% Hydrostatic Analysis of TLP
% 4/25/03; Meg Brogan and Katie Wasserman

% Constants here...

g=32.17;                % gravity  ft/s^2
ro=1.99;                % density  slugs/ft^3
E_steel=4.177e9;        % Youngs MOdulus of Steel lb/ft^2 = 20e10 Pa
nu=35;                  % Specific Volume ft^3/ton

% Basic Vessel Parameters here...

D_water=2985;           % water depth ft
B_hull=245;             % breadth of hull ft
T=85;                   % Draft of the vessel ft
d_cais=66.5;            % diameter of caissons ft
h_cais=166;             % height of caisson ft
w_pont=35.5;            % width of ponttons ft
h_pont=23;              % hight of pontoons ft
d_tend=2.667;           % diameter of tendons,  32in
t_tend=.10412;          % wall thickness of tendons, 1.25in
l_tend=2900;            % length of tendons ft
n=12;                   % number of tendons
a=(B_hull-d_cais)/2;    % arm to center of caissons

% Weights
W_top=20502;                                % total topside weight tons (revised #)
W_hull=12054;                               % hull weight tons (revised #)
W_tend=7500;                                % total weight of all 12 tendons tons
Wtot=W_top+W_hull+0.5*W_tend;               % Total weight of the vessel
Wtot_marg=1.15*Wtot                         % Total weight of the vessel w/ a 15% margin for error
m= Wtot*2200/g;                             % per MIKE T only half the tendon weight is used in these calcs; the 2200 is to get lb from tons

% Displacement, Weight and Tension Determinations

% Caissons

d_sub=T;                                   % submerged depth of caissons ft
A_cais=pi*((d_cais^2)/4);                   % waterplane area per caisson ft^2
V_cais=A_cais*d_sub;                        % submerged volume per caisson ft^3
Vt_cais=4*V_cais ;                          % total submerged volume of caissons ft^3

disp_cais=Vt_cais/nu                       % Total displacement of caisons 

% Pontoons

b_pont=B_hull-d_cais ;                      % breadth of pontoon ft
V_pont=b_pont*w_pont*h_pont;
Vt_pont=4*V_pont;

disp_pont=Vt_pont/nu                       % Total displacement of pontoons

% Tendons

A_tend=pi*(d_tend^2-(d_tend-2*t_tend)^2)/4; %cross sectional area of the tendons
V_tend=l_tend*A_tend;
Vt_tend=12*V_tend;

disp_tend=Vt_tend/nu                       % total displacement of tendons

% Area of the Waterplane

Awp=4*A_cais;

% TOTAL HULL DISPLACEMENT, BOUYANCY

disp_total=disp_cais+disp_pont+disp_tend    % tons

B_tot=disp_total-Wtot_marg                  % Total Bouyant force upwards disp minus weight with fudge factor  

T_tend=B_tot/n                              % Tensions in each tendon is B over # of tendons

% HEAVE analysis

% K=Kdynamic+Kstatic
K_d=n*A_tend*E_steel/l_tend;                % essentially EA/L times n
K_s=ro*g*Awp;                 

K_t=K_d+K_s;

%Mass determinations
m= (W_top+W_hull+0.5*W_tend)*2200/g;        % per MIKE T only half the tendon weight is used in these calcs; the 2200 is to get lb from tons

ma_c=0.5*(4/3)*pi*(d_cais/2)^3*ro*4;
ma_p=4*ro*V_pont;
ma_t=ma_c+ma_p;                               % Total added mass of the pontoon and caisson

% Natural frequency of the Vessel in heave:
w_n3=sqrt(K_t/(m+ma_t));
T_n3=(2*pi)/w_n3;

% PITCH/ROLL Analysis

%C=Cdynamic+Cstatic
a=b_pont/2-d_cais/2;
C_d=6*2*(b_pont/2-d_cais/2)^2*E_steel*A_tend/l_tend;             % 6 represents the number of PAIRS of tendons
C_s=2*(b_pont/2-d_cais/2)^2*g*ro*Awp;   

C_t=C_d+C_s;

%Mass and Inertia Determinations
y=Vt_cais/Vt_pont;
m_hull=W_hull*2200/g;
m_p=m_hull/(1+y);
m_c=m_hull-m_p;

r_ss=(3/8)*B_hull;                          % Gross assumptions made here on the radius of gyration for the SuperStructure, should be refined
I_ss=(0.5*W_top*2200/g)*r_ss^2;             % assumed that superstructure is roughly 1/2 of the total topside weight

r_deck=(1/4)*B_hull;                        % Used conventional assumption about r
I_deck=(0.5*W_top*2200/g)*r_deck^2;

r_cais=d_cais/2;                            % all the caisson weight is at r because its hollow, therefore r=d/2
I_cais=4*(m_c*2200/g)*r_cais^2;

r_pont1=(1/4)*b_pont;
I_pont1=2*(m_p*2200/g)*r_pont1^2;

r_pont2=(1/4)*d_cais;                       %this accounts for the pontoons which are shielded by the caissons
I_pont2=2*(m_p*2200/g)*r_pont2^2;           % ALL these inertias are in the units slug-ft^2

PAT_ss=(0.5*W_top*2200/g)*166.5^2;          % the 166.5 comes from estimates of vcg... these should DEFINATELY be revised
PAT_deck=(0.5*W_top*2200/g)*101^2;          % ditto
PAT_cais=4*(m_c*2200/g)*2^2;
PAT_pont=4*(m_p*2200/g)*73.5^2;

I_tot=I_ss+I_deck+I_cais+I_pont1+I_pont2+PAT_ss+PAT_deck+PAT_cais+PAT_pont;   %total mass moment of inertia of vessel, slug-ft^2

%Added Inertia Determinations

Ia_cais=(1/2)*(4/3)*pi*ro*(a^2)*((d_cais/2)^2); 
Iat_cais=Ia_cais*4;                         % Total added mass moment of inertia of the caissons

Ia_pont1=(1/12)*h_pont*(b_pont^2)*ro*2;     % added moment from two of the pontoons in same direction
Ia_pont2=(h_pont^2)*d_cais*ro*(a^2)*2;      % added moment from the hidden two pontoons in the other direction

Ia_tot=Iat_cais+Ia_pont1+Ia_pont2;

% Natural Frequnecy in pitch/roll

wn_5=sqrt(C_t/(I_tot+Ia_tot));
Tn_5=(2*pi)/wn_5;
                                   

% SAMPLE OUTPUTS:
%disp_total =4.7031e+04
%B_tot =6.2059e+03
%T_tend =517.1593
%w_n3 =1.9217
%T_n3 =3.2697
%wn_5 =0.1670
%Tn_5 =37.6256