author | A.M. Thurnherr <athurnherr@yahoo.com> |
Tue, 18 Jun 2013 11:51:32 +0000 | |
changeset 5 | 033a169071de |
parent 0 | 0a450563f904 |
permissions | -rw-r--r-- |
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%====================================================================== |
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% D R A G M O D E L . M |
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% doc: Wed Jan 7 16:23:52 2009 |
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% dlm: Wed Jan 7 16:24:07 2009 |
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% (c) 2009 A.M. Thurnherr |
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% uE-Info: 11 0 NIL 0 0 72 0 2 4 NIL ofnI |
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%====================================================================== |
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|
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% CHANGES BY ANT: |
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% Jan 7, 2009: - tightened use of exist() |
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|
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% |
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% dragmodel |
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% predict the position of the CTD given the ships position and CTD depth |
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% |
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% DEFINE DRAG MODEL constants |
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% |
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|
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if ~exist('p','var') |
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p.name='dragmodel'; |
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end |
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|
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% CTD/LADCP parameter |
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% Weight of CTD/LADCP system in kg |
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p=setdefv(p,'dmodel_package_weight',400); |
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% Horizontal area of CTD/LADCP system in m^2 |
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p=setdefv(p,'dmodel_package_area_h',.2); |
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% Vertical area of CTD/LADCP system in m^2 |
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p=setdefv(p,'dmodel_package_area_v',0.1); |
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% drag coefficient for CTD/LADCP system (assume cylinder) |
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p=setdefv(p,'dmodel_package_cd',1.3); |
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|
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% Cable parameter |
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% Cable weight in kg per meter length |
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p=setdefv(p,'dmodel_wire_weight',0.5); |
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% Cable wire diameter fraction of inch |
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p=setdefv(p,'dmodel_wire_diameter_inch',0.5); |
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% Cable thickness in m is equal to area |
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p=setdefv(p,'dmodel_wire_area',0.0254*p.dmodel_wire_diameter_inch); |
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% Cable drag coefficient |
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p=setdefv(p,'dmodel_wire_cd',1.3); |
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|
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% Model parameter: |
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% length of wire segments |
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p=setdefv(p,'dmodel_wire_length',10); |
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|
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% Model design: |
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% |
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49 |
% each element has an angle with the vertical: alpha |
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% where 0 means pointing straight down |
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51 |
% |
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% each element had an horizontal angle: beta |
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% where 0 means pointing to the north and positive angles point east |
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% each element has a u,v,w velocity defined at its center |
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% |
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% At each junction between elements the forces are calculated |
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% in the north/east/up direction units are N=kg*m/s^2 |
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58 |
% |
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59 |
% Acceleration of gravity m/s^2 |
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60 |
g=9.81; |
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61 |
|
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% Density of water |
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rho0=1028; |
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64 |
|
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if ~exist('al','var') |
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% initialize model |
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ncable=10; |
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cable_l=ones(ncable,1)*p.dmodel_wire_length; |
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% angle to the vertical |
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al=zeros(ncable+1,1); |
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% angle in horizontal |
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be=zeros(ncable+1,1); |
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% node velocity |
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u=zeros(ncable+1,1); |
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v=zeros(ncable+1,1); |
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% node acceleration |
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dudt=zeros(ncable+1,1); |
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dvdt=zeros(ncable+1,1); |
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% node position |
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X=zeros(ncable+1,1); |
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Y=zeros(ncable+1,1); |
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Z=zeros(ncable+1,1); |
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% node horizontal distance |
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H=zeros(ncable+1,1); |
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85 |
% node vertical distance |
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D=zeros(ncable+1,1); |
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87 |
end |
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88 |
|
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if ~exist('dr','var') |
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dr.z=[0 3000]; |
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dr.u=[0 0]; |
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92 |
dr.v=[0 0]; |
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93 |
d.wm=[0 0]; |
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94 |
end |
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95 |
|
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96 |
|
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% time step |
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98 |
nt=1; |
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99 |
dt=60; |
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100 |
|
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% precalculate |
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sal=sin(al*pi/180); |
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cal=cos(al*pi/180); |
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sbe=sin(be*pi/180); |
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cbe=cos(be*pi/180); |
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106 |
|
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107 |
% get depth of each node |
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108 |
Z=al*0; |
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109 |
for i=1:length(cable_l) |
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110 |
in=length(cable_l)-i+1; |
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111 |
Z(in)=Z(in+1)-p.dmodel_wire_length*cos(al(in)); |
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112 |
end |
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113 |
|
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114 |
% velocity of nodes |
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115 |
vel=u+sqrt(-1)*v; |
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116 |
|
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117 |
% interpolate ocean velocity to drag model points |
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118 |
uo=interp1(-dr.z,dr.u,Z-p.dmodel_wire_length/2,'linear','extrap'); |
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119 |
vo=interp1(-dr.z,dr.v,Z-p.dmodel_wire_length/2,'linear','extrap'); |
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velo=uo+sqrt(-1)*vo; |
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121 |
wctd=d.wm(nt); |
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122 |
|
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123 |
% Compute forces from bottom of CTD up to the ship |
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124 |
% |
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125 |
% CTD/LADCP first |
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126 |
% gravity |
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127 |
Fv(1)=-p.dmodel_package_weight*g; |
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128 |
|
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129 |
% drag |
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130 |
% normal drag Force in direction of flow |
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131 |
Fdn(1)=(-sal(1)*wctd+cal(1)*abs(vel(1)-velo(1))) * ... |
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132 |
abs(sal(1)*wctd+cal(1)*abs(vel(1)-velo(1))) * ... |
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133 |
p.dmodel_package_area_h*p.dmodel_package_cd*rho0; |
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134 |
% along drag Force |
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135 |
Fda(1)=(-cal(1)*wctd+sal(1)*abs(vel(1)-velo(1))) * ... |
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136 |
abs(cal(1)*wctd+sal(1)*abs(vel(1)-velo(1))) * ... |
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137 |
p.dmodel_package_area_h*p.dmodel_package_cd*rho0; |
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138 |
|
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139 |
% project in earth coordinates |
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140 |
% vertical drag |
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141 |
Fv(1)=Fv(1)+Fdn(1)*sal(1)+Fda(1)*cal(1); |
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142 |
|
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143 |
% tension |
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144 |
Ft(1)=Fda(1)*sal(1)+Fv(1)*cal(1); |
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145 |
|
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146 |
% horizontal drag |
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147 |
Fh(1)=Fdn(1)*cal(1)+Ft(1)*sal(1); |
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148 |
Fhx(1)=Fh(1)*cos(angle(vel(1)-velo(1))); |
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149 |
Fhy(1)=Fh(1)*sin(angle(vel(1)-velo(1))); |
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150 |
|
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151 |
% loop over the wire elements to calculate Forces and Tension |
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152 |
for i=1:length(cable_l) |
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153 |
i1=i+1; |
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154 |
% gravity |
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155 |
Fv(i1)=Fv(i)-p.dmodel_wire_weight*p.dmodel_wire_length*g; |
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|
156 |
|
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157 |
% drag |
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158 |
% normal drag Force in direction of flow |
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|
159 |
Fdn(i1)=(-sal(i1)*wctd+cal(i1)*abs(vel(i1)-velo(i1))) * ... |
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|
160 |
abs(sal(i1)*wctd+cal(i1)*abs(vel(i1)-velo(i1))) * ... |
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|
161 |
p.dmodel_wire_area*p.dmodel_wire_cd*p.dmodel_wire_length; |
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|
162 |
% along drag Force |
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|
163 |
Fda(i1)=(-cal(i1)*wctd+sal(i1)*abs(vel(i1)-velo(i1))) * ... |
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|
164 |
abs(cal(i1)*wctd+sal(i1)*abs(vel(i1)-velo(i1))) * ... |
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|
165 |
p.dmodel_wire_area*p.dmodel_wire_cd*p.dmodel_wire_length; |
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|
166 |
|
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167 |
% project in earth coordinates |
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|
168 |
% vertical drag |
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|
169 |
Fv(i1)=Fv(i1)+Fdn(i1)*sal(i1)+Fda(i1)*cal(i1); |
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|
170 |
|
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171 |
% tension |
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|
172 |
Ft(i1)=Fda(i1)*sal(i1)+Fv(i1)*cal(i1); |
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|
173 |
|
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174 |
% horizontal drag |
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|
175 |
Fh(i1)=Fdn(i1)*cal(i1)+Ft(i1)*sal(i1); |
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|
176 |
Fhx(i1)=Fh(i1)*cos(angle(vel(i1)-velo(i1))); |
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|
177 |
Fhy(i1)=Fh(i1)*sin(angle(vel(i1)-velo(i1))); |
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|
178 |
|
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179 |
end |
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|
180 |
|
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|
181 |
% loop over wire elements to calculate accelation from F = m*a |
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|
182 |
% a = F/m |
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|
183 |
% use "dynamical mass" Fv/g |
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|
184 |
|
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|
185 |
dudt(1) = Fhx(1)/abs(Fv(1)/g); |
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|
186 |
dvdt(1) = Fhy(1)/abs(Fv(1)/g); |
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|
187 |
|
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|
188 |
|
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|
189 |
for i=1:(length(cable_l)) |
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|
190 |
i1=i+1; |
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|
191 |
dudt(i1) = 0.5*(Fhx(i1)+Fhx(i))/abs(Fv(i1)/g); |
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|
192 |
dvdt(i1) = 0.5*(Fhy(i1)+Fhy(i))/abs(Fv(i1)/g); |
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193 |
end |
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|
194 |
|
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|
195 |
% loop to update velocity of nodes |
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196 |
|
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197 |
for i=0:(length(cable_l)) |
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198 |
i1=i+1; |
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|
199 |
u(i1) = u(i1) + dudt(i1)*dt/1000; |
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|
200 |
v(i1) = v(i1) + dvdt(i1)*dt/1000; |
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201 |
end |
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|
202 |
|
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203 |
|
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204 |
% loop to calculate horizontal position of nodes |
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205 |
for i=0:(length(cable_l)) |
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206 |
i1=i+1; |
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207 |
X(i1)=X(i1)+u(i1)*dt; |
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208 |
Y(i1)=Y(i1)+v(i1)*dt; |
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209 |
end |
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210 |
|
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211 |
% loop to calculate vertical position of nodes |
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Z(length(cable_l)+1)=0; |
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for i=1:(length(cable_l)) |
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in=length(cable_l)+1-i; |
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in1=in+1; |
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H(in1)=sqrt((X(in1)-X(in)).^2 + (Y(in1)-Y(in)).^2); |
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D(in1)=sqrt(p.dmodel_wire_length.^2 - H(in).^2); |
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Z(in)=Z(in1)-D(in1); |
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al(in)=atan2(H(in),D(in))*180/pi; |
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be(in)=atan2(Y(in1)-Y(in),X(in1)-X(in))*180/pi; |
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end |
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222 |