Questions: Floating Body Stability and Metacentric Height
5 questions to test your understanding
Score: 0 / 5
Question 1 Multiple Choice
A container ship loads cargo into stacks high above the deck. How does this affect the vessel's stability, and why?
AStability improves because the added mass increases the displaced volume and raises the center of buoyancy
BStability decreases because high cargo raises the center of gravity G toward or above the metacenter M, reducing metacentric height GM
CStability is unchanged because metacentric height depends only on the hull geometry, not the cargo position
DStability improves because the weight of high cargo increases the waterline draft, lowering the center of buoyancy and increasing GM
Metacentric height GM = height of metacenter M minus height of center of gravity G. The metacenter M is determined primarily by the hull geometry and waterplane area — it changes relatively little with loading. But G rises when cargo is loaded high above the waterline. As G approaches M, GM decreases. If G rises above M, GM becomes negative and the vessel is unstable — any heel will be amplified rather than corrected. This is why cargo ships have strict loading plans specifying maximum heights and require ballast calculations.
Question 2 Multiple Choice
A vessel heels 8° to starboard. For the ship to self-right (generate a righting moment), where must the metacenter M lie relative to the center of gravity G?
AM must lie above the center of buoyancy B, which always ensures stability
BM must lie above G so that the offset buoyant force acts to windward of G, creating a restoring torque
CM must lie at the same height as G so that gravity and buoyancy are balanced
DM must lie below G to create a downward pull that rights the vessel
When the vessel heels, the center of buoyancy B shifts toward the submerged side. The buoyant force acts vertically upward through the displaced B. The righting moment is the couple formed by this upward buoyant force and the downward weight through G. If M (where the new buoyant force line intersects the original centerline) is above G, the buoyant force has a moment arm that generates a restoring torque. If M is below G, the geometry reverses and the torque amplifies the heel — the vessel capsizes. The condition GM > 0 (M above G) is the stability criterion.
Question 3 True / False
A ship with a very large metacentric height (GM much greater than zero) is typically preferable to one with a moderate GM because maximum stability minimizes capsizing risk.
TTrue
FFalse
Answer: False
Excessive GM causes rapid, violent rolling — the righting moment is so strong that the ship snaps back too quickly after each wave, producing short-period rolling that causes discomfort, can injure crew, damage cargo, and stress structural joints. Well-designed vessels target an appropriate GM range: enough for safety under all loading conditions but not so large as to create operationally problematic stiffness. Naval architects balance stability and seakeeping comfort by specifying a target GM range, not simply maximizing it.
Question 4 True / False
When a floating body heels by a small angle, the center of buoyancy shifts laterally toward the submerged (lower) side because more of the hull volume is submerged on that side.
TTrue
FFalse
Answer: True
This shift of B is the fundamental mechanism of floating body stability. At rest, B is at the centroid of the displaced volume. When the vessel heels, the wedge of hull volume on the descending side enters the water while a corresponding wedge on the rising side emerges. The net effect shifts the centroid of the entire submerged volume toward the newly submerged side. The buoyant force — always vertical — now acts through this displaced B location, creating the righting or overturning moment depending on whether M lies above or below G.
Question 5 Short Answer
Why is metacentric height not a fixed property of a vessel, and what are the consequences for ship design and operation?
Think about your answer, then reveal below.
Model answer: Metacentric height GM depends on both the position of the metacenter M and the center of gravity G, and both change with loading. M depends on the vessel's waterplane area and submerged volume geometry, which change as the ship sinks deeper with load. G changes dramatically depending on how much cargo is loaded and where it is placed — high cargo raises G; ballast water in keel tanks lowers G. A ship with moderate GM when fully loaded in a standard configuration may have dangerously low GM if top-heavy cargo replaces ballast, or uncomfortably high GM when sailing empty. Designers must calculate GM for all planned loading conditions — from empty to fully loaded, with and without ballast — ensuring positive GM throughout. Operators must follow loading plans and ballast procedures to maintain GM in the design range; taking on water in upper compartments during flooding can shift G above M within minutes, causing capsizing.
This is why maritime disasters sometimes occur even to seemingly seaworthy vessels: a loading or damage condition that was not analyzed can bring G above M even on a well-designed ship.