GM and Booms

GMp = Zm – zgp

GMp = yg / tgα 

GMp = ( 2 * c * B / T(sec) ) 2

c = 0.373 + 0.023 B/T – 0.043 L/100 ó 0.4

ΔGMp = ( m /  ( D +m )) * ( hd –zgp )

tgα = yg /  GMp            (boom hight)

tgα = ( m * Δy ) / ( D’ * GMp’ )

Ib = ( l * b3 ) / 12

Load

              ZG * D + m * Z

ZG’ =

                      D + m

                                m * Z

GM’ = GM –

                                    D

Offload

               ZG * D + m * ( Z2 – Z1 )

ZG’ =

                            D + m

                              m *( Z2 – Z1 )

GM’ = GM –

                                       D

yg = ( m * Δy ) / D

yg = GMp * tgα  (small angles)

yg = ( lk - zgp * sinα ) / cosα  (big angles)

xg = (t * Mj ) / D1.025 + xf

Δzg = m / ( D +m ) * ( z – zg )

V = D / ( δ * k )

D = V * δ * k

m = D * ( xgk – xgp ) /  Δxg lad

(weight to shift)

Simpson

Split to 6 areas or 4 and ½, ½

1.  cs = ½, 2, 1, 2, 1, 2, ½

2.  cs = ¼, 1, ¾, 2, 1, 2, ½

S = 2/3 * ( π/180 * d/6 ) * Σ( cs * y )

Static and Dynamic curves

Gz = lk - zgp sinα – yg cosα

ld = 0.08727 * ΣGz

Wind

P * Aw * (Zw+T/2 )

lws =

                   1000 * g * D

     P * Aw * Zw

lwd =

                    1000 * g * D

Towing

             Ft * (Zt+T/2 )

lt =

             1000 * g * D

Cyrculation

                   ( 0.8 * Ve  (m/s))2

lc = 0.24 *                          * (zg – T/2 )

                        l * g

Δmh

          L * B3

IB =

             12

IB = IPS – S * yS2

S = 2/3 * Σ Cs * y * x

MPS = 2/3 * ½ * Σ Cs * y2 * x

IPS = 2/3 * 1/3 * Σ Cs * y3 * x

yS = MPS / S

Δmh = 2 * ( IPS * δ ) (both sides)

Δmh = IB * δ (one side)

Docking

          Δt * Mj              Δt = tD – t0

R =

            xk - xs

                            zGP0 * D

GM’ = Zm  –

                           D – I R I

GM’ > 0

keel block

Grounding

R = 100 * TPC * ΔT

R = DA – D0

Δt = tm – t0

               Δt * Mjm

xp =                                 + xS

                    R

              Tgα * GMm * Dm

yP =

                          R

                                  zgp0 * D0

GMm = Zmm –

                                        Dm

                              tn * xp

TPN = TRN +

                                 Lpp

                        tm * xp

Hw = (TRN +                 ) * cosα  +  y * sinα

                          Lpp

From aft particular

Draft Survey

T = ( Td + TR + 6 * To ) / 8

t * xs * 100 * TPC

c1 =

        lpp

              t2 * ΔMj

c2 =

              2 lpp

D1.025 = D1.025 + c1 +c2

              D1.025 * δ

Dδ =

              1.025

Draft

              D1.025 * ( xg – xf )

t =

                        Mj

Td = T + t / lpp * (lpp / 2 – xs)

Tr = Td – t

Δt = m / Mj * ( xgk – xgp )

Shering Forces – Bending Moments

Kc = ( mcargo + mV/L ) / lcompartment

Kw = - D / lV/L       (Always negative D = V/L + cargo)

Q = Kc + Kw

ST0 = m0 * d0                                                        ( m= Q )

ST1 = ST0 + ( m1 * d1 )

MG0 = ST0 * d0/2        ( field under ST graph till d0 )

MG1 = MG0 + ( ST1 * d1/2)

Barge with Trim

t = D / Mj * (xG – xF)   ( Xf = 0 )

Mj = ( D * GML ) / L

GML = ZmL - ZG

ZmL = ZF + R

R = IL / V

R = (( l3 * b ) / 12 ) / V

because ZF ó ZG so GM...