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 GM_L is small when compared with BM_L]
                  100 x L

               where Δ = displacement [tonnes]

                     GM _L = Longitudinal Metacentric Height

                     BM _L = height of the longitudinal metacentre, M_L
                               above centre of buoyancy, B

GM_L = KB + BM_L - KG [metre]

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

                 =  I _L [metre]
                     V

Change of draught aft, t_a =  l _a x change of trim [metre]
                                     L

Change of draught forward, t_f =  l _f x change of trim [metre]
                                            L

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

TPC = Tonnes per Centimetre Immersion

       = Aw x ρ
            100

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