The metacentric radius (BM) is the vertical distance between the center of buoyancy and the metacenter of a ship[2][4][5][6]. The metacentric radius can be calculated using the formula BM = I/V, where I is the moment of inertia of the waterplane area of the ship around the axis of rotation under consideration, and V is the volume of the underwater part of the ship[4][5]. The metacentric radius is used to compare the stability of different vessels[2][5]. The metacentric height (GM) is calculated as the distance between the center of gravity (G) of a ship and its metacenter (M)[1][4][6]. The formula for calculating the metacentric height is GM = KM - KG, where KM is the height of the metacenter above the keel and KG is the height of the center of gravity above the keel[4][6]. The metacentric height is an approximation for the vessel stability at a small angle (0-15 degrees) of heel[1][6]. The metacentric height and the metacentric radius are both important parameters for a ship's stability, and they are used together to determine the stability of a ship[6].

Citations:

[1] How do you calculate the metacentric height of a ship with a complex hull shape? - LinkedIn https://www.linkedin.com/advice/1/how-do-you-calculate-metacentric-height-ship

[2] Metacentric Radius - an overview | ScienceDirect Topics https://www.sciencedirect.com/topics/engineering/metacentric-radius

[3] Lecture 21 -Derivation of Metacentric Radius (BM) - YouTube https://youtube.com/watch?v=37PdV1ySoO4

[4] Naval architecture - Metacentric Stability, Buoyancy, Stability - Britannica https://www.britannica.com/technology/naval-architecture/Metacentric-stability

[5] FORMULAE AND DEFINITIONS https://pms2004.tripod.com/formulae_and_definitions.html

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

By Perplexity at https://www.perplexity.ai/search/837d939e-2b18-4d05-9bea-3baa8bfaff2b?s=m

How is the metacentric radius related to the metacentric height

The metacentric height and the metacentric radius are related but distinct concepts used in naval architecture to describe the stability of a floating body, such as a ship. Here are the ways in which the two are related:

- The metacentric height is calculated as the distance between the center of gravity (G) of a ship and its metacenter (M), while the metacentric radius is the vertical distance between the center of buoyancy and the metacenter of a ship[1][4].

- The metacentric height and the metacentric radius are both important parameters for a ship's stability, but they are calculated differently and have different applications[2].

- The metacentric height is a measure of initial stability, while the metacentric radius is used to compare the stability of different vessels[1][2].

- The metacentric radius can be calculated from the formula BM = I/V, where I is the moment of inertia of the waterplane area of the ship around the axis of rotation under consideration, and V is the volume of the underwater part of the ship[3].

- The metacentric height is an approximation for the vessel stability at a small angle (0-15 degrees) of heel, while the metacentric radius is used to compare the stability of different vessels[1][2].

- The metacentric height and the metacentric radius are both important parameters for a ship's stability, and they are used together to determine the stability of a ship[6].

In summary, the metacentric height and the metacentric radius are related but distinct concepts used in naval architecture to describe the stability of a floating body, such as a ship. The metacentric height is a measure of initial stability, while the metacentric radius is used to compare the stability of different vessels. The two are used together to determine the stability of a ship.

Citations:

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

[2] Metacentric Radius - an overview | ScienceDirect Topics https://www.sciencedirect.com/topics/engineering/metacentric-radius

[3] Naval architecture - Metacentric Stability, Buoyancy, Stability - Britannica https://www.britannica.com/technology/naval-architecture/Metacentric-stability

[4] Metacentric Height | Boat Design Net https://www.boatdesign.net/threads/metacentric-height.5696/

[5] How do you calculate the metacentric height of a ship with a complex hull shape? - LinkedIn https://www.linkedin.com/advice/1/how-do-you-calculate-metacentric-height-ship

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

By Perplexity at https://www.perplexity.ai/search/aa59d45a-c780-4061-8a64-6de16097313c?s=m

What is the difference between metacentric height and metacentric radius

The metacentric height and the metacentric radius are two related but distinct concepts used in naval architecture to describe the stability of a floating body, such as a ship. Here are the differences between the two:

Metacentric height:

- The metacentric height (GM) is a measurement of the initial static stability of a floating body.

- It is calculated as the distance between the center of gravity (G) of a ship and its metacenter (M).

- A larger metacentric height implies greater initial stability against overturning.

- The metacentric height also influences the natural period of rolling of a hull, with very large metacentric heights being associated with shorter periods of roll which are uncomfortable for passengers.

- The metacentric height is an approximation for the vessel stability at a small angle (0-15 degrees) of heel.

Metacentric radius:

- The metacentric radius (BM) is the vertical distance between the center of buoyancy and the metacenter of a ship.

- It can be calculated from the formula BM = I/V, where I is the moment of inertia of the waterplane area of the ship around the axis of rotation under consideration, and V is the volume of the underwater part of the ship.

- The metacentric radius can be used to compare the stability of different vessels.

- The metacentric radius is the radius of the circle for the movements of the center of buoyancy at small angles of heel.

In summary, the metacentric height and the metacentric radius are both important parameters for a ship's stability, but they are calculated differently and have different applications. The metacentric height is a measure of initial stability, while the metacentric radius is used to compare the stability of different vessels.

Citations:

[1] Metacentric Radius - an overview | ScienceDirect Topics https://www.sciencedirect.com/topics/engineering/metacentric-radius

[2] Naval architecture - Metacentric Stability, Buoyancy, Stability - Britannica https://www.britannica.com/technology/naval-architecture/Metacentric-stability

[3] How do you calculate the metacentric height of a ship with a complex hull shape? - LinkedIn https://www.linkedin.com/advice/1/how-do-you-calculate-metacentric-height-ship

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

[5] Ship Stability - Introduction to Hydrostatics and Stability of Surface Ships - Marine Insight https://www.marineinsight.com/naval-architecture/ship-stability-introduction-hydrostatics-stability-surface-ships/

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

By Perplexity at https://www.perplexity.ai/search/e3b404d9-c808-4a04-b60d-7ea19ee01400?s=m

What is the formula for calculating the metacentric height

The metacentric height (GM) is calculated as the distance between the center of gravity (G) and the metacenter (M) of a ship[1][4]. The formula for calculating the metacentric height is GM = KM - KG, where KM is the height of the metacenter above the keel and KG is the height of the center of gravity above the keel[4]. The metacentric height can also be calculated by dividing the metacentric radius by the roll or pitch angle[2]. The metacentric radius is the distance between the center of buoyancy and the metacenter[2]. The metacentric height is an approximation for the vessel stability at a small angle (0-15 degrees) of heel[1]. The height of the intersection above the base (YZ), when measured on the GZ scale, will give the initial metacentric height[6]. The formula for calculating the metacentric radius is BM = I / V, where I is the moment of inertia of the waterplane area of the ship around the axis of rotation under consideration, and V is the volume of the underwater part of the ship[5].

Citations:

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

[2] How do you calculate the metacentric height of a ship with a complex hull shape? - LinkedIn https://www.linkedin.com/advice/1/how-do-you-calculate-metacentric-height-ship

[3] Determination of Metacentric Height of a Floating Body - The Constructor https://theconstructor.org/practical-guide/metacentric-height-floating-body/30000/?amp=1

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

[5] Formula of metacentric height - Physics Forums https://www.physicsforums.com/threads/formula-of-metacentric-height.860585/

[6] Initial Metacentric Height - an overview | ScienceDirect Topics https://www.sciencedirect.com/topics/engineering/initial-metacentric-height

By Perplexity at https://www.perplexity.ai/search/42cd622a-5dfe-4aa4-8c25-bfe03c2bb0bc?s=m

How is the metacentric height calculated

The metacentric height (GM) is calculated as the distance between the center of gravity (G) and the metacenter (M) of a ship[1][4]. The metacentric height is an approximation for the vessel stability at a small angle (0-15 degrees) of heel[1]. Here are some ways to calculate the metacentric height:

- The metacentric height can be calculated by subtracting the height of the center of gravity (KG) from the height of the metacenter (KM), which can be found using the draft diagram and functions of form curves in the DC Book[4].

- The laboratory procedure to find out the metacentric height of a floating body on water involves adding weight to the body and measuring the height of the water level before and after the weight is added[3].

- The formula for calculating the metacentric height is GM = KM - KG[4].

- The metacentric radius can be used to compare the stability of different vessels[2].

- The height of the intersection above the base (YZ), when measured on the GZ scale, will give the initial metacentric height[5].

In summary, the metacentric height is a crucial parameter for a ship's stability, and it is calculated as the distance between the center of gravity and the metacenter. The metacentric height can be calculated using various methods, including subtracting the height of the center of gravity from the height of the metacenter or by measuring the height of the water level before and after adding weight to the body.

Citations:

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

[2] How do you calculate the metacentric height of a ship with a complex hull shape? - LinkedIn https://www.linkedin.com/advice/1/how-do-you-calculate-metacentric-height-ship

[3] Determination of Metacentric Height of a Floating Body - The Constructor https://theconstructor.org/practical-guide/metacentric-height-floating-body/30000/?amp=1

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

[5] Initial Metacentric Height - an overview | ScienceDirect Topics https://www.sciencedirect.com/topics/engineering/initial-metacentric-height

[6] Metacentric Height - an overview | ScienceDirect Topics https://www.sciencedirect.com/topics/engineering/metacentric-height

By Perplexity at https://www.perplexity.ai/search/5dba5ba1-616c-494d-bf62-5c82d481bda9?s=m

What is the metacentric height and how is it related to the angle of heel

The metacentric height (GM) is a measurement of the initial static stability of a floating body, such as a ship. It is calculated as the distance between the center of gravity (G) and the metacenter (M), which is a fixed point determined by the geometry of the ship and the distribution of its buoyancy forces[2][3]. The metacentric height is an approximation for the vessel's stability at small angles (0-15 degrees) of heel[2].

The angle of heel of a ship is the angle between its upright position and the position it takes when inclined due to external forces. The metacentric height is directly related to the ship's stability and the angle of heel. A higher metacentric height generally indicates greater stability, while a lower metacentric height can lead to reduced stability or even instability[2].

The relationship between the metacentric height and the angle of heel can be seen in the curve of static stability, which is a plot of the righting lever (GZ) against the angle of heel. The righting lever is the moment created by the horizontal distance between the forces of gravity and buoyancy. The metacentric height multiplied by the sine of the angle of heel gives the value of the righting lever, highlighting the importance of the metacentric height to stability[6].

In summary, the metacentric height is a crucial parameter for a ship's stability, and it is related to the angle of heel through the righting lever. A higher metacentric height generally leads to greater stability, while a lower metacentric height can result in reduced stability or even instability.

Citations:

[1] Is the metacentric height independent of heel angle? - Engineering Stack Exchange https://engineering.stackexchange.com/questions/26380/is-the-metacentric-height-independent-of-heel-angle

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

[3] Metacentric Height | Boat Design Net https://www.boatdesign.net/threads/metacentric-height.27171/

[4] Initial Metacentric Height - an overview | ScienceDirect Topics https://www.sciencedirect.com/topics/engineering/initial-metacentric-height

[5] Metacentric Height - an overview | ScienceDirect Topics https://www.sciencedirect.com/topics/engineering/metacentric-height

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

By Perplexity at https://www.perplexity.ai/search/0ba0fe34-5f32-49a9-9229-54eb4a83dba6?s=m

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

How is the maximum angle of heel determined for a ship

The maximum angle of heel that a ship can withstand depends on various factors, including the vessel's design, stability, and the external forces acting on it. Here are some ways to determine the maximum angle of heel for a ship:

- The angle of heel due to the combined effect of crowding, wind pressure, and centrifugal force should not exceed 12° in calculations[1].

- The curve of static stability is a plot between the righting lever and angle of heel, and the maximum righting lever (GZMAX), represented by point ‘B’ in the graph, is proportional to the largest static heeling moment that is required to bring the ship back to its upright position[2].

- The area under the GZ curve, up to a given angle, is proportional to the energy needed to heel the ship to that angle[3].

- The maximum righting arm is the angle of heel at which the maximum righting lever occurs[5].

- The estimated maximum angle of heel before equalization must be approved on a vessel required to survive assumed damage[5].

- The vessel's metacentric height (GM) must be at least 2 inches (5 cm) when the vessel is in the upright position[5].

- The maximum righting arm should occur at an angle of heel preferably exceeding 30° but not less than 25° [4].

- The final angle of equilibrium must not exceed 7 degrees after equalization on a vessel required to survive assumed damage with a longitudinal extent of 10 feet (3 meters) plus 0.03L, and it must not exceed 15 degrees after equalization on a vessel required to survive assumed damage with a longitudinal extent of 20 feet (6.1 meters) plus 0.04L[5].

In summary, the maximum angle of heel that a ship can withstand depends on various factors, and there is no single value that applies to all vessels. The angle of heel is limited by the vessel's stability, design, and the external forces acting on it. The maximum angle of heel can be determined by analyzing the vessel's stability and the external forces acting on it.

Citations:

[1] Heel Angle - an overview | ScienceDirect Topics https://www.sciencedirect.com/topics/engineering/heel-angle

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

[3] Dynamical Stability - an overview | ScienceDirect Topics https://www.sciencedirect.com/topics/engineering/dynamical-stability

[4] Wind speed vs angle of heel | Boat Design Net https://www.boatdesign.net/threads/wind-speed-vs-angle-of-heel.45588/

[5] [PDF] Chapter 2 - Review of Intact Statical Stability https://www.usna.edu/NAOE/_files/documents/Courses/EN455/EN455_Chapter2.pdf

[6] Stability at Large angles of heel - YouTube https://youtube.com/watch?v=nka4RqCfpdI

By Perplexity at https://www.perplexity.ai/search/6bfaf105-6e8e-469f-aad9-8e677c9fd97f?s=m

What is the maximum angle of heel that a ship can withstand

The maximum angle of heel that a ship can withstand depends on various factors, including the vessel's design, stability, and the external forces acting on it. Here are some relevant points from the search results:

- The "Law of 15's" is a rule of thumb that sets list/heel angle limits for Navy and Coast Guard surface ships[2].

- The angle of heel due to the combined effect of crowding, wind pressure, and centrifugal force should not exceed 12° in calculations[1].

- Fast displacement ships with Fn > 0.25 may feature dangerously large heel angles in turning circles, with the heel always outwards, i.e., away from the center of the turn[2].

- The estimated maximum angle of heel before equalization must be approved on a vessel required to survive assumed damage[5].

- The vessel's metacentric height (GM) must be at least 2 inches (5 cm) when the vessel is in the upright position[5].

- The maximum righting arm should occur at an angle of heel preferably exceeding 30° but not less than 25°[4].

- The final angle of equilibrium must not exceed 7 degrees after equalization on a vessel required to survive assumed damage with a longitudinal extent of 10 feet (3 meters) plus 0.03L[5].

- The angle of equilibrium must not exceed 15 degrees after equalization on a vessel required to survive assumed damage with a longitudinal extent of 20 feet (6.1 meters) plus 0.04L[5].

Citations:

[1] Chapter 11 - Stability - imorules https://www.imorules.com/GUID-395B2213-38E4-4D30-A520-1A9B42D46F8B.html

[2] list caused by off-center weight and negative gm - LESSON TOPIC: https://man.fas.org/dod-101/navy/docs/swos/dca/stg4-06.html

[3] [PDF] Chapter 2 - Review of Intact Statical Stability https://www.usna.edu/NAOE/_files/documents/Courses/EN455/EN455_Chapter2.pdf

[4] Intact stability criteria - Wärtsilä https://www.wartsila.com/encyclopedia/term/intact-stability-criteria

[5] 46 CFR § 171.080 - Damage stability standards for vessels with Type I or Type II subdivision. - Law.Cornell.Edu https://www.law.cornell.edu/cfr/text/46/171.080

[6] Heeling Moment - an overview | ScienceDirect Topics https://www.sciencedirect.com/topics/engineering/heeling-moment

By Perplexity at https://www.perplexity.ai/search/046fbcd5-a48f-4089-bca3-5601767f5520?s=m

What is the angle of heel in ships

The angle of heel in ships refers to the inclination of a vessel to one side or the other, measured as the angle between the waterline and the deck[1][2]. It is caused by external forces such as wind, waves, or uneven loading of the vessel[5]. The angle of heel can have various effects on the stability and safety of the ship, depending on its magnitude and the vessel's design[2].

- The angle of heel due to the combined effect of crowding, wind pressure, and centrifugal force should not exceed 12° in calculations[1].

- Fast displacement ships with Fn > 0.25 may feature dangerously large heel angles in turning circles, with the heel always outwards, i.e., away from the center of the turn[2].

- The stability of a ship is significantly reduced due to the build-up of ice on its superstructure, causing unwanted angles of list and trim conditions[5].

To measure the angle of heel, a device that can sense the change in the ship's orientation relative to the vertical is used[6]. Monitoring and controlling the angle of heel is crucial for the safety and stability of the vessel, and appropriate actions should be taken to maintain it within safe limits.

Citations:

[1] Heel Angle - an overview | ScienceDirect Topics https://www.sciencedirect.com/topics/engineering/heel-angle

[2] Heeling Angle - an overview | ScienceDirect Topics https://www.sciencedirect.com/topics/engineering/heeling-angle

[3] Heel & Angle of Heel https://sailskills.co.uk/Stability/sailskills_stability_stability_explained_heel_&_angle_of_heel.html

[4] What is Angle Of Loll in Ships? - Marine Insight https://www.marineinsight.com/naval-architecture/angle-of-loll/

[5] Ship Stability - What Makes a Ship Unstable? - Marine Insight https://www.marineinsight.com/naval-architecture/ship-stability-makes-ship-unstable/

[6] How to Measure Heel Angle and Shift of Weights in an Inclining Experiment - LinkedIn https://www.linkedin.com/advice/1/what-best-methods-measure-heel-angle-shift-weights

By Perplexity at https://www.perplexity.ai/search/72a3e57d-faf4-4ac7-9039-92d0ddec3e5d?s=m

What is the difference between angle of loll and angle of heel

The angle of loll and the angle of heel are two different concepts related to the stability of a ship. Here are the differences between the two:

Angle of loll:

- Occurs when a ship is in an unstable condition when upright, i.e., has a negative metacentric height.

- The vessel takes on an angle of heel to either port or starboard.

- The angle of loll is the angle of heel at which the vessel goes to neutral equilibrium.

- The angle of loll is determined by the values of GM and BM.

- A vessel at the angle of loll displays features of stable equilibrium, but it is a dangerous situation, and rapid remedial action is required to prevent the vessel from capsizing.

Angle of heel:

- Occurs when a ship is inclined to one side or the other.

- The angle of heel is the angle between the waterline and the deck.

- The angle of heel is caused by external forces such as wind, waves, or uneven loading of the vessel.

- The angle of heel is limited by the vessel's stability and the free surface effect of liquids on board.

- A vessel can return to its upright position after a heel, depending on its stability and the external forces acting on it.

In summary, the angle of loll occurs when a vessel is unstable when upright, while the angle of heel occurs when a vessel is inclined to one side or the other due to external forces acting on it.

Citations:

[1] Angle of loll https://en.wikipedia.org/wiki/Angle_of_loll

[2] What is Angle Of Loll in Ships? - Marine Insight https://www.marineinsight.com/naval-architecture/angle-of-loll/

[3] Angle of Loll - an overview | ScienceDirect Topics https://www.sciencedirect.com/topics/engineering/angle-of-loll

[4] Angle of Loll: Hidden Dangers to Stability - DMS Marine Consultant https://www.dmsonline.us/angle-loll-hidden-dangers-stability/

[5] What is Angle of Loll? - MarineGyaan https://marinegyaan.com/what-is-angle-of-loll/

[6] Angle of loll - Wärtsilä https://www.wartsila.com/encyclopedia/term/angle-of-loll

By Perplexity at https://www.perplexity.ai/search/269ebb9b-0adf-4756-84fa-274c90afd923?s=m

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This Privacy Policy applies only to our online activities and is valid for visitors to our website with regards to the information that they shared and/or collect in Naftilosgr. This policy is not applicable to any information collected offline or via channels other than this website.

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By using our website, you hereby consent to our Privacy Policy and agree to its Terms and Conditions.

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