88 lines
2.4 KiB
JSON
88 lines
2.4 KiB
JSON
{
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"tool": "hampton-root-cellar-calculator",
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"version": "1.0.0",
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"author": "Cathy Mcmasters",
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"location": "Hampton, Virginia",
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"date": "2026-07-17",
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"model": {
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"description": "Fourier's Law of Heat Conduction adapted for subterranean thermal equilibrium in clay-loam substrates",
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"equation": "d_min = α × (T_ambient_min − T_target)",
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"variables": {
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"d_min": {
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"description": "minimum burial depth",
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"unit": "meters"
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},
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"α": {
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"description": "thermal resistance coefficient for saturated Hampton clay-loam",
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"value": 0.15,
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"unit": "m/K",
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"source": "USDA Soil Survey Manual Ch.6; de Vries (1963)"
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},
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"T_ambient_min": {
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"description": "lowest expected external temperature",
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"unit": "Kelvin",
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"conversion_from_F": "(F - 32) × 5/9 + 273.15"
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},
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"T_target": {
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"description": "desired internal temperature",
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"unit": "Kelvin",
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"default_F": 36
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}
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}
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},
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"material_properties": {
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"hampton_clay_loam": {
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"thermal_conductivity": {
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"value": 1.4,
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"unit": "W/(m·K)",
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"wikidata": "Q487005"
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},
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"moisture_content": "field saturation (winter)",
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"density": {
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"value": 1.6,
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"unit": "g/cm³"
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}
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},
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"alternative_substrates": {
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"sand": {
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"thermal_conductivity_range": [0.3, 0.5],
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"unit": "W/(m·K)"
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},
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"pure_clay": {
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"thermal_conductivity_range": [1.5, 2.0],
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"unit": "W/(m·K)"
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}
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}
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},
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"operational_parameters": {
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"default_target_temp_F": 36,
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"default_safety_margin_percent": 15,
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"historical_hampton_min_F": -15,
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"record_hampton_low_F": -15
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},
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"work_example": {
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"scenario": "Hampton, VA. Historical minimum: -15°F. Target: 36°F.",
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"steps": [
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"ΔT = (-15°F − 36°F) = -51°F = -28.33 K",
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"d_min = 0.15 m/K × 28.33 K = 4.25 meters",
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"Converted: 4.25 m = 13.94 feet",
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"Safety margin (15%): 16.03 feet"
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],
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"result_ft": 16.03
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},
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"assumptions": [
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"Hampton clay-loam at field saturation (winter conditions)",
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"Steady-state thermal equilibrium (long-duration cold snap)",
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"No active heating or cooling systems",
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"Structural integrity maintained by timber or reinforced brick"
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],
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"license": "CC0",
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"machine_readable": true
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}
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