When displacement increases, what happens to the free surface corrections for slack tanks?

When displacement increases, the free surface corrections for slack tanks decrease. This is because free surface effects arise when liquid in a tank can slosh or shift due to the motion of the vessel. As the displacement of the vessel increases, the vessel's overall buoyancy and stability also increase, which can lead to a relatively smaller impact from the free surface effect.

The correction for free surface is calculated based on the geometry of the tank and the position of the liquid. When the total weight of the vessel (displacement) rises, the same slack in the tank causes a diminishing relative effect on the stability of the vessel because a larger body of water does not produce as strong an adverse effect on the center of gravity and righting moment compared to smaller displacements.

In simpler terms, with a higher displacement, the effects of free surfaces in slack tanks become less significant, leading to a decrease in the overall free surface corrections required to maintain stability.