1. K = Keel
2. G = Center of gravity
3. B = Center of Buoyancy
4. M = Metacentre
5. ø = Angle of Heel
6. BM = Metacentric Radius
7. GM = Metacentric Height
8. GZ = Righting Lever measured from G
9. KB = Height of Center of Buoyancy from keel
10. KG = Height of Center of Gravity from keel
11. KM = Height of Metacenter from keel

KM = KG + GM
KM = KB + BM
GZ = KN - KG x sin ø where KN can be found from KN curves
Righting Moment = Δ x GZ where Δ = displacement

KG = Total Vertical Moment of Weights about keel [metre.tonnes]
                                       Δ [tonnes]

GG¹ = Moment of Weight,W shifted over Distance, D [metre.tonnes]
                                       Δ [tonnes]
       : vertical shift of G

KM = KB + BM

KB = 0.53 x Draft   [metre]

BM =    2nd moment of waterplane area       =   I   [metre]
                volume of displacement                    V

              where I = L x B³  [metre⁴]  for a rectangular barge
                               12

GM = KM - KG

VIRTUAL LOSS OF GM DUE TO FREE SURFACE

GG_v =          s.g. of Liquid in the Tank             x    I     x    1 
           s.g. of Water in which vessel floats           V          n²

where GG_v = virtual rise in G or deduction in G

              I =  2nd moment of the free surface about the centre line

                =  L x B³  [metre⁴]  for a rectangular compartment
                      12

              L = Length of the Tank [metre]

              B = Breadth of the Tank [metre]

              V = Volume of the Tank [metre³]

              n = number of longitudinal compartments into which the tank is
                    subdivided

LARGE ANGLE STABILITY
- where the force of buoyancy can no longer be considered to act vertically upwards through the initial metacentre, M

GZ = (GM + ½BM.tan² ø) sin ø

      : for ship's side that are "WALL-SIDED" in the vicinity of the water line

            ∴     GZ = GM.sin ø