An automatic dumping car uses a discharge mechanism at a designated unloading point to empty its load. This animation shows an end view of a side-tipping body, a retaining latch and the loaded center of gravity. Enter the center-of-gravity offset and height to find the body angle at which that point crosses the vertical line through the pivot.
Automatic Dumping Car Interactive Calculator
Compare the loaded-CG balance angle with an illustrative 10-15 degree band. This is a static geometric comparison, not a dumping-time or vehicle-stability approval.
Equation Used
The calculation finds the body rotation angle at which the loaded centre of gravity passes the pivot line: theta_tip = atan(e / h_cg). The 10–15° range is an example comparison band. This geometric crossing does not determine latch force, discharge time or whether an empty body will return upright.
- Loaded centre of gravity is treated as a point mass relative to the trunnion pivot.
- Positive offset e is the horizontal pivot offset toward the discharge side.
- The 10–15° comparison is illustrative, not a required tip margin or a product specification.
The supplied offset and height determine the original loaded CG crossing. Material movement changes the CG during discharge. The example 10-15 degree band is not a universal Granby specification.
Releasing the latch and tipping the body
The illustrated car has a tipping body carried on a wheeled truck. A retaining latch holds the body in its travel position. At the discharge station a trip releases the latch, and an external tipping rail supplies the initial rotation.
The gold marker represents the original combined center of gravity of the body and its load. Initially it lies on the restoring side of the pivot. As the body turns toward discharge, the marker moves toward the dotted vertical through the pivot. At the calculated angle it reaches that line, where its gravitational moment about the pivot is zero.
Beyond that point the fixed point-mass model gives a moment in the tipping direction. Ore moving or leaving the body changes the actual combined center of gravity, so the original marker no longer describes the complete load throughout discharge.
Parts to follow
- Truck and wheels: support the body and carry the car along the track.
- Body and pivot: allow the container to rotate relative to the truck.
- Retaining latch and trip: represent holding and release at the station.
- Tipping rail: supplies the initial movement in this example.
- CG marker: shows the selected loaded point for the geometric comparison.
The return motion is also prescribed for the animation. An empty-body center of gravity, return cam, counterweight, stops and latch behavior would need separate analysis to establish an actual automatic reset.
Comparing a side-tipping arrangement
A fixed discharge station can coordinate a car’s arrival, latch release and container movement. A side-tipping body needs room beside the track for its sweep and the discharged material. Other arrangements, such as bottom doors or a rotary dumper, use different moving parts and require their own analysis.
This calculator helps distinguish the initial CG crossing from the complete discharge process. It does not determine throughput, rail gauge, payload capacity or the size of a chute.
The actual vehicle and dump station need compatible geometry and documented operating limits. The two inputs do not justify moving a pivot, rebuilding a latch or prescribing a minimum fill level.
The balance-crossing angle
Let e be the horizontal offset from the loaded CG vertical to the pivot, toward the discharge side, and h be the loaded CG height above the pivot. Both inputs use millimeters. For rotation toward the illustrated discharge side, the CG reaches the pivot vertical when h sin θ − e cos θ = 0.
Therefore Tip Angle θ = atan(e/h), converted to degrees. Increasing e at fixed h increases the required rotation. Increasing h at fixed e decreases it. Mass cancels from this geometric condition, although it would be needed to calculate the actual gravitational moment.
The 10 deg Offset is h tan 10°, and the 15 deg Offset is h tan 15°. Example-band margin is the distance to the nearer band edge when θ lies within 10–15°. It is negative by the distance outside the band otherwise, and zero at either edge.
The band is not a stability approval. Whole-car tipping about a wheel or rail contact uses a different pivot and the complete vehicle’s center of gravity. Latch force, material flow, impact, friction and return motion are not included here.
Worked example: a selected loaded CG
Enter e = 89 mm and h = 420 mm. Tip Angle = atan(89/420) = 11.964264°. The two reference offsets are 420 tan 10° = 74.057332 mm and 420 tan 15° = 112.538661 mm. The example-band margin is 1.964264°.
For the same height, an exact 12° crossing would require e = 420 tan 12° = 89.273756 mm. That is a geometric result, not a historical or manufacturer-approved pivot dimension.
Changing only e to 59 mm gives 7.996368°, with a margin of −2.003632°. At e = 136 mm the angle is 17.942447° and the margin is −2.942447°. Neither negative value predicts a fault: it only places the selected geometry outside the example band.
A partially filled body may have a different combined CG. It needs its own e and h; changing fill can move the CG both horizontally and vertically. The tool does not infer those values from volume or material density.
What the angle can and cannot explain
| Quantity | Interpretation |
|---|---|
| CG crossing angle | Where the original loaded point lies vertically above the body pivot. |
| Example-band margin | A signed comparison with 10–15°, not a machine acceptance test. |
| Dumping time | Needs dynamics and bulk-material flow information. |
| Automatic return | Needs empty-body geometry and return/latch mechanisms. |
| Rail stability | Needs the whole vehicle, load and wheel-support geometry. |
Dumping-car geometry questions
No. If the loaded CG is still on the restoring side, initial rotation needs another cause, such as the tipping rail shown. Friction and other forces also matter.
For positive h, atan(e/h) increases with e. The CG must rotate farther before reaching the pivot vertical.
No. Return depends on the empty-body geometry and return mechanism, which are not calculated.
No. It is an illustrative comparison range in this tool.
No. It follows the original full-load point. Real material redistribution and discharge change the combined center of gravity.
The location of the zero gravity-moment crossing depends on geometry. Calculating moment magnitude would also require mass.
No. It has no latch, suspension, vibration or wear model and provides no repair dimensions.
No. It means the body-CG crossing angle is outside a selected example range. Whole-vehicle stability is a different calculation.
Moment-balance reference
OpenStax, Conditions for Static Equilibrium, gives the moment-balance principles used to interpret the CG crossing.
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