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Mariner's Formulae Quick reference guide
Change of Trim
- the difference between initial trim and final trim i.e. change of draught forward + change   of draught aft
Trimming Moment = Weight x Distance shifted = W x d [tonnes.metre]

Change of Trim, t = Trimming Moment [metre]
                               100 x MCT.1cm

MCT.1cm = Moment To Change Trim by 1 cm

              = Δ x GM L [tonnes.metre]
                  100 x L

              ≅ Δ x BM L [as GML is small when compared with BML]
                  100 x L

               where Δ = displacement [tonnes]

                     GM L = Longitudinal Metacentric Height

                     BM L = height of the longitudinal metacentre, ML
                               above centre of buoyancy, B

GML = KB + BML - KG [metre]

where BML = long. 2nd mmt of waterplane about centre of flotation, F
                                              volume of displacement

                 =  I L [metre]

Change of draught aft, ta =  l a x change of trim [metre]

Change of draught forward, tf =  l f x change of trim [metre]

Change in mean draught = Weight loaded or discharged [metre]

TPC = Tonnes per Centimetre Immersion

       = Aw x ρ

         where Aw = area of waterplane [metre2]
                        = L x B x Cw (waterplane area coefficient)

                     ρ = density of sea water [tonnes per metre3]


Trimming Moment = Δ x (longitudinal separation LCG and LCB)

           where LCG = Longitudinal centre of gravity [metre]

                     LCB = Longitudinal centre of buoyancy [metre]

Change in Mean draught due to change in density =   Δ   x (ρ1 - ρ2)
                                                                            Aw     (ρ1.ρ2)

Trimming Moment = Δ x (horizontal shift of LCB)

     or (mass of layer of water added or removed due to change in density) x
          (horizontal distance between initial LCB & final LCF of waterplane)

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