Crabwise · Library
How can moving a load change centre of gravity without changing total weight?
Moving 60 of 200 units from arm 30 to arm 70 keeps total weight at 1300 but adds 2400 to the moment, shifting the CG from 41.54 to 43.38.
Only the moved load's moment changes
In Crabwise's station list a moved load is the same weight with a new arm. Total weight stays the same; the moment of that load changes by weight × (new arm − old arm), and the CG shifts by that change divided by total weight. The fastest way to show this in the app is to split the original row: keep the part that stays and add a row for the part that moves, at its new arm.
The per-station moment lines in the step list make the change visible, because only the rows you touched produce different products.
Worked example
The total remains 1100 units, while moving the 100-unit load from arm 80 to arm 60 reduces moment from 48000 to 46000 and CG from about 43.636 to 41.818.
- Unchanged total weight
- 1100
- Moment after moving the load
- 46000
- CG arm after moving the load
- 41.818182
Represent the move
- Start from the full list as loaded, with every station's weight and arm.
- Reduce the source row by the amount that moves, or delete it if everything moves.
- Add a row with the moved weight at the arm of its new position.
- Confirm total weight is unchanged, then read the new total moment and CG.
Splitting a 200-unit row
The Library worksheet's default rows are 1000 at 40, 200 at 30 and 100 at 80: total weight 1300, total moment 54000, CG ≈ 41.538462. Move 60 units from arm 30 to arm 70 by changing the second row to 140 at 30 and adding 60 at 70. Total weight is still 1300; total moment becomes 40000 + 4200 + 4200 + 8000 = 56400 and the CG ≈ 43.384615.
- Total weight before and after
- 1300
- Moment change, 60 × (70 − 30)
- 2400
- CG before the move
- 41.538462
- CG after the move
- 43.384615
Dividing 2400 by 1300 gives the same 1.846154 shift directly.
Common mistakes
- Adding the moved weight at the new arm without removing it from the old row, which counts it twice.
- Moving the whole 200-unit row when only part of it moves.
- Using an arm for the new position measured from a different datum.
Scope
The arithmetic does not check whether the new position can take the load or whether the result is within the aircraft's limits. The FAA weight-and-balance chapter below explains shifting weight; the aircraft's data sets the limits.
Educational calculation only. Check current aircraft limits, weather, performance and reserve requirements with approved information.