IERS Dashboard
| ▼ Track Rotational forces | ||||
| ☰ | \( M_{\text{track}} \) | Total Optimized Track Mass (kg) | 32,717.800233 |
View Help GuidePurpose: Defines the mass used for all inertial and gravitational calculations. - Total Optimized Track Mass (kg)
Logic: Imported directly from the Track structural sheet. This is the raw physical mass that our lifting motors (the DLLS) have to heave around during every single swivel.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$M_{\text{track}} = \Sigma M_{\text{skeleton}} + M_{\text{outer, structure}} + \Sigma M + \text{Chain Total Mass (kg)} + M_{\text{shielding}} + ( \Sigma M_{\text{permanent, magnet}} \times 2 )$$ Python Logic:
v["Total Skeleton Mass (kg)"] + v["Outer Structure Weight (kg)"] + v["Internal Gears Total Mass (kg)"] + v["Chain Total Mass (kg)"] + v["Shielding Weight (kg)"] + ( v["Total Permanent Magnet Mass Per Side (kg)"] * 2 )Live Evaluation: [ROUTE: STATIC/GLOBAL] 4,485.1444 + 19,203.0493 + 5,789.9167 + 899.1553 + 720.5347 + ( 810.0000 * 2 ) = 32,717.8002
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| ☰ | \( I_{\text{track}} \) | Track Moment of Inertia (I) | 161,334.024685 |
View Help GuidePurpose: Quantifies the structural resistance of the track to angular acceleration during the TAR.
Logic: A long, heavy seesaw is much harder to rotate than a compact block of the exact same weight. This standard physics formula quantifies exactly how much resistance the long track puts up against our lifting motors.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$I_{\text{track}} = ( 1 / 12 ) \times M_{\text{track}} \times ( L_{\text{end-to-end}} ^ 2)$$ Python Logic:
( 1 / 12 ) * v["Total Optimized Track Mass (kg)"] * ( v["Total Track End-to-End Length (m)"] ^ 2)Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 1 / 12 ) * 32,717.8002 * ( 7.6924 ** 2) = 161,334.0247
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| ☰ | \( \Delta\theta \) | Angle (Radians) | 1.047198 |
View Help GuidePurpose: Defines the total angular displacement required for a full Track Arc Rotation.
Logic: The track goes from fully tilted one way to fully tilted the other way (double the baseline angle). We convert this full sweep into radians so the simulator can run pure rotational physics equations.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Delta\theta = RADIANS ( \theta_{\text{tilt}} \times 2 )$$ Python Logic:
RADIANS ( v["Angle tilt (degrees)"] * 2 )Live Evaluation: [ROUTE: STATIC/GLOBAL] RADIANS ( 30.0000 * 2 ) = 1.0472
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| ☰ | \( t_{\text{lift}}^{2} \) | TAR Time Squared | 1 |
View Help GuidePurpose: Intermediate value used to determine the rate of angular acceleration.
Logic: Because rotational acceleration inherently occurs over "time squared" (s^2), isolating this calculation keeps the downstream physics formulas clean and traceable.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$t_{\text{lift}}^{2} = t_{\text{lift}} ^ 2$$ Python Logic:
v["Lift Time (s)"] ^ 2Live Evaluation: [ROUTE: STATIC/GLOBAL] 1.0000 ** 2 = 1.0000
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| ☰ | \( \alpha \) | Angular Acceleration | 4.18879 |
View Help GuidePurpose: Calculates the constant angular acceleration required to complete the rotation in the specified time.
Logic: The track must speed up for the first half of the tilt, then hit the brakes for the second half. This tells us the exact rate of acceleration required to complete the full swivel within our budgeted "Lift Time."
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\alpha = ( 4 \times \Delta\theta ) / t_{\text{lift}}^{2}$$ Python Logic:
( 4 * v["Angle (Radians)"] ) / v["TAR Time Squared"]Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 4 * 1.0472 ) / 1.0000 = 4.1888
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| ☰ | \( \tau_{\text{peak, inertial}} \) | Peak Inertial Torque (Nm) | 675,794.382302 |
View Help GuidePurpose: Defines the maximum rotational torque required to overcome the track's inertia (acceleration and deceleration).
Logic: Multiplies the track's physical stubbornness (Inertia) by how hard we are pushing it (Acceleration). This reveals the absolute maximum torque the flywheels must generate before we even factor in the heavy payload.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\tau_{\text{peak, inertial}} = I_{\text{track}} \times \alpha$$ Python Logic:
v["Track Moment of Inertia (I)"] * v["Angular Acceleration"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 161,334.0247 * 4.1888 = 675,794.3823
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| ☰ | \( \omega_{\text{max}} \) | Max Angular Velocity | 2.094395 |
View Help GuidePurpose: Calculates the peak rotational speed achieved at the midpoint of the Track Arc Rotation.
Logic: The track accelerates until it is perfectly level with the floor, then immediately starts decelerating. This gives us the top velocity right at that horizontal midpoint.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\omega_{\text{max}} = \alpha \times (t_{\text{lift}} / 2)$$ Python Logic:
v["Angular Acceleration"] * (v["Lift Time (s)"] / 2)Live Evaluation: [ROUTE: STATIC/GLOBAL] 4.1888 * (1.0000 / 2) = 2.0944
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| ☰ | \( E_{\text{k}} \) | Kinetic Energy (J) | 353,845.111131 |
View Help GuidePurpose: Defines the total inertial work required to accelerate the track mass to its peak speed
Logic: Calculates the absolute amount of work (in Joules) the DLLS system must burn to accelerate the massive track structure up to its top swivel speed.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$E_{\text{k}} = ( 0.5 ) \times I_{\text{track}} \times \omega_{\text{max}}^ 2$$ Python Logic:
( 0.5 ) * v["Track Moment of Inertia (I)"] * v["Max Angular Velocity"]^ 2Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 0.5 ) * 161,334.0247 * 2.0944** 2 = 353,845.1111
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| ▼ Spring support system | ||||
| ☰ | \( \eta_{\text{spring}} \) | Spring system efficiency (%) |
View Help GuidePurpose: Defines the proportion of the track's inertial work that is counteracted by the spring system.
Logic: Why burn electricity if springs can do the work? This slider lets us tune how much of the track's rotational mass is balanced and absorbed by physical spring tension, taking the massive peak loads off the motors.
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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| ☰ | \( W_{\text{spring}} \) | Inertial Work Supplied by Springs (J) | 265,383.833348 |
View Help GuidePurpose: Calculates the mechanical work performed by the spring system to aid in accelerating the track structure.
Logic: Quantifies the brute mechanical work the springs do to help heave the track. Every Joule absorbed by the springs here is a Joule we don't have to drain from the flywheel.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$W_{\text{spring}} = E_{\text{k}} \times \eta_{\text{spring}}$$ Python Logic:
v["Kinetic Energy (J)"] * v["Spring system efficiency (%)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 353,845.1111 * 0.7500 = 265,383.8333
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| ☰ | \( W_{\text{deficit}} \) | Inertial Work Deficit for Flywheel (J) | 88,461.277783 |
View Help GuidePurpose: Determines the net amount of inertial work that must be supplied by the DLLS flywheel to complete the track rotation. - Kinetic Energy (J) - Inertial Work Supplied by Springs (J)
Logic: The springs can't do 100% of the work. This calculates the exact energy shortfall that the DLLS active drive system must step in and inject to successfully complete the seesaw tilt.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$W_{\text{deficit}} = E_{\text{k}}-W_{\text{spring}}$$ Python Logic:
v["Kinetic Energy (J)"]-v["Inertial Work Supplied by Springs (J)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 353,845.1111-265,383.8333 = 88,461.2778
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| ☰ | \( F_{\text{torque}} \) | Flywheel Torque Contribution Factor | 0.25 |
View Help GuidePurpose: Quantifies the fraction of the track's peak inertial torque the flywheel system is responsible for supplying.
Logic: If the springs handle 75% of the heavy lifting, the flywheel only has to push the remaining 25%. This factor mathematically shifts the torque burden away from the active electrical drivetrain.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$F_{\text{torque}} = 1 - \eta_{\text{spring}}$$ Python Logic:
1 - v["Spring system efficiency (%)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 1 - 0.7500 = 0.2500
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| ☰ | \( \tau_{\text{net, flywheel}} \) | Net Peak Flywheel Torque (Nm) | 168,948.595575 |
View Help GuidePurpose: Calculates the maximum instantaneous torque the flywheel must deliver to overcome the remaining inertial resistance.
Logic: The bottom line for sizing the DLLS gearbox. It strips away the spring assistance to tell us exactly how hard the flywheel shaft needs to twist to overcome the track's remaining stubbornness.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\tau_{\text{net, flywheel}} = \tau_{\text{peak, inertial}} \times F_{\text{torque}}$$ Python Logic:
v["Peak Inertial Torque (Nm)"]* v["Flywheel Torque Contribution Factor"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 675,794.3823* 0.2500 = 168,948.5956
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