Why does the axis of rotation pass through the metacentre?

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SUMMARY

The discussion centers on the concept of the metacentre in naval architecture, specifically addressing the axis of rotation when a ship heels. The metacentre is defined as the point where a vertical line through the heeled center of buoyancy intersects with the original vertical center of buoyancy. Participants debate the position of the center of rotation, asserting that it typically remains near the waterline, while the metacentre is often perceived to be above it. This highlights a critical understanding of ship stability and oscillation during small angular displacements.

PREREQUISITES
  • Understanding of buoyancy principles in naval architecture
  • Familiarity with ship stability concepts
  • Knowledge of angular displacement and its effects on vessels
  • Basic grasp of the relationship between the center of buoyancy and metacentre
NEXT STEPS
  • Research the mathematical derivation of the metacentric height
  • Explore the effects of different hull shapes on metacentre positioning
  • Learn about stability criteria for small-angle oscillations in ships
  • Investigate the role of the center of gravity in ship stability
USEFUL FOR

Naval architects, marine engineers, and students studying ship design and stability will benefit from this discussion, particularly those focused on understanding the dynamics of ship heeling and metacentric principles.

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When a ship heels, the centre of buoyancy of the ship moves laterally. It might also move up or down with respect to the water line. The point at which a vertical line through the heeled centre of buoyancy crosses the line through the original, vertical centre of buoyancy is called the metacentre. But how can we prove that point, about which the ship rotates (starts oscillating for the small angular displacements), is the metacentre?
 
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I don’t think it is. When a ship heels, the center of rotation is usually near the waterline. The metacentre, based on your description, sounds like it would always be above the waterline.
 
LURCH said:
I don’t think it is. When a ship heels, the center of rotation is usually near the waterline. The metacentre, based on your description, sounds like it would always be above the waterline.
Thank you. You are right
 

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