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Stability
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For box-shaped vessels :
Draught is defined as the vertical distance between the keel and the waterline, measured either forward, aft or amidships in metres.Consider a box-shaped vessel floating upright on an even keel with draught “ d ” having beam “ b ”.
INCREASE IN DRAUGHT DUE TO LIST
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Now consider the same vessel listed to an angle Ө.
The new increased draft on the listed side is “D”.
It is seen; D = AX + AY
In triangle AOX , Sin Ө = AX/OA
So AX = OA Sin Ө, but OA = ½ b (breadth)
therefore AX = ½ b Sin Ө , similarly AY = d Cos Ө
Thus Increased draft, D = ½ b Sin Ө + d Cos Ө
X
For Ship Shape Vessels :
For vessels with a rise of floor the formula can be further
modified as follows;
New draft in listed / heeled condition,
D = ½ b Sin Ө + (d - Rise of floor) Cos Ө
Where b = beam of vessel
d = draft in upright condition
Note : The rise of floor is assumed to be linear
The sketch and example on the following page will make
things clearer.
Example 1 (box shaped vessels)
A box-shaped ship with 12 m. beam is floating upright at a draft of 6.7m.Find the increase in draft if the vessel is now listed 18 degrees.
Figure 1(c). From Previous :AX = 1/2 beam x Sin List = 1/2 x 6 x Sin 18 = 1.85mAY = Old draft x Cos List = 6 x Cos 18 = 6.37mNew Draft - XY = 8.23 mIncrease in draft = 8.23 - 6.7 = 1.526 m
Example 2 (Vessels having a rise of floor)
A ship has 20 m. beam at the waterline and is floating upright at 6 m. draft. If the rise of floor is 0.25 m., calculate the new draft if the ship is now listed 15 degrees. (See Figure 1(d), below)
Fig. 1 (d)The formula is modified form of previous and is given by :New Draft = 1/2 beam x Sin List + (Old draft - Rise of
floor) Cos List. = 1/2 x ( 20 x Sin 15 ) + (Old Draft -Rise of
floor) Cos List = 1/2 x ( 5.176) + ( 6 - 0.25 ) Cos 15 = 2.588 + 5.555 = 8.14 metres Ans.