How is the angle of heel related to the ship's center of gravity

How is the angle of heel related to the ship's center of gravity

The angle of heel of a ship is related to the ship's center of gravity in the following ways:

- When a ship is inclined through all angles of heel, the center of buoyancy shifts off-centerline while the center of gravity remains in the same location[4].

- The distance between the forces of buoyancy and gravity is known as the ship's righting arm, which is a perpendicular line drawn from the center of gravity to the point of intersection on the force of buoyancy line[4].

- For small angles of heel (0° through 7° to 10°), the value for the ship's righting arm (GZ) may be found by using trigonometry[4].

- The dynamic stability of a ship may be determined by measuring the area under the righting lever curve (GZ curve) up to a certain angle of heel[5].

- The larger the area under the GZ curve, the greater the ship's stability[5].

- The equilibrium trim angle is reached when the final center of gravity (G1) lies in line with the final center of buoyancy (B1)[3].

- Movement of any weight athwartship (in a transverse direction) will alter the position of the center of gravity of the ship (from G to G1), creating a heeling moment[3].

In summary, the angle of heel of a ship is related to the ship's center of gravity through the righting arm, which is the distance between the forces of buoyancy and gravity. The dynamic stability of a ship is also related to the area under the GZ curve, which is affected by the position of the center of gravity.

Citations:

[1] Metacentric height - Wikipedia https://en.wikipedia.org/wiki/Metacentric_height

[2] Ship Stability - Understanding Curves of Static Stability - Marine Insight https://www.marineinsight.com/naval-architecture/ship-stability-understanding-curves-static-stability/

[3] Understanding Intact Stability of Ships - Marine Insight https://www.marineinsight.com/naval-architecture/intact-stability-of-surface-ships/

[4] LESSON TOPIC: 4 https://man.fas.org/dod-101/navy/docs/swos/dca/stg4-01.html

[5] [PDF] The vessel's centre of gravity (G) has a distinct effect on the righting lever (GZ) and consequently the ability of a vessel t - Fao.org https://www.fao.org/3/i0625e/i0625e02d.pdf

[6] [PDF] Chapter 2 - Review of Intact Statical Stability https://www.usna.edu/NAOE/_files/documents/Courses/EN455/AY20_Notes/EN455CourseNotesAY20_Chapter2.pdf

By Perplexity at https://www.perplexity.ai/search/db18805f-53fe-4afb-9912-36f328519bbe?s=m