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Free Surface Effect Of Ships:
When any tank or a compartment is partially filled, the motion of the liquid (due to the ship’s rolling and pitching motions) would reduce the stability of the ship. Why? Because, when the ship is inclined, the liquid in the tank shifts to the lower side of the tank, as shown in the following figure.
Figure 1: Free surface effect.
In the above figure, the ship tank extends from the bottom to the tank top (shown in red), and is only partially filled. When the ship is in upright position, the free surface of liquid in the tank is shown as AA1. When the ship inclines to a certain angle of heel (say ‘theta’ Ɵ) the free surface of the liquid now changes to TT1. Also, the center of buoyancy shifts from ‘B’ to ‘B1’.
What happens as a result of this? Do note that when the liquid in the tank is transferred to the lower side, the volume of the liquid within the wedge between points ‘A’ and ‘T’ has now shifted to the lower side between the points A1 and T1. So basically, the center of gravity of that volume of liquid has shifted from ‘g’ to ‘g1’.
As a result of the weight shift within the ship, the center of gravity of the ship now shifts from ‘G’ to ‘G1’. The effect of this shift of liquid is such that the resultant weight of the entire system acts through a virtual point which is much higher than the actual center of gravity of the ship. This virtual center of gravity ‘GV’ is obtained by extending a vertical line from the new center of gravity ‘G1’ to the centerline of the ship. So the resultant KG increases, therefore reducing the metacentric height of the ship.
The new metacentric height with free surface effect is now ‘GVM’, and the new righting lever is ‘GVZV’, both of which are significantly less than the original values (without free surface effect). It is this reduction in the metacentric height, or rise in the CG of the ship due to free surface effect, that reduces the stability of the ship or may even render it unstable.
This reduction in metacentric height due to free surface effect can be calculated by the following expression:
In the above expression,
?L = Density of the liquid in the tank.
?S = Density of seawater.
IL = Area moment of the free surface about the tank’s longitudinal centre line.
∇S = Mass displacement of the ship in sea water.
There are some very important conclusions that can be drawn from the above expression, and these are used to develop design methods to combat free surface effect on ships. They can be enlisted as:
- The effect of free surface is independent of the position of the tank. That is, a tank may be at any height within the ship, or at any longitudinal position, and the development of any free surface in it would affect the ship in the same way irrespective of its location.
- Reduction of metacentric height due to free surface effect is more for denser liquids.
- The shape of the tank plays a major role in the evaluation of free surface effect. That is because, reduction in the stability of the ship is directly proportional to the area moment of the free surface about the tank’s longitudinal centerline. What does this imply? The lesser transverse surface area of the free surface, lesser its area moment of inertia about the tank’s longitudinal centerline, lesser the reduction in GM due to free surface effect.
In order to attain this, a design priority during the design of tanks is to reduce the longitudinal moment of the free surface by providing longitudinal bulkheads in tanks having large surface area, as shown in the figure below.
source: https://www.marineinsight.com/naval-architecture/ship-stability-makes-ship-unstable/
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