The DEEP DRILLER, at 60.0 feet draft in sea water, has VM = 974,441 foot-long tons, LM = 40,301 foot-long tons, TM =3 foot-long tons, FSML = 30,572 foot-long tons, and FSMT = 18,732 foot-long tons. What is the metacentric height corrected for longitudinal free surface effects?
• Relationship between metacentric height (GM), displacement volume, and transverse/longitudinal moments • Effect of free surface on metacentric height using FSML and FSMT • Distinguishing between transverse and longitudinal stability corrections and which one affects GM used for initial stability in roll
• Write the basic formula linking GM to the given moments (VM, LM, TM) and identify which terms belong to transverse vs longitudinal stability. • Ask yourself: does longitudinal free surface directly change the metacentric height used for assessing the vessel’s ability to roll, or does it mainly affect trim-related parameters? • Compute the uncorrected GM first, then determine whether you should subtract a free surface correction based on FSML or FSMT, and check the magnitude to see which answer choices are realistic.
• Confirm the units: all moments are in foot-long tons, and volume/dispacement is in long tons or cubic feet as appropriate. • Verify which free surface moment (FSML vs FSMT) is used to correct transverse metacentric height (GM for rolling) and which relates primarily to trim (longitudinal). • After choosing the relevant free surface term, ensure the correction is in feet, not moment units, by dividing by the proper displacement/volume term before comparing to the answer choices.
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