Uncoupled Heaving Motion|dynamics ship

Hii!
I am currently studying about ship dynamic of marine vessel , and for the reference/ book I used :
Dynamics of Marine Vehicles
by Rameswar Bhattacharyya

There are something I don't understand how to determine value added mass coefficient ( C ) for heaving motion. I get the 3 data: [(We^2/2g) x Bn, Bn/Tn, dan βn] to obtain the value added mass coefficient for heaving and the data for determine which curve should used . And I still don't get the value of C , added mass coefficient even there are curve and 3 data .

And I give the picture of curve to determine coefficient C and table of data.

What I am worrying is there are formula to get the value of C , and I can't find the source of information of that . Please Help me.

(this is part of finding added mass )

And Thank you for the time !

 

Hi Arton, welcome to the forum.

If I understand you correctly, you first need to understand what the coef. "C" is representing.
It is all related to what is termed "added mass". It is cornered with a certain amount of the fluid that moves with the body that is oscillating. Simply because the F=ma, means the 'm' is greater than its displacement/mass when oscillating in a fluid compare to air. Hence the term "added mass". d

The original data first used to describe and measure this is related to a deeply submerged cylinder, that is oscillating normal to the axis.

However, ships, or boats are not precisely cylindrical, their shapes are very different.

The curves in DMVs you cite are related to a Lewis form cross section, which is a kind of "ship shape".
The C in fig.s 4.4 etc, relate to that.

So, a shape that is not the same as the Lewis form, you need its added mass coeff. data to obtain the "C". As it will be a different C from that presented.

 

Thank you so much for the answer!
However, I have questions relate to that .... you said I need its added mass coeff.data to obtain the "C" . How to get the added mass coeff.data when it's different "C" from that represented?

 

Firstly there are graphs, like those that you posted from DMVs, in many publications, for "shapes" of different types, related to typical ship shapes.
Publications like, Principles of Naval Architecture, covers useful graphs of variations of B/T ratio, or like the one attached for ref:

Or, if your maths is up to it, you can use a generalisation of Lagrange's equations.

 

Okay, you really help me ! Thanks