Track Master Settings and Dynamic Inputs Dashboard

Primary Inputs
\( SF_{\text{safety, factor}} \) Safety Factor Slider
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Purpose: Structural Headroom.
Logic: Establishes the global multiplier used to define the margin between operational loads and material failure limits.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( \Delta_{\text{max, allowable}} \) Max Allowable Deflection (mm)
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Purpose: Precision Benchmark.
Logic: The strict operational tolerance required to maintain electromagnetic air-gap stability during high-speed rotation.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
User Adjustable Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( \Delta_{\text{max, allowable}} \) Max Allowable Deflection (m) 0.000075
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Purpose: Calculation Datum.
Logic: Normalizes the precision benchmark into meters for integration with SI-based structural stiffness formulas.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Delta_{\text{max, allowable}} = \Delta_{\text{max, allowable}} / 1000$$
Python Logic: v["Max Allowable Deflection (mm)"] / 1000
Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0750 / 1000 = 0.0001
\( M_{\text{unit}} \) Enabler Mass per Unit (kg) 2,522.727273
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Purpose: Unit Mass Datum.
Logic: The specific gravitational weight of a single enabler unit and its dedicated carrier hardware.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$M_{\text{unit}} = W_{\text{unit}} + M_{\text{holder}}$$
Python Logic: v["Weight per gravity enabler (kg)"] + v["Gravity enabler holder weight (kg)"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 2,272.7273 + 250.0000 = 2,522.7273
\( \Sigma X_{\text{units}} \) Total Enabler Units 11.000000
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Purpose: Payload Scale.
Logic: Defines the quantity of individual mass units circulating within the active train for energy generation.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma X_{\text{units}} = N_{\text{enablers}}$$
Python Logic: v["Number of Gravity Enablers"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 11.0000 = 11.0000
\( \Sigma M_{\text{train}} \) Total Enabler Train Mass (kg) 27,750.000000
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Purpose: Total Payload Mass.
Logic: The aggregate dynamic mass that must be supported and contained by the housing structure.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma M_{\text{train}} = M_{\text{unit}} \times \Sigma X_{\text{units}}$$
Python Logic: v["Enabler Mass per Unit (kg)"] * v["Total Enabler Units"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 2,522.7273 * 11.0000 = 27,750.0000
\( n_{\text{operating}} \) Operating Speed (m/s) 8.320000
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Purpose: Linear Velocity.
Logic: The fixed operational speed used to derive kinetic energy, centripetal acceleration, and impact loads.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$n_{\text{operating}} = v$$
Python Logic: v["Operational Velocity (m/s)"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 8.3200 = 8.3200
\( \theta_{\text{operating, slant}} \) Operating Slant Angle (deg) 32.000000
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Purpose: Orientation Constraint.
Logic: Defines the angular orientation of the track plane to resolve vertical gravity into lateral shear force components.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\theta_{\text{operating, slant}} = \theta_{\text{tilt}}$$
Python Logic: v["Angle tilt (degrees)"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 32.0000 = 32.0000
\( \rho_{\text{carbon, fiber}} \) Carbon Fiber Density (kg/m3)
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Purpose: Mass Modeling Base.
Logic: The volumetric density of the composite material used to synthesize the weight of all structural components.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
User Adjustable Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( X_{\text{carbon, fibre}} \) Carbon Fibre Modulus (GPa)
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Purpose: Young's Modulus (E).
Logic: The material stiffness constant used to calculate deflection resistance and structural stability under load.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
User Adjustable Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( X_{\text{carbon, fiber}} \) Carbon Fiber Tensile Limit (MPa)
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Purpose: Ultimate Tensile Strength.
Logic: The material threshold used to size elements subjected to axial pulling or stretching forces.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
User Adjustable Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( X_{\text{carbon, fiber}} \) Carbon Fiber Compressive Limit (MPa)
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Purpose: Ultimate Compressive Strength.
Logic: The material threshold used to size elements subjected to crushing loads or structural buckling.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
User Adjustable Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( \varepsilon_{\text{strain, limit}} \) Strain Limit (%)
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Purpose: Elastic Threshold.
Logic: Defines the maximum allowable fiber elongation to ensure the housing remains within its linear elastic memory range.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
User Adjustable Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( \tau_{\text{carbon, fiber}} \) Carbon Fiber Shear Limit (MPa)
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Purpose: Material Threshold.
Logic: Interlaminar Material Grade Constant shear limit for the CF rod.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
User Adjustable Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( \sigma_{\text{material, yield}} \) Material Yield Strength (MPa) 598.000000
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Purpose: Ultimate Threshold.
Logic: The calculated peak stress the material can endure before reaching permanent, non-recoverable deformation.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\sigma_{\text{material, yield}} = X_{\text{carbon, fibre}} \times 1000 \times \varepsilon_{\text{strain, limit}}$$
Python Logic: v["Carbon Fibre Modulus (GPa)"] * 1000 * v["Strain Limit (%)"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 230.0000 * 1000 * 0.0026 = 598.0000
Master Kinetic Inputs
\( R_{\text{drive}} \) Drive Gear Radius (m) 2.037183
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Purpose: Dimensional Datum.
Logic: The primary geometric radius used to calculate centripetal acceleration and outward kinetic pressure at the curved end-caps.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$R_{\text{drive}} = r_{gear}$$
Python Logic: v["Internal Gear Radius (m)"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 2.0372 = 2.0372
\( \Sigma L_{\text{train}} \) Total Train Length (m) 6.561500
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Purpose: Load Footprint.
Logic: The total longitudinal distance of the enabler chain used to distribute point-loads into a continuous structural pressure.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma L_{\text{train}} = L_{\text{train}}$$
Python Logic: v["Enabler train length (m)"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 6.5615 = 6.5615
\( F_{\text{gross, centrifugal}} \) Gross Centrifugal Force (N) 942,930.185419
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Purpose: Total Outward Load.
Logic: The aggregate kinetic force generated by the rotating mass attempting to move tangentially away from the center shaft.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$F_{\text{gross, centrifugal}} = (M_{\text{total}} \times ( v ^ 2 ) ) / R_{\text{int}}$$
Python Logic: (v["TOTAL WEIGHT (KG)"] * ( v["Operational Velocity (m/s)"] ^ 2 ) ) / v["Internal Gear Radius (m)"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] (27,750.0000 * ( 8.3200 ** 2 ) ) / 2.0372 = 942,930.1854
\( F_{\text{linear, distributed}} \) Linear Distributed Load (N/m) 143,706.497816
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Purpose: True Corner Pressure.
Logic: The operational force exerted against every linear meter of the track curve, representing a shared-load scenario.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$F_{\text{linear, distributed}} = F_{\text{gross, centrifugal}} / \Sigma L_{\text{train}}$$
Python Logic: v["Gross Centrifugal Force (N)"] / v["Total Train Length (m)"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 942,930.1854 / 6.5615 = 143,706.4978
\( F_{\text{design, distributed}} \) Design Distributed Load (N/m) 359,266.244540
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Purpose: Ultimate Limit State (ULS) Corner Load.
Logic: The worst-case radial force used to synthesize the structural thickness of the track curves to ensure zero failure.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$F_{\text{design, distributed}} = F_{\text{linear, distributed}} \times SF_{\text{safety, factor}}$$
Python Logic: v["Linear Distributed Load (N/m)"] * v["Safety Factor Slider"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 143,706.4978 * 2.5000 = 359,266.2445
\( F_{\text{lateral, component}} \) Gravity Lateral Force Component (N) 144,258.596504
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Purpose: Side Shear Load.
Logic: The vector of gravitational force attempting to displace the entire track housing sideways due to the system's tilt.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$F_{\text{lateral, component}} = \Sigma M_{\text{train}} \times N \times SIN ( RADIANS ( \theta_{\text{operating, slant}} ) )$$
Python Logic: v["Total Enabler Train Mass (kg)"] * v["Gravitational Field Strength (N/kg)"] * SIN ( RADIANS ( v["Operating Slant Angle (deg)"] ) )
Live Evaluation: [ROUTE: STATIC/GLOBAL] 27,750.0000 * 9.8100 * SIN ( RADIANS ( 32.0000 ) ) = 144,258.5965
\( \tau_{\text{design, lateral}} \) Design Lateral Shear (N) 360,646.491260
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Purpose: ULS Lateral Load.
Logic: The maximum side-loading force the internal skeleton and X-frames must absorb while maintaining sub-millimeter precision.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\tau_{\text{design, lateral}} = F_{\text{lateral, component}} \times SF_{\text{safety, factor}}$$
Python Logic: v["Gravity Lateral Force Component (N)"] * v["Safety Factor Slider"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 144,258.5965 * 2.5000 = 360,646.4913