Each Mars Exploration Rover carries a Rock Abrasion Tool (RAT) whose intended use was to abrade the outer surfaces of rocks to expose more pristine material. Motor currents drawn by the RAT motors are related to the strength and hardness of rock surfaces undergoing abrasion, and these data can be used to infer more about a target rock's physical properties. However, no calibration of the RAT exists. Here, we attempt to derive an empirical correlation using an assemblage of terrestrial rocks and apply this correlation to data returned by the rover Spirit. The results demonstrate a positive correlation between rock strength and RAT grind energy for rocks with compressive strengths less than about 150 MPa, a category that includes all but the strongest intact rocks. Applying this correlation to rocks abraded by Spirit's RAT, the results indicate a large divide in strength between more competent basaltic rocks encountered in the plains of Gusev crater (Adirondack-class rocks) and the weaker variety of rock types measured in the Columbia Hills. Adirondack-class rocks have estimated compressive strengths in the range of 70–130 MPa and are significantly less strong than fresh terrestrial basalts; this may be indicative of a degree of weathering-induced weakening. Rock types in the Columbia Hills (Wishstone, Watchtower, Clovis, and Peace class) all have compressive strengths <50 MPa and are consistent with impactites or volcanoclastic materials. In general, when considered alongside chemical, spectral, and rock textural data, these inferred compressive strength results help inform our understanding of rock origins and modification history.
 A fundamental goal of geologic exploration on any planetary body is to determine the origin and evolution of rocks and outcrop materials. Chemistry and mineralogy are the principal means of inferring the nature of rocks, but their physical properties provide an additional rich source of information. These include compressive strength, mechanical behavior, density, hardness, and texture, which are reflective of formation conditions and weathering and alteration processes. When analyzed in concert with other data, physical properties measurements provide a fuller picture of the nature of surface and subsurface materials (e.g., alteration rinds and fresh, unweathered materials).
 The Rock Abrasion Tool (RAT) that is carried onboard both of the Mars Exploration Rovers [Gorevan et al., 2003; Squyres et al., 2003] can be used in this way to improve in situ compositional analysis of Martian rocks. Just as a field geologist would use a rock hammer to cleave open rocks to expose fresh surfaces for examination, the rovers use the RAT to grind off the outer surface layers of rock and outcrop targets to expose fresher interior surfaces. Analyses of surfaces before and after RAT brushes and grinds reveal the near-ubiquitous presence of surface coatings and alteration rinds on exposed surfaces on Mars [e.g., Herkenhoff et al., 2004; Arvidson et al., 2006; Hurowitz et al., 2006].
 In addition to providing access to fresher interior surfaces for other instruments to analyze, the RAT itself provides a wealth of information about the physical properties of the target being abraded. Motor currents consumed during RAT grinding operations provide an indication of the amount of energy required to abrade a given volume of rock, a quantity encapsulated as specific grind energy (expressed in units of J/mm3, equivalent to 109 Pa). The specific grind energy is related to bulk physical properties of the rock, i.e., the compressive strength, mechanical behavior, hardness, and density. Despite the utility of this parameter, it remains difficult to infer much about a rock's formation and evolution from this parameter alone. To date, the RAT team has provided data showing the specific grind energy of a few terrestrial test rocks that allow for general comparison with the Mars results [e.g., Myrick et al., 2004; Wang et al., 2006]. But despite extensive pre- and postflight RAT testing, no data catalog exists that is necessary to create an empirical correlation between grind energy and more typical rock strength parameters. Because of this fundamental gap in knowledge, the goal of this paper is to experimentally establish a direct, empirical correlation between the specific grind energy measurement recorded by the RAT and the more traditional, lab-measured rock strength parameter of compressive strength. Using a fully characterized suite of terrestrial rocks will benefit current and future missions by providing a calibration data set that can be used to infer rock strength properties, thereby providing additional information on the formation and modification of Mars surface materials.
1.1 Rock Abrasion Tool Instrument Description
 A detailed description of the RAT is given in Gorevan et al.  and is summarized here. Mounted on the rover's robotic arm, or IDD (Instrument Deployment Device), the RAT instrument is composed of three separate motors in a cylindrical housing 8.5 cm in diameter and 12.8 cm in length (Figure 1). The cutting surfaces of the RAT grinding bit consist of two diamond-impregnated phenolic resin pads attached to either end of a “paddle wheel.” This grinding bit is mounted off the RAT's central axis and rotates up to 3000 rpm about its own axis via one motor (“grind motor”) and 0–2 rpm about the central axis via a second motor (“revolve motor”). The RAT grinding routine is a closed-loop procedure whereby the speed of the revolve motor varies based on the current reading from the grind motor; on a harder rock, the grind motor draws more current, and the revolve motor slows down, whereas on a softer rock, the grind motor current approaches its no-load value, and the revolve motor speeds up. A third motor controls the grinding depth, which is increased in small, quantized steps after each revolution (nominally 0.05 mm per step). A successful grind produces an abraded circular area that is 4.5 cm in diameter and nominally 0.5 cm deep. Each motor's power consumption is recorded at a nominal rate of 2 Hz (i.e., 0.5 s per sample interval). Other ancillary data captured include motor positions, contact switch states, temperature sensor values, bus voltage, and various software states. Both the grind current (rotation motor current) and voltage (rover bus voltage) are encoded as 64 bit binary numbers, i.e., double-precision floating-point numbers.
 The grinding bits of the RAT were designed such that the resin matrix slowly wears away, and the microdiamonds at the surface fall out as the resin around them loses its grip. This continually exposes new microdiamonds from deeper within the bit, so there are always fresh diamonds at the bit surface. This refreshment mechanism ensures that the ability to grind does not degrade over time, but it also means the bit gets slowly consumed, and the RAT's grind capability ceases abruptly once the bits have worn away.
2 Experimental Methods
 We assembled a suite of terrestrial rocks for testing. This assemblage was selected to span a wide range of rock strengths that, although not necessarily matching Martian rock chemistry or mineralogy, spans the range of physical properties expected on the planet. Samples included sandstone, limestone, kaolinite, and three varieties of basalt (Table 1). Major and trace element data were determined for each sample by crushing and analyzing via X-ray fluorescence (XRF) and inductively coupled plasma mass spectrometry (ICP-MS); chemical data are given in Table 2. Compression tests and RAT grinding tests were conducted on each sample.
Table 1. Terrestrial Rock Samples Used in This Study
glassy texture with abundant irregular vesicles
St. George, UT
quartz arenite, no obvious banding
Mojave Desert, CA
dull glassy texture
Mammoth Mountain, CA
very fine-grained texture
Santa Barbara, CA
Table 2. XRF-derived Chemistry of Rock Sample Suite
Unnormalized Major Elements (wt%)
Normalized Major Elements (wt%)
Unnormalized Trace Elements (ppm)
2.1 Compressive Strength Test Procedure
 The most widely quoted index mechanical property of rock is the uniaxial compressive strength of an unconfined cylindrical test specimen [e.g., Attewell and Farmer, 1976]. We performed compressive strength tests on the samples listed in Table 1 using an Instron 8502 mechanical load frame (with 8800R control electronics) at Johns Hopkins University's Applied Physics Laboratory equipped with a 250 kN load cell. Samples were prepared for testing by extracting cylindrical cores using a diamond-tipped rotary drill bit on a Bridgeport drill press. These cores were 24 mm in diameter and ideally 48 mm in length, although lengths varied (Table 3). The core ends were trimmed and precision ground to create two parallel surfaces. Each test was run by loading the rock core in the Instron until brittle failure occurred, and the mode of failure (e.g., axial splitting, shear failure, etc.) was noted in Table 3. All specimens were run at a strain rate of 10−4 s−1 (0.0001 mm/mm/s). The displacement rate in microns/s was therefore the length in millimeters divided by 10 (e.g., 51.25 mm ⇒ 5.125 µm/s). The peak force withstood by the sample divided by its cross-sectional area yields the unconfined compressive strength (UCS) in units of MPa (1 Pa = 1 N m−2 = 1 kg m−1 s−2).
Table 3. Compressive Strength Test Results
Peak Load (kN)
Stress area (mm2)
Peak Stress (MPa)
By “total destruction,” what is meant is that the sample completely (and violently) disaggregated along multiple shear planes.
 A constant strain rate of 10−4s−1 was chosen based on the requirements of the industry standard test protocol that states that a constant strain rate (or stress rate) should be chosen such that the specimen will fail in unconfined compression in a time between 2 and 15 min [ASTM, 2010]. Based on that protocol, we selected a strain rate such that the sample with the shortest anticipated failure time (based on a combination of the expected fracture strength and elastic modulus) would be slightly greater than 120 s.
 An example of a displacement versus calculated stress curve is given in Figure 2a, and corresponding stress-strain curve is given in Figure 2b. Here, displacement refers to the progressive upward advance of the mobile platen as referenced to its starting position. These data have been corrected for machine compliance by subtracting out the displacement of the instrument assemblage under load.
2.2 RAT Grinding Test Procedure
 An engineering flight spare of the RAT is kept at Honeybee's facility in New York. The RAT is mounted in a vertical position along a linear stage and can be raised or lowered to preload its contact switches onto a planar facet of a rock sample. Natural rock surfaces were ground in order to better replicate field conditions for the RAT. Each grind began with a calibration routine used to assess the no-load current of the grind motor, followed by a standard “seek-scan” preprogrammed routine that was designed for autonomous operation on Mars. This routine locates the highest point of the rock surface within the grind area and ensures that the grind starts just above this point. Due to the irregular texture of natural samples, the surface area ground tended to increase with depth into the rock as the paddle wheel attained full contact with the rock surface. Therefore, motor currents were averaged over the last 0.25 mm depth of the RAT grind to determine the specific grind energy (SGE, units J/mm3), which is a measure of the work done per unit volume of abraded material:
 Here, V is the voltage (in volts), is the mean grind current (in mA), ANL is the no-load current (in mA), s is the grind duration (of the last 0.25 mm in seconds), and vol is the grind volume (in mm3). The target depth of each grind ranged from 2 to 5 mm, depending on the estimated depth required to penetrate the uneven top surface. Where possible, multiple grinds were performed in the same spot on a rock to obtain additional SGE data points.
 Motor currents versus time for a grind test (on sample ls-02a) are given in Figure 3. Note that the grind current rises rapidly over the first 2000 s (~33 min) to a value >200 mA as the grinding bit fully engages with the target substrate. Following the convention established previously, SGE was obtained using equation (1) from the last 0.25 mm of the grind where the mean grind current was 271 mA. The mean grind voltage was 25.6 V, the no-load current was 51.5 mA, and the last 0.25 mm took 1329 s to grind. The energy expended was therefore 7456 J, and with a grind volume of 397.6 mm3, the SGE was 18.7 ± 2.3 J/mm3. A discussion of how the uncertainty in the SGE value was estimated is given in section A1.
2.3 Chemical Analytical Procedure
 Small pieces (total ~50 g) of each sample were provided to the Washington State University GeoAnalytical Laboratory (WSU) in sealed glass containers for analysis of major and trace elements by combined X-ray fluorescence (XRF) and inductively couple plasma mass spectroscopy (ICP-MS), in addition to loss on ignition (LOI) analysis. These samples were ground to a fine powder by WSU in a tungsten carbide ring mill. The major and trace elements Si, Al, Ti, Fe, Mn, Ca, Mg, K, Na, P, Sc, V, Ni, Cr, Ba, Sr, Zr, Y, Rb, Nb, Ga, Cu, Zn, Pb, La, Ce, Th, Nd, and U were analyzed by XRF on glass fusion beads of sample powder using a ThermoARL Advant'XP + sequential XRF. Details of the analytical procedures and precision and accuracy of analyses can be found in Johnson et al.  and http://www.sees.wsu.edu/Geolab/note/xrf.html. The trace elements Ba, Th, Nb, Y, Hf, Ta, U, Pb, Rb, Cs, Sr, Sc, Zr, and the rare earth elements were determined on acid digested powder samples using an Agilent 7700 ICP-MS; details of the analytical procedures and precision and accuracy of analyses can be found at http://www.sees.wsu.edu/Geolab/note/icpms.html. Chemical data will be used in an upcoming manuscript that is currently in preparation; they are included here for completeness.
 Compressive strength test results are given in Table 3 and plotted in Figure 4. Despite the variability inherent in natural rock samples, the results show a high degree of self-consistency (average departure from the mean value is 10.2%). With the exception of the vesicular basalt (sample bas-02), the standard deviation of the mean was less than a few MPa. The mean peak stress withstood by the samples ranged from a high of 429 MPa for the aphanitic basalt to a low of 18 MPa for the kaolinite. The samples that exhibited the greatest range of UCS values were the vesicular basalt samples. Void spaces in the vesicular basalt have a heterogeneous distribution, and the measured strength values are likely sensitive to their specific distribution and orientation within a given sample core.
 RAT grinding test results are compiled in Table 4 and Figure 5. Green horizontal lines are mean SGE (specific grind energy) values as given in Figure 4; individual measurements are indicated by multiple symbols per sample type. The results are more scattered than the compression tests and have an average departure from the mean value of about 43%. Measured SGE values ranged from 1.1 to 82 J/mm3. As with the compressive strength tests, the vesicular basalt sample (bas-02) displays the largest range of measured values. For reference, these values are two to three orders of magnitude greater than the specific cutting strength for water ice drilled at 140 K, which was found to be 60 MJ/m3 (or 0.06 J/mm3) using a metal-toothed coring tool [Garry and Wright, 2004]. Such a difference is consistent with the operational dissimilarities between the grinding action of the RAT versus the coring action of a drill.
Material removed determined over last 0.25 mm of grind.
lost preload after ~1.8 mm due to rock shifting
lost preload on second grind attempt
seek/scan “found” top of rim so higher grind depth commanded to compensate
seek/scan “found” top of rim so higher grind depth commanded to compensate
stalled at ~3.4 mm due to rock shift
one switch “chattered” causing Z step backwards; bit did not remove full 0.25 mm
revolve timeout after 3.20 mm
revolve timeout after 2.03 mm
revolve timeout after 2.39 mm
revolve timeout after 2.80 mm
revolve timeout after 0.71 mm
revolve timeout after 0.71 mm
revolve timeout after 2.13 mm, but grind recovered
revolve timeout after 0.76 mm
large grind depth used due to uneven surface
grind failed to achieve contact over full area
end of grind broke through thin edge of rock
 A comparison of UCS versus SGE is given in Figures 6a and 6b. As expected, more competent samples that withstood greater compressive force required more energy to grind with the RAT. However, the results indicate that there are two distinct regimes of rock strength as sampled by the RAT. In the lower strength regime (less than about 150 MPa), an approximate linear correlation can be determined between specific grind energy as recorded by the RAT and lab-measured compressive strength values (R2 values of linear and power-law fits are 0.914 and 0.952, respectively). Above this lower strength regime, the SGE values appear to reach a “plateau point”: a strength above which RAT grinding operates with reduced effectiveness. Grinding still continues but at a very small rate of advancement into the rock. This is due in part to the software control law in place that establishes an upper limit on the RAT's motor current draw (thus limiting the maximum energy available per unit time or per unit volume of target rock). As a result, the compressive strength-SGE relationships established in Figures 6a and 6b for materials with strength values less than ~150 MPa are not applicable to stronger materials.
 Within the lower strength regime, some complications are evident even in this limited sample set. The sandstone sample (ss-01), which is composed of medium-sized, rounded quartz grains held by a diagenetic cement, falls below the trend line. Although resistive to compression (as compared to the kaolinite sample, for example), it may be that the grinding action of the RAT dislodges or plucks individual quartz grains more efficiently than for a non-granular target, thus lowering the amount of energy necessary to grind such a sample.
4 Discussion and Application to MER Spirit Results
 Our study indicates that an approximate correlation can be determined between specific grind energy as recorded by the RAT and lab-measured compressive strength values. As expected, more competent samples tend to require more energy to grind. However, extremely competent rocks (>150 MPa) are ground progressively less efficiently by the RAT (requiring long grind times to achieve minimal depth into the target substrate). Given that the original design objective of the RAT was to grind away and remove the outer weathered rinds of Martian rocks, this objective is expected to be satisfied as it is unlikely that weathering products will exceed the strength of intact, hard rock. In other words, whereas some range of intact rocks strength may exceed the capabilities of the RAT to efficiently grind it, the RAT should be able to remove any weathering rinds during nominal grinding activity. A notable exception to the general trend of weakening with increased weathering is the formation of more resilient, thin surface crusts (such as case hardening or rock varnish [e.g., Conca and Rossman, 1982]). On Earth, such crusts are often mediated by an active biologic component [e.g., Dorn and Oberlander, 1981; Kurtz and Netoff, 2001] that is likely absent on exposed surfaces on Mars. Therefore, martian rock varnish may be weaker than its terrestrial counterpart.
 A potential source of variability in both grind and compressive strength measurements is sample anisotrophy, e.g., rock texture and fabric. Texture is more relevant to the RAT grinds as natural surfaces were used for grind tests, although this is partially mitigated by focusing on the last 0.25 mm of the grind for the SGE calculation. The original surface textures were not preserved in the cores prepared for compression tests, so texture is not a critical factor in these measurements. Rock fabric effects, however, are relevant to both test methods. Aligned grains, phenocrysts, microcrysts, vesicles, bedding plains, laminae, or other banding or grading could affect the results by artificially weakening (or in a few cases, strengthening) the material relative to a bulk isotropic medium. However, no macroscopic anisotropies were observed in the samples prior to testing. Indeed, the absence of foliation and other visible planar fabrics was a criterion for sample selection.
4.1 Estimated Strength Values for Spirit RAT Grind Targets
 A general question is how relatable are the compressive strength results to the grind results—what are the differences and similarities between them in terms of the modes of failure, and how much can the results from one set of tests inform us about the other? In the compressive strength tests, the samples are compressed along a vertical axis and experience a tensional force that is orthogonal to the direction of compression. The ends of the cylindrical samples are not fixed to the spherical platens, and the sample responds to compression in part by expansion in the orthogonal direction. Many of the samples failed by axial splitting, i.e., one or more longitudinal cracks propagating parallel to the direction of the load (see Table 3). These are Mode I cracks that are due to tensile stress normal to the plane of the crack. Another common failure mode was along one or more inclined planes, labeled here as shear planes to distinguish them from the more simple geometry of the axial fracture failure mode. But whether or not all of these inclined fractures are true shear features is debatable [e.g., Slate and Hover, 1984; Yang and Jing, 2011]. Since friction restricts lateral expansion near the ends of the specimens, the resulting stress distribution in the specimen may be neither uniform nor uniaxial [e.g., Wang and Shrive, 1995]. Therefore, while some of these inclined fracture planes may have included a shearing component, others may be only apparent shear displacements that occurred after vertical cracking parallel to the direction of uniaxial compressive load had taken place.
 The RAT grinds are a combination of fracture and frictional sliding. As tensional force is required to break interatomic bonds, the specific mechanism of material removal in RAT grinds must be compression-induced tension, and in that respect it is broadly similar to the uniaxial compression case. Microdiamond particles embedded in the RAT cutting heads are compressed against small surface asperities in the target material due to the rotary action of the cutting heads, akin to the action of a blunt, chisel-like tool. Given the geometry of this cutting action, the role of shear may be more important here than in uniaxial compression. The situation where strong particles are plucked from a weakly bonded matrix (e.g., in a coarse sandstone) is a separate case—here the RAT grinding action attains a special efficiency relative to a more uniform target medium. In summary, while the failure mechanism in each strength test is distinctive, they share the basic commonality of compression-induced tensional failure.
 An additional consideration is loading (or strain) rate sensitivity. As noted previously, the compression tests were conducted at a strain rate of 10−4s−1. The characteristic strain rate of the RAT is less straightforward to determine, but it can be constrained by the maximum linear velocity of the grind heads. Based on a grind bit diameter of 23.3 mm and a maximum rotational rate of 3000 rpm, the maximum linear velocity is about 3.7 m/s. While this value is higher than for the compression tests, in general, brittle materials are relatively rate insensitive until the loading rate becomes very high, i.e., on the same order of magnitude as a crack propagation speed (see Figure 12 of Bhat et al. ). While some supersonic shear crack speeds have been measured [Rosakis et al., 1999], the upper limit of crack propagation is typically considered to be roughly equal to the Rayleigh (elastic) wave speed. For basalt, assuming conservative values for Poisson's ratio of 0.1 and an elastic modulus of 50 GPa, the Rayleigh wave speed is roughly 2400 m/s. As this value is several orders of magnitude lower than the likely RAT strain rate, we do not consider the difference in strain rates between the compression tests and the RAT grinds to be a factor that precludes their comparison.
 Using our experimentally determined correlation given in Figure 6, we provide a first-order estimate of the compressive strength values for target surfaces ground by the Mars Exploration Rover (MER) Spirit (Figure 7). The rocks investigated by the Spirit rover span a greater range of apparent strengths than targets probed by the Opportunity rover; hence, we focus our attention on the former. Table 5 provides a summary of RAT grinding activity on Spirit through Sol 416. After this point, due to wear of the grinding bits of Spirit's RAT paddle wheel, further grind operations of rock targets were not attempted. A full list of RAT-related activity is given in the general mission timeline summary tables of Arvidson et al. [2006, Sols 1–512, 2008, Sols 513–1476].
 Rock and outcrop targets encountered by Spirit were classified according to their geochemical, spectral, and physical properties [Ming et al., 2006; Morris et al., 2006; Squyres et al., 2006; McCoy et al., 2008; Crumpler et al., 2011]. The largest division in inferred strength between rock types is between Adirondack-class rocks (including Adirondack, Mazatzal, and Humphrey) and rock and outcrop materials found in the Columbia Hills, a distinction noted previously [e.g., Squyres et al., 2006]. Adirondack-class rocks are the strongest rocks measured by Spirit and have inferred compressive strength values in the range of 70–130 MPa. Although this falls within the “strong” to “very strong” fields of the rock hardness classification scheme (Table 6), it is significantly weaker than the strength of intact, fresh basalt. No in-place outcrops of Adirondack material were observed by the rover—all contact and remote measurements were conducted on float (i.e., isolated, displaced rock fragments). Ruff et al.  identified numerous examples of rocks of likely Adirondack class in the Columbia Hills, although none were investigated by RAT grinds. As these pieces of float were likely ballistically emplaced during impact events [e.g., Grant et al., 2006], some weakening during the impact process coupled with pre- or post-impact weathering likely accounts for their relative weakness compared to their fresh terrestrial counterparts.
Table 6. Classification of Rock Strength After Hoek and Brown 
Uniaxial Comp. Strength (MPa)
Specimen can only be chipped with a geologic hammer
Crumbles under firm blows with point of geologic hammer, can be peeled with a pocket knife
Highly weathered or altered rock
Indented by thumbnail
Stiff fault gouge
 The second strongest class of rocks is Wishstone class (i.e., Wishstone and Champagne); inferred compressive strengths range from 40 to 55 MPa, straddling the classification division between medium strong to strong materials (Table 6). Their relative strength compared to Clovis, Watchtower, and Peace-class rocks is consistent with their low inferred degree of alteration based on their low ferric iron content (Fe3+/Fetotal [Morris et al., 2006]) and also low S, Cl, and Br [Ming et al., 2006; Squyres et al., 2006]. Although only pieces of float were abraded by the RAT, clasts of Wishstone-class materials were identified in the Voltaire outcrop [Arvidson et al., 2008; Ming et al., 2008]. Given the observed textural characteristics, which include an absence of layering and 1–2 mm angular clasts in a fine-grained matrix, an origin as impact ejecta or volcanic ash flow (e.g., an ignimbrite) is inferred [Squyres et al., 2006; Crumpler et al., 2011].
 Clovis-class material was abraded at the outcrops Clovis, Wooly Patch, and Uchben and the float sample Ebenezer. These materials are massive to layered poorly sorted clastic rocks of basaltic bulk composition [Squyres et al., 2006] with elevated Ni concentrations [Yen et al., 2006]. Inferred compressive strengths for this material are in the range of 15–30 MPa (weak/medium strong). A significant percentage of phyllosilicate minerals (14–17%) is inferred in Wooly Patch [Wang et al., 2006], which lies at the lower end of the range of strengths exhibited by Clovis-class material and is broadly consistent with the strength of pure kaolinite (terrestrial sample kal-01). Overlapping the strength regime of Wishstone-class rocks is Watchtower class, of which only a single example (Watchtower itself) was abraded by the RAT. The inferred strength, 39 ± 9 MPa to 47 ± 11 MPa, nominally falls in the “medium strong” category (Figure 7; Table 6). The inferred strength of Watchtower is subject to higher uncertainty because the RAT's progress stalled while grinding, likely due to a combination of bit wear and clogging by cuttings.
 Weaker still are the inferred strengths of Peace-class material, which is the weakest non-soil material investigated at the Spirit site. Compressive strengths of Peace-class material is ~1–10 MPa, in the “weak” to “extremely weak” strength classification. These low strength values are consistent with a poorly consolidated sandstone [Squyres et al., 2006], one with ultramafic grains weakly bound by sulfate minerals.
 The rock types abraded by the RAT in the Columbia Hills share many common elements. They are all relatively weak compared to the more competent Adirondack-class basalts (UCS < 50 MPa) and, with the exception of Peace-class rocks, have been inferred to be impactites or volcanoclastic in nature. In terrestrial samples of tuffs, rock strength varies with factors such as welding intensity, which is the sintering and compaction of glassy pyroclasts under compressive load at temperatures above the glass transition temperature [e.g., Ross and Smith, 1980]. The reported strengths of tuffs and similar material also vary widely due to differences in density, porosity, fabric, and water content, among other factors. But with inferred compressive strengths of ~40–55 MPa, Wishstone-class materials lie at the higher end of this range, consistent with a more competent or welded tuff-like material, while Clovis-class materials lie at the lower, weaker end [e.g., Quane and Russell, 2003].
 In summary, these data provide an approximate estimate of the compressive strength of rocks on Mars. When considered alongside chemical, spectral, and rock textural data, these results help inform our understanding of rock origins and modification history. Future work on this topic includes an attempt to better constrain the linked effects that weathering has on the chemistry and strength of basalt with the goal of better constraining Martian weathering processes. In addition, a similar approach to that developed here could be applied to future surface studies, for example using the rotary-percussive drill on the Mars Science Laboratory rover Curiosity [Anderson et al., 2012].
Appendix A: Specific Grind Energy Error Analysis
 To assess the level of uncertainty in the specific grind energy (SGE) determinations, we perform a basic error analysis. SGE values are determined by five factors in equation (A1).
 Here, V is the voltage (in volts), is the mean grind current (in mA), ANL is the no-load current (in mA), s is the grind duration (of the last 0.25 mm in seconds), and vol is the grind volume (in mm3). The relative uncertainty in SGE is the sum of the squares of the relative errors of the individual factors.
 The factor with the lowest uncertainty is the grind voltage V; values in the lab-based RAT grind tests varied from 25.5 to 27.2 V, with an uncertainty level <0.1 V (a relative error of less than 0.4%). The no-load current values ANL were determined by rotating the grinding paddle wheel in free space prior to grinding and ranged from 36.1 to 58.9 mA. The level of variability within a given test was low, and the uncertainty level is <0.5 mA (equivalent to a relative error of less than 1.4%).
 Variation in the mean grind voltage is also relatively low. As indicated in the example grind current versus time record given in Figure 3, the current level exhibits a pseudoperiodic variation. In this example, the current spikes correspond to instances where the Z axis incrementally advances. The median value, however, remains relatively constant (black curve in Figure 3), and the relative uncertainty in the mean value is <5%.
 Since the SGE is calculated over the last 0.25 mm of the grind, the volume ground is defined as
 which is the grind surface area multiplied by depth times 1 minus the pore space ϕ. Pore space is determined using post-RAT images of the abraded area, and the uncertainty in the volume ground is dominated by the pore space estimate. For the lab measurements, the post-RAT surfaces were cleared of cuttings using compressed air, and the pore space estimate is fairly straightforward (this factor has a typical uncertainty ±2–3% based on repeated measurements). The uncertainty will be slightly higher in situations where the cuttings are not cleared after grinding is completed; if the cuttings partially fill the pore space, the uncertainty level rises to ~5%. This uncertainty is partially mitigated by the fact that on Mars, post-RAT brushing is part of the standard command sequence to help clear out cuttings from the abraded hole.
 Perhaps non-intuitively, the overall uncertainty in SGE is dominated by the uncertainty in the final term s. Although the number of seconds during which the last 0.25 mm is ground is readily determined with millisecond precision from the test telemetry, the real uncertainty is driven by the inherent uncertainty of the Z axis position. Grind depth measurements (Z axis) are determined from readings of the Z axis motor. While the precision of this measurement is high, its accuracy is lessened due to the unknown amount of strain accommodated by the RAT instrument itself (as well as mounting assembly in the lab version or, on Mars, by the rover's arm and chassis). Consequently, the actual grind depth achieved is typically less than that indicated via the Z axis position. A plausible fractional error of ±10% of the grind duration was used to calculate the uncertainty in the specific grind energy. Using equation (A2) and the values given above, the relative uncertainty in SGE is 12.3%. For reference, if each factor in equation (A1) has a relative error of 5%, the SGE uncertainty would be 11.2%.
 In the future, the overall accuracy of the specific grind energy determination could be improved if more precise depth measurements were available. For a few targets investigated by at the MER landing sites, post-RAT Digital Terrain Models were painstakingly constructed from sets of stereo pairs of Microscopic Imager frames [e.g., Herkenhoff et al., 2006]. However, practical considerations precluded this from being done for all abraded surfaces. Yet even this methodology produces only a single post-activity volume estimate. More precise depth measurements, preferably made while grinding was being conducted, would permit greater insight into the nature of abrasive wear of the target surfaces.
 This project has benefitted from helpful discussions with current and former Honeybee Robotics engineers; insightful and constructive reviews from Ralph Lorenz and an anonymous reviewer also improved the manuscript. Support for this research was provided by a NASA Mars Fundamental Research Program grant to BJT. The authors also gratefully acknowledge Robert Anderson and Gregory Peters from JPL for help with rock sample procurement.