GMEG Engineering Simulator

Covers Dashboard

▼ Cover Impact Logic
☰	$ H_{\text{drop}} $	Drop Height (m)	0.000000	View Help Guide Purpose: Impact Datum. Logic: The calculated vertical distance an enabler "falls" within the internal clearance gap before striking the protective cover. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $( Total Runner Cavity Height (m) - Dynamic Diameter Clearance Buffer (m) ) / 2$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ n_{\text{operating}} $	Operating Speed (m/s)	8.320000	View Help Guide Purpose: Forward Momentum. Logic: The horizontal velocity of the enabler train at the moment of mechanical failure, used to calculate translational kinetic energy. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $DLLS Velocity (m/s)$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ E_{\text{potential, drop}} $	Potential Energy - Drop (J)	0.000000	View Help Guide Purpose: Vertical Energy Component. Logic: The gravitational energy generated by the enabler's vertical fall during a derailment event. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $( 2 * Enabler Mass per Unit (kg) ) * 9.81 * Drop Height (m)$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ v_{\text{ke, velocity}} $	Kinetic Energy - Velocity (J)	0.000000	View Help Guide Purpose: Horizontal Energy Component. Logic: The massive energy stored in the forward motion of the dual-mass units during high-speed operation. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $0.5 * ( 2 * Enabler Mass per Unit (kg) ) * ( Operating Speed (m/s) ^ 2 )$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ \Sigma E_{\text{impact}} $	Total Impact Energy (J)	0.000000	View Help Guide Purpose: Total Crash Load. Logic: The aggregate dynamic energy the cover must absorb and dissipate during a worst-case high-speed failure. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Potential Energy - Drop (J) + Kinetic Energy - Velocity (J)$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ \eta_{\text{cover, aspect}} $	Cover Aspect Ratio (h:w)		View Help Guide Purpose: Profile Strategy. Logic: Defines the structural shape of the cover segments to optimize impact distribution and structural depth. Type: Manual Entry Render on Grids: None Mathematical Formula: $Adjustable User Input$ Python Logic: `N/A` Live Evaluation: N/A (Input Variable)
☰	$ E_{\text{density}} $	Energy Density (%)		View Help Guide Purpose: Elastic Strain Limit. Logic: Represents the safe percentage of shock energy the carbon fiber can absorb while staying within its elastic recovery range. Type: Manual Entry Render on Grids: None Mathematical Formula: $Adjustable User Input$ Python Logic: `N/A` Live Evaluation: N/A (Input Variable)
☰	$ A_{\text{req, cover}} $	Required Cover Area (m2)	0.000000	View Help Guide Purpose: Strength Demand. Logic: The solid cross-sectional area required to absorb the kinetic strike without exceeding the material's elastic threshold. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $( Total Impact Energy (J) * Safety Factor Slider ) / ( Carbon Fiber Tensile Limit (MPa) * 1,000,000 * Energy Density (%) )$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ H_{\text{predicted, cover}} $	Predicted Cover Height (m)	0.000000	View Help Guide Purpose: Architectural Output. Logic: The calculated vertical thickness required for the cover to act as a structural impact buffer. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $SQRT ( Required Cover Area (m2) * Cover Aspect Ratio (h:w) )$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ W_{\text{predicted, cover}} $	Predicted Cover Width (m)	0.000000	View Help Guide Purpose: Architectural Output. Logic: The optimal width of the cover segments designed to match the structural load paths of the inner skeleton. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Predicted Cover Height (m) / Cover Aspect Ratio (h:w)$ Python Logic: `N/A` Live Evaluation: N/A
▼ Cover Impact Safety Audit
☰	$ X_{\text{max, impact}} $	Max Impact Flex (m)		View Help Guide Purpose: Dynamic Crash Buffer. Logic: Defines the allowable elastic "spring" distance of the cover required to safely dissipate kinetic energy during an emergency impact. Type: Manual Entry Render on Grids: None Mathematical Formula: $Adjustable User Input$ Python Logic: `N/A` Live Evaluation: N/A (Input Variable)
☰	$ F_{\text{dynamic, impact}} $	Dynamic Impact Force (N)	0.000000	View Help Guide Purpose: Peak Strike Force. Logic: Calculates the instantaneous load generated as the cover decelerates the falling mass over the specified flex distance. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Total Impact Energy (J) / Max Impact Flex (m)$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ \sigma_{\text{impact, stress}} $	Impact Stress (MPa)	0.000000	View Help Guide Purpose: Material Shock Intensity. Logic: Measures the actual physical pressure the carbon fiber strands must endure during the peak deceleration phase. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $( Dynamic Impact Force (N) / Required Cover Area (m2) ) / 1,000,000$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ \sigma_{\text{material, yield}} $	Material Yield Strength (MPa)	598.000000	View Help Guide Purpose: Ultimate Elastic Threshold. Logic: Establishes the maximum stress the material can handle before reaching permanent, non-recoverable deformation. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Carbon Fibre Modulus (GPa) * 1000 * Strain Limit (%)$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ SF_{\text{impact, safety}} $	Impact Safety Factor	0.000000	View Help Guide Purpose: Crash Margin. Logic: Evaluates the structural headroom available during a failure event; a factor above 1.0 ensures the material stays within its "Safe Stretch" zone. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Material Yield Strength (MPa) / Impact Stress (MPa)$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ X_{\text{cover, impact}} $	Cover Impact Safety Blueprint Validation	0.000000	View Help Guide Purpose: Status Validation. Logic: Final automated confirmation that the cover geometry will successfully catch and contain the enabler without structural shattering. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $IF ( Impact Safety Factor >= 1.0 , "ULTRA-SAFE" , "REVISE" )$ Python Logic: `N/A` Live Evaluation: N/A
▼ Inner Cover Corner Weight
☰	$ R_{\text{inner, cover}} $	Inner Cover Inner Radius (m)	0.000000	View Help Guide Purpose: Internal Boundary. Logic: The starting radial coordinate for the inner protective shell, flush with the skeleton. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Cage Corner Radius (m)$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ R_{\text{inner, cover}} $	Inner Cover Outer Radius (m)	0.000000	View Help Guide Purpose: External Boundary. Logic: The total radial reach of the inner cover, including its calculated structural thickness. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Inner Cover Inner Radius (m) + Predicted Cover Height (m)$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ D_{\text{inner, cover}} $	Inner Cover Outer Diameter (m)	0.000000	View Help Guide Purpose: Spatial Envelope. Logic: The full circular footprint of the inner corner assembly for clearance verification. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Inner Cover Outer Radius (m) * 2$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ A_{\text{req, cover}} $	Required Cover Area (m2)	0.000000	View Help Guide Purpose: Stiffness Demand. Logic: Inherits the solid cross-sectional area required to survive a dynamic crash event. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Required Cover Area (m2) (from Impact Logic)$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ M_{\text{cover, unit}} $	Cover Module Unit Mass (kg)	0.000000	View Help Guide Purpose: Unit Mass Datum. Logic: The calculated weight of a single crash-rated cover segment. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Required Cover Area (m2) * Module Length (m) * Carbon Fiber Density (kg/m3)$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ C_{\text{corner, circ}} $	Corner Circumference (m)	0.000000	View Help Guide Purpose: Arc Path. Logic: The total linear distance of the circular path for both 180-degree inner ends. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $PI() * Inner Cover Outer Radius (m)$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ X_{\text{modules, corner}} $	Modules per Corner	0.000000	View Help Guide Purpose: Modular Scaling. Logic: Determines the number of blocks required to fully skin the inner curved sections. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $ROUNDUP ( Corner Circumference (m) / Module Length (m) , 0)$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ M_{\text{corner}} $	Weight per Corner (kg)	0.000000	View Help Guide Purpose: Sectional Mass. Logic: The total weight of the curved cover segments for a single end-cap assembly. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Modules per Corner * Cover Module Unit Mass (kg)$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ X_{\text{corners}} $	Corners		View Help Guide Purpose: System Multiplier. Logic: Defines the number of curved ends in the track layout (typically two 180-degree turns). Type: Manual Entry Render on Grids: None Mathematical Formula: $Adjustable User Input$ Python Logic: `N/A` Live Evaluation: N/A (Input Variable)
☰	$ \Sigma M_{\text{inner, cover}} $	Total Inner Cover Corner Weight (kg)	0.000000	View Help Guide Purpose: Aggregate Inner Arc Mass. Logic: The total combined weight of all inner curved protective covers. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Weight per Corner (kg) * Corners$ Python Logic: `N/A` Live Evaluation: N/A
▼ Outer Cover Corner Weight
☰	$ R_{\text{outer, cover}} $	Outer cover inner radius (m)	0.000000	View Help Guide Purpose: Internal Boundary. Logic: Defines the starting radial coordinate for the exterior protective shell, perfectly positioned at the top of the support riser. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Drive Gear Radius (m) + ( Runner Profile Height (m) / 2 ) + Top Support Height (m)$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ R_{\text{outer, cover}} $	Outer cover outer radius (m)	0.000000	View Help Guide Purpose: External Boundary. Logic: The absolute maximum radial reach of the machine's exterior impact shield. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Outer Cover Inner Radius (m) + Predicted Cover Height (m)$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ D_{\text{outer, cover}} $	Outer cover outer diameter (m)	0.000000	View Help Guide Purpose: Total Machine Footprint. Logic: The full external diameter of the GMEG housing ends, used for site planning and facility clearance verification. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Outer Cover Outer Radius (m) * 2$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ A_{\text{req, cover}} $	Required Cover Area (m2)	0.000000	View Help Guide Purpose: Stiffness Demand. Logic: Inherits the solid cross-sectional area required to successfully dissipate the massive kinetic energy of a high-speed failure event. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $( Total Impact Energy (J) * Safety Factor Slider ) / ( Carbon Fibre Tensile Limit (Mpa) * 10^6 * Energy Density (%) )$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ M_{\text{outer, cover}} $	Outer Cover Unit Mass (kg)	0.000000	View Help Guide Purpose: Unit Mass Datum. Logic: The calculated dead-weight of a single one-meter crash-rated exterior cover segment. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Required Cover Area (m2) * Module Length (m) * Carbon Fiber Density (kg/m3)$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ C_{\text{corner, circ}} $	Corner circumference (m)	0.000000	View Help Guide Purpose: Arc Path. Logic: The linear distance of a single 180-degree outer curved end-cap. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $PI() * Outer Cover Outer Radius (m)$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ X_{\text{modules, corner}} $	Modules per corner	0.000000	View Help Guide Purpose: Modular Scaling. Logic: Determines the number of 1-meter blocks required to fully skin the outer curved section of one end. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $ROUNDUP ( Corner Circumference (m) / Module Length (m), 0 )$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ M_{\text{corner}} $	Weight per corner (kg)	0.000000	View Help Guide Purpose: Sectional Mass. Logic: The total weight of the curved cover segments for a single outer end-cap assembly. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Modules per Corner * Outer Cover Unit Mass (kg)$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ X_{\text{corners}} $	Corners		View Help Guide Purpose: System Multiplier. Logic: Defines the number of curved 180-degree ends in the track layout (typically two). Type: Manual Entry Render on Grids: None Mathematical Formula: $Adjustable User Input$ Python Logic: `N/A` Live Evaluation: N/A (Input Variable)
☰	$ \Sigma M_{\text{outer, cover}} $	Total Outer Cover Corner Weight (kg)	0.000000	View Help Guide Purpose: Aggregate Outer Arc Mass. Logic: The total combined weight of all exterior curved protective covers. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Weight per Corner (kg) * Corners$ Python Logic: `N/A` Live Evaluation: N/A

▼ Cover Impact Logic
☰	\( H_{\text{drop}} \)	Drop Height (m)	0.000000	View Help Guide Purpose: Impact Datum. Logic: The calculated vertical distance an enabler "falls" within the internal clearance gap before striking the protective cover. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $( Total Runner Cavity Height (m) - Dynamic Diameter Clearance Buffer (m) ) / 2$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( n_{\text{operating}} \)	Operating Speed (m/s)	8.320000	View Help Guide Purpose: Forward Momentum. Logic: The horizontal velocity of the enabler train at the moment of mechanical failure, used to calculate translational kinetic energy. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $DLLS Velocity (m/s)$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( E_{\text{potential, drop}} \)	Potential Energy - Drop (J)	0.000000	View Help Guide Purpose: Vertical Energy Component. Logic: The gravitational energy generated by the enabler's vertical fall during a derailment event. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $( 2 * Enabler Mass per Unit (kg) ) * 9.81 * Drop Height (m)$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( v_{\text{ke, velocity}} \)	Kinetic Energy - Velocity (J)	0.000000	View Help Guide Purpose: Horizontal Energy Component. Logic: The massive energy stored in the forward motion of the dual-mass units during high-speed operation. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $0.5 * ( 2 * Enabler Mass per Unit (kg) ) * ( Operating Speed (m/s) ^ 2 )$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( \Sigma E_{\text{impact}} \)	Total Impact Energy (J)	0.000000	View Help Guide Purpose: Total Crash Load. Logic: The aggregate dynamic energy the cover must absorb and dissipate during a worst-case high-speed failure. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Potential Energy - Drop (J) + Kinetic Energy - Velocity (J)$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( \eta_{\text{cover, aspect}} \)	Cover Aspect Ratio (h:w)		View Help Guide Purpose: Profile Strategy. Logic: Defines the structural shape of the cover segments to optimize impact distribution and structural depth. Type: Manual Entry Render on Grids: None Mathematical Formula: $Adjustable User Input$ Python Logic: `N/A` Live Evaluation: N/A (Input Variable)
☰	\( E_{\text{density}} \)	Energy Density (%)		View Help Guide Purpose: Elastic Strain Limit. Logic: Represents the safe percentage of shock energy the carbon fiber can absorb while staying within its elastic recovery range. Type: Manual Entry Render on Grids: None Mathematical Formula: $Adjustable User Input$ Python Logic: `N/A` Live Evaluation: N/A (Input Variable)
☰	\( A_{\text{req, cover}} \)	Required Cover Area (m2)	0.000000	View Help Guide Purpose: Strength Demand. Logic: The solid cross-sectional area required to absorb the kinetic strike without exceeding the material's elastic threshold. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $( Total Impact Energy (J) * Safety Factor Slider ) / ( Carbon Fiber Tensile Limit (MPa) * 1,000,000 * Energy Density (%) )$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( H_{\text{predicted, cover}} \)	Predicted Cover Height (m)	0.000000	View Help Guide Purpose: Architectural Output. Logic: The calculated vertical thickness required for the cover to act as a structural impact buffer. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $SQRT ( Required Cover Area (m2) * Cover Aspect Ratio (h:w) )$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( W_{\text{predicted, cover}} \)	Predicted Cover Width (m)	0.000000	View Help Guide Purpose: Architectural Output. Logic: The optimal width of the cover segments designed to match the structural load paths of the inner skeleton. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Predicted Cover Height (m) / Cover Aspect Ratio (h:w)$ Python Logic: `N/A` Live Evaluation: N/A
▼ Cover Impact Safety Audit
☰	\( X_{\text{max, impact}} \)	Max Impact Flex (m)		View Help Guide Purpose: Dynamic Crash Buffer. Logic: Defines the allowable elastic "spring" distance of the cover required to safely dissipate kinetic energy during an emergency impact. Type: Manual Entry Render on Grids: None Mathematical Formula: $Adjustable User Input$ Python Logic: `N/A` Live Evaluation: N/A (Input Variable)
☰	\( F_{\text{dynamic, impact}} \)	Dynamic Impact Force (N)	0.000000	View Help Guide Purpose: Peak Strike Force. Logic: Calculates the instantaneous load generated as the cover decelerates the falling mass over the specified flex distance. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Total Impact Energy (J) / Max Impact Flex (m)$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( \sigma_{\text{impact, stress}} \)	Impact Stress (MPa)	0.000000	View Help Guide Purpose: Material Shock Intensity. Logic: Measures the actual physical pressure the carbon fiber strands must endure during the peak deceleration phase. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $( Dynamic Impact Force (N) / Required Cover Area (m2) ) / 1,000,000$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( \sigma_{\text{material, yield}} \)	Material Yield Strength (MPa)	598.000000	View Help Guide Purpose: Ultimate Elastic Threshold. Logic: Establishes the maximum stress the material can handle before reaching permanent, non-recoverable deformation. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Carbon Fibre Modulus (GPa) * 1000 * Strain Limit (%)$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( SF_{\text{impact, safety}} \)	Impact Safety Factor	0.000000	View Help Guide Purpose: Crash Margin. Logic: Evaluates the structural headroom available during a failure event; a factor above 1.0 ensures the material stays within its "Safe Stretch" zone. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Material Yield Strength (MPa) / Impact Stress (MPa)$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( X_{\text{cover, impact}} \)	Cover Impact Safety Blueprint Validation	0.000000	View Help Guide Purpose: Status Validation. Logic: Final automated confirmation that the cover geometry will successfully catch and contain the enabler without structural shattering. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $IF ( Impact Safety Factor >= 1.0 , "ULTRA-SAFE" , "REVISE" )$ Python Logic: `N/A` Live Evaluation: N/A
▼ Inner Cover Corner Weight
☰	\( R_{\text{inner, cover}} \)	Inner Cover Inner Radius (m)	0.000000	View Help Guide Purpose: Internal Boundary. Logic: The starting radial coordinate for the inner protective shell, flush with the skeleton. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Cage Corner Radius (m)$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( R_{\text{inner, cover}} \)	Inner Cover Outer Radius (m)	0.000000	View Help Guide Purpose: External Boundary. Logic: The total radial reach of the inner cover, including its calculated structural thickness. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Inner Cover Inner Radius (m) + Predicted Cover Height (m)$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( D_{\text{inner, cover}} \)	Inner Cover Outer Diameter (m)	0.000000	View Help Guide Purpose: Spatial Envelope. Logic: The full circular footprint of the inner corner assembly for clearance verification. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Inner Cover Outer Radius (m) * 2$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( A_{\text{req, cover}} \)	Required Cover Area (m2)	0.000000	View Help Guide Purpose: Stiffness Demand. Logic: Inherits the solid cross-sectional area required to survive a dynamic crash event. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Required Cover Area (m2) (from Impact Logic)$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( M_{\text{cover, unit}} \)	Cover Module Unit Mass (kg)	0.000000	View Help Guide Purpose: Unit Mass Datum. Logic: The calculated weight of a single crash-rated cover segment. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Required Cover Area (m2) * Module Length (m) * Carbon Fiber Density (kg/m3)$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( C_{\text{corner, circ}} \)	Corner Circumference (m)	0.000000	View Help Guide Purpose: Arc Path. Logic: The total linear distance of the circular path for both 180-degree inner ends. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $PI() * Inner Cover Outer Radius (m)$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( X_{\text{modules, corner}} \)	Modules per Corner	0.000000	View Help Guide Purpose: Modular Scaling. Logic: Determines the number of blocks required to fully skin the inner curved sections. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $ROUNDUP ( Corner Circumference (m) / Module Length (m) , 0)$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( M_{\text{corner}} \)	Weight per Corner (kg)	0.000000	View Help Guide Purpose: Sectional Mass. Logic: The total weight of the curved cover segments for a single end-cap assembly. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Modules per Corner * Cover Module Unit Mass (kg)$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( X_{\text{corners}} \)	Corners		View Help Guide Purpose: System Multiplier. Logic: Defines the number of curved ends in the track layout (typically two 180-degree turns). Type: Manual Entry Render on Grids: None Mathematical Formula: $Adjustable User Input$ Python Logic: `N/A` Live Evaluation: N/A (Input Variable)
☰	\( \Sigma M_{\text{inner, cover}} \)	Total Inner Cover Corner Weight (kg)	0.000000	View Help Guide Purpose: Aggregate Inner Arc Mass. Logic: The total combined weight of all inner curved protective covers. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Weight per Corner (kg) * Corners$ Python Logic: `N/A` Live Evaluation: N/A
▼ Outer Cover Corner Weight
☰	\( R_{\text{outer, cover}} \)	Outer cover inner radius (m)	0.000000	View Help Guide Purpose: Internal Boundary. Logic: Defines the starting radial coordinate for the exterior protective shell, perfectly positioned at the top of the support riser. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Drive Gear Radius (m) + ( Runner Profile Height (m) / 2 ) + Top Support Height (m)$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( R_{\text{outer, cover}} \)	Outer cover outer radius (m)	0.000000	View Help Guide Purpose: External Boundary. Logic: The absolute maximum radial reach of the machine's exterior impact shield. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Outer Cover Inner Radius (m) + Predicted Cover Height (m)$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( D_{\text{outer, cover}} \)	Outer cover outer diameter (m)	0.000000	View Help Guide Purpose: Total Machine Footprint. Logic: The full external diameter of the GMEG housing ends, used for site planning and facility clearance verification. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Outer Cover Outer Radius (m) * 2$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( A_{\text{req, cover}} \)	Required Cover Area (m2)	0.000000	View Help Guide Purpose: Stiffness Demand. Logic: Inherits the solid cross-sectional area required to successfully dissipate the massive kinetic energy of a high-speed failure event. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $( Total Impact Energy (J) * Safety Factor Slider ) / ( Carbon Fibre Tensile Limit (Mpa) * 10^6 * Energy Density (%) )$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( M_{\text{outer, cover}} \)	Outer Cover Unit Mass (kg)	0.000000	View Help Guide Purpose: Unit Mass Datum. Logic: The calculated dead-weight of a single one-meter crash-rated exterior cover segment. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Required Cover Area (m2) * Module Length (m) * Carbon Fiber Density (kg/m3)$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( C_{\text{corner, circ}} \)	Corner circumference (m)	0.000000	View Help Guide Purpose: Arc Path. Logic: The linear distance of a single 180-degree outer curved end-cap. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $PI() * Outer Cover Outer Radius (m)$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( X_{\text{modules, corner}} \)	Modules per corner	0.000000	View Help Guide Purpose: Modular Scaling. Logic: Determines the number of 1-meter blocks required to fully skin the outer curved section of one end. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $ROUNDUP ( Corner Circumference (m) / Module Length (m), 0 )$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( M_{\text{corner}} \)	Weight per corner (kg)	0.000000	View Help Guide Purpose: Sectional Mass. Logic: The total weight of the curved cover segments for a single outer end-cap assembly. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Modules per Corner * Outer Cover Unit Mass (kg)$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( X_{\text{corners}} \)	Corners		View Help Guide Purpose: System Multiplier. Logic: Defines the number of curved 180-degree ends in the track layout (typically two). Type: Manual Entry Render on Grids: None Mathematical Formula: $Adjustable User Input$ Python Logic: `N/A` Live Evaluation: N/A (Input Variable)
☰	\( \Sigma M_{\text{outer, cover}} \)	Total Outer Cover Corner Weight (kg)	0.000000	View Help Guide Purpose: Aggregate Outer Arc Mass. Logic: The total combined weight of all exterior curved protective covers. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $Weight per Corner (kg) * Corners$ Python Logic: `N/A` Live Evaluation: N/A

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