Ships float because buoyancy pushes upward with a force equal to the weight of the water they displace. Stability is about what happens after a ship is tilted by wind, waves, or turning. A stable ship develops a turning effect that brings it back toward upright instead of rolling farther over.
Metacentric height, written GM, is one of the most useful measurements for predicting this initial stability.
The metacentre is the point where the upward buoyant force line meets the ship's centerline after a small heel. The center of gravity, G, is where the ship's weight acts downward, and the center of buoyancy, B, is where the buoyant force acts upward. If M is above G, then GM is positive and the weight and buoyancy forces create a righting moment.
A larger positive GM usually means a ship returns upright more strongly, but if it is too large the ship may roll quickly and uncomfortably.
Key Facts
- Metacentric height is GM = distance from G to M along the ship's centerline.
- Positive stability occurs when M is above G, so GM > 0.
- For small heel angles, righting arm GZ is approximately GZ = GM sin(theta).
- Righting moment is approximately Moment = displacement weight × GZ.
- The center of buoyancy B shifts toward the lower side of the hull when a ship heels.
- A ship becomes unstable when GM < 0 because the forces create an overturning moment.
Vocabulary
- Metacentre
- The metacentre is the point where the buoyant force line for a slightly heeled ship intersects the original vertical centerline.
- Metacentric height
- Metacentric height is the vertical distance GM between the center of gravity G and the metacentre M.
- Center of gravity
- The center of gravity is the point where the total weight of the ship and its cargo acts downward.
- Center of buoyancy
- The center of buoyancy is the center of the displaced water volume where the buoyant force acts upward.
- Righting moment
- A righting moment is a turning effect produced by weight and buoyancy that rotates a tilted ship back toward upright.
Common Mistakes to Avoid
- Confusing G and B, which is wrong because G depends on the mass distribution of the ship while B depends on the underwater shape of the displaced water.
- Thinking buoyancy always acts through the middle of the ship, which is wrong because B shifts sideways when the hull heels.
- Assuming any positive GM is equally safe, which is wrong because a very small GM gives weak righting ability and a very large GM can cause fast, harsh rolling.
- Using GZ = GM sin(theta) for large angles, which is wrong because this approximation is only reliable for small heel angles.
Practice Questions
- 1 A ship has GM = 1.8 m and heels by 10 degrees. Use GZ = GM sin(theta) to estimate the righting arm.
- 2 A vessel has displacement weight 500000 N and a righting arm GZ = 0.35 m. Calculate the approximate righting moment.
- 3 A ship is loaded so that its center of gravity rises above the metacentre. Explain what happens to GM and why the ship may become unstable when it rolls.