Support Layer Dashboard
| ▼ Support Layer Synthesis (The Hollow Risers) | ||||
| ☰ | \( \Sigma X_{\text{support, gap}} \) | Total Support Gap (m) | 0.376437 |
View Help GuidePurpose: Vertical Envelope.
Logic: Defines the total remaining vertical space available for the support layers within the housing stack.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma X_{\text{support, gap}} = \Sigma H_{\text{layer}} - ( H_{\text{top, cover}} + H_{\text{bottom, cover}} + H_{\text{runner, profile}} )$$ Python Logic:
v["Total Layer Height (m)"] - ( v["Top Cover Height (m)"] + v["Bottom Cover Height (m)"] + v["Runner Profile Height (m)"] )Live Evaluation: [ROUTE: STATIC/GLOBAL] 1.2383 - ( 0.3591 + 0.3591 + 0.1436 ) = 0.3764
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| ☰ | \( H_{\text{individual, support}} \) | Support Layer Individual Support Height (m) | 0.188219 |
View Help GuidePurpose: Sectional Depth.
Logic: The vertical dimension of each individual hollow riser (Top and Bottom) within the module.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$H_{\text{individual, support}} = \Sigma X_{\text{support, gap}} / 2$$ Python Logic:
v["Total Support Gap (m)"] / 2Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.3764 / 2 = 0.1882
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| ☰ | \( W_{\text{support, profile}} \) | Support Layer Profile Width (m) | 0.178957 |
View Help GuidePurpose: Load Path Alignment.
Logic: Matches the riser width to the inner skeleton rails to ensure a perfectly direct, linear compression load path.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$W_{\text{support, profile}} = W_{\text{prescribed, rail}}$$ Python Logic:
v["Prescribed Rail Width (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.1790 = 0.1790
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| ☰ | \( A_{\text{req, support}} \) | Support Layer Required Support Area (m2) | 0.013753 |
View Help GuidePurpose: Stiffness Transfer.
Logic: Inherits the exact cross-sectional material demand required to successfully maintain the specified deflection limit.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$A_{\text{req, support}} = A_{\text{req, runner}}$$ Python Logic:
v["Required Runner Area (m2)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0138 = 0.0138
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| ☰ | \( X_{\text{synthesized, support}} \) | Support Layer Synthesized Support Wall (m) | 0.020649 |
View Help GuidePurpose: The Blueprint.
Logic: The mathematically calculated wall thickness of the hollow carbon fiber riser required to meet structural area demands.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{synthesized, support}} = ( W_{\text{support, profile}} / 2 ) \times ( 1 - SQRT ( MAX ( 0, 1 - ( A_{\text{req, support}} / ( H_{\text{individual, support}} \times W_{\text{support, profile}} ) ) ) ) )$$ Python Logic:
( v["Support Layer Profile Width (m)"] / 2 ) * ( 1 - SQRT ( MAX ( 0, 1 - ( v["Support Layer Required Support Area (m2)"] / ( v["Support Layer Individual Support Height (m)"] * v["Support Layer Profile Width (m)"] ) ) ) ) )Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 0.1790 / 2 ) * ( 1 - SQRT ( MAX ( 0, 1 - ( 0.0138 / ( 0.1882 * 0.1790 ) ) ) ) ) = 0.0206
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| ☰ | \( X_{\text{support, layer}} \) | Support Layer Infill (%) | 0.408294 |
View Help GuidePurpose: Material Efficiency.
Logic: Represents the ratio of solid composite material versus hollow empty space within the riser profile.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{support, layer}} = A_{\text{req, support}} / ( H_{\text{individual, support}} \times W_{\text{support, profile}} )$$ Python Logic:
v["Support Layer Required Support Area (m2)"] / ( v["Support Layer Individual Support Height (m)"] * v["Support Layer Profile Width (m)"] )Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0138 / ( 0.1882 * 0.1790 ) = 0.4083
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| ☰ | \( M_{\text{modular, supports}} \) | Support Layer Modular Weight (kg) | 49.509249 |
View Help GuidePurpose: Unit Mass.
Logic: The combined dry weight of both top and bottom hollow support risers for a single one-meter module.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$M_{\text{modular, supports}} = A_{\text{req, support}} \times 2 \times L_{\text{cover}} \times \text{Fossil Carbon Fibre Density (kg.m3)}$$ Python Logic:
v["Support Layer Required Support Area (m2)"] * 2 * v["Cover Module Length (m)"] * v["Fossil Carbon Fibre Density (kg.m3)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0138 * 2 * 1.0000 * 1,800.0000 = 49.5092
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| ☰ | \( \Sigma L_{\text{run}} \) | Support Layer Total Run Length (m) | 19.6 |
View Help GuidePurpose: System Span.
Logic: The total cumulative length of the track used for global mass modeling.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma L_{\text{run}} = L_{\text{run}}$$ Python Logic:
v["Track full run length (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 19.6000 = 19.6000
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| ☰ | \( X_{\text{modules}} \) | Support Layer Modules | 20 |
View Help GuidePurpose: Component Multiplier.
Logic: The total number of one-meter segments required to complete the full track run.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{modules}} = ROUNDUP ( \Sigma L_{\text{run}} / L_{\text{cover}}, 0 )$$ Python Logic:
ROUNDUP ( v["Support Layer Total Run Length (m)"] / v["Cover Module Length (m)"], 0 )Live Evaluation: [ROUTE: STATIC/GLOBAL] ROUNDUP ( 19.6000 / 1.0000, 0 ) = 20.0000
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| ☰ | \( \Sigma V_{\text{support, layer}} \) | Support Layer Total Volume (m3) | 0.550103 |
View Help GuidePurpose: Support Layer Total Volume
Logic: Support Layer Total Volume for material sizing
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma V_{\text{support, layer}} = A_{\text{req, support}} \times 2 \times L_{\text{cover}} \times X_{\text{modules}}$$ Python Logic:
v["Support Layer Required Support Area (m2)"] * 2 * v["Cover Module Length (m)"] * v["Support Layer Modules"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0138 * 2 * 1.0000 * 20.0000 = 0.5501
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| ☰ | \( \Sigma M_{\text{support, layers}} \) | Support Layers Total Mass (kg) | 990.184982 |
View Help GuidePurpose: Cumulative Riser Mass.
Logic: The huge total weight of all support risers across the full operational run length of the system.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma M_{\text{support, layers}} = \text{Support Layer Total Volume (m3)} \times D_{\text{FCF}}$$ Python Logic:
v["Support Layer Total Volume (m3)"] * v["Fossil Carbon Fibre Density (kg.m3)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.5501 * 1,800.0000 = 990.1850
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| ▼ Support Layer Safety & Buckling Audit | ||||
| ☰ | \( I_{\text{hollow, inertia}} \) | Support Layer Hollow Moment of Inertia (I) | 0.000063 |
View Help GuidePurpose: Geometric Stiffness.
Logic: Quantifies the specific structural resistance of the hollow rectangular profile against buckling or bowing laterally.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$I_{\text{hollow, inertia}} = ( ( W_{\text{support, profile}} \times ( H_{\text{individual, support}} ^ 3) ) / 12 ) - ( ( ( W_{\text{support, profile}} - ( 2 \times X_{\text{synthesized, support}} ) ) \times ( ( H_{\text{individual, support}} - ( 2 \times X_{\text{synthesized, support}} ) ) ^ 3 ) ) / 12 )$$ Python Logic:
( ( v["Support Layer Profile Width (m)"]* ( v["Support Layer Individual Support Height (m)"] ^ 3) ) / 12 ) - ( ( ( v["Support Layer Profile Width (m)"] - ( 2 * v["Support Layer Synthesized Support Wall (m)"] ) ) * ( ( v["Support Layer Individual Support Height (m)"] - ( 2 * v["Support Layer Synthesized Support Wall (m)"] ) ) ^ 3 ) ) / 12 )Live Evaluation: [ROUTE: STATIC/GLOBAL] ( ( 0.1790* ( 0.1882 ** 3) ) / 12 ) - ( ( ( 0.1790 - ( 2 * 0.0206 ) ) * ( ( 0.1882 - ( 2 * 0.0206 ) ) ** 3 ) ) / 12 ) = 0.0001
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| ☰ | \( F_{\text{critical, buckling}} \) | Support Layer Critical Buckling Load (N) | 4,040,619,033.237661 |
View Help GuidePurpose: Stability Limit.
Logic: The theoretical peak force required to cause the hollow riser walls to undergo sudden geometric failure (Euler buckling).
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$F_{\text{critical, buckling}} = ( \pi^2 \times ( \text{Fossil Carbon Fibre Modulus (GPa)} \times 10^9 ) \times I_{\text{hollow, inertia}}) / ( H_{\text{individual, support}} ^ 2 )$$ Python Logic:
( PI()^2 * ( v["Fossil Carbon Fibre Modulus (GPa)"] * 10^9 ) * v["Support Layer Hollow Moment of Inertia (I)"]) / ( v["Support Layer Individual Support Height (m)"] ^ 2 )Live Evaluation: [ROUTE: STATIC/GLOBAL] ( PI()**2 * ( 230.0000 * 10**9 ) * 0.0001) / ( 0.1882 ** 2 ) = 4,040,619,033.2377
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| ☰ | \( SF_{\text{buckling, safety}} \) | Support Layer Buckling Safety Factor | 17,032.365512 |
View Help GuidePurpose: Stability Margin.
Logic: Evaluates the ratio between the calculated buckling resistance and the actual applied operational load to ensure absolute structural headroom.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$SF_{\text{buckling, safety}} = F_{\text{critical, buckling}} / F_{\text{net, structural}}$$ Python Logic:
v["Support Layer Critical Buckling Load (N)"] / v["Net Structural Load (N)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 4,040,619,033.2377 / 237,231.8179 = 17,032.3655
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| ☰ | \( X_{\text{support, layer}} \) | Support Layer Safety & Buckling Blueprint Validation | ULTRA-SAFE |
View Help GuidePurpose: Status Validation.
Logic: Automated confirmation that the newly hollowed support geometry safely meets stability requirements for high-precision operation.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{support, layer}} = IF ( SF_{\text{buckling, safety}} > SF_{\text{safety, factor}} , 1 , 0 )$$ Python Logic:
IF ( v["Support Layer Buckling Safety Factor"] > v["Safety Factor Slider"] , 1 , 0 )Live Evaluation: [ROUTE: STATIC/GLOBAL] IF ( 17,032.3655 > 2.5000 , 1 , 0 ) = 1.0000
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| ▼ Support Layer Safety Audit | ||||
| ☰ | \( X_{\text{contact, pressure}} \) | Support Layer Contact Pressure (MPa) | 17.25 |
View Help GuidePurpose: Internal Material Stress.
Logic: Measures the compressive pressure aggressively exerted on the carbon fiber riser walls at the structural interface.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{contact, pressure}} = ( F_{\text{net, structural}} / A_{\text{req, support}} ) / 1000000$$ Python Logic:
( v["Net Structural Load (N)"] / v["Support Layer Required Support Area (m2)"] ) / 1000000Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 237,231.8179 / 0.0138 ) / 1000000 = 17.2500
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| ☰ | \( SF_{\text{structural, safety}} \) | Support Layer Structural Safety Factor | 34.666667 |
View Help GuidePurpose: Material Safety Margin.
Logic: Evaluates the final headroom between the material’s raw physical capacity and the applied operational pressure.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$SF_{\text{structural, safety}} = \text{Fossil Carbon Fibre Material Yield Strength (MPa)} / X_{\text{contact, pressure}}$$ Python Logic:
v["Fossil Carbon Fibre Material Yield Strength (MPa)"] / v["Support Layer Contact Pressure (MPa)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 598.0000 / 17.2500 = 34.6667
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| ☰ | \( X_{\text{support, layer}} \) | Support Layer Safety Blueprint Validation | ULTRA-SAFE |
View Help GuidePurpose: Status Validation.
Logic: Automated confirmation that the support wall thickness is sufficient to prevent long-term fatigue or material crushing.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{support, layer}} = IF ( SF_{\text{structural, safety}} > SF_{\text{safety, factor}} , 1 , 0 )$$ Python Logic:
IF ( v["Support Layer Structural Safety Factor"] > v["Safety Factor Slider"] , 1 , 0 )Live Evaluation: [ROUTE: STATIC/GLOBAL] IF ( 34.6667 > 2.5000 , 1 , 0 ) = 1.0000
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