A side-dump rail car carries a body that pivots relative to its underframe. This calculator is limited to an ideal rigid combined mass at a selected fixed centre-of-gravity radius from the pivot; it does not predict whether a real load will tip, slide, discharge or return.
Side-Dump Body · Selected Rigid-CG Ledger
Explore an ideal rigid combined mass at a selected fixed CG radius from a side-dump pivot.
Equation Used
- Load and body masses are combined into one ideal point mass fixed to the body.
- e is the selected centre-to-centre CG radius from the pivot at the level reference.
- theta is measured from that level reference in the illustrated direction.
- Gravity is 9.80665 m/s².
- Cargo shift, friction, latches, springs, impact, strength, stability, discharge and safety are excluded.
The secondary figure keeps the entered CG radius fixed to the body; real cargo redistribution is not represented.
Selected rigid-CG ledger
With combined entered mass m, selected fixed CG radius e and body angle theta measured from the level reference, the ideal gravity moment magnitude is mge cos(theta) and the potential-energy decrease from level is mge sin(theta).
Real granular or fluid cargo redistributes, so its centre of gravity is generally not fixed to the body.
What the calculator determines
Use it only to inspect the stated rigid-body proxy and entered load mass per entered box volume. It does not size trunnions, latches, springs, actuators, frames or rails.
Exact selected relationships
m=m_load+m_body; tau0=mge; tau(theta)=mge cos(theta); Delta U=mge sin(theta); entered average load density=m_load/V.
Selected-input example
At V=0.5 m³, load mass 750 kg, body mass 200 kg, e=50 mm and theta=45°, the rigid-CG proxy gives tau0=466.0 N·m, tau=329.5 N·m, Delta U=329.5 J and entered average load density 1500 kg/m³.
Not a dumping or safety model
Load shifting, free-surface effects, discharge opening, latch and pivot friction, springs, impacts, stops, structural stress, wheel and rail stability, tipping time, return motion and safety are excluded.
Questions
Does a positive moment prove the car will dump?
No. The model omits restraint, friction and cargo redistribution.
Is the density a material property?
No. It is only entered load mass divided by entered box volume.
Can the result size a latch or trunnion?
No. Dynamic and structural loads are excluded.
Primary references
- US3807317A, Articulated railway tilting dump car — pivoted container and trunnion arrangements.
- US1228540A, Automatic dumping and righting mechanism for tiltable dump-cars — mechanism-specific dumping and return geometry.
- USPTO Class 105 definition — railway dumping receptacle and offset-pivot classifications.
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