Inner Dashboard

Inner Structural Synthesis
\( R \) Gear Radius (m) 2.037183
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Purpose: Radial Limit.
Logic: Establishes the primary distance from the center shaft to the pitch circumference of the drive system.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$R = R_{\text{drive}}$$
Python Logic: v["Drive Gear Radius (m)"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 2.0372 = 2.0372
\( X_{\text{track, int}} \) Track Internal Offset (m) 0.334310
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Purpose: Internal Encroachment.
Logic: The total distance the "Bottom Sandwich" extends inward from the gear centerline.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{track, int}} = ( H_{\text{runner, profile}} / 2 ) + H_{\text{bottom, support}} + H_{\text{bottom, cover}}$$
Python Logic: ( v["Runner Profile Height (m)"] / 2 ) + v["Bottom Support Height (m)"] + v["Bottom Cover Height (m)"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 0.0000 / 2 ) + 0.0000 + 0.0000 = 0.3343
\( H_{\text{track}} \) Track Height (m) 4.074367
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Purpose: Total Machine Envelope.
Logic: The absolute vertical footprint of the GMEG housing from its highest to lowest outermost edges.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$H_{\text{track}} = ( R + ( ( H_{\text{runner, profile}} / 2 ) + H_{\text{top, support}} + H_{\text{top, cover}} ) ) \times 2$$
Python Logic: ( v["Gear Radius (m)"] + ( ( v["Runner Profile Height (m)"] / 2 ) + v["Top Support Height (m)"] + v["Top Cover Height (m)"] ) ) * 2
Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 2.0372 + ( ( 0.0000 / 2 ) + 0.0000 + 0.0000 ) ) * 2 = 4.0744
\( R_{\text{cage, corner}} \) Cage Corner Radius (m) 1.702873
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Purpose: Skeletal Radius.
Logic: Defines the rounded profile of the inner skeleton to ensure zero interference with the enabler cavity.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$R_{\text{cage, corner}} = R - X_{\text{track, int}}$$
Python Logic: v["Gear Radius (m)"] - v["Track Internal Offset (m)"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 2.0372 - 0.3343 = 1.7029
\( H_{\text{cage, section}} \) Cage Section Height (m) 1.702873
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Purpose: Inner Frame Height.
Logic: Sets the vertical dimension for the internal cage walls based on the available skeletal radius.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$H_{\text{cage, section}} = R_{\text{cage, corner}}$$
Python Logic: v["Cage Corner Radius (m)"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 1.7029 = 1.7029
\( H_{\text{xbrace, frame}} \) X-Brace Frame Height (m) 1.702873
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Purpose: Internal Clearance.
Logic: Defines the vertical span available for the primary diagonal X-brace reinforcements.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$H_{\text{xbrace, frame}} = H_{\text{cage, section}}$$
Python Logic: v["Cage Section Height (m)"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 1.7029 = 1.7029
\( L_{\text{straight, track}} \) Straight Track Length (m) 6.000000
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Purpose: Longitudinal Span.
Logic: The total distance of the flat track runs used to map the distribution of internal support frames.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$L_{\text{straight, track}} = L_{\text{straight}}$$
Python Logic: v["Straight track length (m)"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 6.0000 = 6.0000
Side Frame Structure
\( X_{\text{straight, side}} \) Straight Side Rails
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Purpose: Member Count.
Logic: Defines the total number of longitudinal bars used to distribute lateral loads across the chassis.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( \Sigma L_{\text{straight, rail}} \) Total Straight Rail Length (m) 18.000000
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Purpose: Cumulative Rail Distance.
Logic: The total linear length of all horizontal structural rails combined, used for mass modeling.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma L_{\text{straight, rail}} = L_{\text{straight, track}} \times X_{\text{straight, side}}$$
Python Logic: v["Straight Track Length (m)"] * v["Straight Side Rails"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 6.0000 * 3.0000 = 18.0000
\( F_{\text{applied, rail}} \) Applied Force per Rail (N) 120,215.497087
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Purpose: Dynamic Rail Load.
Logic: The specific side-shear force allocated to each individual rail member under peak operation.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$F_{\text{applied, rail}} = \tau_{\text{design, lateral}} / X_{\text{straight, side}}$$
Python Logic: v["Design Lateral Shear (N)"] / v["Straight Side Rails"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0000 / 3.0000 = 120,215.4971
\( A_{\text{req, rail}} \) Required Rail Material Area (m2) 0.041814
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Purpose: Stiffness Demand.
Logic: The actual cross-sectional area of solid carbon fiber required to maintain the sub-millimeter precision limit.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$A_{\text{req, rail}} = ( F_{\text{applied, rail}} \times L_{\text{straight, track}} ) / ( ( X_{\text{carbon, fibre}} \times 10^9 ) \times \Delta_{\text{max, allowable}} )$$
Python Logic: ( v["Applied Force per Rail (N)"] * v["Straight Track Length (m)"] ) / ( ( v["Carbon Fibre Modulus (GPa)"] * 10^9 ) * v["Max Allowable Deflection (m)"] )
Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 120,215.4971 * 6.0000 ) / ( ( 230.0000 * 10**9 ) * 0.0001 ) = 0.0418
\( \eta_{\text{target, aspect}} \) Target Aspect Ratio (h:w)
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Purpose: Geometry Strategy.
Logic: Controls the height-to-width ratio of the rail profile to optimize it for specific directional loads.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( H_{\text{prescribed, rail}} \) Prescribed Rail Height (m) 0.228621
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Purpose: Architectural Output.
Logic: The optimal vertical dimension of the rail profile, mathematically derived from load and material constants.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$H_{\text{prescribed, rail}} = SQRT ( A_{\text{req, rail}} \times \eta_{\text{target, aspect}} )$$
Python Logic: SQRT ( v["Required Rail Material Area (m2)"] * v["Target Aspect Ratio (h:w)"] )
Live Evaluation: [ROUTE: STATIC/GLOBAL] SQRT ( 0.0418 * 1.2500 ) = 0.2286
\( W_{\text{prescribed, rail}} \) Prescribed Rail Width (m) 0.182897
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Purpose: Architectural Output.
Logic: The optimal horizontal dimension of the rail profile derived from the target aspect ratio.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$W_{\text{prescribed, rail}} = H_{\text{prescribed, rail}}/ \eta_{\text{target, aspect}}$$
Python Logic: v["Prescribed Rail Height (m)"]/ v["Target Aspect Ratio (h:w)"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.2286/ 1.2500 = 0.1829
\( W_{\text{synthesized, thickness}} \) Synthesized Wall Thickness (m) 0.091448
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Purpose: The Blueprint.
Logic: The precise manufacturing wall thickness required to ensure the hollow carbon fiber rail remains structurally rigid and doesn't buckle.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$W_{\text{synthesized, thickness}} = ( W_{\text{prescribed, rail}} / 2 ) \times ( 1 - SQRT ( 1 - ( A_{\text{req, rail}} / (H_{\text{prescribed, rail}} \times W_{\text{prescribed, rail}} ) ) ) )$$
Python Logic: ( v["Prescribed Rail Width (m)"] / 2 ) * ( 1 - SQRT ( 1 - ( v["Required Rail Material Area (m2)"] / (v["Prescribed Rail Height (m)"] * v["Prescribed Rail Width (m)"] ) ) ) )
Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 0.1829 / 2 ) * ( 1 - SQRT ( 1 - ( 0.0418 / (0.2286 * 0.1829 ) ) ) ) = 0.0914
\( V_{\text{rail, output}} \) Rail Volume Output (m3) 0.752654
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Purpose: Calculated Volume.
Logic: The total solid material volume required for the entire horizontal rail system.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$V_{\text{rail, output}} = A_{\text{req, rail}} \times \Sigma L_{\text{straight, rail}}$$
Python Logic: v["Required Rail Material Area (m2)"] * v["Total Straight Rail Length (m)"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0418 * 18.0000 = 0.7527
\( M_{\text{predicted, rail}} \) Predicted Rail Mass (kg) 1,354.776385
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Purpose: Blueprint Weight.
Logic: The total dead-weight of the longitudinal rails required to guarantee stability at the precision limit.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$M_{\text{predicted, rail}} = V_{\text{rail, output}} \times \rho_{\text{carbon, fiber}}$$
Python Logic: v["Rail Volume Output (m3)"] * v["Carbon Fiber Density (kg/m3)"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.7527 * 1,800.0000 = 1,354.7764
Side Rail Safety & Stress Audit
\( X_{\text{bending, moment}} \) Bending Moment (Nm) 180,323.245630
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Purpose: Flexural Loading.
Logic: Calculates the peak internal torque experienced at the dead-center of the rail span under maximum payload.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{bending, moment}} = ( F_{\text{applied, rail}} \times L_{\text{straight, track}} ) / 4$$
Python Logic: ( v["Applied Force per Rail (N)"]* v["Straight Track Length (m)"] ) / 4
Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 120,215.4971* 6.0000 ) / 4 = 180,323.2456
\( I_{\text{inertia}} \) Moment of Inertia (I) 0.000182
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Purpose: Geometric Stiffness.
Logic: Quantifies the hollow profile's structural resistance to bending based purely on its newly synthesized geometric shape.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$I_{\text{inertia}} = ( W_{\text{prescribed, rail}} \times (H_{\text{prescribed, rail}} ^ 3 ) / 12 ) \times ( 1 - ( ( 1 - ( 2 \times W_{\text{synthesized, thickness}} / W_{\text{prescribed, rail}} ) ) ^ 4 ) )$$
Python Logic: ( v["Prescribed Rail Width (m)"] * (v["Prescribed Rail Height (m)"] ^ 3 ) / 12 ) * ( 1 - ( ( 1 - ( 2 * v["Synthesized Wall Thickness (m)"] / v["Prescribed Rail Width (m)"] ) ) ^ 4 ) )
Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 0.1829 * (0.2286 ** 3 ) / 12 ) * ( 1 - ( ( 1 - ( 2 * 0.0914 / 0.1829 ) ) ** 4 ) ) = 0.0002
\( \sigma_{\text{peak, operating}} \) Peak Operating Stress (MPa) 113.178530
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Purpose: Peak Fiber Stress.
Logic: Measures the maximum physical pressure experienced by the outermost carbon fibers at peak operational deflection.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\sigma_{\text{peak, operating}} = ( ( X_{\text{bending, moment}} \times (H_{\text{prescribed, rail}} / 2 ) ) / I_{\text{inertia}} ) / 1000000$$
Python Logic: ( ( v["Bending Moment (Nm)"] * (v["Prescribed Rail Height (m)"] / 2 ) ) / v["Moment of Inertia (I)"] ) / 1000000
Live Evaluation: [ROUTE: STATIC/GLOBAL] ( ( 180,323.2456 * (0.2286 / 2 ) ) / 0.0002 ) / 1000000 = 113.1785
\( SF_{\text{structural, safety}} \) Structural Safety Factor 5.283688
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Purpose: Structural Margin.
Logic: The ratio between the material's absolute breaking point and the actual stress encountered, ensuring a massive operational safety buffer.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$SF_{\text{structural, safety}} = \sigma_{\text{material, yield}} / \sigma_{\text{peak, operating}}$$
Python Logic: v["Material Yield Strength (MPa)"] / v["Peak Operating Stress (MPa)"]
Live Evaluation: [ROUTE: STATIC/GLOBAL] 598.0000 / 113.1785 = 5.2837
\( \sigma_{\text{side, rail}} \) Side Rail Safety & Stress Blueprint Validation 1.000000
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Purpose: Status Validation.
Logic: An automated traffic light confirming that the rail geometry satisfies the prescribed safety protocols for high-precision track components.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\sigma_{\text{side, rail}} = 1 if SF_{\text{structural, safety}} > SF_{\text{safety, factor}} else 0$$
Python Logic: 1 if v["Structural Safety Factor"] > v["Safety Factor Slider"] else 0
Live Evaluation: [ROUTE: STATIC/GLOBAL] 1 if 5.2837 > 2.5000 else 0 = 1.0000
Inner Skeleton
\( W_{\text{cage, inner}} \) Cage Inner Width (m) 0.000000
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Purpose: Internal Span.
Logic: Defines the horizontal spacing between the left and right side-frame structures.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Total width (m)
Python Logic: N/A
Live Evaluation: N/A
\( L_{\text{diagonal, strut}} \) Diagonal Strut Length (m) 0.000000
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Purpose: Hypotenuse Datum.
Logic: Uses Pythagoras to calculate the exact linear length of a single diagonal brace within the internal X-frame assembly.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
SQRT ( ( X-Brace Frame Height (m) ^ 2 ) + ( Cage Inner Width (m) ^ 2) )
Python Logic: N/A
Live Evaluation: N/A
\( X_{\text{centre, xbrace}} \) Centre X-Brace
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Purpose: Primary Core Count.
Logic: Defines the number of central bracing units within the inner skeleton.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( X_{\text{side, xbraces}} \) Side X-Braces
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Purpose: Secondary Brace Count.
Logic: Defines the number of supplemental bracing units distributed toward the outer ends of the chassis.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( X_{\text{sides}} \) Sides
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Purpose: Symmetry Constant.
Logic: A multiplier ensuring that bracing units are mirrored equally on both lateral faces of the skeleton.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( \Sigma X_{\text{xbraces}} \) Total X-Braces 0.000000
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Purpose: Aggregate Brace Count.
Logic: The cumulative number of X-frame assemblies providing torsional stability to the chassis.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Centre X-Brace + ( Side X-Braces * Sides )
Python Logic: N/A
Live Evaluation: N/A
\( X_{\text{xbrace, struts}} \) X-Brace Struts per X-Brace
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Purpose: Member Density.
Logic: Defines the number of diagonal members required to complete a single X-brace unit.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( \Sigma X_{\text{xbrace, struts}} \) Total X-Brace Struts 0.000000
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Purpose: Global Member Count.
Logic: The total physical number of diagonal carbon fiber struts required for the entire inner skeleton assembly.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
X-Brace Struts per X-Brace * ( Centre X-Brace + ( Side X-Braces * Sides ) )
Python Logic: N/A
Live Evaluation: N/A
\( \Sigma L_{\text{xbrace, strut}} \) Total X-Brace Strut Length (m) 0.000000
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Purpose: Cumulative Linear Mass.
Logic: The total length of bracing material used to synthesize the mass and volume of the torsional core.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Diagonal Strut Length (m) * Total X-Brace Struts
Python Logic: N/A
Live Evaluation: N/A
\( F_{\text{applied, strut}} \) Applied Force per Strut (N) 0.000000
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Purpose: Diagonal Load Allocation.
Logic: Resolves the total lateral side-shearing force into individual pushing/pulling loads for each bracing member.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
( Design Lateral Shear (N) / Total X-Braces ) / 2
Python Logic: N/A
Live Evaluation: N/A
\( X_{\text{expansion, factor}} \) Expansion Factor (Hollow)
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Purpose: Rigidity Multiplier.
Logic: Controls the "stretching" of solid material into a hollow profile to maximize bending resistance without adding dead weight.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( A_{\text{req, strut}} \) Required Strut Area (m2) 0.000000
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Purpose: Stiffness Demand.
Logic: The cross-sectional area of solid carbon fiber actually required to maintain longitudinal and torsional precision under load.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
( Applied Force per Strut (N) * Diagonal Strut Length (m) ) / ( ( Carbon Fibre Modulus (GPa) * 10^9 ) * Max Allowable Deflection (m) )
Python Logic: N/A
Live Evaluation: N/A
\( \eta_{\text{strut, aspect}} \) Strut Aspect Ratio (h:w)
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Purpose: Profile Strategy.
Logic: Defines the rectangular footprint of the strut to optimize it for directional stiffness versus weight.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( W_{\text{prescribed, strut}} \) Prescribed Strut Width (m) 0.000000
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Purpose: Architectural Output.
Logic: The calculated external width of the hollow strut required to satisfy both stiffness and geometry constraints.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
SQRT ( Required Strut Area (m2) / Strut Aspect Ratio ) * Expansion Factor
Python Logic: N/A
Live Evaluation: N/A
\( H_{\text{prescribed, strut}} \) Prescribed Strut Height (m) 0.000000
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Purpose: Architectural Output.
Logic: The calculated external height of the hollow strut based on the prescribed width and target aspect ratio.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Prescribed Strut Width (m) * Strut Aspect Ratio
Python Logic: N/A
Live Evaluation: N/A
\( W_{\text{synthesized, thickness}} \) Synthesized Wall Thickness (m) 0.091448
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Purpose: The Blueprint.
Logic: The exact manufacturing wall thickness required to ensure the hollow diagonal brace remains structurally stable.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
( Prescribed Strut Width (m) / 2 ) * ( 1 - SQRT ( MAX ( 0, 1 - ( 1 / ( Expansion Factor (Hollow) ^ 2) ) ) ) )
Python Logic: N/A
Live Evaluation: N/A
\( M_{\text{predicted, xbrace}} \) Predicted X-Brace Mass (kg) 0.000000
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Purpose: Mass Output.
Logic: The calculated dead-weight of the torsional bracing system required to guarantee the precision of the electromagnetic path.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Required Strut Area (m2) * Total X-Brace Strut Length (m) * Carbon Fiber Density (kg/m3)
Python Logic: N/A
Live Evaluation: N/A
X-Brace Safety & Torsional Audit
\( \sigma_{\text{axial, stress}} \) Axial Stress (MPa) 0.000000
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Purpose: Strut Pressure.
Logic: Measures the intense internal tensile (pulling) or compressive (pushing) pressure felt by the diagonal carbon fibers.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
( Applied Force per Strut (N) / Required Strut Area (m2) ) / 1,000,000
Python Logic: N/A
Live Evaluation: N/A
\( \sigma_{\text{material, yield}} \) Material Yield Strength (MPa) 598.000000
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Purpose: Ultimate Threshold.
Logic: Establishes the maximum stress the material can withstand before entering the plastic deformation zone (permanent damage).
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
\( SF_{\text{structural, safety}} \) Structural Safety Factor 5.283688
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Purpose: Safety Margin.
Logic: Evaluates the massive headroom available in the material compared to the applied torsional load.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Material Yield Strength (MPa) / Axial Stress (MPa)
Python Logic: N/A
Live Evaluation: N/A
\( X_{\text{xbrace, safety}} \) X-Brace Safety & Torsional Blueprint Validation 0.000000
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Purpose: Status Validation.
Logic: Automated confirmation that the X-brace geometry provides absolute torsional stability for the electromagnetic path.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
IF ( Structural Safety Factor > Safety Factor Slider, "ULTRA-SAFE", "REVISE" )
Python Logic: N/A
Live Evaluation: N/A
Vertical Pillars
\( X_{\text{central, pillars}} \) Central Pillars
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Purpose: Primary Uprights.
Logic: Defines the count of main vertical members located at the longitudinal center of each side frame.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( X_{\text{corner, pillars}} \) Corner Pillars
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Purpose: End-Cap Uprights.
Logic: Defines the count of vertical members positioned at the critical transition points between the straight and curved track sections.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( X_{\text{xbrace, support}} \) X-Brace Support Pillars 0.000000
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Purpose: Intermediate Bracing Uprights.
Logic: Calculates the supplemental vertical members required to properly anchor all the distributed X-brace frames.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Total X-Braces - Centre X-Brace
Python Logic: N/A
Live Evaluation: N/A
\( X_{\text{pillars, side}} \) Pillars per Side 0.000000
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Purpose: Lateral Support Count.
Logic: The total number of vertical compression members integrated into a single side of the internal skeleton.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Central Pillars + Corner Pillars + X-Brace Support Pillars
Python Logic: N/A
Live Evaluation: N/A
\( \Sigma X_{\text{pillars}} \) Total Pillars 0.000000
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Purpose: Global Component Count.
Logic: The cumulative number of vertical pillars required within the entire internal chassis.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Pillars per Side * Sides
Python Logic: N/A
Live Evaluation: N/A
\( \Sigma L_{\text{vertical, pillar}} \) Total Vertical Pillar Length (m) 0.000000
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Purpose: Cumulative Vertical Span.
Logic: The total linear length of all upright members, used to synthesize the mass and volume of the skeleton.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Total Pillars * X-Brace Frame Height (m)
Python Logic: N/A
Live Evaluation: N/A
\( F_{\text{applied, pillar}} \) Applied Force per Pillar (N) 0.000000
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Purpose: Structural Node Load.
Logic: The resolved lateral design force allocated specifically to each individual upright member.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Design Lateral Shear (N) / Total Pillars
Python Logic: N/A
Live Evaluation: N/A
\( A_{\text{req, pillar}} \) Required Pillar Area (m2) 0.000000
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Purpose: Stiffness Demand.
Logic: The minimum cross-sectional area of solid carbon fiber required to prevent the pillars from bowing sideways beyond the precision limit.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
( Applied Force per Pillar (N) * X-Brace Frame Height (m) ) / ( ( Carbon Fibre Modulus (GPa) * 10^9 ) * Max Allowable Deflection (m) )
Python Logic: N/A
Live Evaluation: N/A
\( \eta_{\text{pillar, aspect}} \) Pillar Aspect Ratio (h:w)
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Purpose: Profile Strategy.
Logic: Defines the square or rectangular footprint of the pillar to perfectly balance vertical load capacity versus lateral stiffness.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( H_{\text{prescribed, pillar}} \) Prescribed Pillar Depth (m) 0.000000
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Purpose: Architectural Output.
Logic: The mathematically calculated optimal depth dimension for the pillar's cross-section.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
SQRT ( Required Pillar Area (m2) * Pillar Aspect Ratio (h:w) )
Python Logic: N/A
Live Evaluation: N/A
\( W_{\text{prescribed, pillar}} \) Prescribed Pillar Width (m) 0.000000
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Purpose: Architectural Output.
Logic: The calculated optimal width dimension for the pillar's cross-section.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Prescribed Pillar Depth (m) / Pillar Aspect Ratio (h:w)
Python Logic: N/A
Live Evaluation: N/A
\( W_{\text{synthesized, thickness}} \) Synthesized Wall Thickness (m) 0.091448
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Purpose: The Blueprint.
Logic: The precise manufacturing wall thickness required to ensure the hollow pillar remains axially stable without carrying unneeded weight.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
( Prescribed Pillar Width (m) / 2 ) * ( 1 - SQRT ( MAX ( 0, 1 - ( Required Pillar Area (m2) / ( Prescribed Pillar Depth (m) * Prescribed Pillar Width (m) ) ) ) ) )
Python Logic: N/A
Live Evaluation: N/A
\( M_{\text{predicted, pillar}} \) Predicted Pillar Mass (kg) 0.000000
View Help Guide
Purpose: Blueprint Weight.
Logic: The calculated dead-weight of a single vertical upright required to maintain the skeleton's geometric integrity.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Required Pillar Area (m2) * Total Vertical Pillar Length (m) * Carbon Fiber Density (kg/m3)
Python Logic: N/A
Live Evaluation: N/A
\( \Sigma M_{\text{pillar}} \) Total Pillar Mass (kg) 0.000000
View Help Guide
Purpose: Blueprint Weight.
Logic: The combined mass of all vertical uprights required for the entire track skeleton.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Predicted Pillar Mass (kg) x Total Pillars
Python Logic: N/A
Live Evaluation: N/A
Vertical Pillar Safety & Buckling Audit
\( F_{\text{critical, buckling}} \) Critical Buckling Load (N) 0.000000
View Help Guide
Purpose: Stability Limit.
Logic: The theoretical load threshold at which the vertical pillar would undergo sudden, catastrophic lateral collapse (Euler Buckling).
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
( PI()^2 * ( Carbon Fibre Modulus (GPa) * 10^9 ) * ( ( ( Prescribed Pillar Width (m) * ( Prescribed Pillar Depth (m) ^ 3 ) ) / 12 ) - ( ( ( Prescribed Pillar Width (m) - ( 2 * Synthesized Wall Thickness (m) ) ) * ( ( Prescribed Pillar Depth (m) - ( 2 * Synthesized Wall Thickness (m) ) ) ^ 3 ) ) / 12 ) ) ) / ( X-Brace Frame Height (m) ^ 2 )
Python Logic: N/A
Live Evaluation: N/A
\( \sigma_{\text{peak, compressive}} \) Peak Compressive Stress (MPa) 0.000000
View Help Guide
Purpose: Peak Axial Stress.
Logic: Measures the internal crushing pressure experienced by the carbon fiber molecules under maximum operational load.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
( Applied Force per Pillar (N) / Required Pillar Area (m2) ) / 1,000,000
Python Logic: N/A
Live Evaluation: N/A
\( SF_{\text{structural, safety}} \) Structural Safety Factor 5.283688
View Help Guide
Purpose: Safety Margin.
Logic: The ratio between the material's elastic limit and the applied crushing stress, verifying the column's ultimate capacity.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Material Yield Strength (MPa) / Peak Compressive Stress (MPa)
Python Logic: N/A
Live Evaluation: N/A
\( X_{\text{vertical, pillar}} \) Vertical Pillar Safety & Buckling Blueprint Validation 0.000000
View Help Guide
Purpose: Status Validation.
Logic: Automated confirmation that the newly synthesized hollow vertical pillar geometry is completely immune to buckling and crushing failure.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
IF ( Structural Safety Factor > Safety Factor Slider, "ULTRA-SAFE", "REVISE" )
Python Logic: N/A
Live Evaluation: N/A
Corner Arc Skeleton
\( R_{\text{corner, arc}} \) Corner Arc Radius (m) 0.000000
View Help Guide
Purpose: Curve Geometry.
Logic: Defines the physical radius of the rounded inner frame ends to ensure perfect skeletal alignment.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Cage Corner Radius (m)
Python Logic: N/A
Live Evaluation: N/A
\( C_{\text{circ, side}} \) Circumference per Side (m) 0.000000
View Help Guide
Purpose: Full Loop Path.
Logic: The combined linear distance of the two 180-degree arcs on a single side-frame assembly.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
2 * PI() * Corner Arc Radius (m)
Python Logic: N/A
Live Evaluation: N/A
\( \Sigma L_{\text{curved, rail}} \) Total Curved Rail Length (m) 0.000000
View Help Guide
Purpose: Cumulative Arc Length.
Logic: The total longitudinal distance of all curved rails across both side frames for mass synthesis.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Circumference per Side (m) * Sides
Python Logic: N/A
Live Evaluation: N/A
\( F_{\text{applied, curves}} \) Applied Force to Curves (N) 0.000000
View Help Guide
Purpose: Radial Outward Thrust.
Logic: The peak distributed centripetal force violently pressing against every meter of the curved frame.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Design Distributed Load (N/m)
Python Logic: N/A
Live Evaluation: N/A
\( A_{\text{req, curve}} \) Required Curve Area (m2) 0.000000
View Help Guide
Purpose: Stiffness Area.
Logic: The cross-sectional solid carbon fiber area required per arc meter to maintain the strict sub-millimeter precision limit.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
( Applied Force to Curves (N) * Corner Arc Radius (m) ) / ( ( Carbon Fibre Modulus (GPa) * 10^9 ) * Max Allowable Deflection (m) )
Python Logic: N/A
Live Evaluation: N/A
\( W_{\text{prescribed, arc}} \) Prescribed Arc Width (m) 0.000000
View Help Guide
Purpose: Structural Continuity.
Logic: Matches the horizontal width of the straight rails to ensure a perfectly seamless load path and flush physical transition.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Prescribed Rail Width (m)
Python Logic: N/A
Live Evaluation: N/A
\( W_{\text{synthesized, arc}} \) Synthesized Arc Thickness (m) 0.000000
View Help Guide
Purpose: The Blueprint.
Logic: The mathematically calculated vertical thickness of the carbon fiber arc required to prevent the curve from expanding outward under load.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Required Curve Area (m2) / Prescribed Arc Width (m)
Python Logic: N/A
Live Evaluation: N/A
\( M_{\text{curved, rail}} \) Curved Rail Mass (kg) 0.000000
View Help Guide
Purpose: Arc Mass Output.
Logic: The calculated total dead-weight of the curved skeletal components engineered for the deflection target.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Required Curve Area (m2) * Total Curved Rail Length (m) * Carbon Fiber Density (kg/m3)
Python Logic: N/A
Live Evaluation: N/A
Corner Arc Safety & Stress Audit
\( F_{\text{hoop, tension}} \) Hoop Tension Load (N) 0.000000
View Help Guide
Purpose: Radial Internal Tension.
Logic: Calculates the massive "bursting" force attempting to stretch and elongate the curved carbon fiber strands.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Applied Force to Curves (N) * Corner Arc Radius (m)
Python Logic: N/A
Live Evaluation: N/A
\( \sigma_{\text{peak, tensile}} \) Peak Tensile Stress (MPa) 0.000000
View Help Guide
Purpose: Fiber Tensile Pressure.
Logic: Measures the actual physical pull experienced by the carbon fiber filaments within the curve under peak load.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
( Hoop Tension Load (N) / Required Curve 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 Threshold.
Logic: Establishes the absolute peak stress the material can endure before permanently losing its precision elastic memory.
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
\( SF_{\text{structural, safety}} \) Structural Safety Factor 5.283688
View Help Guide
Purpose: Safety Margin.
Logic: The ratio between material capacity and peak centrifugal pull, ensuring the arcs remain perfectly circular.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Material Yield Strength (MPa) / Peak Tensile Stress (MPa)
Python Logic: N/A
Live Evaluation: N/A
\( \sigma_{\text{corner, arc}} \) Corner Arc Safety & Stress Blueprint Validation 0.000000
View Help Guide
Purpose: Status Validation.
Logic: Automated confirmation that the newly synthesized curved end-caps are structurally immune to expansion or failure.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
IF ( Structural Safety Factor > Safety Factor Slider, "ULTRA-SAFE", "REVISE" )
Python Logic: N/A
Live Evaluation: N/A
T-Connections
\( X_{\text{pillar, tspokes}} \) Pillar T-Spokes per Curve
View Help Guide
Purpose: Internal Radius Bars.
Logic: Defines the exact count of horizontal reinforcement spokes used to rigidly anchor the curve arc back to the central shaft axis.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( \Sigma X_{\text{tspokes}} \) Total T-Spokes 0.000000
View Help Guide
Purpose: Global Spoke Count.
Logic: The cumulative number of horizontal radial bracing bars across the entire internal chassis.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Pillar T-Spokes per Curve * 2 * Sides
Python Logic: N/A
Live Evaluation: N/A
\( \Sigma L_{\text{tspoke}} \) Total T-Spoke Length (m) 0.000000
View Help Guide
Purpose: Cumulative Spoke Distance.
Logic: The total linear length of all horizontal radial members combined, used for volume and mass modeling.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Total T-Spokes * Corner Arc Radius (m)
Python Logic: N/A
Live Evaluation: N/A
\( \eta_{\text{tspoke, aspect}} \) T-Spoke Aspect Ratio (h:w)
View Help Guide
Purpose: Profile Strategy.
Logic: Sets the square or rectangular cross-sectional footprint for the internal radial bracing struts.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( W_{\text{prescribed, spoke}} \) Prescribed Spoke Width (m) 0.000000
View Help Guide
Purpose: Architectural Output.
Logic: The calculated physical width of the radial spoke required to match the material strength demand of the associated curve.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
SQRT ( Required Curve Area (m2) / T-Spoke Aspect Ratio (h:w) )
Python Logic: N/A
Live Evaluation: N/A
\( H_{\text{prescribed, spoke}} \) Prescribed Spoke Height (m) 0.000000
View Help Guide
Purpose: Architectural Output.
Logic: The calculated vertical dimension of the spoke cross-section.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Prescribed Spoke Width (m) / T-Spoke Aspect Ratio (h:w)
Python Logic: N/A
Live Evaluation: N/A
\( M_{\text{tspoke}} \) T-Spoke Mass (kg) 0.000000
View Help Guide
Purpose: Spoke Mass Output.
Logic: The total calculated dead-weight of the radial internal anchors holding the skeletal system together.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Required Curve Area (m2) * Total T-Spoke Length (m) * Carbon Fiber Density (kg/m3)
Python Logic: N/A
Live Evaluation: N/A
T-Spoke Safety & Buckling Audit
\( X_{\text{applied, compression}} \) Applied Compression (N) 0.000000
View Help Guide
Purpose: Radial Load.
Logic: The specific compressive force being aggressively pushed back into the center shaft by each individual spoke.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Applied Force to Curves (N) / Total T-Spokes
Python Logic: N/A
Live Evaluation: N/A
\( \sigma_{\text{peak, compressive}} \) Peak Compressive Stress (MPa) 0.000000
View Help Guide
Purpose: Spoke Pressure.
Logic: Measures the internal crushing pressure actually felt by the horizontal carbon fiber reinforcement bars.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
( Applied Compression (N) / Required Curve Area (m2) ) / 1,000,000
Python Logic: N/A
Live Evaluation: N/A
\( F_{\text{critical, buckling}} \) Critical Buckling Load (N) 0.000000
View Help Guide
Purpose: Stability Limit.
Logic: The mathematical maximum force the spoke can handle before it suddenly bows or "pops" sideways under pressure.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
( PI()^2 * ( Carbon Fibre Modulus (GPa) * 10^9 ) * ( ( Prescribed Spoke Width^4 ) / 12 ) ) / ( Corner Arc Radius (m)^2 )
Python Logic: N/A
Live Evaluation: N/A
\( SF_{\text{buckling, safety}} \) Buckling Safety Factor 0.000000
View Help Guide
Purpose: Stability Margin.
Logic: Evaluates the headroom before lateral structural failure; absolutely critical to ensure the cage remains perfectly circular.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Critical Buckling Load (N) / Applied Compression (N)
Python Logic: N/A
Live Evaluation: N/A
\( \sigma_{\text{material, yield}} \) Material Yield Strength (MPa) 598.000000
View Help Guide
Purpose: Ultimate Threshold.
Logic: Defines the maximum stress the material can handle before losing its precision elastic memory.
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
\( SF_{\text{material, safety}} \) Material Safety Factor 0.000000
View Help Guide
Purpose: Material Margin.
Logic: The ratio of the material's raw crushing strength compared to the applied axial pressure.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Material Yield Strength (MPa) / Peak Compressive Stress (MPa)
Python Logic: N/A
Live Evaluation: N/A
\( X_{\text{tspoke, safety}} \) T-Spoke Safety & Buckling Blueprint Validation 0.000000
View Help Guide
Purpose: Status Validation.
Logic: Automated confirmation that the radial spokes remain perfectly rigid, keeping the drive gear completely center-locked.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
IF ( AND ( Buckling Safety Factor > Safety Factor Slider, Material Safety Factor > Safety Factor Slider ) , "ULTRA-SAFE" , "REVISE" )
Python Logic: N/A
Live Evaluation: N/A
Final Skeleton Aggregation
\( M_{\text{predicted, rail}} \) Predicted Rail Mass (kg) 1,354.776385
View Help Guide
Purpose: Longitudinal Mass.
Logic: Total accumulated weight of the horizontal straight skeletal rails.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Predicted Rail Mass (kg)
Python Logic: N/A
Live Evaluation: N/A
\( M_{\text{predicted, xbrace}} \) Predicted X-Brace Mass (kg) 0.000000
View Help Guide
Purpose: Torsional Mass.
Logic: Total accumulated weight of all internal diagonal X-bracing struts.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Predicted X-Brace Mass (kg)
Python Logic: N/A
Live Evaluation: N/A
\( \Sigma M_{\text{pillar}} \) Total Pillar Mass (kg) 0.000000
View Help Guide
Purpose: Vertical Mass.
Logic: Total accumulated weight of the vertical compression uprights.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Total Pillar Mass (kg)
Python Logic: N/A
Live Evaluation: N/A
\( M_{\text{curved, rail}} \) Curved Rail Mass (kg) 0.000000
View Help Guide
Purpose: Arc Mass.
Logic: Total accumulated weight of the curved skeletal end-caps.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Curved Rail Mass (kg)
Python Logic: N/A
Live Evaluation: N/A
\( M_{\text{tspoke}} \) T-Spoke Mass (kg) 0.000000
View Help Guide
Purpose: Radial Mass.
Logic: Total accumulated weight of the horizontal internal support spokes.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
T-Spoke Mass (kg)
Python Logic: N/A
Live Evaluation: N/A
\( \Sigma M_{\text{skeleton}} \) Total Skeleton Mass (kg) 0.000000
View Help Guide
Purpose: Aggregate Chassis Mass.
Logic: The final, combined dry weight of the entire internal carbon fiber skeleton.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Predicted Rail Mass (kg) + Predicted X-Brace Mass (kg) + Total Pillar Mass (kg) + Curved Rail Mass (kg) + T-Spoke Mass (kg)
Python Logic: N/A
Live Evaluation: N/A