Metacentric height correction due to free surface effect

In summary, Russ_waters is trying to calculate the moment of a floating structure with open compartments filled with water. His opinion is that the moment of the free water surface with respect to it's axis of transverse rotation is the moment of the free water surface with respect to the structure's axis of transverse rotation. His collegues opinion is that the moment of the free water surface with respect to the structure's axis of transverse rotation is the moment of the free water surface with respect to the structure's centerline. Without considering the effect of the free water surface, Russ_waters calculates that the metacentric height of the structure is 1.88 m.
  • #1
ar
2
0
Hi
regarding the above subject there is a conflict of opinion between me and a collegue. So i need your help
In order to calculate the corrected metacentric height of a floating structure that have a open compartment, filled with water, that is located eccentrically i have to use
GMnew = GM - (density of tank fluid * accel. of gravity * second moment of inertia / structure displacement)
Which is the second moment of inertia that i have to use?
My opinion : is the moment of the free water surface with respect to it's axis of transverse rotation
My collegues opinion : is the moment of the free water surface with respect to the structure's axis of transverse rotation
I will appreciate your reply
Thanks
ar
 
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  • #2
I'm a little ways away from my last statics/dynamics class and I'm not sure of all of your terms, so I'm not quite sure what you are asking, but perhaps drawing a simplified version of your problem would help:

A 2d, square-cross section ship with 4 compartments floats 3/4 of the way out of the water. If the bottom-right compartment is opened, it fills halfway and the moment generated on the ship can be calculated by using a point-force at the cog of the water in relation to the cog of the ship.
 
  • #3
Dear russ_waters
thank you for your reply
I will try to make the problem more specific.
Let's say we have concrete box structure with plan dimensions 10m (transverse) & 20m(longitudinal) that is closed at the bottom with a slab and open on the top. The structure is divided in two symmetrical parts by a wall running on the longitudinal axis. So we have the concrete box structure with two empty tanks (20 by 5) that we are going to float (assume that height is sufficient, let's say 15m). The wall & slab thickness is, let's say 50cm.
Now we add 1m of water inside the two tanks.
Checking the transverse stability of the structure
Weight = 1880 tons (1440 ton walls + 240 tons slab +200 ton water)
Draft should be 1880/(20*10)= 9.4 m, for displaced volume = 1880 m3
Center of gravity located at 5.7m
Center of boyancy located at 4.7m

Now, let's calculate the following values
2nd moment of inertia of waterplane area Jw= 20 x 10^3/12 = 1667 m4

2nd moment of inertia of each tank free surface with respect to tank centerline Jf1 = Jf2 = 20 x 5^3/12 = 208 m4

2nd moment of inertia of each tank free surface with respect to structure's centerline Jf1' = Jf2' = (20 x 5^3/12) + (( 20 x 5) x 2.5^2)= 833 m4

Metacentric height without considering the free water surface effect will be
GM0=(J of waterplane area / displaced vol) + (5.7-4.7) = (1667/1880)+1 = 1.88 m

NOW, MY QUESTION IS
In order to consider the effect of free surfaces to the GM0 we have to reduce GMo by a value equal
a) (Jf1+Jf2)/displ volume = 2 x 208/1880 = 0.22m so the GMcorrect=1.66m
or
b) (Jf1'+Jf2')/dipl volume = 2 x 833/1880 = 0.87, so the GMcorrect=1.01 m

Thank you again for your interest to my inquiry
ar
 

1. What is metacentric height correction due to free surface effect?

Metacentric height correction due to free surface effect is a measurement of the stability of a floating body, such as a ship, with respect to its metacentric height. It takes into account the impact of the free surface effect, which is the movement of liquids on board a floating body, on the stability of the body.

2. Why is metacentric height correction due to free surface effect important?

This correction is important because it helps to determine the safety and stability of a floating body, such as a ship, during its operation. If the metacentric height is too low, the body may be prone to capsizing, while a high metacentric height can cause excessive rolling and discomfort for those on board.

3. How is metacentric height correction due to free surface effect calculated?

The calculation of this correction involves measuring the volume and weight distribution of the liquids on board a floating body, as well as the distance between the center of gravity and the metacenter. This information is then used to determine the corrected metacentric height.

4. What factors can affect the metacentric height correction due to free surface effect?

The amount and distribution of liquids on board, as well as the shape and size of the floating body, can all affect the metacentric height correction due to free surface effect. Weather conditions such as waves and wind can also impact the correction.

5. How can the metacentric height correction due to free surface effect be minimized?

The free surface effect can be minimized by reducing the amount of liquids on board, keeping them evenly distributed, and using anti-roll tanks or other stability-enhancing measures. Proper loading and ballasting of the floating body can also help to minimize the correction and improve its stability.

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