Rear Gear-Box Core Dashboard
| ▼ Rear Gear-Box Core | ||||
| ☰ | \( F_{\text{rear, gearbox}} \) | Rear Gear-Box Core Vertical Load (N) | 196,808.949729 |
View Help GuidePurpose: Primary Axial Compression.
Logic: Calculates the massive total gravitational "crush" force acting specifically on this single main pillar.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$F_{\text{rear, gearbox}} = ( M_{\text{top, base}} \times N) \times X_{\text{rear, gearbox}}$$ Python Logic:
( v["Top Base Static Mass (kg)"] * v["Gravitational Field Strength (N/kg)"]) * v["Rear Gear-Box Gravity Share (%)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 47,783.1612 * 9.8066) * 0.4200 = 196,808.9497
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| ☰ | \( \tau_{\text{rear, gearbox}} \) | Rear Gear-Box Core Torque (Nm) | 1,226,652.398518 |
View Help GuidePurpose: Torsional Resolve.
Logic: Calculates the violent twisting force this core must anchor into the foundation to keep the whole machine perfectly aligned.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\tau_{\text{rear, gearbox}} = \tau_{\text{reaction}} \times \tau_{\text{rear, gearbox}}$$ Python Logic:
v["Reaction Torque (Nm)"] * v["Rear Gear-Box Core Torque Share (%)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 1,443,120.4688 * 0.8500 = 1,226,652.3985
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| ☰ | \( H_{\text{rear, gearbox}} \) | Rear Gear-Box Core Pillar Height (m) | 10 |
View Help GuidePurpose: Vertical Alignment Datum.
Logic: Establishes the exact vertical run from the concrete floor up to the underside of the Top Base bridge.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$H_{\text{rear, gearbox}} = \Sigma H_{\text{arc}}$$ Python Logic:
v["Arc Total Wall Height (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 10.0000 = 10.0000
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| ☰ | \( A_{\text{rear, gearbox}} \) | Rear Gear-Box Core Available Footprint Width (m) | 0.881653 |
View Help GuidePurpose: Lateral Space Constraint.
Logic: Defines the absolute maximum physical width allowed for the base of the pillar within the facility floor plan.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$A_{\text{rear, gearbox}} = W_{\text{int, spine}}$$ Python Logic:
v["Internal Spine Wall Predicted Min. Width (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.8817 = 0.8817
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| ☰ | \( L_{\text{rear, gearbox}} \) | Rear Gear-Box Core Length Benefit (%) |
View Help GuidePurpose: Longitudinal Efficiency.
Logic: Applies a scaling factor to account for the pillar's extended structural reach along the track axis, giving it extra leverage.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input Python Logic:
N/ALive Evaluation: N/A (Input Variable)
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| ☰ | \( L_{\text{rear, gearbox}} \) | Rear Gear-Box Core Pillar Length (m) | 3.119437 |
View Help GuidePurpose: Longitudinal Load Distribution.
Logic: Defines the front-to-back depth of the pillar, ensuring it has a wide enough footprint to absolutely prevent tipping.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$L_{\text{rear, gearbox}} = L_{\text{gantry}} \times ( 1 + L_{\text{rear, gearbox}} )$$ Python Logic:
v["Gantry Wall Length (m)"] * ( 1 + v["Rear Gear-Box Core Length Benefit (%)"] )Live Evaluation: [ROUTE: STATIC/GLOBAL] 2.7852 * ( 1 + 0.1200 ) = 3.1194
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| ☰ | \( I_{\text{rear, gearbox}} \) | Rear Gear-Box Core Required Inertia (I) | 2.370343 |
View Help GuidePurpose: Minimum Geometric Stiffness.
Logic: Calculates the required mathematical stiffness score to keep this tower from flexing beyond our ultra-tight precision limits.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$I_{\text{rear, gearbox}} = (\tau_{\text{rear, gearbox}} \times H_{\text{pillars, pillar}}^2) / (3 \times ( \text{Fossil Carbon Fibre Modulus (GPa)} \times 10^9 ) \times ( \Delta_{\text{max, allowable}}))$$ Python Logic:
(v["Rear Gear-Box Core Torque (Nm)"] * v["Pillars Pillar Height (m)"]^2) / (3 * ( v["Fossil Carbon Fibre Modulus (GPa)"] * 10^9 ) * ( v["Max Allowable Deflection (m)"]))Live Evaluation: [ROUTE: STATIC/GLOBAL] (1,226,652.3985 * 10.0000**2) / (3 * ( 230.0000 * 10**9 ) * ( 0.0001)) = 2.3703
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| ☰ | \( W_{\text{rear, gearbox}} \) | Rear Gear-Box Core Required Border Thickness (m) | 0.162925 |
View Help GuidePurpose: Shear Flow Efficiency.
Logic: Determines the razor-thin minimum thickness required for the outer carbon fiber shell to successfully absorb twisting loads.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$W_{\text{rear, gearbox}} = I_{\text{rear, gearbox}} / (6 \times L_{\text{rear, gearbox}} \times A_{\text{rear, gearbox}}^2)$$ Python Logic:
v["Rear Gear-Box Core Required Inertia (I)"] / (6 * v["Rear Gear-Box Core Pillar Length (m)"] * v["Rear Gear-Box Core Available Footprint Width (m)"]^2)Live Evaluation: [ROUTE: STATIC/GLOBAL] 2.3703 / (6 * 3.1194 * 0.8817**2) = 0.1629
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| ☰ | \( X_{\text{rear, gearbox}} \) | Rear Gear-Box Core SPS Block Selection (m) | 0.2 |
View Help GuidePurpose: Modular Production Alignment.
Logic: Matches that theoretical razor-thin requirement to a standard, manufacturable, and physically thicker block size.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{rear, gearbox}} = ROUNDUP ( W_{\text{rear, gearbox}} , 1 )$$ Python Logic:
ROUNDUP ( v["Rear Gear-Box Core Required Border Thickness (m)"] , 1 )Live Evaluation: [ROUTE: STATIC/GLOBAL] ROUNDUP ( 0.1629 , 1 ) = 0.2000
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| ☰ | \( X_{\text{rear, gearbox}} \) | Rear Gear-Box Core Final Module Skin (m) | 0.024463 |
View Help GuidePurpose: Solid Material Specification.
Logic: Defines exactly how thick the solid carbon fiber skin needs to be inside the hollowed-out block to maintain track precision.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{rear, gearbox}} = (W_{\text{rear, gearbox}} / 6.66)$$ Python Logic:
(v["Rear Gear-Box Core Required Border Thickness (m)"] / 6.66)Live Evaluation: [ROUTE: STATIC/GLOBAL] (0.1629 / 6.66) = 0.0245
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| ☰ | \( X_{\text{rear, gearbox}} \) | Rear Gear-Box Core Module Solidity (%) | 0.244632 |
View Help GuidePurpose: Internal Density Balance.
Logic: Calculates the exact ratio of solid material to empty air inside the block, optimizing the balance between structural integrity and weight savings.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{rear, gearbox}} = (X_{\text{rear, gearbox}} \times 2) / X_{\text{rear, gearbox}}$$ Python Logic:
(v["Rear Gear-Box Core Final Module Skin (m)"] * 2) / v["Rear Gear-Box Core SPS Block Selection (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] (0.0245 * 2) / 0.2000 = 0.2446
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| ☰ | \( A_{\text{rear, gearbox}} \) | Rear Gear-Box Core Footprint Area (m2) | 2.750262 |
View Help GuidePurpose: Ground Interface Area.
Logic: The total square meters of facility floor space physically occupied by the base of the pillar.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$A_{\text{rear, gearbox}} = L_{\text{rear, gearbox}} \times A_{\text{rear, gearbox}}$$ Python Logic:
v["Rear Gear-Box Core Pillar Length (m)"] * v["Rear Gear-Box Core Available Footprint Width (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 3.1194 * 0.8817 = 2.7503
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| ☰ | \( L_{\text{rear, gearbox}} \) | Rear Gear-Box Core Internal Void Length (m) | 2.719437 |
View Help GuidePurpose: Mass Reduction Strategy.
Logic: Determines the physical length of the empty hollow chamber inside the pillar, turning it into an ultra-strong "Box Girder."
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$L_{\text{rear, gearbox}} = L_{\text{rear, gearbox}} - (X_{\text{rear, gearbox}} \times 2)$$ Python Logic:
v["Rear Gear-Box Core Pillar Length (m)"] - (v["Rear Gear-Box Core SPS Block Selection (m)"] * 2)Live Evaluation: [ROUTE: STATIC/GLOBAL] 3.1194 - (0.2000 * 2) = 2.7194
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| ☰ | \( W_{\text{rear, gearbox}} \) | Rear Gear-Box Core Internal Void Width (m) | 0.481653 |
View Help GuidePurpose: Mass Reduction Strategy.
Logic: Determines the physical width of the empty hollow chamber.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$W_{\text{rear, gearbox}} = A_{\text{rear, gearbox}} - (X_{\text{rear, gearbox}} \times 2)$$ Python Logic:
v["Rear Gear-Box Core Available Footprint Width (m)"] - (v["Rear Gear-Box Core SPS Block Selection (m)"] * 2)Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.8817 - (0.2000 * 2) = 0.4817
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| ☰ | \( A_{\text{rear, gearbox}} \) | Rear Gear-Box Core Void Area (m2) | 1.309826 |
View Help GuidePurpose: Material Displacement Calculation.
Logic: Calculates the total square area of the empty hollow center to verify our overall material reduction and cost savings.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$A_{\text{rear, gearbox}} = L_{\text{rear, gearbox}} \times W_{\text{rear, gearbox}}$$ Python Logic:
v["Rear Gear-Box Core Internal Void Length (m)"] * v["Rear Gear-Box Core Internal Void Width (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 2.7194 * 0.4817 = 1.3098
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| ☰ | \( X_{\text{rear, gearbox}} \) | Rear Gear-Box Core Wall Fill Factor (%) | 0.523745 |
View Help GuidePurpose: Sectional Efficiency Metric.
Logic: Measures what percentage of the physical footprint is actually made of solid, load-bearing carbon fiber shell versus empty air.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{rear, gearbox}} = (A_{\text{rear, gearbox}} - A_{\text{rear, gearbox}}) / A_{\text{rear, gearbox}}$$ Python Logic:
(v["Rear Gear-Box Core Footprint Area (m2)"] - v["Rear Gear-Box Core Void Area (m2)"]) / v["Rear Gear-Box Core Footprint Area (m2)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] (2.7503 - 1.3098) / 2.7503 = 0.5237
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| ☰ | \( \Sigma V_{\text{rear, gearbox}} \) | Rear Gear-Box Core Total Volume (m3) | 3.523771 |
View Help GuidePurpose: Determines the total physical volume of the primary core structure within the rear gear-box assembly.
Logic: Calculates the aggregated cubic displacement of the rear gear-box core to establish its spatial footprint and provide the volumetric baseline required for subsequent mass and inertia calculations.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma V_{\text{rear, gearbox}} = A_{\text{rear, gearbox}} \times H_{\text{rear, gearbox}} \times X_{\text{rear, gearbox}} \times X_{\text{rear, gearbox}}$$ Python Logic:
v["Rear Gear-Box Core Footprint Area (m2)"] * v["Rear Gear-Box Core Pillar Height (m)"] * v["Rear Gear-Box Core Wall Fill Factor (%)"] * v["Rear Gear-Box Core Module Solidity (%)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 2.7503 * 10.0000 * 0.5237 * 0.2446 = 3.5238
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| ☰ | \( \Sigma M_{\text{rear, gearbox}} \) | Rear Gear-Box Core Total Wall Mass (kg) | 6,342.787281 |
View Help GuidePurpose: Assembly Logistics.
Logic: The definitive final weight of the completed tower. This is the exact number used to plan crane lifts and logistics.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma M_{\text{rear, gearbox}} = (A_{\text{rear, gearbox}} \times H_{\text{rear, gearbox}} \times \text{Fossil Carbon Fibre Density (kg.m3)} ) \times X_{\text{rear, gearbox}} \times X_{\text{rear, gearbox}}$$ Python Logic:
(v["Rear Gear-Box Core Footprint Area (m2)"] * v["Rear Gear-Box Core Pillar Height (m)"] * v["Fossil Carbon Fibre Density (kg.m3)"] ) * v["Rear Gear-Box Core Wall Fill Factor (%)"] * v["Rear Gear-Box Core Module Solidity (%)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] (2.7503 * 10.0000 * 1,800.0000 ) * 0.5237 * 0.2446 = 6,342.7873
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| ▼ Rear Gear-Box Safety Audit | ||||
| ☰ | \( F_{\text{rear, gearbox}} \) | Rear Gear-Box Core Effective Load Area (m2) | 0.352377 |
View Help GuidePurpose: Net Stress Plane.
Logic: After accounting for all the hollowed-out empty space, this calculates the actual remaining square meters of solid carbon fiber carrying the vertical load.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$F_{\text{rear, gearbox}} = A_{\text{rear, gearbox}} \times X_{\text{rear, gearbox}} \times X_{\text{rear, gearbox}}$$ Python Logic:
v["Rear Gear-Box Core Footprint Area (m2)"] * v["Rear Gear-Box Core Wall Fill Factor (%)"] * v["Rear Gear-Box Core Module Solidity (%)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 2.7503 * 0.5237 * 0.2446 = 0.3524
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| ☰ | \( \sigma_{\text{rear, gearbox}} \) | Rear Gear-Box Core Applied Axial Stress (MPa) | 0.558518 |
View Help GuidePurpose: Compressive Pressure.
Logic: Measures the intense downward crushing pressure on the remaining carbon fiber walls from the weight of the machine.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\sigma_{\text{rear, gearbox}} = (F_{\text{rear, gearbox}} / F_{\text{rear, gearbox}}) / 10^6$$ Python Logic:
(v["Rear Gear-Box Core Vertical Load (N)"] / v["Rear Gear-Box Core Effective Load Area (m2)"]) / 10^6Live Evaluation: [ROUTE: STATIC/GLOBAL] (196,808.9497 / 0.3524) / 10**6 = 0.5585
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| ☰ | \( \sigma_{\text{rear, gearbox}} \) | Rear Gear-Box Core Applied Shear Stress (MPa) | 1.368767 |
View Help GuidePurpose: Torsional Skin Stress.
Logic: Measures the "sliding" and "tearing" stress generated in the outer skin as the tower desperately fights the twisting torque.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\sigma_{\text{rear, gearbox}} = (\tau_{\text{rear, gearbox}} / (2 \times A_{\text{rear, gearbox}} \times W_{\text{rear, gearbox}})) / 10^6$$ Python Logic:
(v["Rear Gear-Box Core Torque (Nm)"] / (2 * v["Rear Gear-Box Core Footprint Area (m2)"] * v["Rear Gear-Box Core Required Border Thickness (m)"])) / 10^6Live Evaluation: [ROUTE: STATIC/GLOBAL] (1,226,652.3985 / (2 * 2.7503 * 0.1629)) / 10**6 = 1.3688
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| ☰ | \( \sigma_{\text{rear, gearbox}} \) | Rear Gear-Box Core Combined Von Mises Stress (MPa) | 2.435675 |
View Help GuidePurpose: Universal Failure Analysis.
Logic: The "Global Truth." This advanced engineering formula combines the downward crush and the twisting tear into a single, ultimate stress score.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\sigma_{\text{rear, gearbox}} = \sqrt{\sigma_{\text{rear, gearbox}}^2 + 3 \times \sigma_{\text{rear, gearbox}}^2)$$ Python Logic:
SQRT(v["Rear Gear-Box Core Applied Axial Stress (MPa)"]^2 + 3 * v["Rear Gear-Box Core Applied Shear Stress (MPa)"]^2)Live Evaluation: [ROUTE: STATIC/GLOBAL] SQRT(0.5585**2 + 3 * 1.3688**2) = 2.4357
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| ☰ | \( SF_{\text{rear, gearbox}} \) | Rear Gear-Box Core Structural Safety Factor | 245.517175 |
View Help GuidePurpose: Global Safety Buffer.
Logic: The ratio proving that the material's strength vastly exceeds the worst-case combined load state.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$SF_{\text{rear, gearbox}} = \text{Fossil Carbon Fibre Material Yield Strength (MPa)} / \sigma_{\text{rear, gearbox}}$$ Python Logic:
v["Fossil Carbon Fibre Material Yield Strength (MPa)"] / v["Rear Gear-Box Core Combined Von Mises Stress (MPa)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 598.0000 / 2.4357 = 245.5172
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| ☰ | \( X_{\text{rear, gearbox}} \) | Rear Gear-Box Core Safety Blueprint Validation | ULTRA-SAFE |
View Help GuidePurpose: Technical Validation.
Logic: 1 if v["Rear Gear-Box Core Structural Safety Factor"] > v["Safety Factor Slider"] else 0
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{rear, gearbox}} = IF(SF_{\text{rear, gearbox}} > SF_{\text{safety, factor}}, 1, 0)$$ Python Logic:
1 if v["Rear Gear-Box Core Structural Safety Factor"] > v["Safety Factor Slider"] else 0Live Evaluation: [ROUTE: STATIC/GLOBAL] 1 if 245.5172 > 2.5000 else 0 = 1.0000
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