GMEG Engineering Simulator

Operational Environment Dashboard

▼ Track
☰	$ N_{\text{links, straight}} $	Links per straight track run length		View Help Guide Purpose: Set links to determine length of straight track section Logic: A physical building block. You dictate the track's length by telling the simulator how many links to use, ensuring the design remains perfectly modular and manufacturable. Type: Manual Entry Render on Grids: None Mathematical Formula: $\text{User Input}$ Python Logic: `N/A` Live Evaluation: N/A (Input Variable)
☰	$ L_{\text{straight}} $	Straight track length (m)	6.000000	View Help Guide Purpose: Length of straight track Logic: Establishes the core dimension of the straightaway. By calculating this using whole chain links, we guarantee the drive chain will fit perfectly without needing awkward "half-links" during assembly. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $L_{\text{straight}} = N_{\text{links, straight}} \times L_{\text{link}}$ Python Logic: `v["Links per straight track run length"]v["Chain link (m)"]` Live Evaluation:* [ROUTE: STATIC/GLOBAL] 60.00000.1000 = 6.0000*
☰	$ L_{\text{straight}}/2 $	Half straight track length (m)	3.000000	View Help Guide Purpose: Half straight track length to determine centre point which is also in line with the pivot point Logic: This locates the absolute center of gravity for the machine. This spot is the central pivot point (the fulcrum) where the entire track will tilt like a massive seesaw. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $L_{\text{straight}}/2 = L_{\text{straight}}/2$ Python Logic: `v["Straight track length (m)"]/2` Live Evaluation: [ROUTE: STATIC/GLOBAL] 6.0000/2 = 3.0000
☰	$ L_{\text{end-to-end}} $	Total Track End-to-End Length (m)	10.074367	View Help Guide Purpose: Total end to end length of the track footprint Logic: Defines the machine's true longitudinal footprint. It combines the straight sections and the radius of the curved end-caps to tell us exactly how much space the track takes up. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $L_{\text{end-to-end}} = D_{\text{int}}+L_{\text{straight}}$ Python Logic: `v["Internal Gear Diameter (m)"]+v["Straight track length (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 4.0744+6.0000 = 10.0744
☰	$ R_{\text{max}} $	Maximum lever arm (m)	5.037183	View Help Guide Purpose: Maximum lever arm from the central pivot point to the centre of the rounded corner, also to ensure this distance is not exceeded in the Ratational Torque lever arm calculations Logic: The master torque dimension. Torque is force multiplied by distance; this represents the maximum "distance" a heavy enabler can reach, defining the absolute highest twisting force the lifting system (DLLS) has to fight. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $R_{\text{max}} = L_{\text{end-to-end}}/2$ Python Logic: `v["Total Track End-to-End Length (m)"]/2` Live Evaluation: [ROUTE: STATIC/GLOBAL] 10.0744/2 = 5.0372
☰	$ L_{\text{run}} $	Track full run length (m)	24.800000	View Help Guide Purpose: Total revolution around the track circumference Logic: The master path length. It maps both straightaways and both curves to determine exactly how much physical track exists in the loop. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $L_{\text{run}} = C_{\text{int}}+(L_{\text{straight}} \times 2)$ Python Logic: `v["Internal Gear Circumference (m)"]+(v["Straight track length (m)"]2)` Live Evaluation:* [ROUTE: STATIC/GLOBAL] 12.8000+(6.00002) = 24.8000*
☰	$ N_{\text{links, run}} $	Links per track run length	248.000000	View Help Guide Purpose: Number of links around the internal gears Logic: Essential for the Bill of Materials, but also acts as a geometric proof to confirm the full track path perfectly aligns with a whole number of unbroken chain links. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $N_{\text{links, run}} = L_{\text{run}}/L_{\text{link}}$ Python Logic: `v["Track full run length (m)"]/v["Chain link (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 24.8000/0.1000 = 248.0000
☰	$ t_{\text{run}} $	Run time across GMEG track (s)	2.980769	View Help Guide Purpose: Based on speedv time for the enabler train for a full revolution around the track Logic: The master clock for the system. It connects distance and speed to give us a precise time window, which is critical for timing the lifts, drops, and flywheel energy recovery cycles. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $t_{\text{run}} = L_{\text{run}}/v$ Python Logic: `v["Track full run length (m)"]/v["Operational Velocity (m/s)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 24.8000/8.3200 = 2.9808
☰	$ \theta_{\text{tilt}} $	GMEG Angle tilt (degrees)	32.000000	View Help Guide Purpose: User input to determine base parallel force input Logic: The DLLS is the mechanism that actually performs the lifting. Pulling this number ensures the lifting motors are mathematically synced to the exact angle required to harvest gravity. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $\theta_{\text{tilt}} = \theta_{\text{tilt}}$ Python Logic: `v["Angle tilt (degrees)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 32.0000 = 32.0000
☰	$ \theta_{seg,rad} $	Angle Per Segment radians (rad/s)	0.017453	View Help Guide Purpose: Radians for each segment during a track arc rotation Logic: Converts the physical tilt degrees into radians to accurately calculate rotational physics per simulation tick. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $\theta_{seg,rad} = \text{rad}((\theta_{\text{tilt}} \times 2)/(\theta_{\text{tilt}} \times 2))$ Python Logic: `RADIANS((v["GMEG Angle tilt (degrees)"]2)/(v["GMEG Angle tilt (degrees)"]2))` Live Evaluation: [ROUTE: STATIC/GLOBAL] RADIANS((32.00002)/(32.00002)) = 0.0175
▼ Track Dimensions
☰	$ L_{\text{end-to-end}} $	Total Track End-to-End Length (m)	10.074367	View Help Guide Purpose: Total end to end length of the track footprint Logic: Carried down from the previous section. In our tilt math, this acts as the "hypotenuse" of the triangle, allowing us to calculate the exact vertical lift and horizontal shadow of the tilted track. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $L_{\text{end-to-end}} = L_{\text{end-to-end}}$ Python Logic: `v["Total Track End-to-End Length (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 10.0744 = 10.0744
☰	$ H_{\text{track}} $	Track Height (m)	4.074367	View Help Guide Purpose: Estimate height of the track for the runner design purposes Logic: Directly linked to the diameter of the internal gear. This dictates the vertical clearance required inside the housing to ensure the enablers can pass cleanly over and under the center axle. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $H_{\text{track}} = D_{\text{int}}$ Python Logic: `v["Internal Gear Diameter (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 4.0744 = 4.0744
☰	$ L_{\text{bottom}} $	Bottom length at Angle Titl degrees (m)	8.543547	View Help Guide Purpose: Estimate bottom length if the track is tilted Logic: When you tilt a seesaw, its horizontal "shadow" gets shorter. This trigonometric calculation (Cosine) tells us exactly how much ground clearance the machine occupies at maximum tilt. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $L_{\text{bottom}} = COS ( RADIANS ( \theta_{\text{tilt}} ) ) \times L_{\text{end-to-end}}$ Python Logic: `COS ( RADIANS ( v["Angle tilt (degrees)"] ) ) * v["Total Track End-to-End Length (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] COS ( RADIANS ( 32.0000 ) ) * 10.0744 = 8.5435
☰	$ W_{\text{track}} $	Width (m)	0.000000	View Help Guide Purpose: Adjustable user input which influences size of gravity enabler weight dimensions and also operational footprint Logic: Pulled directly from the structural Track simulator. This is critical for facility floor planning and ensuring the stand has a wide enough stance to prevent lateral tipping. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $N/A$ Python Logic: `N/A` Live Evaluation: N/A
☰	$ h_{\text{lift}} $	Lift height (m)	5.338601	View Help Guide Purpose: Indication of potential height of the system Logic: This trigonometric calculation (Sine) defines the maximum Z-axis from a central point during a Track Arc Rotation recharge. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $h_{\text{lift}} = SIN ( RADIANS ( \theta_{\text{tilt}}) ) \times L_{\text{end-to-end}}$ Python Logic: `SIN ( RADIANS ( v["Angle tilt (degrees)"]) ) * v["Total Track End-to-End Length (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] SIN ( RADIANS ( 32.0000) ) * 10.0744 = 5.3386
☰	$ t_{\text{lift}} $	Lift Time (s)		View Help Guide Purpose: Influences speed of track arc rotation and DLLS performance and energy needs Logic: A massive tuning variable. Lifting the heavy track faster requires exponentially more power from the DLLS motors, while lifting it too slowly could throw off the gravity harvesting sequence. Type: Manual Entry Render on Grids: None Mathematical Formula: $\text{User Input}$ Python Logic: `N/A` Live Evaluation: N/A (Input Variable)
▼ Velocity
☰	$ n_{\text{rps}} $	GMEG Input Rotations per second	0.650000	View Help Guide Purpose: GMEG operational RPM Logic: This is the internal speed of the GMEG to help determine the operational velocity. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $n_{\text{rps}} = n_{\text{rps}}$ Python Logic: `v["Internal Gear rotations per second"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.6500 = 0.6500
☰	$ v $	Operational Velocity (m/s)	8.320000	View Help Guide Purpose: The actual physical speed of the train moving along the track in meters per second. Logic: Converts the rotational spin of the internal gears back into straight-line speed. This is the baseline variable for all kinetic energy, momentum, and impact calculations. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $v = C_{\text{int}} \times n_{\text{rps}}$ Python Logic: `v["Internal Gear Circumference (m)"]v["GMEG Input Rotations per second"]` Live Evaluation:* [ROUTE: STATIC/GLOBAL] 12.80000.6500 = 8.3200*
☰	$ D_{\text{centre}} $	Centre enabler distance from rounded corner centre (m)	4.160000	View Help Guide Purpose: Determine Centre enabler distance from rounded corner centre for TAR activation Logic: We need to know exactly where the middle of the train travels needs to be to activate the lifting phase. This maps that distance so the track swivels at the absolute perfect moment. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $D_{\text{centre}} = v/2$ Python Logic: `v["Operational Velocity (m/s)"]/2` Live Evaluation: [ROUTE: STATIC/GLOBAL] 8.3200/2 = 4.1600
▼ Track Spatial Operational Environment
☰	$ L_{s1} $	Physical End Straight1 (m)	6.000000	View Help Guide Purpose: Determining the distance across the top straight track. Logic: Establishes the exact meter mark where the first linear propulsion zone ends. Type: Calculated (Math Output) Render on Grids: Spatial Mathematical Formula: $L_{s1} = L_{\text{straight}}$ Python Logic: `v["Straight track length (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 6.0000 = 6.0000
☰	$ L_{s2} $	Physical End Corner1 (m)	12.400000	View Help Guide Purpose: Determining the distance across the right rounded corner. Logic: Adds the 180-degree arc length to the straight, marking the physical end of the first turn. Type: Calculated (Math Output) Render on Grids: Spatial Mathematical Formula: $L_{s2} = L_{\text{straight}}+C_{\text{half}}$ Python Logic: `v["Straight track length (m)"]+v["Half Internal Gear Circumference (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 6.0000+6.4000 = 12.4000
☰	$ L_{c1} $	Physical End Straight2 (m)	18.400000	View Help Guide Purpose: Determining the distance across the bottom straight track. Logic: Adds the return straight length to the running total, marking the start of the final curve. Type: Calculated (Math Output) Render on Grids: Spatial Mathematical Formula: $L_{c1} = (L_{\text{straight}} \times 2)+C_{\text{half}}$ Python Logic: `(v["Straight track length (m)"]2)+v["Half Internal Gear Circumference (m)"]` Live Evaluation:* [ROUTE: STATIC/GLOBAL] (6.00002)+6.4000 = 18.4000*
☰	$ L_{c2} $	Physical End Corner2 (m)	24.800000	View Help Guide Purpose: Determining the distance across the left rounded corner. Logic: Completes the loop, representing the total track perimeter used to trigger the lap wrap-around resets. Type: Calculated (Math Output) Render on Grids: Spatial Mathematical Formula: $L_{c2} = (L_{\text{straight}}+C_{\text{half}}) \times 2$ Python Logic: `(v["Straight track length (m)"]+v["Half Internal Gear Circumference (m)"])2` Live Evaluation:* [ROUTE: STATIC/GLOBAL] (6.0000+6.4000)2 = 24.8000*
☰	$ R_{z1, start} $	RotZone1 Start (m)	5.040000	View Help Guide Purpose: Determining the distance point on the right rounded corner to enable a track arc rotation Logic: Calculates the exact spatial trigger point where the track begins its physical tilt mechanism on the first curve. Type: Calculated (Math Output) Render on Grids: Spatial Mathematical Formula: $R_{z1, start} = L_{\text{straight}}-((v/2)-C_{\text{corner, dist}})$ Python Logic: `v["Straight track length (m)"]-((v["Operational Velocity (m/s)"]/2)-v["Half semi corner Circumference (m)"])` Live Evaluation: [ROUTE: STATIC/GLOBAL] 6.0000-((8.3200/2)-3.2000) = 5.0400
☰	$ R_{z1, end} $	RotZone1 End (m)	13.360000	View Help Guide Purpose: Determining the distance point on the right rounded corner to disable a track arc rotation Logic: Identifies the exact meter mark where the first corner tilt sequence finishes and locks back into a flat plane. Type: Calculated (Math Output) Render on Grids: Spatial Mathematical Formula: $R_{z1, end} = R_{z1, start}+v$ Python Logic: `v["RotZone1 Start (m)"]+v["Operational Velocity (m/s)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 5.0400+8.3200 = 13.3600
☰	$ R_{z2, start} $	RotZone2 Start (m)	17.440000	View Help Guide Purpose: Determining the distance point on the left rounded corner to enable a track arc rotation Logic: Calculates the trigger point for the second corner's tilting mechanism. Type: Calculated (Math Output) Render on Grids: Spatial Mathematical Formula: $R_{z2, start} = (L_{\text{straight}} \times 2)+C_{\text{half}}+C_{\text{corner, dist}}-D_{\text{centre}}$ Python Logic: `(v["Straight track length (m)"]2)+v["Half Internal Gear Circumference (m)"]+v["Half semi corner Circumference (m)"]-v["Centre enabler distance from rounded corner centre (m)"]` Live Evaluation:* [ROUTE: STATIC/GLOBAL] (6.00002)+6.4000+3.2000-4.1600 = 17.4400*
☰	$ R_{z2, end} $	RotZone2 End (m)	25.760000	View Help Guide Purpose: Determining the distance point on the left rounded corner to disable a track arc rotation Logic: Identifies the finish line for the second corner's tilt, returning the track to its default flat state. Type: Calculated (Math Output) Render on Grids: Spatial Mathematical Formula: $R_{z2, end} = R_{z2, start}+v$ Python Logic: `v["RotZone2 Start (m)"]+v["Operational Velocity (m/s)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 17.4400+8.3200 = 25.7600
▼ Rotational Torque Grid
☰	$ r_{gear} $	Internal Gear Radius (m)	2.037183	View Help Guide Purpose: Referencing the internal gear radius for torque calculations Logic: This is the main "Lever Arm" for the machine. It is the master variable used to convert the linear chain pull into rotational torque. Type: Calculated (Math Output) Render on Grids: Rotational Torque Mathematical Formula: $r_{gear} = r_{gear}$ Python Logic: `v["Internal Gear Radius (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 2.0372 = 2.0372
☰	$ v $	Velocity (m/s)	8.320000	View Help Guide Purpose: Desired operational speed Logic: Converts the rotational spin of the internal gears back into straight-line speed. This is the baseline variable for all kinetic energy, momentum, and impact calculations. Type: Calculated (Math Output) Render on Grids: Rotational Torque Mathematical Formula: $$$v = v$$$ Python Logic: `v["Operational Velocity (m/s)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 8.3200 = 8.3200
☰	$ d_{gap} $	Enabler gap (m)	0.596500	View Help Guide Purpose: Enabler spacing Logic: Ensures the cylinders have enough breathing room (with a safety buffer) so they don't grind against each other as the chain bends around the gears. Type: Calculated (Math Output) Render on Grids: Rotational Torque Mathematical Formula: $d_{gap} = L_{\text{gap}}$ Python Logic: `v["Enabler gap length (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.5965 = 0.5965
☰	$ \eta_{DLLS} $	Energy Transfer Efficiency DLLS (%)		View Help Guide Purpose: Set custom efficiency for DLLS power transfer to GMEG Logic: Defines the baseline power retention factor when shifting energy from the linear drive to the generator. Type: Manual Entry Render on Grids: None Mathematical Formula: $\text{User Input}$ Python Logic: `N/A` Live Evaluation: N/A (Input Variable)
☰	$ \mu $	Friction factor (%)		View Help Guide Purpose: Set custom friction factor for moving gravity enabler train Logic: Injects standard mechanical drag into the dynamic tracking equations. Type: Manual Entry Render on Grids: None Mathematical Formula: $\text{User Input}$ Python Logic: `N/A` Live Evaluation: N/A (Input Variable)

▼ Track
☰	\( N_{\text{links, straight}} \)	Links per straight track run length		View Help Guide Purpose: Set links to determine length of straight track section Logic: A physical building block. You dictate the track's length by telling the simulator how many links to use, ensuring the design remains perfectly modular and manufacturable. Type: Manual Entry Render on Grids: None Mathematical Formula: $\text{User Input}$ Python Logic: `N/A` Live Evaluation: N/A (Input Variable)
☰	\( L_{\text{straight}} \)	Straight track length (m)	6.000000	View Help Guide Purpose: Length of straight track Logic: Establishes the core dimension of the straightaway. By calculating this using whole chain links, we guarantee the drive chain will fit perfectly without needing awkward "half-links" during assembly. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $L_{\text{straight}} = N_{\text{links, straight}} \times L_{\text{link}}$ Python Logic: `v["Links per straight track run length"]v["Chain link (m)"]` Live Evaluation:* [ROUTE: STATIC/GLOBAL] 60.00000.1000 = 6.0000*
☰	\( L_{\text{straight}}/2 \)	Half straight track length (m)	3.000000	View Help Guide Purpose: Half straight track length to determine centre point which is also in line with the pivot point Logic: This locates the absolute center of gravity for the machine. This spot is the central pivot point (the fulcrum) where the entire track will tilt like a massive seesaw. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $L_{\text{straight}}/2 = L_{\text{straight}}/2$ Python Logic: `v["Straight track length (m)"]/2` Live Evaluation: [ROUTE: STATIC/GLOBAL] 6.0000/2 = 3.0000
☰	\( L_{\text{end-to-end}} \)	Total Track End-to-End Length (m)	10.074367	View Help Guide Purpose: Total end to end length of the track footprint Logic: Defines the machine's true longitudinal footprint. It combines the straight sections and the radius of the curved end-caps to tell us exactly how much space the track takes up. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $L_{\text{end-to-end}} = D_{\text{int}}+L_{\text{straight}}$ Python Logic: `v["Internal Gear Diameter (m)"]+v["Straight track length (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 4.0744+6.0000 = 10.0744
☰	\( R_{\text{max}} \)	Maximum lever arm (m)	5.037183	View Help Guide Purpose: Maximum lever arm from the central pivot point to the centre of the rounded corner, also to ensure this distance is not exceeded in the Ratational Torque lever arm calculations Logic: The master torque dimension. Torque is force multiplied by distance; this represents the maximum "distance" a heavy enabler can reach, defining the absolute highest twisting force the lifting system (DLLS) has to fight. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $R_{\text{max}} = L_{\text{end-to-end}}/2$ Python Logic: `v["Total Track End-to-End Length (m)"]/2` Live Evaluation: [ROUTE: STATIC/GLOBAL] 10.0744/2 = 5.0372
☰	\( L_{\text{run}} \)	Track full run length (m)	24.800000	View Help Guide Purpose: Total revolution around the track circumference Logic: The master path length. It maps both straightaways and both curves to determine exactly how much physical track exists in the loop. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $L_{\text{run}} = C_{\text{int}}+(L_{\text{straight}} \times 2)$ Python Logic: `v["Internal Gear Circumference (m)"]+(v["Straight track length (m)"]2)` Live Evaluation:* [ROUTE: STATIC/GLOBAL] 12.8000+(6.00002) = 24.8000*
☰	\( N_{\text{links, run}} \)	Links per track run length	248.000000	View Help Guide Purpose: Number of links around the internal gears Logic: Essential for the Bill of Materials, but also acts as a geometric proof to confirm the full track path perfectly aligns with a whole number of unbroken chain links. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $N_{\text{links, run}} = L_{\text{run}}/L_{\text{link}}$ Python Logic: `v["Track full run length (m)"]/v["Chain link (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 24.8000/0.1000 = 248.0000
☰	\( t_{\text{run}} \)	Run time across GMEG track (s)	2.980769	View Help Guide Purpose: Based on speedv time for the enabler train for a full revolution around the track Logic: The master clock for the system. It connects distance and speed to give us a precise time window, which is critical for timing the lifts, drops, and flywheel energy recovery cycles. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $t_{\text{run}} = L_{\text{run}}/v$ Python Logic: `v["Track full run length (m)"]/v["Operational Velocity (m/s)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 24.8000/8.3200 = 2.9808
☰	\( \theta_{\text{tilt}} \)	GMEG Angle tilt (degrees)	32.000000	View Help Guide Purpose: User input to determine base parallel force input Logic: The DLLS is the mechanism that actually performs the lifting. Pulling this number ensures the lifting motors are mathematically synced to the exact angle required to harvest gravity. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $\theta_{\text{tilt}} = \theta_{\text{tilt}}$ Python Logic: `v["Angle tilt (degrees)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 32.0000 = 32.0000
☰	\( \theta_{seg,rad} \)	Angle Per Segment radians (rad/s)	0.017453	View Help Guide Purpose: Radians for each segment during a track arc rotation Logic: Converts the physical tilt degrees into radians to accurately calculate rotational physics per simulation tick. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $\theta_{seg,rad} = \text{rad}((\theta_{\text{tilt}} \times 2)/(\theta_{\text{tilt}} \times 2))$ Python Logic: `RADIANS((v["GMEG Angle tilt (degrees)"]2)/(v["GMEG Angle tilt (degrees)"]2))` Live Evaluation: [ROUTE: STATIC/GLOBAL] RADIANS((32.00002)/(32.00002)) = 0.0175
▼ Track Dimensions
☰	\( L_{\text{end-to-end}} \)	Total Track End-to-End Length (m)	10.074367	View Help Guide Purpose: Total end to end length of the track footprint Logic: Carried down from the previous section. In our tilt math, this acts as the "hypotenuse" of the triangle, allowing us to calculate the exact vertical lift and horizontal shadow of the tilted track. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $L_{\text{end-to-end}} = L_{\text{end-to-end}}$ Python Logic: `v["Total Track End-to-End Length (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 10.0744 = 10.0744
☰	\( H_{\text{track}} \)	Track Height (m)	4.074367	View Help Guide Purpose: Estimate height of the track for the runner design purposes Logic: Directly linked to the diameter of the internal gear. This dictates the vertical clearance required inside the housing to ensure the enablers can pass cleanly over and under the center axle. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $H_{\text{track}} = D_{\text{int}}$ Python Logic: `v["Internal Gear Diameter (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 4.0744 = 4.0744
☰	\( L_{\text{bottom}} \)	Bottom length at Angle Titl degrees (m)	8.543547	View Help Guide Purpose: Estimate bottom length if the track is tilted Logic: When you tilt a seesaw, its horizontal "shadow" gets shorter. This trigonometric calculation (Cosine) tells us exactly how much ground clearance the machine occupies at maximum tilt. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $L_{\text{bottom}} = COS ( RADIANS ( \theta_{\text{tilt}} ) ) \times L_{\text{end-to-end}}$ Python Logic: `COS ( RADIANS ( v["Angle tilt (degrees)"] ) ) * v["Total Track End-to-End Length (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] COS ( RADIANS ( 32.0000 ) ) * 10.0744 = 8.5435
☰	\( W_{\text{track}} \)	Width (m)	0.000000	View Help Guide Purpose: Adjustable user input which influences size of gravity enabler weight dimensions and also operational footprint Logic: Pulled directly from the structural Track simulator. This is critical for facility floor planning and ensuring the stand has a wide enough stance to prevent lateral tipping. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $N/A$ Python Logic: `N/A` Live Evaluation: N/A
☰	\( h_{\text{lift}} \)	Lift height (m)	5.338601	View Help Guide Purpose: Indication of potential height of the system Logic: This trigonometric calculation (Sine) defines the maximum Z-axis from a central point during a Track Arc Rotation recharge. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $h_{\text{lift}} = SIN ( RADIANS ( \theta_{\text{tilt}}) ) \times L_{\text{end-to-end}}$ Python Logic: `SIN ( RADIANS ( v["Angle tilt (degrees)"]) ) * v["Total Track End-to-End Length (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] SIN ( RADIANS ( 32.0000) ) * 10.0744 = 5.3386
☰	\( t_{\text{lift}} \)	Lift Time (s)		View Help Guide Purpose: Influences speed of track arc rotation and DLLS performance and energy needs Logic: A massive tuning variable. Lifting the heavy track faster requires exponentially more power from the DLLS motors, while lifting it too slowly could throw off the gravity harvesting sequence. Type: Manual Entry Render on Grids: None Mathematical Formula: $\text{User Input}$ Python Logic: `N/A` Live Evaluation: N/A (Input Variable)
▼ Velocity
☰	\( n_{\text{rps}} \)	GMEG Input Rotations per second	0.650000	View Help Guide Purpose: GMEG operational RPM Logic: This is the internal speed of the GMEG to help determine the operational velocity. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $n_{\text{rps}} = n_{\text{rps}}$ Python Logic: `v["Internal Gear rotations per second"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.6500 = 0.6500
☰	\( v \)	Operational Velocity (m/s)	8.320000	View Help Guide Purpose: The actual physical speed of the train moving along the track in meters per second. Logic: Converts the rotational spin of the internal gears back into straight-line speed. This is the baseline variable for all kinetic energy, momentum, and impact calculations. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $v = C_{\text{int}} \times n_{\text{rps}}$ Python Logic: `v["Internal Gear Circumference (m)"]v["GMEG Input Rotations per second"]` Live Evaluation:* [ROUTE: STATIC/GLOBAL] 12.80000.6500 = 8.3200*
☰	\( D_{\text{centre}} \)	Centre enabler distance from rounded corner centre (m)	4.160000	View Help Guide Purpose: Determine Centre enabler distance from rounded corner centre for TAR activation Logic: We need to know exactly where the middle of the train travels needs to be to activate the lifting phase. This maps that distance so the track swivels at the absolute perfect moment. Type: Calculated (Math Output) Render on Grids: None Mathematical Formula: $D_{\text{centre}} = v/2$ Python Logic: `v["Operational Velocity (m/s)"]/2` Live Evaluation: [ROUTE: STATIC/GLOBAL] 8.3200/2 = 4.1600
▼ Track Spatial Operational Environment
☰	\( L_{s1} \)	Physical End Straight1 (m)	6.000000	View Help Guide Purpose: Determining the distance across the top straight track. Logic: Establishes the exact meter mark where the first linear propulsion zone ends. Type: Calculated (Math Output) Render on Grids: Spatial Mathematical Formula: $L_{s1} = L_{\text{straight}}$ Python Logic: `v["Straight track length (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 6.0000 = 6.0000
☰	\( L_{s2} \)	Physical End Corner1 (m)	12.400000	View Help Guide Purpose: Determining the distance across the right rounded corner. Logic: Adds the 180-degree arc length to the straight, marking the physical end of the first turn. Type: Calculated (Math Output) Render on Grids: Spatial Mathematical Formula: $L_{s2} = L_{\text{straight}}+C_{\text{half}}$ Python Logic: `v["Straight track length (m)"]+v["Half Internal Gear Circumference (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 6.0000+6.4000 = 12.4000
☰	\( L_{c1} \)	Physical End Straight2 (m)	18.400000	View Help Guide Purpose: Determining the distance across the bottom straight track. Logic: Adds the return straight length to the running total, marking the start of the final curve. Type: Calculated (Math Output) Render on Grids: Spatial Mathematical Formula: $L_{c1} = (L_{\text{straight}} \times 2)+C_{\text{half}}$ Python Logic: `(v["Straight track length (m)"]2)+v["Half Internal Gear Circumference (m)"]` Live Evaluation:* [ROUTE: STATIC/GLOBAL] (6.00002)+6.4000 = 18.4000*
☰	\( L_{c2} \)	Physical End Corner2 (m)	24.800000	View Help Guide Purpose: Determining the distance across the left rounded corner. Logic: Completes the loop, representing the total track perimeter used to trigger the lap wrap-around resets. Type: Calculated (Math Output) Render on Grids: Spatial Mathematical Formula: $L_{c2} = (L_{\text{straight}}+C_{\text{half}}) \times 2$ Python Logic: `(v["Straight track length (m)"]+v["Half Internal Gear Circumference (m)"])2` Live Evaluation:* [ROUTE: STATIC/GLOBAL] (6.0000+6.4000)2 = 24.8000*
☰	\( R_{z1, start} \)	RotZone1 Start (m)	5.040000	View Help Guide Purpose: Determining the distance point on the right rounded corner to enable a track arc rotation Logic: Calculates the exact spatial trigger point where the track begins its physical tilt mechanism on the first curve. Type: Calculated (Math Output) Render on Grids: Spatial Mathematical Formula: $R_{z1, start} = L_{\text{straight}}-((v/2)-C_{\text{corner, dist}})$ Python Logic: `v["Straight track length (m)"]-((v["Operational Velocity (m/s)"]/2)-v["Half semi corner Circumference (m)"])` Live Evaluation: [ROUTE: STATIC/GLOBAL] 6.0000-((8.3200/2)-3.2000) = 5.0400
☰	\( R_{z1, end} \)	RotZone1 End (m)	13.360000	View Help Guide Purpose: Determining the distance point on the right rounded corner to disable a track arc rotation Logic: Identifies the exact meter mark where the first corner tilt sequence finishes and locks back into a flat plane. Type: Calculated (Math Output) Render on Grids: Spatial Mathematical Formula: $R_{z1, end} = R_{z1, start}+v$ Python Logic: `v["RotZone1 Start (m)"]+v["Operational Velocity (m/s)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 5.0400+8.3200 = 13.3600
☰	\( R_{z2, start} \)	RotZone2 Start (m)	17.440000	View Help Guide Purpose: Determining the distance point on the left rounded corner to enable a track arc rotation Logic: Calculates the trigger point for the second corner's tilting mechanism. Type: Calculated (Math Output) Render on Grids: Spatial Mathematical Formula: $R_{z2, start} = (L_{\text{straight}} \times 2)+C_{\text{half}}+C_{\text{corner, dist}}-D_{\text{centre}}$ Python Logic: `(v["Straight track length (m)"]2)+v["Half Internal Gear Circumference (m)"]+v["Half semi corner Circumference (m)"]-v["Centre enabler distance from rounded corner centre (m)"]` Live Evaluation:* [ROUTE: STATIC/GLOBAL] (6.00002)+6.4000+3.2000-4.1600 = 17.4400*
☰	\( R_{z2, end} \)	RotZone2 End (m)	25.760000	View Help Guide Purpose: Determining the distance point on the left rounded corner to disable a track arc rotation Logic: Identifies the finish line for the second corner's tilt, returning the track to its default flat state. Type: Calculated (Math Output) Render on Grids: Spatial Mathematical Formula: $R_{z2, end} = R_{z2, start}+v$ Python Logic: `v["RotZone2 Start (m)"]+v["Operational Velocity (m/s)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 17.4400+8.3200 = 25.7600
▼ Rotational Torque Grid
☰	\( r_{gear} \)	Internal Gear Radius (m)	2.037183	View Help Guide Purpose: Referencing the internal gear radius for torque calculations Logic: This is the main "Lever Arm" for the machine. It is the master variable used to convert the linear chain pull into rotational torque. Type: Calculated (Math Output) Render on Grids: Rotational Torque Mathematical Formula: $r_{gear} = r_{gear}$ Python Logic: `v["Internal Gear Radius (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 2.0372 = 2.0372
☰	\( v \)	Velocity (m/s)	8.320000	View Help Guide Purpose: Desired operational speed Logic: Converts the rotational spin of the internal gears back into straight-line speed. This is the baseline variable for all kinetic energy, momentum, and impact calculations. Type: Calculated (Math Output) Render on Grids: Rotational Torque Mathematical Formula: $$$v = v$$$ Python Logic: `v["Operational Velocity (m/s)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 8.3200 = 8.3200
☰	\( d_{gap} \)	Enabler gap (m)	0.596500	View Help Guide Purpose: Enabler spacing Logic: Ensures the cylinders have enough breathing room (with a safety buffer) so they don't grind against each other as the chain bends around the gears. Type: Calculated (Math Output) Render on Grids: Rotational Torque Mathematical Formula: $d_{gap} = L_{\text{gap}}$ Python Logic: `v["Enabler gap length (m)"]` Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.5965 = 0.5965
☰	\( \eta_{DLLS} \)	Energy Transfer Efficiency DLLS (%)		View Help Guide Purpose: Set custom efficiency for DLLS power transfer to GMEG Logic: Defines the baseline power retention factor when shifting energy from the linear drive to the generator. Type: Manual Entry Render on Grids: None Mathematical Formula: $\text{User Input}$ Python Logic: `N/A` Live Evaluation: N/A (Input Variable)
☰	\( \mu \)	Friction factor (%)		View Help Guide Purpose: Set custom friction factor for moving gravity enabler train Logic: Injects standard mechanical drag into the dynamic tracking equations. Type: Manual Entry Render on Grids: None Mathematical Formula: $\text{User Input}$ Python Logic: `N/A` Live Evaluation: N/A (Input Variable)

Operational Environment Dashboard

Add New Variable & Layout Control

Global Find & Replace

✏️ Edit Variable

🔒 Isolated Bucket & Aggregator