Stability:
Appendix 2
Example of Calculating Stability Conditions
The following pages show various examples of calculating whether or not a barge’s stability
complies with the stability criteria contained within her stability book for different combinations
of cargo. Although the examples are for a barge, the principles apply equally to all vessels.
The data used in the examples are from an actual stability book, and the limiting values in the summary table below are used in each example.
Summary Table
Deck Cargo Barge (210ft x 52ft x 12ft)
Notes:
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Example 1
1st and 2nd tiers heavy 20ft containers (20t), 3rd and 4th tiers empty 20ft containers (2.4t).
Assumption for calculation:-
- Each tier fully stacked at 5 rows across by 8 containers fore and aft
- Vertical Centre of Gravity, VCG, of containers is half height = half 2.59m = 1.295m
- Weight of heavy container = 20t, weight of empty container = 2.4t
Taking moments about the deck to calculate the total cargo vertical centre of gravity, CVCG, above the deck
CVCG = total moment = 5635.84 ÷ 1792 (total cargo weight) = 3.15m
From the Summary Table on page 31 we derive by interpolation that for a cargo weight (deadweight) of 1792 we find that extreme draft is 2.48m and the maximum permissible cargo VCG above deck is 4.24m
The calculated CVCG of 3.15m is less than the maximum permissible CVCG of 4.24m and therefore is within the permissible stability criteria and is safe.
With the extreme draft of 2.48m and the CVCG of 3.15m we can also determine using the maximum cargo VCG curve that the load plan is in the Safe Zone (see figure below).
Example 2
1st and 2nd tiers heavy 40ft containers (30t), 3rd and 4th tiers empty 40ft containers (4t)
Assumption for calculation:-
- Each tier fully stacked at 5 rows across by 4 containers fore and aft
- Vertical Centre of Gravity, VCG, of containers is half height = half 2.59m = 1.295m
- Weight of heavy container = 30T, weight of empty container = 4.0T
Taking moments about the deck to calculate the total cargo vertical centre of gravity, CVCG, above the deck
CVCG = total moment = 4351.2 ÷ 1360 (total cargo weight) = 3.20m
From the Summary Table on page 31 we derive by interpolation that for a cargo weight (deadweight) of 1360 we find that extreme draft is 2.03m and the maximum permissible cargo VCG above deck is 7.34m.
The calculated CVCG of 3.20m is less than the maximum permissible CVCG of 7.34m and therefore is within the permissible stability criteria and is safe.
With the extreme draft of 2.03m and the CVCG of 3.20m we can also determine using the maximum cargo VCG curve that the load plan is in the Safe Zone (see below).
Example 3
1st and 2nd tiers 20ft containers of 15t in weight, 3rd tier 20ft containers of 8t in weight,
4th tier empty 20ft containers (2.4t).
Assumption for calculation:-
- Each tier fully stacked at 5 rows across by 8 containers fore and aft Vertical Centre of Gravity, VCG, of containers is half height = half 2.59m = 1.295m
- Weight of empty 20ft containers is 2.4t
Taking moments about the deck to calculate the total cargo vertical centre of gravity, CVCG, above the deck
CVCG = total moment = 6050.24 ÷ 1616 (total cargo weight) = 3.74m
From the Summary Table on page 31 we derive by interpolation that for a cargo weight (deadweight) of 1616T we find that extreme draft is 2.30m and the maximum permissible Cargo VCG above deck is 5.60m
The calculated CVCG of 3.74m is less than the maximum permissible CVCG of 5.60m and therefore is within the permissible stability criteria and is safe.
With the extreme draft of 2.30m and the CVCG of 3.74m we can also determine using the maximum cargo VCG curve that the load plan is in the Safe Zone (see below)
Example 4
1st and 2nd tiers heavy 20ft containers (20t) and 3rd tier 20ft containers of 10 t in weight.
Assumption for calculation:-
- Each tier fully stacked at 5 rows across by 8 containers fore and aft
- Vertical Centre of Gravity, VCG, of containers is half height = half 2.59m = 1.295m
Taking moments about the deck to calculate the total cargo vertical centre of gravity, CVCG, above the deck
CVCG = total moment = 6734 ÷ 2000 (total cargo weight) = 3.37m
From the Summary Table on page 31 we derive by interpolation that for a cargo weight (deadweight) of 2000T we find that extreme draft is 2.68m and the maximum permissible Cargo VCG above deck is 2.42m
The calculated CVCG of 3.37m is greater than the maximum permissible CVCG of 2.42m and therefore is outside the permissible stability criteria and is NOT SAFE.
With the extreme draft of 2.68m and the CVCG of 3.37m we can also determine using the maximum cargo VCG curve that the load plan is in the UNSAFE ZONE (see figure below).
Example 5
Mixed Cargo - Container and General Cargo Stowage: Containers, tier 1 and 2 heavy (20t),
tiers 3 and 4 empty (2.4t) x 4 bays, Frames 2 – 16 Boxes, General, Stowed to 3.8m high, total
325T, Frames 16 - 20 Steel Coils, 1.5m dia x 2.4 width x 12t, stowed fore and aft ‘on the roll’, 3
rows x 9 coils per row, Frames 20 -24 Pipes, 40ft x 30ins dia x 7t, stowed across the barge,
stacked 3 high, Frames 24 - 30
Assumption for calculation
- Vertical Centre of Gravity, VCG, of containers is half height = half 2.59m = 1.295m
- Vertical Centre of Gravity, VCG, of boxes is half height = half 3.8m = 1.9m
- Vertical Centre of Gravity of coils is half diameter = half 1.5m = 0.75m
- Vertical Centre of Gravity of pipe is half diameter = half 0.762m = 0.381m
Taking moments about the deck to calculate the total cargo vertical centre of gravity, CVCG, above the deck CVCG = total moment = 3979.79 ÷ 1818 (total cargo weight) = 2.19m
From the Summary Table on page 31 we derive by interpolation that for a cargo weight (deadweight) of 1818T we find that extreme draft is 2.50m and the maximum permissible Cargo VCG above deck is 4.04m.*
The calculated CVCG of 2.19m is less than the maximum permissible CVCG of 4.04m and therefore is within the permissible stability criteria and is safe.
With the extreme draft of 2.50m and the CVCG of 2.19m we can also determine using the maximum cargo VCG curve that the load plan is in the Safe Zone (see below).
