Center of buoyancy is the point in a floating or submerged object where the buoyant force (or upthrust) effectively acts. It is the centroid (geometric center) of the displaced volume of fluid, meaning it’s the average position of all the fluid pushed aside by the object. The buoyant force, which keeps the object afloat or determines its behavior underwater, acts vertically upward through this point. There isn’t a single, universal formula for the center of buoyancy, its location is determined by calculating the centroid of the volume of fluid displaced by an object. This depends on the object’s shape, orientation, and how much of it is submerged. The process involves geometry and sometimes calculus, rather than a plug-and-play equation.
Regular Shapes - If a rectangular object is fully submerged, the center of buoyancy is simply the geometric center of the submerged portion.
Floating Objects - For a floating object like a ship, you calculate the CB based on the submerged portion of the hull. This requires knowing the shape of the hull below the waterline and integrating over that volume.
Center of Bouyancy Formula
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| \( B_c \;=\; \dfrac{ I }{ V } - M \) | ||
| Symbol | English | Metric |
| \( B_c \) = Center of Buoyancy | \(in\) | \(mm\) |
| \( I \) = Moment of Inertia | \(lbm \;/\; ft^2-sec\) | \(kg \;/\; m^2\) |
| \( V \) = Object Volume | \(in^3\) | \(mm^3\) |
| \( M \) = Metacenter | \(dimensionless\) | \(dimensionless\) |
