Crabwise · Library
How can an extra load change total weight, moment and centre of gravity?
Add a station to a weight-and-balance list and recompute total weight, total moment and CG from the new sums, not from an average of two arms.
How an added station enters the sums
Crabwise's weight-and-balance screen treats every row as a station with a weight and an arm. For each row it computes the moment M = W × arm, then adds all weights into ΣW and all moments into ΣM. The centre of gravity is CG = ΣM ÷ ΣW. When you add a row, both sums change at once, so the new CG is a weighted result: a light load far aft moves it less than a heavy load at the same arm.
The step-by-step view lists one moment line per station, then the total weight, the total moment and the division that gives the CG. Comparing the list before and after the new row shows exactly which product was added.
Worked example
Starting with 1000 weight units at arm 40, adding 100 at arm 80 moves the calculated CG from 40 to about 43.636. These are educational quantities, not aircraft loading limits.
- Weight after the addition
- 1100
- Moment after the addition
- 48000
- CG arm after the addition
- 43.636364
Add the row and read the change
- Enter the existing stations exactly as before, with the same weight unit and the same arm unit.
- Add one new row with the load's weight and the arm of the position where it will actually sit.
- Check the new station's moment line: weight multiplied by arm, nothing else.
- Read the new total weight and total moment, then the CG they produce.
- If you entered envelope points, read the inside or outside result again for the new point.
A second load at a different arm
Start from the two-station case on this page, 1000 at arm 40 and 100 at arm 80, then add 80 units at arm 95. The new moment line is 80 × 95 = 7600. Total weight becomes 1000 + 100 + 80 = 1180 and total moment 40000 + 8000 + 7600 = 55600. Dividing gives 55600 ÷ 1180 ≈ 47.118644.
- Added station moment
- 7600
- Total weight with three stations
- 1180
- Total moment with three stations
- 55600
- CG arm with three stations
- 47.118644
Averaging the previous CG of 43.636364 with the new arm of 95 would give about 69.318182, far aft of the real weighted result. Those are educational quantities only.
Common mistakes
- Replacing an existing row with the new load instead of adding a separate station.
- Using the arm of a nearby seat or bay because the actual position's arm is not at hand.
- Mixing kilograms with inches or pounds with millimetres; the app expects pounds with inches or kilograms with millimetres.
- Reading the new total weight and forgetting that the CG moved as well.
Where this stops
The worksheet adds the numbers you enter. It does not know a compartment's weight limit, whether the load fits, or whether the copied envelope matches the aircraft. Chapter 10 of the FAA Pilot's Handbook, linked below, explains station arithmetic; the aircraft's own weight-and-balance data decides what is permitted.
Educational calculation only. Check current aircraft limits, weather, performance and reserve requirements with approved information.