US Army Engineer Waterways Experiment Station

This is a historical facility. Waterways Experiment Station was a named Army organization from 1 March 1937 to 30 September 1999, when the Corps of Engineers consolidated seven of its laboratories into the Engineer Research and Development Center [8]. The Vicksburg site and its soils work continued: vehicle mobility and terramechanics are run there today by the Mobility Systems Branch of the ERDC Geotechnical and Structures Laboratory, which is the organizational descendant of the Mobility and Environmental Division and still names the Lunar Roving Vehicle among the work its site supported [9]. What did not survive is the specific arrangement described below: the single-wheel dynamometer, the prepared soil bins and the four shear apparatus of the lunar wheel campaigns are documented only in reports from 1968 to 1978, and nothing published establishes that any of that hardware still stands. Contact ERDC for current capability. The parameters below are the conditions the Apollo-era results were measured under.

The Waterways Experiment Station at Vicksburg is the laboratory where the Apollo lunar wheel was chosen. Under NASA sponsorship its Mobility and Environmental Division ran the five candidate wheels of the Lunar Roving Vehicle program on one single-wheel dynamometer in one prepared sand, then swept the selected Boeing/GM wire-mesh wheel over speed, load and soil strength in a crushed basalt simulant [1][2][3]. The drawbar pull against slip method that NASA GRC’s SLOPE laboratory still publishes as a procedure descends from the mobility work done here [6].

Its second output is less well known and more transferable: the division characterized its own soils by four independent shear apparatus at once, and published the disagreement between them [2]. That is the reason a friction angle quoted for a simulant is a property of the apparatus as much as of the soil.

Everything below is the historical record from the test reports themselves. No published source describes a user program, a fee schedule or a lead time under either name, and the test reports all predate the 1999 reorganization [8].

Laboratory data

Parameter	Value
Operator	US Army Corps of Engineers, Mobility and Environmental Division [1][2]
Location	Vicksburg, Mississippi, United States [4]
Commissioned	Not published. Lunar wheel reports span 1968 to 1971 [1][2][4]
Type	Terramechanics laboratory: soil bins, single-wheel dynamometer, test vehicles
Floor area	Not published
Capabilities	Dynamometer, soil bins, vehicles
Simulant or terrain	Yuma sand at five consistencies; crushed Napa basalt at five consistencies [1][2][3]
Instrumentation	Dynamometer carriage with independent wheel drive; WES cone penetrometer
Ground truth	Soil characterized before every traffic run; 170 penetrometer tests behind one condition [1]
Fidelity limits	1 g, in air, on moist terrestrial soil. No vacuum and no offload [1][2][3]
Access	Not published. The lunar program was contract work, not an open user program [1]
Cited by	Apollo LRV, lunar environment

Capabilities

Single-wheel dynamometer

Parameter	Value
Working volume	Prepared soil bin traversed by a carriage; bin dimensions not published
Test article limits	Wheels 47.75 to 107.95 cm diameter run to date; loads 67 to 667 N [1]
Vacuum	None. Tests were run in air at ambient pressure [1][2][3]
Temperature	Not controlled and not reported
Illumination	Not applicable
Simulant or terrain	Yuma sand or crushed Napa basalt, prepared to a target consistency
Slope	Not applicable. Slope capability is inferred from level-ground pull data [1]
Gravity offload	None. Wheel load is commanded instead [1]
Instrumentation	Pull, torque, sinkage and slip; contact-length sensor in the wheel surface [4]

The rig drives carriage and wheel independently, so slip is programmed rather than observed. Freitag’s comparative program used five discrete wheel loads, 67, 133, 311, 489 and 667 N, at about 0.5 m/s translational speed, and read performance at 20 and 60 percent slip [1]. The later Boeing/GM program held a single 254 N wheel load, ran the full programmed slip sweep to 100 percent, and read performance at 20 and 50 percent slip because torque and pull rise only slowly above 20 percent [2]. Both constant-slip and programmed-slip modes were used, in classical, ramped and modified variants [3].

Wheel diameters run in the candidate screening were 101.60 cm for the Bendix I petal elastic wheel, 102.87 cm for the Boeing/GM I wire mesh, 107.95 cm for the Grumman I, 97.4 cm for the pneumatic reference wheel and 47.75 cm for the Surveyor Lunar Roving Vehicle wheel, all at 25.4 cm contact width except the SLRV [1]. The six Boeing/GM development wheels GM IX to GM XIV measured 77.3 to 82.2 cm unloaded, and the GM X baseline with 50 percent chevron cover sat at 6.3 kPa contact pressure at 254 N on an 11.00 by 6.85 in tire print [2].

For the rigid-wheel stress work the bench carried a 71 cm smooth rigid wheel in two widths, 7.6 and 30.5 cm, at loads from 178 to 7108 N and constant slips of 3, 14 and 33 percent, with contact length measured directly by a sensor in the wheel surface rather than inferred [4].

Prepared soil bins

Parameter	Value
Working volume	Not published
Test article limits	Single wheels and 4x4 and 6x6 vehicles on matched soil preparations [1]
Simulant or terrain	Air-dry Yuma sand, and crushed Napa basalt from Basalt Rock Company [1][2]
Instrumentation	WES cone penetrometer reporting cone index gradient G
Ground truth	Density, cone index gradient, cohesion and friction angle before traffic [1][2]

Soil is prepared to a target consistency and characterized before it is driven on, and the characterization is what makes the results reusable. The measured conditions:

Condition	Material	Cone index gradient	Dry density	Relative density	Strength
S1 [1]	air-dry Yuma sand, loose	0.54 MN/m3, average of 170 tests	1.484 g/cm3, average of 75	39 pct	zero cohesion
S2 [1]	Yuma sand, dense	Not published	1.62 g/cm3	87 pct	43.5 deg, zero cohesion
C3 [1]	Yuma sand, 1.8 pct moisture	Not published	1.51 g/cm3	48 pct	38.1 deg, cohesion 1.75 kN/m2
LSS1 [2]	crushed basalt, 0.9 pct moisture	0.22 MN/m3 (0.8 pci)	1.518 g/cm3	31 pct	see below
LSS3 [2]	crushed basalt, 0.9 pct moisture	6.5 pci	1.655 g/cm3	52 pct	40.0 deg by triaxial
LSS4 [3]	crushed basalt, 1.8 to 1.9 pct moisture	0.22 MN/m3	Not published	about 30 pct	cohesion 0 to 2.9 kN/m2
LSS5 [3]	crushed basalt, firm	6.39 MN/m3	Not published	about 60 pct	cohesion 2.9 kN/m2

The S1 range across those 170 penetrometer tests was 0.48 to 0.81 MN/m3 and the S1 density range across 75 gravimetric tests 1.446 to 1.527 g/cm3, so the spread of a nominally single condition is about a factor of 1.7 in strength [1]. Relative density is itself uncertain: for the basalt simulant the value derived from the cone index gradient and the value from the density box disagree badly, 32 against 17 percent for LSS4 and 31 against 54 percent for LSS1, and the report prefers the gradient-derived figure because volumetric readings were erratic in loose soil [2].

Every cohesion figure in the table is apparent cohesion produced by moisture and interlock at 0.5 to 1.9 percent water content [1][2][3]. It has no lunar counterpart, and the sources say so [1][2][3].

Test vehicles

Parameter	Value
Working volume	Prepared soil lanes and constructed slopes; dimensions not published
Test article limits	4x4 and 6x6 test vehicles, built light so wheel loads match lunar weight [1]
Slope	Slope-climbing runs performed; maximum constructed angle not published [1]
Gravity offload	None. Vehicle mass was reduced instead of offloaded [1]
Instrumentation	Drawbar pull through a hitch; axle scales for load transfer [6]

The division ran vehicle-level pull-slip and slope-climbing tests alongside the single-wheel work, on soil prepared to matching consistency, which is what allowed the single-wheel to vehicle transfer to be checked rather than assumed [1]. Hitch geometry was measured rather than ignored: on the WES 4x4 test vehicle with the hitch at one seventh of the wheelbase, applied drawbar pull transferred about 9 percent of the pull force from the front axle to the rear, load transfer being pull force times twice the ratio of hitch height to wheelbase when the center of gravity sits between the axles [6].

Soil strength apparatus

Parameter	Value
Working volume	Bench and in-situ instruments used inside the soil bins
Test article limits	Soil specimens; sample sizes 1 to 4 tests per apparatus per condition [2]
Instrumentation	Vacuum triaxial, in-situ plate shear, bevameter plate and ring shear, Cohron sheargraph, trenching

The bevameter supplies the Bekker pressure-sinkage parameters and the ring shear supplies the Coulomb parameters, both fitted rather than measured directly. On crushed basalt the frictional modulus of sinkage k-phi came out at 4.32 lb/in^(2+n) for LSS1 over four tests with individual fits 3.50 to 5.25, and 8.83 for LSS3 over three tests, with sinkage exponent n of 0.90, 1.15, 1.48 and 1.18 across the four conditions, not monotonic in density [2].

What it does not reproduce

Gravity. Every result is 1 g. The workaround used here, and still used at every terramechanics bench since, was to build the test vehicles light enough that wheel loads matched lunar weight [1]. That reproduces the contact load and leaves the gravitational body force in the soil column at its terrestrial value.

Vacuum, and therefore lunar cohesion. The soils are terrestrial, in air, at 0.5 to 1.9 percent moisture [1]. Freitag’s headline negative result, that adding cohesion did not markedly improve wheel performance, is a result about moist sand, not necessarily about regolith, because the cohesion was imposed by water rather than by the interparticle and electrostatic mechanisms that produce it on the Moon [1]. Melzer’s report goes further and flags unquantified air-pore pressure as a possible artifact of testing in air: the one sand against simulant comparison showed a speed effect on sand that did not appear in the simulant, and the authors recommended vacuum scale-model tests to settle it, which were not run [3].

Agreement between its own instruments. Four apparatus on one soil in one campaign gave friction angles spanning 19 degrees and apparent cohesions spanning a factor of ten [2]. The numbers and the reasoning are on the regolith simulants page; what belongs here is that the disagreement is a property of this laboratory’s method set and not of the sample [2].

A physically meaningful cohesive modulus of sinkage. The Bekker parameter k-c fitted negative on all three LSS3 plate penetration tests, range -2.44 to -0.94 lb/in^(1+n), and on some LSS1 tests, range -0.76 to +1.28 [2]. A negative cohesive modulus has no physical meaning, and this is the measured counterpart to the analytical objection raised from inside the same program, that k-c, k-phi, n and the shear modulus K are curve fits to a particular plate or shear ring rather than soil properties [4].

Statistical weight. Slope-climb figures are single-vehicle observations, not qualification runs, and the 1 to 2 degree penalty for steering while climbing is stated by the authors as an estimate from observation rather than a measured sweep [1]. LSS2 and LSS4 rest on a single bevameter test each [2].

Grouser geometry. The angle-iron grousers that produced the largest pull gains measured here are given a height and a width but never a count or a circumferential spacing, in either report, so the gain cannot be placed on a grouser spacing curve [1][2].

Campaigns run there

Lunar wheel down-select, reported 1970. Five candidate wheels on one dynamometer in one soil, at 220 N wheel load in loose air-dry sand [1]:

Wheel	Diameter	Pull coefficient at 20 pct slip, S1	Max climbable slope	Specific energy
Bendix I, petal elastic	101.60 cm	0.452	28 to 30 deg	4 W-h/km
Boeing/GM I, wire mesh	102.87 cm	0.274	15 to 20 deg	6 W-h/km
Grumman I	107.95 cm	0.281	15 to 20 deg	10 W-h/km
SLRV	47.75 cm	0.426	Not reported	Not reported
Pneumatic reference	97.4 cm	0.448	Not reported	Not reported

None of the original wheels could be relied on to climb the 35 degree slope the program asked for [1]. Adding cohesion helped less than expected: the Bendix wheel went from 0.452 in zero-cohesion S1 to 0.505 in C2 at 1.08 kN/m2 cohesion, and the Boeing/GM wheel from 0.274 to 0.343. Adding grousers helped much more: 3.2 cm angle-iron grousers took the Grumman wheel from 0.580 to 1.010 pull coefficient at 60 percent slip at 310 N in S1, a 74 percent gain, at a cost in power [1].

Two findings from that campaign generalize past the LRV. Below about 220 N wheel load the pull coefficient stops depending on load, and over 0.7 to 3.5 kN/m2 it stops depending on average contact pressure, both in fine sand [1]. A lightly loaded wheel therefore operates in a regime where the classical pressure-sinkage terms do not order the result. And level-ground pull data predicted vehicle slope-climbing ability conservatively by 1 to 2 degrees, with a further 1 to 2 degrees lost to steering while climbing [1].

Boeing LRV wheel design and soil, reported 1971. Six wire-mesh configurations differing in chevron tread cover from 0 to 100 percent and in rim stiffness, at a fixed 254 N wheel load in four simulant consistencies [2]. For the 50 percent chevron wheel that flew, power number relates to pull coefficient exponentially, and the slope of the initial linear portion fell from 1.478 at G = 0.8 pci to 1.314 at G = 6.5 pci: the cost of pull drops as the soil firms [2]. This report is also the source of the soil table above.

Boeing LRV wheel speed and load sweep, reported 1971. Fifty-seven single-wheel tests on the flight-configuration wheel established that pull coefficient, power number and efficiency are insensitive to wheel speed from 0.44 to 3.14 m/s, to wheel acceleration, to the presence of a fender, to travel direction and to wheel load from 178 to 377 N. Only sinkage varied with load [3]. Soil strength is the variable that matters: pull coefficient at 20 percent slip rose 50 percent as G went from 0.22 to 6.39 MN/m3. The slope limits used in Apollo mission planning come from here, 19 +/- 6 degrees in the nominal soil condition and 23 +/- 5 degrees in the firm one, at torque coefficients at maximum efficiency of 0.35 +/- 0.11 and 0.32 +/- 0.10 [3].

Tractor dozer field trials for the Bureau of Mines, reported 1978. Six tractor and blade combinations reclaiming coal-mine spoil banks, measured for blade capacity, production rate, cone index and drawbar pull against slip [7]. Maximum drawbar pull coefficients were 0.88 for a Caterpillar D8H and 0.86 for a D9H, both in first gear at about 20 percent track slip on spoil with a 0 to 6 in cone index above 200 [7]. Measured earthmoving production reached 49.0 to 70.6 percent of the traction-optimum production at the measured speed, averaging 55.9 percent, and every blade tested operated below 67 percent of its measured maximum capacity. The material is wet terrestrial spoil at a cone index where soil strength stops mattering, so nothing in it constrains behavior in weak regolith, but the roughly half-of-optimum gap is the number an excavation sizing argument from blade force alone leaves out.

Retrospective re-analysis, 2009. A curve fit over about 500 slope against slip points drawn from this laboratory’s archived data puts the mean slip required for the LRV wire-mesh wheel to climb its 25 degree requirement slope at 59.5 percent, rising to 72.0, 79.5 and 84.5 percent at one, two and three standard deviations, and identifies 50 percent tread coverage as the optimum from the comparative dynamometer runs, minimum power at the self-propelled point and highest drawbar pull at 20 percent slip in LSS1 [5]. Both figures are analyses performed in 2009 by authors working from the archive, not period results, and the 59.5 percent slip figure is the one that shows the Bekker-method design analysis overpredicted the wheel [5].