{ "status": "Source review complete; matched calibration and revised construction runs pending.", "sources": { "page2022": { "title": "Page et al. (2022), tether friction on natural objects", "url": "https://arxiv.org/pdf/2208.10646", "kind": "Primary experiment, different rope and load", "note": "Uses primarily 1 mm HERCULES Dyneema fishing line and a 225 g sled with a handheld force gauge. Natural-object friction fits range from 0.26 on smooth bark to 0.5 on a fire hydrant. Moisture does not consistently raise or lower friction. This provides a capstan measurement method and shows sensitivity to surface conditions; it does not calibrate 40 mm plant-fibre rope on polished or lubricated timber under kilonewton loads." }, "buchholz": { "title": "Buchholz et al. (1988), palmar skin and handle materials", "url": "https://stacks.cdc.gov/view/cdc/185560/cdc_185560_DS1.pdf", "kind": "Primary experiment, other materials", "note": "Seven subjects tested seven materials, about 9\u201355 N pinch force, dry and moist. Dry paper mean \u03bc=0.27 and dry aluminium mean \u03bc=0.33. Material, moisture and force affected grip. No wood was tested; this does not calibrate a skin/timber coefficient." }, "scheuring": { "title": "Scheuring (2025), counterweight proposal", "url": "https://www.nature.com/articles/s40494-025-02018-w", "kind": "Construction hypothesis", "note": "Uses wood/stone sliding \u03bc=0.2, with a stated range 0.2\u20130.4, citing Engineering Toolbox (reference 24). Proposes polishing and lubricating fixed wooden rope guides, without specifying lubricant or measured rope friction." }, "rabat": { "title": "Rabat et al. (2022), porous limestone tilt tests", "url": "https://doi.org/10.1007/s10064-022-02687-y", "kind": "Primary experiment, material proxy", "note": "Table 5 dry mean basic friction angles: 32.0\u00b0, 37.4\u00b0, 37.2\u00b0, giving tan(\u03c6)=0.625, 0.765, 0.759. Saw-cut Spanish calcarenites, onset of sliding, not Giza limestone or kinetic sliding. Saturation increased friction in one lithotype and decreased it in two." }, "araki": { "title": "Araki et al. (2009), timber column bases on stone", "url": "https://doi.org/10.3130/aijt.15.405", "kind": "Primary experiment, contact proxy", "note": "Initial static coefficients 0.7\u20130.9, with reductions up to 30% on the second loading cycle. Timber building column contacts differ from polished sledge runners and rolling contacts. These values motivate high-friction stress cases, not direct sledge calibration." }, "aira": { "title": "Aira et al. (2014), Scots pine against Scots pine", "url": "https://doi.org/10.3989/mc.2014.03913", "kind": "Primary experiment, wood proxy", "note": "Measured mean static/kinetic pairs: 0.24/0.17 for transverse surfaces, 0.12/0.08 for radial surfaces along grain. Small sample, sawn Spanish pine, approximately 12% moisture, 2435.3 N normal loading and 8 mm/min motion. These wood/wood data do not measure wood/stone." }, "fall": { "title": "Fall et al. (2014), sliding on wet and dry sand", "url": "https://doi.org/10.1103/PhysRevLett.112.175502", "kind": "Primary experiment, granular drag", "note": "Small PVC sled with 35 \u03bcm sandpaper underside, mixed and tapped sand beds. Modest water reduced drag; excess water increased it. Sand type mattered. The minimum around 0.3 for polydisperse sand is effective sled-bed drag, including ploughing, not wood/limestone or roller friction." }, "blakely": { "title": "Blakely & Blakely (2014), Egyptian pulley experiment", "url": "https://exarc.net/issue-2014-3/at/reinventing-egyptian-pulley", "kind": "Primary experiment, different mechanism", "note": "Tested rotating stone cylinders in stone cradles, using animal fat in the prototype and olive oil in the full-size bearing. Rope did not slide on the cylinder. The report cannot calibrate Scheuring\u2019s sliding rope over stationary wood." }, "ayrinhac": { "title": "Ayrinhac (2016), statue hauling and worker traction", "url": "https://doi.org/10.2474/trol.11.466", "kind": "Mechanical analysis and literature review", "note": "Separates steady pulling from brief peaks, discusses teamwork losses and foot-ground traction. Lubricant identity remains uncertain. A force-per-worker allowance alone does not verify footing, posture, fatigue or coordination." }, "mujoco": { "title": "MuJoCo, contact model and coefficient units", "url": "https://mujoco.readthedocs.io/en/stable/computation/index.html#contact", "kind": "Engine documentation", "note": "Sliding coefficient is dimensionless. Rolling and torsional coefficients are lengths. Point-contact regularization approximates deformation; it does not automatically model wood crushing or sand rutting." }, "palmer": { "title": "Palmer (2016), rope/log friction investigation", "url": "https://forestengineering.org/wp-content/uploads/2020/11/2016-Jack-Palmer-Final-Project-pdf.pdf", "kind": "Primary student experiment, different rope", "note": "Uses capstan tension ratios for wire logging rope against pine logs. Supports the test method, not a coefficient for ancient plant-fibre rope on polished, lubricated wood." }, "eisp": { "title": "Van Tilburg & Ralston (2005), loaded roller and sledge experiments", "url": "https://www.eisp.org/544/", "kind": "Primary heavy-load experiment, different materials", "note": "Construction-yard tests used representative 10\u201312-ton loads on a steel plate, palm-wood sledge and irregular 33 cm palm rollers on a hard surface. Breakaway force was about 2800 lbf, effective F/W just over 0.1; rolling force fell to about half. Rollers wandered and jammed after short travel. Separate island trials with eucalyptus sliders on wooden rails reported about 0.2 at starting and about half during sliding. These are assembly drag ratios, not local contact coefficients or limestone-track calibration." } }, "contacts": [ { "id": "human_skin_plant_rope", "pair": "Palmar skin / plant-fibre rope", "condition": "Selected dry grip; fibre, surface finish, moisture, pressure and lubricant contamination remain unmatched.", "status": "Unmeasured grip sensitivity input", "unmeasured_mu_stress_cases": [ 0, 0.1, 0.15, 0.3, 0.6 ], "sources": [ "buchholz", "mujoco" ], "component_test": "qa/rope-surface-grip-comparison.json", "action": "Opposing normal pressure and axial Coulomb friction act at actual finite rope-surface points. Count complete hand-force vectors against the selected 150 N/person cap and preserve force, moment and virtual work. The isolated 1.5 kg proof holds independently at selected \u03bc=0.15, 0.3 and 0.6; \u03bc=0.1 leaves support at the laboratory anchor and fails independent holding. Other skin/handle materials do not calibrate plant-rope grip. Full sling handling remains unverified." }, { "id": "human_skin_wood", "pair": "Palmar skin / round wooden crossbar", "condition": "Selected dry, unlubricated grip. Timber finish, skin moisture and pressure are not matched to a measurement.", "status": "Unmeasured grip sensitivity input", "unmeasured_mu_stress_cases": [ 0, 0.1, 0.2, 0.3, 0.5 ], "sources": [ "buchholz" ], "action": "The transport-cycle trial selects \u03bc=0.3. Circumferential and axial tangential hand forces share one Coulomb cone, sqrt(F_circ\u00b2+F_axial\u00b2)\u2264\u03bc F_n, at each actual surface contact. Count both complete hand-force vectors against the same 150 N/person cap. Compare grip loss and recovery across stated cases; coefficients for other handle materials do not establish measured wood values." }, { "id": "rope_stone_surface", "pair": "Plant-fibre rope / limestone load", "condition": "Dry lifting sling and haul collar, separate from lubricated guides", "status": "Unmeasured sensitivity input", "unmeasured_mu_stress_cases": [ 0.1, 0.3, 0.5 ], "sources": [ "mujoco" ], "action": "The finite-rope experiment selects 0.3. This is an investigator-selected case, not a measured material value. Test slip, contact pressure and surface abrasion; the cited engine documentation supports coefficient units, not this number." }, { "id": "rope_self", "pair": "Plant-fibre rope / plant-fibre rope", "condition": "Dry rope crossings; knots use separate endpoint constraints", "status": "Unmeasured sensitivity input", "unmeasured_mu_stress_cases": [ 0.1, 0.3, 0.5 ], "sources": [ "mujoco" ], "action": "Native capsule contacts select 0.3 for diagnostic crossings. Rope knots, crushing and fibre deformation remain uncalibrated. Avoid treating an ideal endpoint tie as a tested knot." }, { "id": "rope_floor", "pair": "Plant-fibre rope / prepared ground", "condition": "Loose rope recovery and floor contact", "status": "Unmeasured sensitivity input", "unmeasured_mu_stress_cases": [ 0.1, 0.3, 0.5 ], "sources": [ "mujoco" ], "action": "The finite-rope fixture selects 0.3. Ground roughness and contamination need matched measurements. Rope drag and recovery must enter the human work ledger." }, { "id": "stone_bed", "pair": "Limestone block / prepared limestone bed", "condition": "Dry, planar, cleaned, unlubricated", "status": "Measured material proxy for onset only", "static_mu_cases": [ 0.625, 0.65, 0.765 ], "kinetic_mu": null, "sources": [ "rabat" ], "action": "Identify the actual finishing and pressure. Kinetic friction remains unmeasured; constant-Coulomb runs are sensitivity cases. Bed preparation must be shown if needed." }, { "id": "wood_stone", "pair": "Wooden sled runner or receiving timber / smooth limestone", "condition": "Dry; any lubricated variant is separate", "status": "Proposal-based sliding range; static threshold unknown", "sliding_mu_cases": [ 0.2, 0.3, 0.4 ], "static_stress_cases": [ 0.7, 0.9 ], "sources": [ "scheuring", "araki" ], "action": "Do not use the ramp sliding value to guarantee stationary timber supports grip. Test starting, descending, receiving and return separately." }, { "id": "wood_wood", "pair": "Wood roller / wood timber, including roller collisions", "condition": "Species, cut, grain direction and moisture specified", "status": "Primary wood proxy; present generic timber remains uncalibrated", "static_mu_cases": [ 0.12, 0.24 ], "kinetic_mu_cases": [ 0.08, 0.17 ], "sources": [ "aira", "eisp" ], "action": "Use orientation-matched pine tests as small-load proxies. The loaded eucalyptus slider trials provide a separate assembly comparison. Keep these conditions distinct." }, { "id": "roller_stone", "pair": "Wood roller / limestone floor and block", "condition": "Dry, clean stone; loaded roller radius 0.12 m", "status": "Rolling loss unresolved", "rolling_length_m_cases": [ 0.0005, 0.001, 0.002, 0.005, 0.006, 0.01 ], "sources": [ "mujoco", "araki", "eisp" ], "action": "The 0.002 m value in the prototype is an unmeasured experiment parameter. Listed lengths are stress tests. The heavy-load roller comparison gives approximate rolling F/W\u22480.05 under different surfaces; ideal b=r(F/W) maps this to 0.006 m at r=0.12 m, but does not establish a local rolling parameter. Include roundness, crushing, jamming and steering; measure matched drawbar drag." }, { "id": "sand_route", "pair": "Sled or roller / granular transport route", "condition": "Dry, damp and over-wet sand are distinct", "status": "Sand drag cannot be replaced by a stone contact coefficient", "sources": [ "fall" ], "action": "Model settling and ploughing or use a calibrated effective-drag law. Roller/stone trials require a hard track; constructing such a track costs worker effort." }, { "id": "rope_guide", "pair": "Plant-fibre rope / fixed polished wooden guide", "condition": "Dry control and lubricated proposal", "status": "Matched friction measurement missing", "unmeasured_mu_stress_cases": [ 0.05, 0.1, 0.2, 0.3, 0.5 ], "sources": [ "scheuring", "palmer", "page2022", "blakely" ], "action": "Log each wrap angle and slip direction. Account for unequal tensions, wear, bending and frictional work. Match fibre, rope diameter, timber finish, pressure, moisture and speed. The \u03bc=0.1 numerical test case does not establish that a dry guide can achieve it, or that a particular oil will. Link each lubricant and coefficient to a matched measurement or a stated sensitivity case." }, { "id": "rope_clamp", "pair": "Rope / stone clamp or anchor", "condition": "Gripping surfaces treated independently of lubricated guides", "status": "Grip coefficient and clamp pressure unresolved", "sources": [ "scheuring" ], "action": "Calculate normal clamping force, contact area and holding margin from a tested static coefficient. Account for setting and releasing the clamp, and lubricant contamination." }, { "id": "human_footing", "pair": "Human feet / working surface", "condition": "Dry standing route separated from sliding surfaces", "status": "Worker boundary condition requires traction check", "sources": [ "ayrinhac" ], "action": "Cap force using body weight, vertical rope component and available traction as well as strength. 150 N/person remains an illustrative allocation, not a measured ancient capacity. Carrying and bracing also need reach and stance checks." } ], "calculations": { "mass_kg": 2995.2, "gravity_m_s2": 9.81, "ramp_angle_deg": 26.565051177077994, "scope": "Quasistatic sensitivity only. Equal total masses, ideal 2:1 rope system, no guide loss, carrier mass or acceleration. Return column is a loaded counterweight pulled directly along its incline.", "ramp": [ { "mu": 0.2, "downhill_available_n": 7884.262633067318, "worker_assistance_counterweight_end_n": 6807.193366932682, "loaded_return_n": 18396.612810490406 }, { "mu": 0.3, "downhill_available_n": 5256.175088711547, "worker_assistance_counterweight_end_n": 9435.280911288453, "loaded_return_n": 21024.700354846176 }, { "mu": 0.4, "downhill_available_n": 2628.0875443557734, "worker_assistance_counterweight_end_n": 12063.368455644228, "loaded_return_n": 23652.78789920195 }, { "mu": 0.5, "downhill_available_n": 1.6310792716467404e-12, "worker_assistance_counterweight_end_n": 14691.455999999998, "loaded_return_n": 26280.875443557725 }, { "mu": 0.6, "downhill_available_n": -2628.0875443557684, "worker_assistance_counterweight_end_n": 17319.54354435577, "loaded_return_n": 28908.96298791349 } ], "bare_sled_descent_static_threshold_mu": 0.5000000000000001, "roller_estimates": [ { "rolling_length_m": 0.0005, "approx_load_only_drag_n": 122.42880000000001 }, { "rolling_length_m": 0.001, "approx_load_only_drag_n": 244.85760000000002 }, { "rolling_length_m": 0.002, "approx_load_only_drag_n": 489.71520000000004 }, { "rolling_length_m": 0.005, "approx_load_only_drag_n": 1224.288 }, { "rolling_length_m": 0.006, "approx_load_only_drag_n": 1469.1456 }, { "rolling_length_m": 0.01, "approx_load_only_drag_n": 2448.576 } ], "roller_scope": "Ideal no-slip, equal top and bottom rolling-resistance lengths; F\u2248W*b/r. Omits roller own weight, deformation, edge impacts and bunching. These lengths have no matched empirical calibration.", "single_fixed_guide": [ { "mu": 0.05, "wrap_deg": 180, "tension_ratio": 1.1700887874964219 }, { "mu": 0.1, "wrap_deg": 180, "tension_ratio": 1.369107770624847 }, { "mu": 0.2, "wrap_deg": 180, "tension_ratio": 1.8744560875853382 }, { "mu": 0.3, "wrap_deg": 180, "tension_ratio": 2.566332395208135 }, { "mu": 0.5, "wrap_deg": 180, "tension_ratio": 4.810477380965351 } ] }, "lubrication": { "required_by_proposal": "Polish and lubricate stationary wooden rope guides.", "lubricant_identity": "Unspecified by Scheuring. Olive oil or animal fat would be explicit reconstruction choices requiring matched tests.", "animation": "Show carrying, applying and renewing lubricant, worker N labels, quantity and preparation work. Record wear and contamination. Wetting sand and oiling a guide are separate operations." }, "existing_runs": "Transport and first-foundation traces retain their original provisional friction. Their force labels are model outputs, not surface-calibrated predictions." }