Stability
Formulas
KM
= KG + GM
KG = KM - GM
GM = KM - KG
Gg1 = w x d
........W ± w
"w"
is the weight being loaded/discharged/shifted and "d"
is the distance the centre of gravity is going to move
"W"
is the total weight of the boat and "w" is the weight
being taken onboard/discharged/shifted
Table
of Moments
To
find the total moment for the item being used including the
vessel, multiplying the items weight by the items KG
(Weight x KG = Moment)
Find the moments first then - If all items are loaded, add all
the weights together as well as adding all the moments together,
then divide the total weights by the total moments to give you
your new KG
Find the moments first then - If all items are discharged, subtract
all the weights from the vessels weight as well as subtracting
all the moments from the vessels moments, then divide the total
weights by the total moments to give you your new KG
Find the moments first then - If items are loaded/discharged,
add all the weights being loaded to the vessels weight then
subtract the discharged weight from the total loaded weight
then all the loaded moments to the vessels moments then subtract
all the discharged moments from the total loaded moments, then
divide the total weights by the total moments to give you your
new KG
Example
| |
Weight
tonnes |
metres |
Moments |
| Item |
loaded |
discharged |
KG |
Moment
loaded (+) |
Moment
discharged (-) |
| Vessel |
2000
(+) |
|
4.2 |
8400 |
|
| Fuel |
200
(+) |
|
1.9 |
380 |
|
| Stores |
10
(+) |
|
3.9 |
39 |
|
| Grain
(discharged) |
|
500
(-) |
3.4 |
|
1700 |
| Totals |
2300 |
500 |
|
8819 |
1700 |
| |
500
- |
|
|
1700
- |
|
| Final
Totals |
1800 |
|
|
7119 |
|
KG
= Final weight
.......Final moment
KG
= 1800
.......7119
KG
= 0.2528445 metres
KG = 0.253 (3 decimal figures)
More
Formulas
| Centre
of Gravity = |
Total
Moment |
| |
Total
Weight |
| M.S.S.
= W x Gz |
M.S.S.
is Moment of Statical Stability |
| Gz
= GM Sin Θ |
Where
Θ is the angle of heel (Θ Theta symbol) |
| T.P.C.
= |
1.024A.....Where
(A) is the area of waterplane in Metres 2 |
| |
100
|
| Sinkage
from SW to FW = |
Displacement
inches |
| |
40
TPI |
| Sinkage
= |
F.W.A.
x 1.025 - dock water
inches |
| |
1.025
-1.000 |
| GZ
= KN - KG x Sine Θ |
Where
Θ is the angle of heel (Θ Theta symbol) |
Always Add FSE
to KG or Subtract FSE from GM |
