**Ship Intact Stability -Part 2**

*-Raghu Varier*

In the previous post we discussed about the ship intact stability for small angles and neglecting the effect of vertical shift in centre of buoyancy B due to the change in the shape of submerged volume. If you haven’t read the previous post, it is recommended to go through it first, since in this section we will be considering the effect of vertical shift in B as well.

Here we consider a wall sided vessel, i.e a vessel with flat vertical sides as shown below.

Most of the things remain the same as the previous section. The only additional consideration being the vertical shift in B. So that means we have to also consider the vertical shift in B. This is as illustrated above.

(Serious mathematics ahead.)

So the small shift in volume also has a vertical shift by the above value. The value of this small volume as arrived at in the previous post is

So the vertical moment of volume shift is

The Second moment of this area represented by “I” as arrived at in the previous post is

So let us substitute this in the vertical moment expression and we get the value as

The vertical moment of Volume shift can be written as

The horizontal moment of volume shift can be written as

No from the above figure

Now from the above figure,

And can be written much better as

If you observe carefully at the expression, you can see it is the same as that for small angle along with the additional term after the ‘+’. This means that stability lever is increased.

The stability lever i.e stability can be improved by obtaining more volume shift moment and this can be obtained by flaring the ships.

So the flaring of ships is more of a stability aspect than looks. This is why warships conventionally have nice flaring bow sections as it serves the dual purpose of better stability and larger deck area at the bow.

However there are some recent warships that donot have this flaring but instead has a tumblehome structure. And yes I am talking of none other than the DDG-1000 USS Zumwalt. The stability of such a warship is hence an interesting matter of study as the lack of flaring means very small tolerances available for roll motions. We shall be discussing about such tumblehome warships in the near future.

However let us take a look at how powering of a ship is calculated and how propulsion system is selected in the upcoming post.

*Next Post: Resistance and Propulsion*