An automatic tipping scale collects a batch, detects a weighing threshold, empties the container and resets. The illustration separates the counterweighted weighing beam from the bucket’s dumping motion. Use the calculator to compare an ideal balance mass and fill interval; counting batches can estimate total material only when the actual mass delivered per batch is known.
Automatic Tipping Scale Interactive Calculator
Vary counterweight mass, effective arms and inflow to compare ideal batch mass, balance moment and fill interval.
Equation Used
With empty-bucket tare already balanced, the ideal material threshold occurs when its moment equals the counterweight moment. Gravity cancels in m_tip = m_cw L_cw / L_b. Inflow divided by this mass gives an ideal batch rate that excludes emptying and reset time.
- Lever arms are effective horizontal distances from the pivot at the tipping point.
- Counterweight and material forces act vertically, so g cancels in the mass balance.
- Pivot friction, impact loading, tare buildup, and dynamic overshoot are neglected.
Empty-bucket tare is assumed compensated. Ideal fill interval and batch rate exclude discharge/reset delays and do not establish achievable machine throughput.
Weigh a batch, then empty the bucket
Material enters the bucket while its support loads one side of a balance beam. A counterweight supplies the opposing moment. At the selected threshold, the illustrated sequence closes the feed, tips the bucket about its own trunnion, then returns it to the filling position.
The weighing pivot and dumping trunnion have different jobs. The first compares moments; the second allows discharge. The animation provides a conceptual timing sequence rather than calculating the feed-gate linkage, bucket acceleration or return torque.
Parts shown
- Bucket: receives and releases the material.
- Weighing beam: carries the opposing material and counterweight moments.
- Counterweight: establishes an ideal threshold through its effective arm.
- Feed gate: is shown stopping inflow during discharge.
- Bucket trunnion: allows the emptying motion.
Empty-bucket tare is assumed compensated separately. Friction, retained material, inflow impact and material already falling after cutoff can change real batch mass. A geometry calculation therefore does not replace calibration under the intended operating conditions.
Batch counting and direct weighing
A repeated-batch system can estimate total quantity from a known batch amount and count. A weighing hopper can instead measure individual loads, while a belt weigher measures material on a moving conveyor. These approaches require different calibration and performance assessments.
A tipping-bucket rain gauge counts small liquid collections, but not all rain gauges tip. OTT’s Pluvio² uses a weighing principle with a load cell, rather than the tipping mechanism drawn here. Liquid volume, rainfall depth and material mass also require different unit conversions.
Trade use depends on the actual instrument’s approval and local requirements. OIML R 107 covers specified totalizing hopper weighers but explicitly excludes instruments that simply multiply a preset constant load by cycle count. That scope distinction does not establish whether any particular device is legal for trade.
Ideal balance and fill interval
The calculator uses counterweight mass mcw in kg and effective horizontal arms Lcw and Lb in mm. At the ideal threshold, with tare compensated:
mcw × g × Lcw = mtip × g × Lb
mtip = mcw × Lcw/Lb
Both arms use the same unit, so their ratio is dimensionless. Balance moment in N·m is mcw × 9.80665 × (Lcw/1000). Mass in kg and force in N are different quantities; a force-moment expression must be divided by g before it is expressed as mass.
For the entered inflow Q in metric tonnes/hour, ideal batch rate = 1000Q/mtip batches/hour. Ideal fill interval = 3600/(batch rate) seconds. This is filling time alone. Emptying, reset, settling and any feed interruption require additional time.
If a totalizer assigns mcal kg to each counted discharge, its reported total is count × mcal. This is correct only to the extent that actual delivered batches match the assigned amount and counts are complete. A partly filled final batch needs separate treatment.
Worked example: a 25 kg ideal batch
Use mcw = 5 kg, Lcw = 200 mm and Lb = 40 mm. The ideal material threshold is 5 × 200/40 = 25 kg. Balance moment is 5 × 9.80665 × 0.200 = 9.80665 N·m.
At an illustrative inflow of 9 t/h, the ideal rate is 9000/25 = 360 batches/hour and filling takes 10 seconds. At 18 t/h, the rate doubles to 720 batches/hour and filling takes 5 seconds. Neither number includes discharge or reset, so it does not prove achievable machine capacity.
Increasing the counterweight arm to 205 mm raises the threshold to 25.625 kg and moment to 10.05182 N·m. At 9 t/h, ideal rate becomes 351.2195 batches/hour and fill interval 10.25 seconds.
If a counter assigns 25 kg per discharge but the actual delivered mass is 23 kg, 100 discharges report 2500 kg while delivering 2300 kg: an over-reading of 200/2300 = 8.6957%. The error follows batch mass and count, not a generic accuracy claim for all tipping scales.
Interpreting a batch total
| Issue | Effect to assess |
|---|---|
| Variable mass per discharge | A fixed count multiplier may overstate or understate total mass. |
| Missed or repeated pulses | The count differs from actual completed discharges. |
| Material retained after emptying | Tare and delivered quantity may change. |
| Inflow during cutoff or dumping | Material may enter outside the assumed weighing interval. |
| Uncounted partial batch | A count-only total omits material still in the container. |
Accuracy, allowable flow, inspection intervals and usable resolution belong to a tested instrument and installation. Neither a mechanical counter nor an electronic sensor removes the need to verify the actual delivered quantity.
Tipping-scale questions
No. It assumes tare is already balanced. There is no tare input, and the displayed threshold is material mass under that assumption.
They are effective horizontal distances for the vertical forces at the weighing position. A tilted rod’s length is not necessarily its moment arm.
It increases the opposing moment, so more material moment is required at the same bucket arm.
No. It changes the ideal filling rate and interval. The model does not include impact loading or dynamic overshoot.
No. The numerical interval is filling time only, and the illustrated discharge and return do not model real delays.
Yes. If actual batches differ from the assigned mass, or pulses are missed or repeated, the reported total differs from the delivered quantity.
No. Its manufacturer describes a weighing principle using a load cell. It is a useful contrast to tipping collection.
No. Approval and applicable requirements must be checked for the exact instrument and jurisdiction. The drawing and ideal equations supply no metrological certification.
Instrument references
- OTT, Pluvio² operating instructions, describes a weighing precipitation gauge, distinct from a tipping bucket.
- OIML, R 107-1:2007, reconfirmed 2024, defines the scope and testing of specified totalizing hopper weighers. Its scope excludes fixed preset-load multiplication by cycle count.
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