You must have read about the center of gravity of
a body in your high school physics but do you know its importance in the
context of ship stability in the vast oceans? Just read on to find out more!
Introduction
In the previous article we learnt how forces and
moments could be acting on a body at a given point of time and how to find the
net or resultant value of those forces or moments. In this article we will
continue our study of ship stability by learning something about center of
gravity, centroid and their relationship to stability of a ship floating in the
sea.
Center of Gravity
When studying objects, forces and their
inter-relationships we often tend to represent a body by a point for
theoretical purposes of calculations relating to that body. This certainly is a
convenient method of representation but we know that in actual situation there
is hardly any body which is actually the size of a point, so how do we go about
it?
How to find out the center of gravity?
A body can be assumed to be made of small pieces
joined together and let there be small pieces of mass “m” each with the
distance “d” from the center of gravity. The center of gravity can be
calculated as the summation of the moments of all the masses divided by the
total mass of the body i.e.
R = (∑ m * d)/∑m
But you need not do this for all bodies for the
well defined geometrical shapes the center of gravity coincides with the
geometrical center (it is also known as centroid) of the body and here are a
few cases
- In case of circle, the center of gravity is at its center
- In case of square and rectangle, the center of gravity is at the intersection of two diagonals
Change in Mass and change in CG
Since center of gravity depends on mass,
certainly any change in mass would result in a change of center of gravity of
the body. Now if you are thinking in terms of conservation of mass I do not
mean that mass is created or destroyed but I simply mean that some weight is
either place on or removed from the object under discussion. The mathematical
analysis of such a case suggests that whenever some amount of mass is either
added (or removed) from an object the center of gravity of the body move
towards (or away from) the center of gravity of the body by a distance which is
directly proportional to the mass added (or removed) and its distance from the
original center of gravity of the body and inversely proportional to the total
increased (or decreased) mass of the combined bodies.
Mathematically this can be expressed as follows
CG = m * s/M + m
Where “m” is the mass added (or removed), M is
original mass of the body and “s” is the distance between the two centers of
gravities of the separate bodies.
Corollary: another thing which can be concluded
from the above equation is that if the mass is neither removed nor added but
only moved from one position to other on the parent body, the new center of
gravity is given by the same equation except that M remains unchanged,
therefore
CG = m * s/M
How is this relevant to a ship?
If you just remembered that we are talking about ship
stability here then let me explain how this concept is useful in ship
calculations. We know that ships contain huge cargo hatches from where cargo is
removed or added in bulk quantities during loading or discharging operations.
This change of mass will cause a change in the center of gravity of the entire
ship and hence you can start to see a connection between the stuff studied till
now and its application to stability. We will proceed with this study in our next
article.
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