Inner Dashboard
| ▼ Inner Structural Synthesis | ||||
| ☰ | \( R \) | Gear Radius (m) | 1.846197 |
View Help GuidePurpose: 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] 1.8462 = 1.8462
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| ☰ | \( X_{\text{track, int}} \) | Track Internal Offset (m) | 0.619158 |
View Help GuidePurpose: 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] ( 0.1436 / 2 ) + 0.1882 + 0.3591 = 0.6192
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| ☰ | \( H_{\text{track}} \) | Track Height (m) | 4.93071 |
View Help GuidePurpose: 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)"] ) * 2Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 1.8462 + ( 0.1436 / 2 ) + 0.1882+ 0.3591 ) * 2 = 4.9307
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| ☰ | \( R_{\text{cage, corner}} \) | Cage Corner Radius (m) | 1.22704 |
View Help GuidePurpose: 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] 1.8462 - 0.6192 = 1.2270
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| ☰ | \( H_{\text{cage, section}} \) | Cage Section Height (m) | 1.22704 |
View Help GuidePurpose: 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] 1.2270 = 1.2270
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| ☰ | \( H_{\text{xbrace, frame}} \) | X-Brace Frame Height (m) | 1.22704 |
View Help GuidePurpose: 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] 1.2270 = 1.2270
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| ☰ | \( L_{\text{straight, track}} \) | Straight Track Length (m) | 4 |
View Help GuidePurpose: 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] 4.0000 = 4.0000
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| ▼ Side Frame Structure | ||||
| ☰ | \( X_{\text{straight, side}} \) | Straight Side Rails |
View Help GuidePurpose: 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/ALive Evaluation: N/A (Input Variable)
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| ☰ | \( \Sigma L_{\text{straight, rail}} \) | Total Straight Rail Length (m) | 12 |
View Help GuidePurpose: 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] 4.0000 * 3.0000 = 12.0000
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| ☰ | \( F_{\text{applied, rail}} \) | Applied Force per Rail (N) | 172,637.901042 |
View Help GuidePurpose: 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] 517,913.7031 / 3.0000 = 172,637.9010
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| ☰ | \( A_{\text{req, rail}} \) | Required Rail Material Area (m2) | 0.040032 |
View Help GuidePurpose: 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:
$$A_{\text{req, rail}} = ( F_{\text{applied, rail}} \times L_{\text{straight, track}} ) / ( ( \text{Fossil Carbon Fibre Modulus (GPa)} \times 10^9 ) \times \Delta_{\text{max, allowable}} )$$ Python Logic:
( v["Applied Force per Rail (N)"] * v["Straight Track Length (m)"] ) / ( ( v["Fossil Carbon Fibre Modulus (GPa)"] * 10^9 ) * v["Max Allowable Deflection (m)"] )Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 172,637.9010 * 4.0000 ) / ( ( 230.0000 * 10**9 ) * 0.0001 ) = 0.0400
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| ☰ | \( \eta_{\text{target, aspect}} \) | Target Aspect Ratio (h:w) |
View Help GuidePurpose: 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/ALive Evaluation: N/A (Input Variable)
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| ☰ | \( H_{\text{prescribed, rail}} \) | Prescribed Rail Height (m) | 0.223696 |
View Help GuidePurpose: 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 ( 0.0400 * 1.2500 ) = 0.2237
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| ☰ | \( W_{\text{prescribed, rail}} \) | Prescribed Rail Width (m) | 0.178957 |
View Help GuidePurpose: 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] 0.2237/ 1.2500 = 0.1790
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| ☰ | \( W_{\text{synthesized, thickness}} \) | Synthesized Wall Thickness (m) | 0.011036 |
View Help GuidePurpose: 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] ( 0.1790 / 2 ) * ( 1 - SQRT ( 1 - ( 0.0400 / (0.2237 * 0.1790 ) ) ) ) = 0.0110
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| ☰ | \( V_{\text{rail, output}} \) | Side Rail Total Volume (m3) | 0.480384 |
View Help GuidePurpose: 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] 0.0400 * 12.0000 = 0.4804
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| ☰ | \( M_{\text{predicted, rail}} \) | Side Rail Total Mass (kg) | 864.690705 |
View Help GuidePurpose: 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:
$$M_{\text{predicted, rail}} = \text{Side Rail Total Volume (m3)} \times D_{\text{FCF}}$$ Python Logic:
v["Side Rail Total Volume (m3)"] * v["Fossil Carbon Fibre Density (kg.m3)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.4804 * 1,800.0000 = 864.6907
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| ▼ Side Rail Safety & Stress Audit | ||||
| ☰ | \( X_{\text{bending, moment}} \) | Side Rail Bending Moment (Nm) | 172,637.901042 |
View Help GuidePurpose: 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)"] ) / 4Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 172,637.9010* 4.0000 ) / 4 = 172,637.9010
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| ☰ | \( I_{\text{inertia}} \) | Side Rail Moment of Inertia (I) | 0.000167 |
View Help GuidePurpose: 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] ( 0.1790 * (0.2237 ** 3 ) / 12 ) * ( 1 - ( ( 1 - ( 2 * 0.0110 / 0.1790 ) ) ** 4 ) ) = 0.0002
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| ☰ | \( \sigma_{\text{peak, operating}} \) | Side Rail Peak Operating Stress (MPa) | 115.670326 |
View Help GuidePurpose: 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["Side Rail Bending Moment (Nm)"] * (v["Prescribed Rail Height (m)"] / 2 ) ) / v["Side Rail Moment of Inertia (I)"] ) / 1000000Live Evaluation: [ROUTE: STATIC/GLOBAL] ( ( 172,637.9010 * (0.2237 / 2 ) ) / 0.0002 ) / 1000000 = 115.6703
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| ☰ | \( SF_{\text{structural, safety}} \) | Side Rail Structural Safety Factor | 5.169865 |
View Help GuidePurpose: 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["Fossil Carbon Fibre Material Yield Strength (MPa)"]/v["Side Rail Peak Operating Stress (MPa)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 598.0000/115.6703 = 5.1699
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| ☰ | \( \sigma_{\text{side, rail}} \) | Side Rail Safety & Stress Blueprint Validation | ULTRA-SAFE |
View Help GuidePurpose: 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["Side Rail Structural Safety Factor"] > v["Safety Factor Slider"] else 0Live Evaluation: [ROUTE: STATIC/GLOBAL] 1 if 5.1699 > 2.5000 else 0 = 1.0000
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| ▼ Inner Skeleton | ||||
| ☰ | \( W_{\text{cage, inner}} \) | Cage Inner Width (m) | 3.102591 |
View Help GuidePurpose: 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:
$$W_{\text{cage, inner}} = \Sigma W$$ Python Logic:
v["Total Track width (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 3.1026 = 3.1026
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| ☰ | \( L_{\text{diagonal, strut}} \) | Diagonal Strut Length (m) | 3.336419 |
View Help GuidePurpose: 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:
$$L_{\text{diagonal, strut}} = SQRT ( ( H_{\text{xbrace, frame}} ^ 2 ) + ( W_{\text{cage, inner}} ^ 2) )$$ Python Logic:
SQRT ( ( v["X-Brace Frame Height (m)"] ^ 2 ) + ( v["Cage Inner Width (m)"] ^ 2) )Live Evaluation: [ROUTE: STATIC/GLOBAL] SQRT ( ( 1.2270 ** 2 ) + ( 3.1026 ** 2) ) = 3.3364
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| ☰ | \( X_{\text{centre, xbrace}} \) | Centre X-Brace |
View Help GuidePurpose: 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/ALive Evaluation: N/A (Input Variable)
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| ☰ | \( X_{\text{side, xbraces}} \) | Side X-Braces |
View Help GuidePurpose: 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/ALive Evaluation: N/A (Input Variable)
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| ☰ | \( X_{\text{sides}} \) | Inner Skeleton Sides |
View Help GuidePurpose: 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/ALive Evaluation: N/A (Input Variable)
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| ☰ | \( \Sigma X_{\text{xbraces}} \) | Total X-Braces | 3 |
View Help GuidePurpose: 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:
$$\Sigma X_{\text{xbraces}} = X_{\text{centre, xbrace}} + ( X_{\text{side, xbraces}} \times X_{\text{sides}} )$$ Python Logic:
v["Centre X-Brace"] + ( v["Side X-Braces"] * v["Inner Skeleton Sides"] )Live Evaluation: [ROUTE: STATIC/GLOBAL] 1.0000 + ( 1.0000 * 2.0000 ) = 3.0000
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| ☰ | \( X_{\text{xbrace, struts}} \) | X-Brace Struts per X-Brace |
View Help GuidePurpose: 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/ALive Evaluation: N/A (Input Variable)
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| ☰ | \( \Sigma X_{\text{xbrace, struts}} \) | Total X-Brace Struts | 6 |
View Help GuidePurpose: 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:
$$\Sigma X_{\text{xbrace, struts}} = X_{\text{xbrace, struts}} \times ( X_{\text{centre, xbrace}} + ( X_{\text{side, xbraces}} \times X_{\text{sides}} ) )$$ Python Logic:
v["X-Brace Struts per X-Brace"] * ( v["Centre X-Brace"] + ( v["Side X-Braces"] * v["Inner Skeleton Sides"] ) )Live Evaluation: [ROUTE: STATIC/GLOBAL] 2.0000 * ( 1.0000 + ( 1.0000 * 2.0000 ) ) = 6.0000
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| ☰ | \( \Sigma L_{\text{xbrace, strut}} \) | Total X-Brace Strut Length (m) | 20.018517 |
View Help GuidePurpose: 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:
$$\Sigma L_{\text{xbrace, strut}} = L_{\text{diagonal, strut}} \times \Sigma X_{\text{xbrace, struts}}$$ Python Logic:
v["Diagonal Strut Length (m)"] * v["Total X-Brace Struts"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 3.3364 * 6.0000 = 20.0185
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| ☰ | \( F_{\text{applied, strut}} \) | Applied Force per Strut (N) | 86,318.950521 |
View Help GuidePurpose: 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:
$$F_{\text{applied, strut}} = ( \tau_{\text{design, lateral}} / \Sigma X_{\text{xbraces}}) / 2$$ Python Logic:
( v["Design Lateral Shear (N)"] / v["Total X-Braces"]) / 2Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 517,913.7031 / 3.0000) / 2 = 86,318.9505
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| ☰ | \( X_{\text{expansion, factor}} \) | Expansion Factor (Hollow) |
View Help GuidePurpose: 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/ALive Evaluation: N/A (Input Variable)
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| ☰ | \( A_{\text{req, strut}} \) | Required Strut Area (m2) | 0.016695 |
View Help GuidePurpose: 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:
$$A_{\text{req, strut}} = ( F_{\text{applied, strut}} \times L_{\text{diagonal, strut}} ) / ( ( \text{Fossil Carbon Fibre Modulus (GPa)} \times 10^9 ) \times \Delta_{\text{max, allowable}} )$$ Python Logic:
( v["Applied Force per Strut (N)"] * v["Diagonal Strut Length (m)"] ) / ( ( v["Fossil Carbon Fibre Modulus (GPa)"] * 10^9 ) * v["Max Allowable Deflection (m)"] )Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 86,318.9505 * 3.3364 ) / ( ( 230.0000 * 10**9 ) * 0.0001 ) = 0.0167
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| ☰ | \( \eta_{\text{strut, aspect}} \) | Strut Aspect Ratio (h:w) |
View Help GuidePurpose: 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/ALive Evaluation: N/A (Input Variable)
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| ☰ | \( W_{\text{prescribed, strut}} \) | Prescribed Strut Width (m) | 0.086677 |
View Help GuidePurpose: 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:
$$W_{\text{prescribed, strut}} = SQRT ( A_{\text{req, strut}} / \eta_{\text{strut, aspect}} ) \times X_{\text{expansion, factor}}$$ Python Logic:
SQRT ( v["Required Strut Area (m2)"] / v["Strut Aspect Ratio (h:w)"] ) * v["Expansion Factor (Hollow)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] SQRT ( 0.0167 / 5.0000 ) * 1.5000 = 0.0867
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| ☰ | \( H_{\text{prescribed, strut}} \) | Prescribed Strut Height (m) | 0.433386 |
View Help GuidePurpose: 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:
$$H_{\text{prescribed, strut}} = W_{\text{prescribed, strut}} \times \eta_{\text{strut, aspect}}$$ Python Logic:
v["Prescribed Strut Width (m)"] * v["Strut Aspect Ratio (h:w)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0867 * 5.0000 = 0.4334
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| ☰ | \( W_{\text{synthesized, thickness}} \) | Synthesized Wall Thickness (m) | 0.011036 |
View Help GuidePurpose: 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:
$$W_{\text{synthesized, thickness}} = ( W_{\text{prescribed, strut}} / 2 ) \times ( 1 - SQRT ( MAX ( 0, 1 - ( 1 / ( X_{\text{expansion, factor}} ^ 2) ) ) ) )$$ Python Logic:
( v["Prescribed Strut Width (m)"] / 2 ) * ( 1 - SQRT ( MAX ( 0, 1 - ( 1 / ( v["Expansion Factor (Hollow)"] ^ 2) ) ) ) )Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 0.0867 / 2 ) * ( 1 - SQRT ( MAX ( 0, 1 - ( 1 / ( 1.5000 ** 2) ) ) ) ) = 0.0110
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| ☰ | \( \Sigma V_{\text{xbrace}} \) | X-Brace Total Volume (m3) | 0.334218 |
View Help GuidePurpose: X-Brace Volume
Logic: The total volume of the x-braces for sizing
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma V_{\text{xbrace}} = A_{\text{req, strut}} \times \Sigma L_{\text{xbrace, strut}}$$ Python Logic:
v["Required Strut Area (m2)"] * v["Total X-Brace Strut Length (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0167 * 20.0185 = 0.3342
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| ☰ | \( M_{\text{predicted, xbrace}} \) | X-Brace Total Mass (kg) | 601.592072 |
View Help GuidePurpose: 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:
$$M_{\text{predicted, xbrace}} = A_{\text{req, strut}} \times \Sigma L_{\text{xbrace, strut}} \times \text{Fossil Carbon Fibre Density (kg.m3)}$$ Python Logic:
v["Required Strut Area (m2)"] * v["Total X-Brace Strut Length (m)"] * v["Fossil Carbon Fibre Density (kg.m3)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0167 * 20.0185 * 1,800.0000 = 601.5921
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| ▼ X-Brace Safety & Torsional Audit | ||||
| ☰ | \( \sigma_{\text{axial, stress}} \) | Axial Stress (MPa) | 5.170213 |
View Help GuidePurpose: 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:
$$\sigma_{\text{axial, stress}} = ( F_{\text{applied, strut}} / A_{\text{req, strut}} ) / 1000000$$ Python Logic:
( v["Applied Force per Strut (N)"] / v["Required Strut Area (m2)"] ) / 1000000Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 86,318.9505 / 0.0167 ) / 1000000 = 5.1702
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| ☰ | \( SF_{\text{structural, safety}} \) | X-brace Structural Safety Factor | 115.662542 |
View Help GuidePurpose: 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:
$$SF_{\text{structural, safety}} = \sigma_{\text{material, yield}} / \sigma_{\text{axial, stress}}$$ Python Logic:
v["Fossil Carbon Fibre Material Yield Strength (MPa)"] / v["Axial Stress (MPa)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 598.0000 / 5.1702 = 115.6625
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| ☰ | \( X_{\text{xbrace, safety}} \) | X-Brace Safety & Torsional Blueprint Validation | ULTRA-SAFE |
View Help GuidePurpose: 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:
$$X_{\text{xbrace, safety}} = IF ( SF_{\text{structural, safety}} > SF_{\text{safety, factor}}, 1,0)$$ Python Logic:
IF ( v["X-brace Structural Safety Factor"] > v["Safety Factor Slider"], 1,0)Live Evaluation: [ROUTE: STATIC/GLOBAL] IF ( 115.6625 > 2.5000, 1,0) = 1.0000
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| ▼ Vertical Pillars | ||||
| ☰ | \( X_{\text{central, pillars}} \) | Central Pillars |
View Help GuidePurpose: 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/ALive Evaluation: N/A (Input Variable)
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| ☰ | \( X_{\text{corner, pillars}} \) | Corner Pillars |
View Help GuidePurpose: 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/ALive Evaluation: N/A (Input Variable)
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| ☰ | \( X_{\text{xbrace, support}} \) | X-Brace Support Pillars | 2 |
View Help GuidePurpose: 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:
$$X_{\text{xbrace, support}} = \Sigma X_{\text{xbraces}} - X_{\text{centre, xbrace}}$$ Python Logic:
v["Total X-Braces"] - v["Centre X-Brace"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 3.0000 - 1.0000 = 2.0000
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| ☰ | \( X_{\text{pillars, side}} \) | Pillars per Side | 5 |
View Help GuidePurpose: 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:
$$X_{\text{pillars, side}} = X_{\text{central, pillars}} + X_{\text{corner, pillars}} + X_{\text{xbrace, support}}$$ Python Logic:
v["Central Pillars"] + v["Corner Pillars"] + v["X-Brace Support Pillars"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 1.0000 + 2.0000 + 2.0000 = 5.0000
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| ☰ | \( \Sigma X_{\text{pillars}} \) | Total Pillars | 10 |
View Help GuidePurpose: 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:
$$\Sigma X_{\text{pillars}} = X_{\text{pillars, side}} \times X_{\text{sides}}$$ Python Logic:
v["Pillars per Side"] * v["Inner Skeleton Sides"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 5.0000 * 2.0000 = 10.0000
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| ☰ | \( \Sigma L_{\text{vertical, pillar}} \) | Total Vertical Pillar Length (m) | 12.270395 |
View Help GuidePurpose: 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:
$$\Sigma L_{\text{vertical, pillar}} = \Sigma X_{\text{pillars}} \times H_{\text{xbrace, frame}}$$ Python Logic:
v["Total Pillars"] * v["X-Brace Frame Height (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 10.0000 * 1.2270 = 12.2704
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| ☰ | \( F_{\text{applied, pillar}} \) | Applied Force per Pillar (N) | 51,791.370312 |
View Help GuidePurpose: 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:
$$F_{\text{applied, pillar}} = \tau_{\text{design, lateral}} / \Sigma X_{\text{pillars}}$$ Python Logic:
v["Design Lateral Shear (N)"] / v["Total Pillars"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 517,913.7031 / 10.0000 = 51,791.3703
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| ☰ | \( A_{\text{req, pillar}} \) | Required Pillar Area (m2) | 0.003684 |
View Help GuidePurpose: 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:
$$A_{\text{req, pillar}} = ( F_{\text{applied, pillar}} \times H_{\text{xbrace, frame}} ) / ( ( \text{Fossil Carbon Fibre Modulus (GPa)} \times 10^9 ) \times \Delta_{\text{max, allowable}} )$$ Python Logic:
( v["Applied Force per Pillar (N)"] * v["X-Brace Frame Height (m)"] ) / ( ( v["Fossil Carbon Fibre Modulus (GPa)"] * 10^9 ) * v["Max Allowable Deflection (m)"] )Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 51,791.3703 * 1.2270 ) / ( ( 230.0000 * 10**9 ) * 0.0001 ) = 0.0037
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| ☰ | \( \eta_{\text{pillar, aspect}} \) | Pillar Aspect Ratio (h:w) |
View Help GuidePurpose: 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/ALive Evaluation: N/A (Input Variable)
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| ☰ | \( H_{\text{prescribed, pillar}} \) | Prescribed Pillar Depth (m) | 0.060696 |
View Help GuidePurpose: 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:
$$H_{\text{prescribed, pillar}} = SQRT ( A_{\text{req, pillar}} \times \eta_{\text{pillar, aspect}})$$ Python Logic:
SQRT ( v["Required Pillar Area (m2)"] * v["Pillar Aspect Ratio (h:w)"])Live Evaluation: [ROUTE: STATIC/GLOBAL] SQRT ( 0.0037 * 1.0000) = 0.0607
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| ☰ | \( W_{\text{prescribed, pillar}} \) | Prescribed Pillar Width (m) | 0.060696 |
View Help GuidePurpose: Architectural Output.
Logic: The calculated optimal width dimension for the pillar's cross-section.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$W_{\text{prescribed, pillar}} = H_{\text{prescribed, pillar}} / \eta_{\text{pillar, aspect}}$$ Python Logic:
v["Prescribed Pillar Depth (m)"] / v["Pillar Aspect Ratio (h:w)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0607 / 1.0000 = 0.0607
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| ☰ | \( W_{\text{synthesized, thickness}} \) | Pillar Synthesized Wall Thickness (m) | 0.030348 |
View Help GuidePurpose: 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:
$$W_{\text{synthesized, thickness}} = ( W_{\text{prescribed, pillar}} / 2 ) \times ( 1 - SQRT ( MAX ( 0, 1 - ( A_{\text{req, pillar}} / ( H_{\text{prescribed, pillar}} \times W_{\text{prescribed, pillar}} ) ) ) ) )$$ Python Logic:
( v["Prescribed Pillar Width (m)"] / 2 ) * ( 1 - SQRT ( MAX ( 0, 1 - ( v["Required Pillar Area (m2)"] / ( v["Prescribed Pillar Depth (m)"] * v["Prescribed Pillar Width (m)"] ) ) ) ) )Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 0.0607 / 2 ) * ( 1 - SQRT ( MAX ( 0, 1 - ( 0.0037 / ( 0.0607 * 0.0607 ) ) ) ) ) = 0.0303
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| ☰ | \( M_{\text{predicted, pillar}} \) | Predicted Pillar Mass (kg) | 81.368798 |
View Help GuidePurpose: 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:
$$M_{\text{predicted, pillar}} = A_{\text{req, pillar}} \times \Sigma L_{\text{vertical, pillar}} \times \text{Fossil Carbon Fibre Density (kg.m3)}$$ Python Logic:
v["Required Pillar Area (m2)"] * v["Total Vertical Pillar Length (m)"] * v["Fossil Carbon Fibre Density (kg.m3)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0037 * 12.2704 * 1,800.0000 = 81.3688
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| ☰ | \( \Sigma V_{\text{vertical, pillar}} \) | Vertical Pillar Total Volume (m3) | 0.452049 |
View Help GuidePurpose: Vertical Pillar total volume
Logic: The total material volume of the vertical pillars for material use
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma V_{\text{vertical, pillar}} = A_{\text{req, pillar}} \times \Sigma L_{\text{vertical, pillar}} \times \Sigma X_{\text{pillars}}$$ Python Logic:
v["Required Pillar Area (m2)"] * v["Total Vertical Pillar Length (m)"] * v["Total Pillars"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0037 * 12.2704 * 10.0000 = 0.4520
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| ☰ | \( \Sigma M_{\text{pillar}} \) | Vertical Pillar Total Mass (kg) | 813.687985 |
View Help GuidePurpose: 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:
$$\Sigma M_{\text{pillar}} = M_{\text{predicted, pillar}} \times \Sigma X_{\text{pillars}}$$ Python Logic:
v["Predicted Pillar Mass (kg)"] * v["Total Pillars"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 81.3688 * 10.0000 = 813.6880
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| ▼ Vertical Pillar Safety & Buckling Audit | ||||
| ☰ | \( F_{\text{critical, buckling}} \) | Critical Buckling Load (N) | 1,705,229.868599 |
View Help GuidePurpose: 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:
$$F_{\text{critical, buckling}} = ( \pi^2 \times ( \text{Fossil Carbon Fibre Modulus (GPa)} \times 10^9 ) \times ( ( ( W_{\text{prescribed, pillar}} \times ( H_{\text{prescribed, pillar}} ^ 3 ) ) / 12 ) - ( ( ( W_{\text{prescribed, pillar}} - ( 2 \times W_{\text{synthesized, thickness}} ) ) \times ( ( H_{\text{prescribed, pillar}} - ( 2 \times W_{\text{synthesized, thickness}} ) ) ^ 3 ) ) / 12 ) ) ) / ( H_{\text{xbrace, frame}} ^ 2 )$$ Python Logic:
( PI()^2 * ( v["Fossil Carbon Fibre Modulus (GPa)"] * 10^9 ) * ( ( ( v["Prescribed Pillar Width (m)"] * ( v["Prescribed Pillar Depth (m)"] ^ 3 ) ) / 12 ) - ( ( ( v["Prescribed Pillar Width (m)"] - ( 2 * v["Pillar Synthesized Wall Thickness (m)"] ) ) * ( ( v["Prescribed Pillar Depth (m)"] - ( 2 * v["Pillar Synthesized Wall Thickness (m)"] ) ) ^ 3 ) ) / 12 ) ) ) / ( v["X-Brace Frame Height (m)"] ^ 2 )Live Evaluation: [ROUTE: STATIC/GLOBAL] ( PI()**2 * ( 230.0000 * 10**9 ) * ( ( ( 0.0607 * ( 0.0607 ** 3 ) ) / 12 ) - ( ( ( 0.0607 - ( 2 * 0.0303 ) ) * ( ( 0.0607 - ( 2 * 0.0303 ) ) ** 3 ) ) / 12 ) ) ) / ( 1.2270 ** 2 ) = 1,705,229.8686
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| ☰ | \( \sigma_{\text{peak, compressive}} \) | Pillar Peak Compressive Stress (MPa) | 14.058227 |
View Help GuidePurpose: 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:
$$\sigma_{\text{peak, compressive}} = ( F_{\text{applied, pillar}} / A_{\text{req, pillar}} ) / 1000000$$ Python Logic:
( v["Applied Force per Pillar (N)"] / v["Required Pillar Area (m2)"] ) / 1000000Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 51,791.3703 / 0.0037 ) / 1000000 = 14.0582
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| ☰ | \( SF_{\text{structural, safety}} \) | Pillar Structural Safety Factor | 42.53737 |
View Help GuidePurpose: 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:
$$SF_{\text{structural, safety}} = \text{Fossil Carbon Fibre Material Yield Strength (MPa)} / \sigma_{\text{peak, compressive}}$$ Python Logic:
v["Fossil Carbon Fibre Material Yield Strength (MPa)"] / v["Pillar Peak Compressive Stress (MPa)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 598.0000 / 14.0582 = 42.5374
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| ☰ | \( X_{\text{vertical, pillar}} \) | Vertical Pillar Safety & Buckling Blueprint Validation | ULTRA-SAFE |
View Help GuidePurpose: 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:
$$X_{\text{vertical, pillar}} = IF ( SF_{\text{structural, safety}} > SF_{\text{safety, factor}}, 1, 0 )$$ Python Logic:
IF ( v["Pillar Structural Safety Factor"] > v["Safety Factor Slider"], 1, 0 )Live Evaluation: [ROUTE: STATIC/GLOBAL] IF ( 42.5374 > 2.5000, 1, 0 ) = 1.0000
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| ▼ Corner Arc Skeleton | ||||
| ☰ | \( R_{\text{corner, arc}} \) | Corner Arc Radius (m) | 1.22704 |
View Help GuidePurpose: 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:
$$R_{\text{corner, arc}} = R_{\text{cage, corner}}$$ Python Logic:
v["Cage Corner Radius (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 1.2270 = 1.2270
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| ☰ | \( C_{\text{circ, side}} \) | Circumference per Side (m) | 7.709717 |
View Help GuidePurpose: 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:
$$C_{\text{circ, side}} = 2 \times \pi \times R_{\text{corner, arc}}$$ Python Logic:
2 * PI() * v["Corner Arc Radius (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 2 * PI() * 1.2270 = 7.7097
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| ☰ | \( \Sigma L_{\text{curved, rail}} \) | Total Curved Rail Length (m) | 15.419433 |
View Help GuidePurpose: 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:
$$\Sigma L_{\text{curved, rail}} = C_{\text{circ, side}} \times X_{\text{sides}}$$ Python Logic:
v["Circumference per Side (m)"] * v["Inner Skeleton Sides"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 7.7097 * 2.0000 = 15.4194
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| ☰ | \( F_{\text{applied, curves}} \) | Applied Force to Curves (N) | 847,256.492413 |
View Help GuidePurpose: 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:
$$F_{\text{applied, curves}} = F_{\text{design, distributed}}$$ Python Logic:
v["Design Distributed Load (N/m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 847,256.4924 = 847,256.4924
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| ☰ | \( A_{\text{req, curve}} \) | Required Curve Area (m2) | 0.060268 |
View Help GuidePurpose: 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:
$$A_{\text{req, curve}} = ( F_{\text{applied, curves}} \times R_{\text{corner, arc}} ) / ( ( \text{Fossil Carbon Fibre Modulus (GPa)} \times 10^9 ) \times \Delta_{\text{max, allowable}} )$$ Python Logic:
( v["Applied Force to Curves (N)"] * v["Corner Arc Radius (m)"] ) / ( ( v["Fossil Carbon Fibre Modulus (GPa)"] * 10^9 ) * v["Max Allowable Deflection (m)"] )Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 847,256.4924 * 1.2270 ) / ( ( 230.0000 * 10**9 ) * 0.0001 ) = 0.0603
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| ☰ | \( W_{\text{prescribed, arc}} \) | Prescribed Arc Width (m) | 0.178957 |
View Help GuidePurpose: 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:
$$W_{\text{prescribed, arc}} = W_{\text{prescribed, rail}}$$ Python Logic:
v["Prescribed Rail Width (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.1790 = 0.1790
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| ☰ | \( W_{\text{synthesized, arc}} \) | Synthesized Arc Thickness (m) | 0.336772 |
View Help GuidePurpose: 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:
$$W_{\text{synthesized, arc}} = A_{\text{req, curve}} / W_{\text{prescribed, arc}}$$ Python Logic:
v["Required Curve Area (m2)"] / v["Prescribed Arc Width (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0603 / 0.1790 = 0.3368
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| ☰ | \( \Sigma V_{\text{curved, rail}} \) | Curved Rail Total Volume (m3) | 0.929293 |
View Help GuidePurpose: Curved Rail Total Volume
Logic: Curved Rail Total Volume for material sizing
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma V_{\text{curved, rail}} = A_{\text{req, curve}} \times \Sigma L_{\text{curved, rail}}$$ Python Logic:
v["Required Curve Area (m2)"] * v["Total Curved Rail Length (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0603 * 15.4194 = 0.9293
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| ☰ | \( M_{\text{curved, rail}} \) | Curved Rail Total Mass (kg) | 1,672.727803 |
View Help GuidePurpose: 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:
$$M_{\text{curved, rail}} = \text{Curved Rail Total Volume (m3)} \times D_{\text{FCF}}$$ Python Logic:
v["Curved Rail Total Volume (m3)"] * v["Fossil Carbon Fibre Density (kg.m3)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.9293 * 1,800.0000 = 1,672.7278
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| ▼ Corner Arc Safety & Stress Audit | ||||
| ☰ | \( F_{\text{hoop, tension}} \) | Hoop Tension Load (N) | 1,039,617.198751 |
View Help GuidePurpose: 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:
$$F_{\text{hoop, tension}} = F_{\text{applied, curves}} \times R_{\text{corner, arc}}$$ Python Logic:
v["Applied Force to Curves (N)"] * v["Corner Arc Radius (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 847,256.4924 * 1.2270 = 1,039,617.1988
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| ☰ | \( \sigma_{\text{peak, tensile}} \) | Corner Arc Peak Tensile Stress (MPa) | 17.25 |
View Help GuidePurpose: 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:
$$\sigma_{\text{peak, tensile}} = ( F_{\text{hoop, tension}} / A_{\text{req, curve}} ) / 1000000$$ Python Logic:
( v["Hoop Tension Load (N)"] / v["Required Curve Area (m2)"] ) / 1000000Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 1,039,617.1988 / 0.0603 ) / 1000000 = 17.2500
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| ☰ | \( SF_{\text{structural, safety}} \) | Corner Arc Structural Safety Factor | 34.666667 |
View Help GuidePurpose: 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:
$$SF_{\text{structural, safety}} = \sigma_{\text{material, yield}} / \sigma_{\text{peak, tensile}}$$ Python Logic:
v["Fossil Carbon Fibre Material Yield Strength (MPa)"] / v["Corner Arc Peak Tensile Stress (MPa)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 598.0000 / 17.2500 = 34.6667
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| ☰ | \( \sigma_{\text{corner, arc}} \) | Corner Arc Safety & Stress Blueprint Validation | ULTRA-SAFE |
View Help GuidePurpose: 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:
$$\sigma_{\text{corner, arc}} = IF ( SF_{\text{structural, safety}} > SF_{\text{safety, factor}}, 1, 2 )$$ Python Logic:
IF ( v["Corner Arc Structural Safety Factor"] > v["Safety Factor Slider"], 1, 2 )Live Evaluation: [ROUTE: STATIC/GLOBAL] IF ( 34.6667 > 2.5000, 1, 2 ) = 1.0000
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| ▼ T-Connections | ||||
| ☰ | \( X_{\text{pillar, tspokes}} \) | Pillar T-Spokes per Curve |
View Help GuidePurpose: 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/ALive Evaluation: N/A (Input Variable)
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| ☰ | \( \Sigma X_{\text{tspokes}} \) | Total T-Spokes | 4 |
View Help GuidePurpose: 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:
$$\Sigma X_{\text{tspokes}} = X_{\text{pillar, tspokes}} \times 2 \times X_{\text{sides}}$$ Python Logic:
v["Pillar T-Spokes per Curve"] * 2 * v["Inner Skeleton Sides"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 1.0000 * 2 * 2.0000 = 4.0000
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| ☰ | \( \Sigma L_{\text{tspoke}} \) | Total T-Spoke Length (m) | 4.908158 |
View Help GuidePurpose: 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:
$$\Sigma L_{\text{tspoke}} = \Sigma X_{\text{tspokes}} \times R_{\text{corner, arc}}$$ Python Logic:
v["Total T-Spokes"] * v["Corner Arc Radius (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 4.0000 * 1.2270 = 4.9082
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| ☰ | \( \eta_{\text{tspoke, aspect}} \) | T-Spoke Aspect Ratio (h:w) |
View Help GuidePurpose: 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/ALive Evaluation: N/A (Input Variable)
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| ☰ | \( W_{\text{prescribed, spoke}} \) | Prescribed Spoke Width (m) | 0.245495 |
View Help GuidePurpose: 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:
$$W_{\text{prescribed, spoke}} = SQRT ( A_{\text{req, curve}} / \eta_{\text{tspoke, aspect}} )$$ Python Logic:
SQRT ( v["Required Curve Area (m2)"] / v["T-Spoke Aspect Ratio (h:w)"] )Live Evaluation: [ROUTE: STATIC/GLOBAL] SQRT ( 0.0603 / 1.0000 ) = 0.2455
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| ☰ | \( H_{\text{prescribed, spoke}} \) | Prescribed Spoke Height (m) | 0.245495 |
View Help GuidePurpose: Architectural Output.
Logic: The calculated vertical dimension of the spoke cross-section.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$H_{\text{prescribed, spoke}} = W_{\text{prescribed, spoke}} / \eta_{\text{tspoke, aspect}}$$ Python Logic:
v["Prescribed Spoke Width (m)"] / v["T-Spoke Aspect Ratio (h:w)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.2455 / 1.0000 = 0.2455
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| ☰ | \( \Sigma V_{\text{tspoke}} \) | T-Spoke Total Volume (m3) | 0.295803 |
View Help GuidePurpose: T-Spoke Total Volume
Logic: T-Spoke Total Volume for material sizing
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma V_{\text{tspoke}} = A_{\text{req, curve}} \times \Sigma L_{\text{tspoke}}$$ Python Logic:
v["Required Curve Area (m2)"] * v["Total T-Spoke Length (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0603 * 4.9082 = 0.2958
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| ☰ | \( M_{\text{tspoke}} \) | T-Spoke Total Mass (kg) | 532.445797 |
View Help GuidePurpose: 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:
$$M_{\text{tspoke}} = \text{T-Spoke Total Volume (m3)} \times D_{\text{FCF}}$$ Python Logic:
v["T-Spoke Total Volume (m3)"] * v["Fossil Carbon Fibre Density (kg.m3)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.2958 * 1,800.0000 = 532.4458
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| ▼ T-Spoke Safety & Buckling Audit | ||||
| ☰ | \( X_{\text{applied, compression}} \) | T-Spoke Applied Compression (N) | 211,814.123103 |
View Help GuidePurpose: 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:
$$X_{\text{applied, compression}} = F_{\text{applied, curves}} / \Sigma X_{\text{tspokes}}$$ Python Logic:
v["Applied Force to Curves (N)"] / v["Total T-Spokes"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 847,256.4924 / 4.0000 = 211,814.1231
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| ☰ | \( \sigma_{\text{peak, compressive}} \) | T-Spoke Peak Compressive Stress (MPa) | 3.514557 |
View Help GuidePurpose: 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:
$$\sigma_{\text{peak, compressive}} = ( X_{\text{applied, compression}} / A_{\text{req, curve}} ) / 1000000$$ Python Logic:
( v["T-Spoke Applied Compression (N)"] / v["Required Curve Area (m2)"] ) / 1000000Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 211,814.1231 / 0.0603 ) / 1000000 = 3.5146
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| ☰ | \( F_{\text{critical, buckling}} \) | T-Spoke Critical Buckling Load (N) | 456,349,886.986231 |
View Help GuidePurpose: 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:
$$F_{\text{critical, buckling}} = ( \pi^2 \times ( \text{Fossil Carbon Fibre Modulus (GPa)} \times 10^9 ) \times ( ( W_{\text{prescribed, spoke}}^4 ) / 12 ) ) / ( R_{\text{corner, arc}}^2 )$$ Python Logic:
( PI()^2 * ( v["Fossil Carbon Fibre Modulus (GPa)"] * 10^9 ) * ( ( v["Prescribed Spoke Width (m)"]^4 ) / 12 ) ) / ( v["Corner Arc Radius (m)"]^2 )Live Evaluation: [ROUTE: STATIC/GLOBAL] ( PI()**2 * ( 230.0000 * 10**9 ) * ( ( 0.2455**4 ) / 12 ) ) / ( 1.2270**2 ) = 456,349,886.9862
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| ☰ | \( SF_{\text{buckling, safety}} \) | T-Spoke Buckling Safety Factor | 2,154.482809 |
View Help GuidePurpose: 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:
$$SF_{\text{buckling, safety}} = F_{\text{critical, buckling}} / X_{\text{applied, compression}}$$ Python Logic:
v["T-Spoke Critical Buckling Load (N)"] / v["T-Spoke Applied Compression (N)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 456,349,886.9862 / 211,814.1231 = 2,154.4828
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| ☰ | \( SF_{\text{material, safety}} \) | T-Spoke Material Safety Factor | 170.14948 |
View Help GuidePurpose: 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:
$$SF_{\text{material, safety}} = \text{Fossil Carbon Fibre Material Yield Strength (MPa)} / \sigma_{\text{peak, compressive}}$$ Python Logic:
v["Fossil Carbon Fibre Material Yield Strength (MPa)"] / v["T-Spoke Peak Compressive Stress (MPa)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 598.0000 / 3.5146 = 170.1495
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| ☰ | \( X_{\text{tspoke, safety}} \) | T-Spoke Safety & Buckling Blueprint Validation | ULTRA-SAFE |
View Help GuidePurpose: 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:
$$X_{\text{tspoke, safety}} = IF ( AND ( SF_{\text{buckling, safety}} > SF_{\text{safety, factor}}, SF_{\text{material, safety}} > SF_{\text{safety, factor}} ) , 1 , 0 )$$ Python Logic:
IF ( AND ( v["T-Spoke Buckling Safety Factor"] > v["Safety Factor Slider"], v["T-Spoke Material Safety Factor"] > v["Safety Factor Slider"] ) , 1 , 0 )Live Evaluation: [ROUTE: STATIC/GLOBAL] IF ( AND ( 2,154.4828 > 2.5000, 170.1495 > 2.5000 ) , 1 , 0 ) = 1.0000
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| ▼ Final Skeleton Aggregation | ||||
| ☰ | \( M_{\text{predicted, rail}} \) | Side Rail Total Mass (kg) | 864.690705 |
View Help GuidePurpose: Longitudinal Mass.
Logic: Total accumulated weight of the horizontal straight skeletal rails.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$M_{\text{predicted, rail}} = M_{\text{predicted, rail}}$$ Python Logic:
v["Side Rail Total Mass (kg)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 864.6907 = 864.6907
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| ☰ | \( M_{\text{predicted, xbrace}} \) | X-Brace Total Mass (kg) | 601.592072 |
View Help GuidePurpose: Torsional Mass.
Logic: Total accumulated weight of all internal diagonal X-bracing struts.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$M_{\text{predicted, xbrace}} = M_{\text{predicted, xbrace}}$$ Python Logic:
v["X-Brace Total Mass (kg)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 601.5921 = 601.5921
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| ☰ | \( \Sigma M_{\text{pillar}} \) | Vertical Pillar Total Mass (kg) | 813.687985 |
View Help GuidePurpose: Vertical Mass.
Logic: Total accumulated weight of the vertical compression uprights.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma M_{\text{pillar}} = \Sigma M_{\text{pillar}}$$ Python Logic:
v["Vertical Pillar Total Mass (kg)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 813.6880 = 813.6880
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| ☰ | \( M_{\text{curved, rail}} \) | Curved Rail Total Mass (kg) | 1,672.727803 |
View Help GuidePurpose: Arc Mass.
Logic: Total accumulated weight of the curved skeletal end-caps.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$M_{\text{curved, rail}} = M_{\text{curved, rail}}$$ Python Logic:
v["Curved Rail Total Mass (kg)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 1,672.7278 = 1,672.7278
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| ☰ | \( M_{\text{tspoke}} \) | T-Spoke Total Mass (kg) | 532.445797 |
View Help GuidePurpose: Radial Mass.
Logic: Total accumulated weight of the horizontal internal support spokes.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$M_{\text{tspoke}} = M_{\text{tspoke}}$$ Python Logic:
v["T-Spoke Total Mass (kg)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 532.4458 = 532.4458
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| ☰ | \( \Sigma M_{\text{skeleton}} \) | Total Skeleton Mass (kg) | 4,485.144362 |
View Help GuidePurpose: 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:
$$\Sigma M_{\text{skeleton}} = M_{\text{predicted, rail}} + M_{\text{predicted, xbrace}} + \Sigma M_{\text{pillar}} + \text{Curved Rail Total Mass (kg)} + M_{\text{tspoke}}$$ Python Logic:
v["Side Rail Total Mass (kg)"] + v["X-Brace Total Mass (kg)"] + v["Vertical Pillar Total Mass (kg)"] + v["Curved Rail Total Mass (kg)"] + v["T-Spoke Total Mass (kg)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 864.6907 + 601.5921 + 813.6880 + 1,672.7278 + 532.4458 = 4,485.1444
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