U-Chain Dashboard
| ▼ Central Enabler Pin Component | ||||
| ☰ | \( \Sigma F_{\text{linear, drive}} \) | Total Linear Drive Force (N) | 243,385.669407 |
View Help GuidePurpose: Total System Loop Load.
Logic: Links the total macro directional driving force down to the mechanical connection axles.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma F_{\text{linear, drive}} = F_{\text{tangential, drive}}$$ Python Logic:
v["Tangential Drive Force (N)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 243,385.6694 = 243,385.6694
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| ☰ | \( N_{\text{active, pins}} \) | Number of Active Enabler Pins | 13 |
View Help GuidePurpose: Load-Bearing Anchors.
Logic: The number of continuous central rods actively distributing the total transit pull force.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$N_{\text{active, pins}} = N_{\text{enablers}}$$ Python Logic:
v["Number of Gravity Enablers"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 13.0000 = 13.0000
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| ☰ | \( F_{\text{individual, pin}} \) | Force Per Individual Pin (N) | 18,721.97457 |
View Help GuidePurpose: Pin Shear Load.
Logic: The raw concentrated cutting force focused on a single structural axle shaft connection point.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$F_{\text{individual, pin}} = \Sigma F_{\text{linear, drive}} / N_{\text{active, pins}}$$ Python Logic:
v["Total Linear Drive Force (N)"] / v["Number of Active Enabler Pins"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 243,385.6694 / 13.0000 = 18,721.9746
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| ☰ | \( \tau_{\text{shear, plane}} \) | Shear Plane Plane Factor |
View Help GuidePurpose: Double Shear Identifier.
Logic: Accounts for continuous rod layout, splitting the shearing stress perfectly across two separate material planes.
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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| ☰ | \( SF_{\text{pin, safety}} \) | Pin Safety Factor | 2.5 |
View Help GuidePurpose: Dave-Proof Cushion.
Logic: Structural design buffer to confidently manage unexpected transient deceleration or extreme load spikes.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$SF_{\text{pin, safety}} = SF_{\text{safety, factor}}$$ Python Logic:
v["Safety Factor Slider"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 2.5000 = 2.5000
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| ☰ | \( X_{\text{req, pin}} \) | Required Pin Cross-Section (m2) | 0.000293 |
View Help GuidePurpose: Axle Cross-Sectional Volume.
Logic: The physical solid material surface area required inside the pin body to resist tearing or shearing apart.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{req, pin}} = ( F_{\text{individual, pin}} \times SF_{\text{pin, safety}} ) / ( 2 \times \text{Fossil Carbon Fibre Shear Limit (MPa)} \times 10^6)$$ Python Logic:
( v["Force Per Individual Pin (N)"] * v["Pin Safety Factor"] ) / ( 2 * v["Fossil Carbon Fibre Shear Limit (MPa)"] * 10^6)Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 18,721.9746 * 2.5000 ) / ( 2 * 80.0000 * 10**6) = 0.0003
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| ☰ | \( D_{\text{calculated, pin}} \) | Calculated Pin Diameter (m) | 0.019299 |
View Help GuidePurpose: The Final Pin Gauge.
Logic: The ultra-precise, solid pin thickness requirement.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$D_{\text{calculated, pin}} = SQRT ( ( 4 \times X_{\text{req, pin}} ) / \pi )$$ Python Logic:
SQRT ( ( 4 * v["Required Pin Cross-Section (m2)"] ) / PI() )Live Evaluation: [ROUTE: STATIC/GLOBAL] SQRT ( ( 4 * 0.0003 ) / PI() ) = 0.0193
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| ▼ U-Chain Geometry Component | ||||
| ☰ | \( W_{\text{int, channel}} \) | Internal Channel Width (m) | 0.300396 |
View Help GuidePurpose: Inner Core Sleeve.
Logic: The interior width clearance of the U-channel cap required to perfectly envelope the structural gear face.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$W_{\text{int, channel}} = W_{\text{predicted}}$$ Python Logic:
v["Predicted Gear Width (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.3004 = 0.3004
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| ☰ | \( X_{\text{sidewall, running}} \) | Sidewall Running Clearance (m) |
View Help GuidePurpose: Thermal Air Gap.
Logic: An operational clearance tolerance on either side to prevent friction-wear against the spinning wheel.
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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| ☰ | \( W_{\text{chain, sidewall}} \) | Chain Sidewall Thickness (m) | 0.020141 |
View Help GuidePurpose: Wall Gauge Thickness.
Logic: Calculates the minimum physical thickness of the outer link flaps to sustain operational chain tension loops.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$W_{\text{chain, sidewall}} = SQRT ( ( F_{\text{tangential, drive}} / 2 ) / ( \text{Fossil Carbon Fibre Tensile Limit (MPa)} \times 10^6 \times H_{\text{chain, sidewall}} ) )$$ Python Logic:
SQRT ( ( v["Tangential Drive Force (N)"] / 2 ) / ( v["Fossil Carbon Fibre Tensile Limit (MPa)"] * 10^6 * v["Chain Side-Wall Hug Depth (m)"] ) )Live Evaluation: [ROUTE: STATIC/GLOBAL] SQRT ( ( 243,385.6694 / 2 ) / ( 1,500.0000 * 10**6 * 0.2000 ) ) = 0.0201
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| ☰ | \( \Sigma W_{\text{ext, chain}} \) | Total External Chain Width (m) | 0.344677 |
View Help GuidePurpose: Maximum Outer Width.
Logic: The final, absolute maximum spatial cross-sectional envelope of the moving chain loop assembly.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma W_{\text{ext, chain}} = W_{\text{int, channel}} + ( X_{\text{sidewall, running}} \times 2) + ( W_{\text{chain, sidewall}} \times 2)$$ Python Logic:
v["Internal Channel Width (m)"] + ( v["Sidewall Running Clearance (m)"] * 2) + ( v["Chain Sidewall Thickness (m)"] * 2)Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.3004 + ( 0.0020 * 2) + ( 0.0201 * 2) = 0.3447
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| ☰ | \( H_{\text{ext, chain}} \) | External Chain Top Height (m) | 0.048248 |
View Help GuidePurpose: Crown Structural Depth.
Logic: The solid material height directly above the gear rim to securely house and reinforce the central pin bore.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$H_{\text{ext, chain}} = D_{\text{calculated, pin}} \times SF_{\text{pin, safety}}$$ Python Logic:
v["Calculated Pin Diameter (m)"] * v["Pin Safety Factor"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0193 * 2.5000 = 0.0482
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| ☰ | \( \Sigma H_{\text{ext, chain}} \) | Total External Chain Height (m) | 0.248248 |
View Help GuidePurpose: Total Link Profile Height.
Logic: The absolute vertical dimension of an individual articulating box-link casing from top to bottom.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma H_{\text{ext, chain}} = H_{\text{chain, sidewall}} + H_{\text{ext, chain}}$$ Python Logic:
v["Chain Side-Wall Hug Depth (m)"] + v["External Chain Top Height (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.2000 + 0.0482 = 0.2482
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| ☰ | \( \theta_{\text{req, taper}} \) | Required Taper Angle (Degrees) | 0.375803 |
View Help GuidePurpose: Wedge Relief Angle.
Logic: The precise trapezoidal cutback required on the link edges so the flaps can clear each other smoothly when rounding the wheels.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\theta_{\text{req, taper}} = DEGREES ( ATAN ( X_{\text{chain, pitch}} / (R_{\text{int}} - H_{\text{chain, sidewall}} ) ) ) - DEGREES ( ATAN ( X_{\text{chain, pitch}} / R_{\text{int}}) )$$ Python Logic:
DEGREES ( ATAN ( v["Chain Pitch (m)"] / (v["Internal Gear Radius (m)"] - v["Chain Side-Wall Hug Depth (m)"] ) ) ) - DEGREES ( ATAN ( v["Chain Pitch (m)"] / v["Internal Gear Radius (m)"]) )Live Evaluation: [ROUTE: STATIC/GLOBAL] DEGREES ( ATAN ( 0.1000 / (1.8462 - 0.2000 ) ) ) - DEGREES ( ATAN ( 0.1000 / 1.8462) ) = 0.3758
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| ☰ | \( \Sigma W \) | Total Track width (m) | 3.102591 |
View Help GuidePurpose: System Footprint Envelope.
Logic: Combines the skeleton length boundaries and rail widths with the chain envelope to track master lane clearances.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma W = ( L_{\text{enab, len}} \times 2 ) + (W_{\text{prescribed, rail}} \times 2 ) + \Sigma W_{\text{ext, chain}}$$ Python Logic:
( v["Length (m)"] * 2 ) + (v["Prescribed Rail Width (m)"] * 2 ) + v["Total External Chain Width (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 1.2000 * 2 ) + (0.1790 * 2 ) + 0.3447 = 3.1026
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| ▼ U-Chain Mass | ||||
| ☰ | \( L_{\text{straight, track}} \) | Straight Track Length (m) | 4 |
View Help GuidePurpose: The Flat Run.
Logic: The direct linear distance of the flat track section spanning between the two large gear centers.
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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| ☰ | \( \Sigma L_{\text{chain, loop}} \) | Total Chain Loop Length (m) | 19.6 |
View Help GuidePurpose: Total Loop Perimeter.
Logic: The absolute continuous length of the entire articulating chain loop wrapping the system.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma L_{\text{chain, loop}} = L_{\text{run}}$$ Python Logic:
v["Track full run length (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 19.6000 = 19.6000
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| ☰ | \( A_{\text{link, crosssectional}} \) | Link Cross-Sectional Area (m2) | 0.025486 |
View Help GuidePurpose: The U-Shape Profile.
Logic: The actual material end-face area of the hollow inverted "U" cap, subtracting the core cutout channel where the gear sits.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$A_{\text{link, crosssectional}} = ( \Sigma W_{\text{ext, chain}} \times \Sigma H_{\text{ext, chain}}) - (W_{\text{int, channel}} \times H_{\text{chain, sidewall}} )$$ Python Logic:
( v["Total External Chain Width (m)"] * v["Total External Chain Height (m)"]) - (v["Internal Channel Width (m)"] * v["Chain Side-Wall Hug Depth (m)"] )Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 0.3447 * 0.2482) - (0.3004 * 0.2000 ) = 0.0255
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| ☰ | \( M_{\text{chain, unit}} \) | Chain Unit Mass (kg/m) | 45.875269 |
View Help GuidePurpose: Linear Weight Profile.
Logic: The calculated physical mass of the heavy-duty box chain per linear meter of length.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$M_{\text{chain, unit}} = A_{\text{link, crosssectional}} \times \text{Fossil Carbon Fibre Density (kg.m3)}$$ Python Logic:
v["Link Cross-Sectional Area (m2)"]* v["Fossil Carbon Fibre Density (kg.m3)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0255* 1,800.0000 = 45.8753
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| ☰ | \( V_{\text{chain, unit}} \) | Chain Unit Volume (m3) | 0.025486 |
View Help GuidePurpose: The volume per chain link
Logic: Calculating the total volume of a single chain link
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$V_{\text{chain, unit}} = M_{\text{chain, unit}} / D_{\text{FCF}}$$ Python Logic:
v["Chain Unit Mass (kg/m)"] / v["Fossil Carbon Fibre Density (kg.m3)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 45.8753 / 1,800.0000 = 0.0255
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| ☰ | \( L_{\text{links, chain}} \) | Links per chain loop length | 196 |
View Help GuidePurpose: Total Link Count.
Logic: The exact number of individual physical modular block links required to assemble the full closed drive loop.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$L_{\text{links, chain}} = \Sigma L_{\text{chain, loop}} / X_{\text{chain, pitch}}$$ Python Logic:
v["Total Chain Loop Length (m)"] / v["Chain Pitch (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 19.6000 / 0.1000 = 196.0000
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| ☰ | \( \Sigma M_{\text{chain}} \) | Chain Total Mass (kg) | 899.155274 |
View Help GuidePurpose: Total Chain Loop Weight.
Logic: The final aggregated weight of the entire moving, articulating loop assembly circling the GMEG track structure.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma M_{\text{chain}} = \Sigma L_{\text{chain, loop}} \times M_{\text{chain, unit}}$$ Python Logic:
v["Total Chain Loop Length (m)"] * v["Chain Unit Mass (kg/m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 19.6000 * 45.8753 = 899.1553
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| ☰ | \( \Sigma V_{\text{chain}} \) | Chain Total Volume (m3) | 4.995307 |
View Help GuidePurpose: The total chain volume
Logic: The volume per link multiplied by the number of chain links to help inform the total expected volume of the entire chain
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma V_{\text{chain}} = V_{\text{chain, unit}} \times L_{\text{links, chain}}$$ Python Logic:
v["Chain Unit Volume (m3)"] * v["Links per chain loop length"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0255 * 196.0000 = 4.9953
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