Ship Stability _ Trim Introduction Part 2_ Formula for MCTC
SAILORSTUBE・8 minutes read
The position of a ship's center of gravity (G) is crucial for stability and is affected by shifting weight aft or forward, changing the ship's trim. The relationship between G, the new position G1, and the longitudinal metacenter (ML) is expressed through specific formulas to determine stability and trim adjustments.
Insights
- Shifting weight from forward to aft alters the ship's center of gravity (G) to G1, impacting its trim, showcasing the critical relationship between weight distribution and stability.
- The formula for Moment to Change Trim by 1 Centimeter (MCTC) reveals the intricate calculation involving ship weight, longitudinal metacenter, and length between perpendiculars, highlighting the precise mathematical considerations crucial for maintaining optimal trim levels.
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Recent questions
What is the center of gravity on a ship?
The center of gravity (G) on a ship is where the total weight (W) of the ship acts vertically downward, calculated by multiplying the mass (m) by the acceleration due to gravity (g).
How does shifting weight affect a ship's trim?
Shifting weight (small W) from forward to aft on a ship changes the position of the center of gravity (G) to G1, which in turn affects the ship's trim.
What determines the shift in the center of gravity on a ship?
The shift in the center of gravity from G to G1 on a ship is determined by the weight shifted (small W) multiplied by the distance shifted (D) and divided by the total weight (W) of the ship.
How is the relationship between center of gravity, G1, and the longitudinal metacenter expressed?
The relationship between the center of gravity (G), G1, and the longitudinal metacenter (ML) on a ship is expressed as tan theta = GG1 / GML.
What is the formula for Moment to Change Trim by 1 Centimeter on a ship?
The formula for Moment to Change Trim by 1 Centimeter (MCTC) on a ship is MCTC = W * GML / 100 * LBP, where W is the total weight, GML is the longitudinal metacenter, and LBP is the length between perpendiculars.
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Summary
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Ship Stability and Weight Distribution Analysis
- Center of gravity (G) is where the ship's total weight (W) acts vertically downward, calculated as mass (m) multiplied by acceleration due to gravity (g).
- Shifting weight (small W) from forward to aft changes the position of G to G1, affecting the ship's trim.
- The shift in G from G to G1 is determined by small W multiplied by the distance shifted (D) divided by capital W.
- The relationship between G, G1, and the longitudinal metacenter (ML) is expressed as tan theta = GG1 / GML.
- Trim, the difference between forward and aft drafts, is related to theta as tan theta = trim / LBP.
- The formula for Moment to Change Trim by 1 Centimeter (MCTC) is MCTC = W * GML / 100 * LBP.
