GM and Booms

GM_p = Zm - z_gp

GM_p = y_g / tgα

GM_p = ( 2 * c * B / T_(sec) ) ²

^{c = 0.373 + 0.023 B/T - 0.043 L/100 0.4}

ΔGM_p = ( m / ( D +m )) * ( h_d -z_gp )

tgα = y_g / GM_p ^{(boom hight)}

tgα = ( m * Δy ) / ( D' * GM_p' )

Ib = ( l * b³ ) / 12

Load

Z_G * D + m * Z

Z_G' =

D + m

m * Z

GM' = GM -

D

Offload

Z_G * D + m * ( Z₂ - Z₁ )

Z_G' =

D + m

m *( Z₂ - Z₁ )

GM' = GM -

D

y_g = ( m * Δy ) / D

y_g = GM_p * tgα (small angles)

y_g = ( lk - z_gp * sinα ) / cosα (big angles)

x_g = (t * Mj ) / D_1.025 + x_f

Δz_g = m / ( D +m ) * ( z - z_g )

V = D / ( δ * k )

D = V * δ * k

m = D * ( x_gk - x_gp ) / Δx_{g 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 - z_gp sinα - y_g cosα

ld = 0.08727 * ΣGz

Wind

P * Aw * (Zw+T/2 )

l_ws =

1000 * g * D

P * Aw * Zw

l_wd =

1000 * g * D

Towing

F_t * (Zt+T/2 )

l_t =

1000 * g * D

Cyrculation

( 0.8 * V_{e (m/s)})²

l_c = 0.24 * * (z_g - T/2 )

l * g

Δmh

L * B³

I_B =

12

I_B = I_PS - S * y_S²

S = 2/3 * Σ C_s * y * x

M_PS = 2/3 * ½ * Σ C_s * y² * x

I_PS = 2/3 * 1/3 * Σ C_s * y³ * x

y_S = M_PS / S

Δmh = 2 * ( I_PS * δ ) (both sides)

Δmh = I_B * δ (one side)

Docking

Δt * Mj Δt = t_D - t₀

R =

x_k - x_s

z_GP0 * D

GM' = Zm -

D - I R I

GM' > 0

keel block

Grounding

R = 100 * TPC * ΔT

R = D_A - D₀

Δt = t_m - t₀

Δt * Mj_m

x_p = + x_S

R

Tgα * GM_m * D_m

y_P =

R

z_gp0 * D₀

GM_m = Zm_m -

D_m

t_n * x_p

T_PN = T_RN +

Lpp

t_m * x_p

H_w = (T_RN + ) * cosα + y * sinα

Lpp

From aft particular

Draft Survey

T = ( T_d + T_R + 6 * T_o ) / 8

t * x_s * 100 * TPC

c₁ =

lpp

t² * ΔMj

c₂ =

2 lpp

D_1.025 = D_1.025 + c₁ +c₂

D_1.025 * δ

D_δ =

1.025

Draft

D_1.025 * ( x_g - x_f )

t =

Mj

T_d = T + t / lpp * (lpp / 2 - x_s)

T_r = T_d - t

Δt = m / Mj * ( x_gk - x_gp )

Shering Forces - Bending Moments

Kc = ( m_cargo + m_V/L ) / l_compartment

Kw = - D / l_{V/L (Always negative D = V/L + cargo)}

Q = Kc + Kw

ST₀ = m₀ * d_{0 ( 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 * (x_G - x_F) _{( Xf = 0 )}

Mj = ( D * GM_L ) / L

GM_L = Zm_L - Z_G

Zm_L = Z_F + R

R = I_L / V

R = (( l³ * b ) / 12 ) / V

because Z_F Z_G so GM_L = R

Z_F = T/2

T = V / ( l * b )

l² * b

Mj =

12IMO - Cryteria

Static

1. GM_p >= 0.15m

2. GZ for φ>= 30˚ >= 0.2m

3. φ for GZ_max >= 25˚ but should be >= 30˚

Dynamic

4. A ( 0 30˚) >= 0.055 mrad

5. A ( 0 40˚) >= 0.09 mrad

6. A ( 30˚ 40˚ ) >= 0.03mrad

Weather

7. B >= A

8. Φ₀ <= 16˚

9. Φ₀ <= 0.8φ_p

Φ₀ is for l_w1

504 * A_w * (z_w+T/2)

l_w1 =

1000 * 9.81 * D

l_w2 = 1.5 * l_w1

end of curve to 50˚ or φ_z or φ_c

total angle

Timber carriers:

Nasiakliwosc 10 - 15 %

Not for Timber carriers

GM_p >= 0.1m

For Timber carriers

Dep GM_p >= 0.1 m

Arr GM_p >= 0 m

For all TC

Gz _max >=0.25m

A ( 0 40˚) >= 0.08 mrad

Φ₀ <= 16˚

Φ₀ is for l_w1

Passenger ships

General +

Φ_c <=10˚ (cyrculation)

Φ_p <=10˚ (passenger muster)

Conteiner carriers

General but limits flexible

Supply vessels

General exept one

Gz_max for φ>= 15˚

HSC and DSC

General +

Cyrculation list and max list <= 8˚

PRS - Cryteria

1. GM_p >= 0.15m

>= 0.20m _{(containers on deck)}

2. Gz_max >=0.2m

3. Φ for Gz_max >= 30˚

4. Φ_R >= 60˚ _{( rightning arms > 0)}

>= 50˚ _{( for ships with ice on deck)}

_{(Φz - flooding angle - end of curve)}

5. l_{wd ( 1250 N/m2 )} for Φ_{A ( from book )} - can not cupsize

l_KR

>= 1

l_Wd

Container carriers

6. Φ_w <= 15˚ (Φ_w l_W = 0.6 * l_DW 1216 N/m2 )

Φ_C <= 0.5 * Φ_P

_{( water on deck )}

7. Φ_w <= <= 15˚

Φ_C <= 0.5 * Φ_P

( 0.8* V_e ^(m/s) )²

Φ_C l_c = 0.24 ( z_GP - T/2 )

L * g

OR Z_{G DOP} >= Z_GP

SOLAS - Grain Code - Cryteria

V/L constructed as Grain Carriers

_{FULL HOLD ( 2% LESS - 15˚ SHIFT ) 1.06 * Mv}

_{NOT FULL HOLD ( 25˚ SHIFT ) 1.12 * Mv}

1. GM_P >= 0.30m

2. Φ_G <= 12˚

3. A ( φG0˚ φ40˚ ) >= 0.075mrad

λ₀ = ΣM_G / D _{( MG = MG / k )}

λ₄₀ = 0.8 * λ₀

φ_KR <= φ_z or 40˚or φ for ΔGz_MAX

OR ΣM_G <= M_GMAX

V/L constructed not as Grain Carriers

1. GM_p >= 0.30m and

GM_p >= GM_GrainCode

2. M_z <= 1/3 * DWT

_{Grain Weight}

3. Vertical h = 1/8 * B or >=2.4m

4. Holds not full secured with bags

Stability in Emergency Situations

V_{W ( volume of water )}

μ =

V_{P ( volume of compartment )}

Hole in the Hull:

Width: 11m or 3m +3%Lpp

Hight: from keel to upperdeck

Depth: 1/3 Breath

Categories of flooded departments

I - flooded completely ( below water line )

II - partly flooded ( constant quantity of water, leak from ballast tanks etc.)

III - flooded in and out ( hole on the water line )

Calculating Methods:

1. Loaded Weight Method (cat I and II, Z_G, Δmh GM_A, Z_GA )

2. Constant Deadweight Method ( cat III, constant Deadweight, new hull shape, new hydrostatic curves )

Passenger Ships

1. GM_A >= 0.05m

2. GZ_MAX >= 0.10m

>= M_pax / D + 0.04

>= M_w(120N/m2) / D + 0.04

>= M_R / D + 0.04

_{( moment from launching lifeboats )}

3. φ_A <= 7˚ - _{( for one department )}

φ_A <= 12˚ - _{( for two departments )}

4. φ_temp <= 15˚

_{( temp pass muster in one place )}

5. l_{d 20˚} = A >= 0.015mrad

RO - PAX

1.

A

>= N ˜ ^{97.5% (possibility to survive the storm)}

A_MAX

A = Σa * p * s

_{( possibility to be a hole in this place )}

_{( possibility to be a hole that big )}

_{( possibility that ship match the cryteria )}

A_MAX = A for s = 1

2. Stockholm Agreement

- N = 1

- In emergency we do have water on each deck above

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