Runner Dashboard
| ▼ Track Module Load Scaling | ||||
| ☰ | \( L \) | Runner Module Length (m) |
View Help GuidePurpose: Modular Basis.
Logic: Defines the longitudinal footprint of a single structural block for manufacturing and logistics scaling.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input Python Logic:
N/ALive Evaluation: N/A (Input Variable)
|
|
| ☰ | \( F_{\text{active, load}} \) | Active Load per Module (N) | 338,902.596965 |
View Help GuidePurpose: Local Load.
Logic: Resolves the total outward kinetic pressure into the specific force acting upon a single modular section.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$F_{\text{active, load}} = F_{\text{gross, centrifugal}} / ( \Sigma L_{\text{train}} / L )$$ Python Logic:
v["Gross Centrifugal Force (N)"] / ( v["Total Train Length (m)"] / v["Runner Module Length (m)"] )Live Evaluation: [ROUTE: STATIC/GLOBAL] 1,970,809.0362 / ( 5.8153 / 1.0000 ) = 338,902.5970
|
| ☰ | \( X_{\text{mag, support}} \) | Magnetic Support Offset (%) |
View Help GuidePurpose: Pre-Stress Assistance.
Logic: Defines the percentage of centripetal load neutralized by external magnetic bracing before it even hits the carbon fiber track.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input Python Logic:
N/ALive Evaluation: N/A (Input Variable)
|
|
| ☰ | \( F_{\text{net, structural}} \) | Net Structural Load (N) | 237,231.817876 |
View Help GuidePurpose: Resultant Operational Stress.
Logic: The final resultant force that the carbon fiber runner must actually resist to maintain operational precision.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$F_{\text{net, structural}} = F_{\text{active, load}} \times ( 1 - X_{\text{mag, support}} )$$ Python Logic:
v["Active Load per Module (N)"] * ( 1 - v["Magnetic Support Offset (%)"] )Live Evaluation: [ROUTE: STATIC/GLOBAL] 338,902.5970 * ( 1 - 0.3000 ) = 237,231.8179
|
| ▼ Prescriptive Runner Design (The Wheel Guide) | ||||
| ☰ | \( A_{\text{req, runner}} \) | Required Runner Area (m2) | 0.013753 |
View Help GuidePurpose: Stiffness Demand.
Logic: The cross-sectional solid carbon fiber area required per module to suppress deflection and stay perfectly within the precision limit.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$A_{\text{req, runner}} = ( F_{\text{net, structural}} \times L ) / ( ( \text{Fossil Carbon Fibre Modulus (GPa)} \times 10^9 ) \times \Delta_{\text{max, allowable}} )$$ Python Logic:
( v["Net Structural Load (N)"] * v["Runner Module Length (m)"] ) / ( ( v["Fossil Carbon Fibre Modulus (GPa)"] * 10^9 ) * v["Max Allowable Deflection (m)"] )Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 237,231.8179 * 1.0000 ) / ( ( 230.0000 * 10**9 ) * 0.0001 ) = 0.0138
|
| ☰ | \( \eta_{\text{runner, aspect}} \) | Runner Aspect Ratio (h:w) |
View Help GuidePurpose: Profile Strategy.
Logic: Defines the vertical-to-horizontal ratio of the guide rail to perfectly optimize it for bending resistance.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input Python Logic:
N/ALive Evaluation: N/A (Input Variable)
|
|
| ☰ | \( H_{\text{predicted, runner}} \) | Predicted Runner Height (m) | 0.143627 |
View Help GuidePurpose: Architectural Output.
Logic: The calculated vertical depth of the wheel guide path strictly required for structural rigidity.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$H_{\text{predicted, runner}} = SQRT ( A_{\text{req, runner}} \times \eta_{\text{runner, aspect}} )$$ Python Logic:
SQRT ( v["Required Runner Area (m2)"] * v["Runner Aspect Ratio (h:w)"] )Live Evaluation: [ROUTE: STATIC/GLOBAL] SQRT ( 0.0138 * 1.5000 ) = 0.1436
|
| ☰ | \( W_{\text{predicted, runner}} \) | Predicted Magnetic Runner Width (m) | 0.095752 |
View Help GuidePurpose: Architectural Output.
Logic: The calculated horizontal width of the guide path required to fully support the enabler wheel footprint.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$W_{\text{predicted, runner}} = H_{\text{predicted, runner}} / \eta_{\text{runner, aspect}}$$ Python Logic:
v["Predicted Runner Height (m)"] / v["Runner Aspect Ratio (h:w)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.1436 / 1.5000 = 0.0958
|
| ☰ | \( M_{\text{modular, runner}} \) | Modular Weight: Runner (kg) | 24.754625 |
View Help GuidePurpose: Unit Mass.
Logic: The dry weight of the solid wheel-guide runner for a single one-meter module.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$M_{\text{modular, runner}} = A_{\text{req, runner}} \times L \times \text{Fossil Carbon Fibre Density (kg.m3)}$$ Python Logic:
v["Required Runner Area (m2)"] * v["Runner Module Length (m)"] * v["Fossil Carbon Fibre Density (kg.m3)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0138 * 1.0000 * 1,800.0000 = 24.7546
|
| ☰ | \( \Sigma L_{\text{run}} \) | Total Run Length (m) | 19.6 |
View Help GuidePurpose: System Span.
Logic: The total cumulative length of the guide track 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
|
| ☰ | \( X_{\text{modules}} \) | Runner Modules | 19.6 |
View Help GuidePurpose: Component Multiplier.
Logic: The total number of one-meter segments required to piece together and complete the full track run.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{modules}} = \Sigma L_{\text{run}} / L$$ Python Logic:
v["Total Run Length (m)"] / v["Runner Module Length (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 19.6000 / 1.0000 = 19.6000
|
| ☰ | \( \Sigma V_{\text{runner}} \) | Runner Total Volume (m3) | 0.26955 |
View Help GuidePurpose: Runner Total Volume
Logic: Runner Total Volume for material sizing
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma V_{\text{runner}} = A_{\text{req, runner}} \times L \times X_{\text{modules}}$$ Python Logic:
v["Required Runner Area (m2)"] * v["Runner Module Length (m)"] * v["Runner Modules"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0138 * 1.0000 * 19.6000 = 0.2696
|
| ☰ | \( \Sigma M_{\text{runner}} \) | Runner Total Mass (kg) | 485.190641 |
View Help GuidePurpose: Cumulative Track Mass.
Logic: The massive total weight of the primary carbon fiber wheel-guides for the entire system.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma M_{\text{runner}} = \text{Runner Total Volume (m3)} \times D_{\text{FCF}}$$ Python Logic:
v["Runner Total Volume (m3)"] * v["Fossil Carbon Fibre Density (kg.m3)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.2696 * 1,800.0000 = 485.1906
|
| ▼ Running Track Safety Audit | ||||
| ☰ | \( X_{\text{contact, pressure}} \) | Running Track Contact Pressure (MPa) | 17.25 |
View Help GuidePurpose: Surface Stress.
Logic: Measures the extreme pressure directly at the tiny contact interface between the enabler wheel and the carbon fiber track.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{contact, pressure}} = ( F_{\text{net, structural}} / A_{\text{req, runner}} ) / 1000000$$ Python Logic:
( v["Net Structural Load (N)"] / v["Required Runner Area (m2)"] ) / 1000000Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 237,231.8179 / 0.0138 ) / 1000000 = 17.2500
|
| ☰ | \( SF_{\text{compressive, safety}} \) | Running Track Compressive Safety Factor | 69.565218 |
View Help GuidePurpose: Crush Margin.
Logic: Evaluates the headroom before the material surface experiences permanent indentation or crushing.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$SF_{\text{compressive, safety}} = \text{Fossil Carbon Fibre Compressive Limit (MPa)} / X_{\text{contact, pressure}}$$ Python Logic:
v["Fossil Carbon Fibre Compressive Limit (MPa)"] / v["Running Track Contact Pressure (MPa)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 1,200.0000 / 17.2500 = 69.5652
|
| ☰ | \( X_{\text{running, track}} \) | Running Track Safety Blueprint Validation | ULTRA-SAFE |
View Help GuidePurpose: Status Validation.
Logic: Automated confirmation that the track surface can effortlessly withstand the highly concentrated rolling wheel loads.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{running, track}} = IF ( SF_{\text{compressive, safety}} > SF_{\text{safety, factor}} , 1 , 0 )$$ Python Logic:
IF ( v["Running Track Compressive Safety Factor"] > v["Safety Factor Slider"] , 1 , 0 )Live Evaluation: [ROUTE: STATIC/GLOBAL] IF ( 69.5652 > 2.5000 , 1 , 0 ) = 1.0000
|
| ▼ Running Track Surface Safety Audit | ||||
| ☰ | \( SF_{\text{structural, safety}} \) | Running Track Structural Safety Factor | 34.666667 |
View Help GuidePurpose: Safety Margin.
Logic: Evaluates the headroom before the track surface experiences permanent fatigue.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$SF_{\text{structural, safety}} = \sigma_{\text{material, yield}}/ X_{\text{contact, pressure}}$$ Python Logic:
v["Fossil Carbon Fibre Material Yield Strength (MPa)"]/ v["Running Track Contact Pressure (MPa)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 598.0000/ 17.2500 = 34.6667
|
| ☰ | \( X_{\text{running, track}} \) | Running Track Surface Safety Blueprint Validation | ULTRA-SAFE |
View Help GuidePurpose: Status Validation.
Logic: Provides an automated confirmation that the predicted track geometry is totally immune to surface crushing.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{running, track}} = IF ( SF_{\text{structural, safety}} > SF_{\text{safety, factor}}, 1 , 0 )$$ Python Logic:
IF ( v["Running Track Structural Safety Factor"] > v["Safety Factor Slider"], 1 , 0 )Live Evaluation: [ROUTE: STATIC/GLOBAL] IF ( 34.6667 > 2.5000, 1 , 0 ) = 1.0000
|