# SLACK TANKS

When you fill a pool aboard a vessel it looses stability for two reasons: The considerable weight (the water in the pool) that’s moved from the tanks, usually placed low down, to the pool that’s generally quite high up, usually on an open deck. The oscillation of the surface water in the pool (free surface effect). If the first cause of stability is somewhat obvious (the ship’s centre of gravity rises as a function of the amount of water moved and the distance it’s raised up), the second cause is a bit less intuitive. So let’s get to grips with it. A liquid load aboard, if its not kept in a sealed tank, will be free to move in its container and change the shape of its volume. In particular it’ll be the surface of this liquid load that’ll change shape: the so-called “free surface effect “. A pool on board is a “free surface”.the mere presence of this liquid surface, in other words of a watery mass free to oscillate, causes a reduction in a vessel’s stability, in that the metacentric radius of the hull “r” is reduced, and consequently also the metacentric height “r-a”. In the case of a pool, where the water contained in the tank is made up of water of a density similar to that of the seawater in which the vessel is sailing, the reduced metacentric height depends solely on the geometry of the liquid surface, or, to be more precise, on the moment of inertia “i” of the liquid surface with respect to the barycentric axis parallel to the symmetric longitudinal plane of the vessel. In effect if a vessel’s righting moment, that is the ability of the vessel to return to its horizontal position after having listed due to an external cause (wind, waves or whatever), is given by the following relation (for small inclinations within the limits of the metametric method): RM = D (r-a) sine a then the presence of a liquid surface (in this case of water) free to oscillate reduces righting moment as follows: RM = D (r-a) sine a - (p i/v) sine a As the event becomes repetitive the relation simplifies and becomes: RM = D (r-a-i/v) sine a Where RM = Right Moment (r-a) = metacentric height a = angle of list p = weight of liquid i = moment of inertia of the surface of the pool v = volume of liquid V = volume of vessel’s hull

In effect the righting motion factor RM reduces as a function of the moment of inertia of the surface water in the pool, a moment of inertia that represents the resistance (inertia indeed) against changing its shape for a simple shape such as

the one for a rectangular pool, said moment of inertia will be given by: i = (L * B3)/12 where L is the length and B the width of the pool that is elevated to the power of 3. The correlation thus tells us that the reduction in stability is solely a function of the size of the surface of the pool, in other words its moment of inertia, and not of the amount of water held in the pool. It is thus evident that the wider the pool the less stable a vessel will be. This is why tanks on board, at least the larger ones, always have baffles that split them up into compartments so as to limit L e B and, thus, reduce moment of inertia. The same expedient is used on tankers. To give an idea of how dangerous an open surface of water can be on board, forgetting for a moment pools and tanks, it is enough to remember the danger represented by a deck flooded with seawater or rain, should it be impossible to discharge the water quickly; this is a grave danger for vessels, even when the quantity of water is minimal.