.ksh2eri.r . I3cz.e the blocks sceni fairly well dist:ributrd

al.ong the slopr (sc-2 tnhlc J+l-XVI) . Blocks for tllis slope irere, nicasurcd

werc c.oirilt~dill 6 squares. A second talus :;l.opc in Sclli:5terrs Valley was couni-eil on 7,7,x and 36x cr?lavgemei?ts of TJunar Orbiten photograplls.

The coz~ntscorrespoild Zaivly well (coinpaireTable D-lX'VII, colwn;~F and

Table D-X.VZ:I.I).

In order to placc: the Ercquencies of blocks around c:raters i.m r-;me

yerspectivc it is necessary to discuss the incercrater areas rcprcsented

by Surveyor L (rough mare) , Surveyor V (smoot-hi mare), and Survcyor VI

(quasi-rough inare). Suxveyor I11 is in an old age crater arid Su-cveyorVII

is on the flanks of a large fresh upl.and crater.

Surveyor resul-ts indicate diffcucnces bcthrecn 1:be rough and snlooth

mare wllicfi are in agrecinentr with thc: block Crequcncics around craters.

For example, the frccpei~cyof bloclis larger than 10 cm arc. higher on

rough mare (Surveyor I) than smooth rnaxc (Surveyor V) and tlie quasi-

rougli marc (Surveyor VS) falls in between. The mlioncnts on the frcqucncy

distributions also change systlematicnlly. Such diflcrcnces arc shown in

the foI1.6wi1xgequations (convcrtccl from eciunti ons furnished by E. C. Morri.~) which represent t.Zu.2 frcql~cncydistri.butians Xor blocks less than a fcw

tens oi: cerlt:irnc:tlcrs : M I 0 ?I x -3 C? 0 r-l

Or) 1 m 0 r a X r-4

Or) m Id Oo r=-1 r+ C') CVf Tab1.e D-XVII::f_

V 11-~204 (235) 33x 1i.n lay p,emeiki:

r~I.al.t~~at base of slope

Bl~clcdi.arnetc:rs Cx~~nzll.rrt:i.vefrcqucncy of

(meters) , blocks /rrrcterZ . P**mw** -I.* ^=~.%~~~I~-~~~~~~*-~~~.:~~~"~~-*"~~.-->~~~~-~~~~L"~."~-"I~~*C-~~~--~~-~~~~-"I-~n*.X-ILI.-,..W*.*rn>W?" (I--* -.,I m.flv**." III.,ww-?.UIIIIYIPn plllll"*,~.w*"m-~~sT".,,-. "-m-a",w,~~.-*~-~-~'m~~ %*-- *. "?'-I"-aI^.AM-mse ma 3 -* 2,@ 7.1 Surveyor I N r= 2,39 x 10 33 -7, **0*11 A - 4-59 x %O D -4 -2.56 Surveyor ZII N .= G,9 x 10 D -3 -0,56 A~3,lGx20 D 4-4 -7,,65 Su~:vcyor V M = I,LI. x 20 33 -4 -0.65 AE5,7x10 D

-n 4 .-2,51. Saxrvcyor V:l N = 5,9 x 10 3)

-2 =-+1*82 Surveyo~rVIP N = 2,74 x 10 D

A = fraction of: area covei.ed by blocks larger than. size x

Al= fraction of area covcrcd Ly blocks :;ion1 3c-r tlian size x

3) - b1oclz d:i.alnetcr ira IIECI'CTS, There is no evidcacc that these block frequencies can be extxapolatcd upward to estimate frequencies of b2.oclcs larger than a few tens of centimeters, Studies of Lunar Orbiter 111 pkotograplls of the Survey~rJ sit83 SUSg68t tha.t:

is a rcautjlir-ll~lecsLinilatc lor frequencies of blocks 1a:r.g~~~,ZZ&X,~ 1 .0 1ncte-r

(see fig. D-~10). For the smooth marc, the frequencjes axe probably one order 01. magnitude less, lns~tfficientda.ta are avai.lable f~rthe Crater

Tycho, but the follo-wing eclzeat ion seems to be reasonabler:

Li:stii~latt>~of: t:he rract:ia;-s sf area. c0-!7~3416!d by blor:ks are slrown in

fi.8u.r~D-%l1.for SU.~.VG~OXSI, V, and V3:I al.o~:~g::$~i.t:Tz t11os.l: for bl.oclis aro:uid

i.denti.ca1- rs.i.,tJr Su~:vcy~l.:1 or' roa.~glarzlaxe,

wi-tl-t size, localc, nr-rd distance frorrz the craker: rim, Frec~uanciesof

blc~cksarouirt.c:l. roug1.a mare cra.tcl?.z:s bemeem. 72 and 500 m.r;:texs are large

eraorz1;b so that at: least 3 percc:~~"i:oE the s~trfacenear tFza rims of craEcrs

72 rnetxxs across wi21 be covered by blocks tll~atare hazardous to rovj-ng

ve1dcl.es and fox the larger crate3: at %cast as ~~itcbas 3.0 percent: of the

surface will be covcrcd by such hazards&,, The ireci.~enc;yof b3,oclis and

pcrccnt:cg;e area covered by hazardous bloclc.,sare higlicst within the craicrc where 30 pcreeslt or so of th,c surfacc IXL~~he covencd by suc1-1b1c;sckn but

only a percent or less of the ~~~rfa&:ci.~cove~ed by hazaxclous bloclis at

distaiice aC one a.nd one-ha.1.fcrater di.amet-er froill the cr;r.tex rim,

Freqzlcncjcs of blocks incrcasc w:i.i:h the six: of tll~crater, For slllall

@a cxakers less tharx 32 -'24 meters across, rtlcrc ziri: srss:laall.y na hazards

but tllose 500 meters across will prcsrnt problems to lunar roving vehicles.

Frequencies of blocks are significantly slilaller Xorm4cratcrson smooth

marc than craters on rough mare. .- Irr.tcr:i..orsof large craters, block f rs'.el~ds,and t-.aI.us slopes may

present- o't~stacl.eswith co1-~ccnt:3-ati.onsctompnrable: r.0 or In:i glzer than thosc!

found around frcaln craters in rougll Inarc.

Firra3.3y, frequencies of blocks l argcr than oxi: rrieter' across are

highca: on roxagIl marc tll~anon smooth rnare, The Iris gcst frcy~~cncicsof blocki: are found ar:oy.ii?d fresh crai:i:rs oil rough iilnr:c, in t:alus s l-opcs, on walls of 13.rge subdu~:dcraters, j.n bloclc fields, ox?, soln-. upl.a,nd slope:; and i~il.l:;, and lli a,ad ncouild very l.a,rge crai:ci-s suck1 a,s :('yc;-io and A3:i.starcf-1:i2se 1nt :r ~~cI~~~J~~~"~~~~" .m*.--,-"

Cra"ic_!rf;,blocks, scarp:;, and I.inear depres:;ioa~s present obstacles which. m!sL Ire crossed or by-passed by %t:rtar ROV~328 Vehicles S:nall cratclrs and bloeks tirith reliefs oT: 11%to 3. mcts-r or lcsk call hc crosscd. Cvatcirs and blocks wi.tli largi?r rcl LcKs nwcL bc circumvenred. )I '

Rillcs or linear tlrprescions can gc:s~az.ally he crclcscd ai: some point- along t:heir l.cilgtl3 but, there arc little dakn on the frcquc:lic~r of occurxencca of crossings, Thus, ozr J:y c.l.'atc~:sand blocks will bc?. CCJIZS~d~r~d

be lt3\,?. @,

Mctllad of -**a=*%.> - ---. "* Proccdxires for ~~zalyzingir-rcx-cased pc?l^h l~?~lgtEisof vc1ticl.c tr-avel required by t:llp. presence of obstacle:; have 1,een di.scuzsed by B~coiis

(19581, Ul.ricll (1968), and liu~cma(unpublisljed data). The a~~alysi~s bcl.ow is *kinlilar to tlllosc above birr: it- diffcx-r.; jri that tzJnc ohstaclns arc clcccribed by a frequency dl.strjl1ut5.on rati~crtllail Ly a discrete

tian is given to t:he vi:il:i.cle t-t;rn:ilrg radius W~I-ich.my ha-ve considcrohlc importanec wl-zen frcq~rcrrcyof smal I. obsi-;tclc?s 3-s hrigl~., dy x!i.$i:!l c.$~~n:i.l~i:oi~a!~i:rity (see fj,t;.

and tlie meair i~i:ri~.t:i.o:i;il.clj..r;i-aace ,kra;ve:l-~:d (p, ) 2

2(~sin 0) sin Q d~ - 2 (I. 2 ) J 0 -- ..--.- =-""a '*.s""*'- -.**.-o 7".%=--.A'*.-+-'-."~..,"z* &"*~*.* li : ( .II ) P2 (3- -. 0) 4. (3 ) ri" 6i..%'4.0 do

clcar thp ohstnclc by half of if-swldil~

r, nl-i J.TI.C~I LoL obstitcl es li~it.;).dirl:ri~ef:ers 19

addit:? oilnl di:: i:anct. trave lcd per

P1 ohstaclt: (p ) is: 3 J."

where :

n $ -2, 3 1 and n:f 0.

Solution of equati-on LO For xi = -1 eivcs: But I? i.~a, fraci:itin t.1~map lent,i:h (M) so that::

and nilm of all. 1-l-te jncrc2nstrd path l.ength5:

Critcron for Lmpass;rbj.l:it:x -----am"?-"-" * --*---a -.. s -% s ., ** *- *%W-w-*-* In orc1c-x to cstsbl-ish if a bloclc field or a cluster of sbwp crat:ers is passah1e or iinpasaable rcquires deiailcd cxaminat ion of that ficld because siratist:i.cal.ap11ro:icl~c.s do not ~ic.ces::nrilyyjcld such P information, Eo-wcvcr, an estirnatc can be nude froill the for~goii-~g ecluatiorlr:. For a firld of obsilncles (lifw) that: cc).vcr all. tilt? area, the area is cl.ea.rly i.mpassablc. Thc .vehiclemi.ghi 8rivc through if trlre area t:o.vel-ed by obsl:aclcr, (Dl-w) i,s less t2lan 1.0, Tiiun t:l,e inf.cgral *' of equation 6 may bu uccd to c:stiniahe passability:

wlrere :

n 5d -2, n # -1, and n :# 0. Solutions fox ~qu;i.i:i.ojl 1.7 ir.,:c s:i,nr:il,;l,j: to tkose fay: cq~~;j~~ioi:k10.

F:n.ci.L~~pler-...- . of 1,;lii:: us:. o:f eqiiat:ions 5, 10, 1.6 tll!: :i.iikcgj,al o~ equai:i.on fi a.re given i.ii i- al.~l-er.13-1 , 1',-1::f , and IZ...'j::''I ,

ReJ;~~~~*n;~-c;~~5; !-;'fbccja R" S"

Brooks, I.'. C, , 1958, EELect of iiill>c.netrahleo1jstacl.e~on vc~hic1.e

opccni:ioiial. 5:pr-c:dr l.:md Locc~motionlicsearct-1 Brancil of U.S. Arrny

Rosixifal, August, 3.898, Ueb::~ gcomcLrLslic2 Ger:tcinsanalyr;ei~: Vc:climdl*~u:gcr~

U.S. Gcol. Survey lrltaragcncy Report: Astrogcology 7, 59 p. l'ab:l.a Eo'el, Exa.r~lpl

-1, * 3- Section A 0,1.00 D I. -. 20 0 ,358;'~ 1,558 178

: Each scci;ic~~-eis 47 x 47 ~rlci:e:rs,

m"m-*"mw -*"-%="-"" 4"- *' NA c-4I/ = ni~inberof craters per squarr rnri:er.

--a/ nTL = ~IU~~I~C-Cof O!ISLE(CICS encouni.ered for each kilonletcr of di.s tai-~cctraveled. I 1 / NA = n~~n&bcro.f crirt:c!rs per sqllare metcr. P

2/ I), 11L3 D are crat:cr diaiucfcrs in ril2tess. I - - - 2 1 3/ I., L 1, = ratio of distance i:ravclcd to map lelilgth .am- B2 C f 4 / -* NL = number of ol~staclcsencolmt-crcd for each kil-oii~et-.erof distance I trauel.cd.