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Stochastic6DOF.m
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Stochastic6DOF.m
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clear variables;
close all;
clc;
%% Load Map of Launch Site
img_far = imread('image1.png');
img_h_mi = 15840; img_w_mi = 26400;
img_h = size(img_far,1); img_w = size(img_far,2);
figure;
hold on;
RI = imref2d(size(img_far));
RI.XWorldLimits = [-img_w_mi/2 img_w_mi/2];
RI.YWorldLimits = [-img_h_mi/2 img_h_mi/2];
imshow(img_far,RI);
%% Run the Trajectory Simulations
numstocsim = 21;
xs = zeros(numstocsim,3);
apogees = zeros(numstocsim);
OTRSs = zeros(numstocsim);
burntime= zeros(numstocsim);
for si = 1:1:numstocsim % First loop is mean
clearvars -except si xs apogees OTRSs
%% Initial values
recovery = 1; % 0 for no recovery / 1 for recovery
turb = 1; % 0 for none / 1 for light / 2 for medium / 3 for severe
h = 2200; % elevation of launch site
if si==1
Temp0 = 70;
kTemp = 10000; % Seems to be the most reasonable "tending to atmospheric model" rate
P0 = 14.24*144;
else
Temp0 = 70*normrnd(1,.1^2);
kTemp = 10000*normrnd(1,.2^2); % Seems to be the most reasonable "tending to atmospheric model" rate
P0 = 14.24*144*normrnd(1,.1^2);
end
hr0 = 0;
%g = 32.174;
lat = 34.0522*pi/180;
glat = 9.7803*((1+0.001932*(sin(lat))^2)/(sqrt(1-0.006694*(sin(lat))^2)));
%g = (glat-3.086*(10^(-6))*(h/3.28))*3.28;
GM = 1.4077*10^16;
re = 20.902*10^6;
g = GM/(re+h)^2;
Eomega = 7.2921*10^(-5);
% vwgx = -5*5280/3600;
% vwgx = -27;
if si==1
vwgx = -5*5280/3600;
vwgy = 5*5280/3600;
else
vwgx = -5*5280/3600*normrnd(1,0.2^2);
vwgy = 5*5280/3600*normrnd(1,0.2^2);
end
k = 0.4;
dref = 0.000;
z1 = 0.1/100;
atm_stability = 1; % 1=neutral, 2=stable, 3=unstable
dw = 95.496;
T0 = readmatrix('352022StaticFire.xlsx');
tstocbool = true;
if si ~= 1
randthrust = 18.08+normrnd(0,1);
if randthrust > 18.08
tstocbool = false;
end
for thrustcounter = 1:length(T0) & tstocbool
if T0(thrustcounter, 1) > randthrust
T0 = T0(1:thrustcounter,:);
tstocbool = false;
end
end
end
% T0 = readmatrix('Odyssey3Thrust.xlsx');
% T0 = readmatrix('PropSimThrust.xlsx');
Imp = trapz(T0(:,1),T0(:,2)); %calculate impulse using Riemanns
Impfactor = 9200/Imp-0.037;
%T0 = T0*Impfactor;
%Imp = trapz(T0(:,1),T0(:,2));
% Isp = 200;
wp = 58.8; %weight of propellant
OF = 34.339/24.461; %oxidizer to fuel ratio
wfi = wp/(OF+1);
woi = wfi*OF;
ww = dw+wfi+woi; %wet weight
Isp = Imp/(ww-dw); %specific impulse
lfi = 26.604/12; %length of fuel tank
loi = 26.604/12; %length of oxidizer tank
cgfi = 92/12 + 1/12 + loi + 0.5*lfi; %center of grav of fuel tank
cgoi = 92/12 + 0.5*loi; %center of grav of ox tank
xfuel0 = cgfi-lfi/2; %position of fuel tank wrt nose
xox0 = cgoi-loi/2; %position of ox tank wrt nose
dtank = 7/12; %diameter of tank
rtank = dtank/2; %radius of tank
% dnoz = 4;
dnoz = 1.5; %diameter of nozzle
cgd = 93.546/12; %dry center of mass
if si==1 %non-stochastic
Ecg = 1; %center of grav error
RLa = 3*pi/180; %rail angle
else
Ecg = normrnd(1,0.025^2);
RLa = normrnd(3*pi/180,0.1^2);
end
RL = 55; %rail length
p0 = RLa; %initial direction
RLv = [-RL*sin(RLa),RL*cos(RLa)]; %rail vector
df = (wfi/g)/(lfi*pi*rtank^2); %density of fuel
dox = (woi/g)/(loi*pi*rtank^2); %density of oxidizer
ejection = 0;
ti = 0;
tb = T0(end,1);
% tb = round(find(T0(:,2),1,'last')/1000,2); %PropSim
tf = 400;
dt = 0.01;
t_steps = tf/dt;
Tt = interp1(T0(:,1),T0(:,2),ti:dt:tb);
% if dt==0.001
% Tt = Tt(121:end); %If Odyssey Motor is used
% tb = tb-0.12;
% elseif dt==0.01
% Tt = Tt(13:end); %If Odyssey Motor is used
% tb = tb-0.12;
% end
% Tx = zeros(t_steps,1);
% Tz = zeros(t_steps,1);
T = zeros(t_steps,3);
% mach_cd = readmatrix('varCD.CSV');
% ma = mach_cd(:,1);
% cdv = mach_cd(:,6);
vs = zeros(t_steps,1);
gamma = 1.4;
R = 1717;
mach = zeros(t_steps,1);
cd8 = zeros(t_steps,1);
cl8 = zeros(t_steps,1);
d = 7;
Aref = pi*(d/12/2)^2;
n = 4;
CNan = 2;
dr = 5.5/12;
DR = dr/2;
CNat = 2*((dr/(d/12))^2-1);
r0 = d/2;
S = 7.8/12;
% S = 1/12;
Cr = 14/12;
Ct = 4/12;
Lf = sqrt(S^2+(Cr/2-Ct/2)^2);
dfa = dr;
Kf = 1+(dr/2)/(S+(dr/2));
CNaf = Kf*((4*n*(S/(d/12))^2)/(1+sqrt(1+(2*Lf/(Cr+Ct))^2)));
Ln = 35/12;
xn = 0.466*Ln;
LB = (175.5-35-19.7)/12;
xp = Ln+LB;
Lt = 19.70/12;
xt = xp+Lt/3*((1+(1-(d/12)/dr)/(1-((d/12)/dr)^2)));
Rl = Ln+LB+Lt;
xB = Rl-Cr;
xr = Cr-Ct;
xf = xB+xr/3*(Cr+2*Ct)/(Cr+Ct)+(1/6*((Cr+Ct)-(Cr*Ct)/(Cr+Ct)));
xBody = Ln+0.5*LB;
K = 1.5;
ApB = (d/12)*LB;
Apb = Lt/2*((d/12)+dr);
Apn = (d/12)*Ln/2*1.3; % Factor of 1.3 to account for cone to ogive difference
Ap = ApB+Apb+Apn;
CNab = 0;
Tf = 0.6/12;
thetaLE = atan(xr/S);
thetaTE = atan((Cr-xr-Ct)/S);
Afe2 = 2*(Cr*S-0.5*S^2*(tan(thetaLE)+tan(thetaTE)))+Tf*S*0.3;
Afe = S*(Cr+Ct);
Afp = Afe+0.5*(1/12)*Cr;
Rs = (2*S+d/12)/dfa;
kfb = 0.8065*Rs^2+1.1553*Rs;
kbf = 0.1935*Rs^2+0.8174*Rs+1;
tr = Ct/Cr;
if si==1
Ecp = 1;
Ecl = 1;
Ecd = 1;
else
Ecp = normrnd(1,0.05^2);
Ecl = normrnd(1,0.1^2);
Ecd = normrnd(1,0.2^2);
end
Apf = Afe;
Apf = 0;
Apt = Ap + Apf;
CPcut = (Apn*xn+ApB*xB+Apb*xt+Apf*xf)/Apt;
Iapogee2 = 1;
Aprime = 2*Tf/3/Cr;
% Afin = (2*S)^2/(Afe/2);
Sfin = (Cr+Ct)*S;
Afin = (2*S)^2/Sfin;
K_wb = 1 + (((d/12)/2)/S)^1.15;
beta2 = sqrt(3);
MAC = (Cr+Ct)/2;
CPiFM2r = ((Afin*beta2-0.67)/(2*Afin*beta2-1));
CPiFM0 = xf-xB;
CPiFM2 = (xf-xB)*CPiFM2r/0.25;
theta = rad2deg(atan(((d/12)/2)/Ln));
msCNa = 0.05525641*theta - 0.067948718;
bsCNa = -0.044717949*theta + 2.03025641;
% machD = 0.8;
machD = -0.0156*(Ln/(d/12))^2+0.136*(Ln/(d/12))+0.6817;
if (Ln/Rl)<0.2
A = 2.4;
b = -1.05;
else
A = -321.94*(Ln/Rl)^2+264.07*(Ln/Rl)-36.348;
b = 19.634*(Ln/Rl)^2-18.369*(Ln/Rl)+1.7434;
end
machF = A*(Rl/(d/12))^b+1.0275;
c = 50.676*(Ln/Rl)^2-51.734*(Ln/Rl)+15.642;
G = -2.2538*(Ln/Rl)^2+1.3108*(Ln/Rl)-1.7344;
if (Rl/(d/12))>=6
dCDmax = c*(Rl/(d/12))^G;
else
dCDmax = c*(6)^G;
end
% dCDmax = 0.086;
% dCDmax = 0.115;
dCDmax = 0.1956;
Rec = 5*10^5;
mu0 = 3.62*10^(-7);
temp0 = 518.7;
Kb = 0.0274*atan((Rl-Ln)/(d/12)+0.0116);
nb = 3.6542*((Rl-Ln)/(d/12))^(-0.2733);
rpro = 1.35/12; %radius
Apro = pi/2*rpro^2; %Projected Area
Lp = 55.74/12; %Length of Protuberance
aPro = 76.78; %Distance from nosecone to Protuberance
Spro = 2*2*Apro+2*pi*rpro*Lp; %Surface Area of protuberance
All = 1/144; %in
% All = 0/144; %in
rll = sqrt(All/pi);
Lll = 6/12;
Sll = 2*All+2*2*pi*rll*Lll;
aLL = Rl/2; %Midway on rocket
muk = 0.12; %Steel on steel lubricated
mus = 0.16; %Steel on steel lubricated
% muk = 0; %Steel on steel lubricated
% mus = 0; %Steel on steel lubricated
if p0<0
% mus = -mus;
end
Lc = [Rl,Cr,Lp,Lll];
%Find cg formulas later
cgn = 24.36/12;
cgb = Ln+LB/2;
cgt = 166/12;
cgfin = 172/12;
cgi = [cgn, cgb, cgt, cgfin];
vwg = zeros(t_steps,3); % Wind model in loop
ustar = zeros(t_steps,1);
% ustar(:) = abs(vwgx)/3.28*k/log((RLv(2)/3.28-dref/3.28)/(z1/3.28));
cv = 0.25; % 0.1 to 0.4
fv = 2*Eomega*sin(lat);
% ustar(:) = vwgx*k/log(RLv(2)/z1);
if atm_stability == 1
Lv = 500*3.281;
ustar(:) = abs(vwgx)*k/log(RLv(2)/z1);
vstar(:) = abs(vwgy)*k/log(RLv(2)/z1);
hv = cv*ustar(1)/abs(fv);
hv2 = cv*vstar(1)/abs(fv);
vA = 4.9;
vB = 1.9;
LMBL = hv/2*(((log(ustar(1)/abs(fv)/z1)-vB)^2+vA^2)^0.5-log(hv/z1))^(-1);
LMBL2 = hv2/2*(((log(vstar(1)/abs(fv)/z1)-vB)^2+vA^2)^0.5-log(hv2/z1))^(-1);
elseif atm_stability == 2 % How to find hv without ustar
Lv = 125*3.281;
% ustar(:) = abs(vwgx)*k/(log(RLv(2)/z1)+4.7*RLv(2)/Lv*(1-RLv(2)/2/hv));
% hv = 0.5*sqrt(ustar(1)*Lv/abs(fv));
vA = log(hv/Lv)-2.2*hv/Lv+2.9;
vB = 3.5*hv/Lv;
LMBL = hv/2*(((log(ustar(1)/abs(fv)/z1)-vB)^2+vA^2)^0.5-log(hv/z1)-4.7*hv/2/Lv)^(-1);
elseif atm_stability == 3
Lv = -150*3.281;
vx = (1-12*RLv(2)/Lv)^(1/3);
fzl = 1.5*log((1+vx+vx^2)/3)-sqrt(3)*atan((1+2*vx)/sqrt(3))+pi/sqrt(3);
ustar(:) = abs(vwgx)*k/(log(RLv(2)/z1)-fzl);
hv = cv*ustar(1)/abs(fv);
vxh = (1-12*hv/Lv)^(1/3);
fhl = 1.5*log((1+vxh+vxh^2)/3)-sqrt(3)*atan((1+2*vxh)/sqrt(3))+pi/sqrt(3);
vA = log(hv/abs(Lv))+log(abs(fv)*hv/ustar(1))+1.5;
vB = k*ustar(1)/fv/hv+1.8*fv*hv/ustar(1)*exp(1)^(0.2*hv/Lv);
LMBL = hv/2*(((log(ustar(1)/abs(fv)/z1)-vB)^2+vA^2)^0.5-log(hv/z1)+fhl)^(-1);
else
error('Fix atm stability');
end
if vwgx<0
ustar(:) = -ustar(:);
end
if vwgy<0
vstar(:) = -vstar(:);
end
% tgust = 5.82;
tgust = 15.93;
dtgust = 3;
dtrise = 0*dtgust;
if (si > 1 && rand<0.1)
gust = -30;
else
gust = 0;
end
% tma = [0.16/180*pi,0];
if si==1
tmap = 0;
tma = 0.32/180*pi*[cos(tmap),sin(tmap)];
else
tmap = pi/20*rand(1);
tma = 0.32/180*pi*[cos(tmap),sin(tmap)];
end
% tmap = 0.7;
% tma = 0.32/180*pi*[cos(tmap),sin(tmap)];
% cant = 1/180*pi;
if si==1
cant = 0;
else
cant = normrnd(0,(.5/180*pi)^2);
end
% rf = r0/12;
% CR = 0.04;
%% Initialize arrays
ts = ti:dt:tf;
rho = zeros(t_steps,1);
%temp = zeros(t_steps,1);
%P = zeros(t_steps,1);
wfr = zeros(t_steps,1);
w = zeros(t_steps,1);
w(1) = ww;
W = zeros(t_steps,3);
wf = zeros(t_steps,1);
wf(1) = wfi;
wo = zeros(t_steps,1);
wo(1) = woi;
cgf = zeros(t_steps,1);
cgf(1) = cgfi;
cgo = zeros(t_steps,1);
cgo(1) = cgoi;
lf = zeros(t_steps,1);
lf(1) = lfi;
lo = zeros(t_steps,1);
lo(1) = loi;
cg = zeros(t_steps,1);
wfrf = zeros(t_steps,1);
wfro = zeros(t_steps,1);
cgp = zeros(t_steps,1);
Mt = zeros(t_steps,3);
stab = zeros(t_steps,1);
% Reb = zeros(t_steps,1);
% Ref = zeros(t_steps,1);
Rnc = zeros(t_steps,4);
mu = zeros(t_steps,1);
% Bb = zeros(t_steps,1);
% Bf = zeros(t_steps,1);
B = zeros(t_steps,2);
% Cfb = zeros(t_steps,1);
% Cff = zeros(t_steps,1);
Cf = zeros(t_steps,4);
% CDfb = zeros(t_steps,1);
% CDb = zeros(t_steps,1);
% CDf = zeros(t_steps,1);
% CDi = zeros(t_steps,1);
% CD0 = zeros(t_steps,4);
Cfi = zeros(t_steps,4);
CfiT = zeros(t_steps,4);
CfT = zeros(t_steps,4);
CDf6 = zeros(t_steps,1);
% CDb6 = zeros(t_steps,1);
p = zeros(t_steps,1);
p(1) = p0;
y = zeros(t_steps,1);
y(1) = 0;
r = zeros(t_steps,1);
r(1) = 0;
omega = zeros(t_steps,3);
ihat = [-sin(p(1)),0,cos(p(1))];
jhat = [0,1,0];
khat = [cos(p(1)),0,sin(p(1))];
yA = zeros(3,t_steps);
pA = zeros(3,t_steps);
rA = zeros(3,t_steps);
q = zeros(4,t_steps);
qdot = zeros(4,t_steps);
omega(1,:) = [0,0,0]; %1=y,2=p,3=r
q(:,1) = [cos(r(1)/2)*cos(p(1)/2)*cos(y(1))+sin(r(1)/2)*sin(p(1)/2)*sin(y(1));...
sin(r(1)/2)*cos(p(1)/2)*cos(y(1))-cos(r(1)/2)*sin(p(1)/2)*sin(y(1));...
cos(r(1)/2)*sin(p(1)/2)*cos(y(1))+sin(r(1)/2)*cos(p(1)/2)*sin(y(1));...
cos(r(1)/2)*cos(p(1)/2)*sin(y(1))-sin(r(1)/2)*sin(p(1)/2)*cos(y(1))];
qdot(:,1) = 0.5*([0,-omega(1,1),-omega(1,2),-omega(1,3);omega(1,1),0,omega(1,3),-omega(1,2);...
omega(1,2),-omega(1,3),0,omega(1,1);omega(1,3),omega(1,2),-omega(1,1),0]*q(:,1));
% roll0 = atan2(2*(q(1)*q(2)+q(3)*q(4)),1-2*(q(2)^2+q(3)^2));
% pitch0 = asin(2*(q(1)*q(3)-q(4)*q(2)));
% yaw0 = atan2(2*(q(1)*q(4)+q(2)*q(3)),1-2*(q(3)^2+q(4)^2));
RM = [1-2*q(3)^2-2*q(4)^2, 2*q(2)*q(3)-2*q(1)*q(4), 2*q(2)*q(4)+2*q(1)*q(3);...
2*q(2)*q(3)+2*q(1)*q(4), 1-2*q(2)^2-2*q(4)^2, 2*q(3)*q(4)-2*q(1)*q(2);...
2*q(2)*q(4)-2*q(1)*q(3), 2*q(3)*q(4)+2*q(1)*q(2), 1-2*q(2)^2-2*q(3)^2];
RM(1:2,:) = -RM(1:2,:);
RMrec{1} = RM;
yA(:,1) = RM*[1;0;0];
pA(:,1) = RM*[0;1;0];
rA(:,1) = RM*[0;0;1];
% rA(1,1) = -rA(1,1);
tA(:,1) = [cos(tma(2)),-sin(tma(2)),0;sin(tma(2)),cos(tma(2)),0;0,0,1]*...
[cos(tma(1)),0,sin(tma(1));0,1,0;-sin(tma(1)),0,cos(tma(1))]*rA(:,1);
L = zeros(t_steps,3);
%Lx = zeros(t_steps,1);
%Lz = zeros(t_steps,1);
CNa = zeros(t_steps,4);
CNa(1,:) = [CNan,CNab,CNat,CNaf];
CP8 = zeros(t_steps,1);
CPi = zeros(t_steps,4);
CPi(1,:) = [xn,xBody,xt,xf];
D = zeros(t_steps,3);
MN = zeros(t_steps,3);
% Dx = zeros(t_steps,1);
% Dz = zeros(t_steps,1);
phi = zeros(t_steps,1);
F = zeros(t_steps,3);
% Fx = zeros(t_steps,1);
% Fz = zeros(t_steps,1);
C = zeros(t_steps,3);
Md = zeros(t_steps,1);
M = zeros(t_steps,3);
Frk = zeros(t_steps,3);
Frfk = zeros(t_steps,1);
Reac = zeros(t_steps,3);
Lw = zeros(t_steps,1);
Lu = zeros(t_steps,1);
xTurb = zeros(t_steps,1);
zTurb = zeros(t_steps,2);
a = zeros(t_steps,3);
% ax = zeros(t_steps,1);
% az = zeros(t_steps,1);
% vx = zeros(t_steps,1);
% vz = zeros(t_steps,1);
v = zeros(t_steps,3);
v(1,1) = 0;
v(1,2) = 0;
v(1,3) = 0;
x = zeros(t_steps,3);
%z = zeros(t_steps,1);
x(1,1) = 282;
x(1,2) = 30.5;
x(1,3) = h;
dist = zeros(t_steps,1);
dist(1) = 0;
s = zeros(t_steps,1);
s(1) = 0;
%zs = zeros(t_steps,1);
Ixx = zeros(t_steps,1);
Iyy = zeros(t_steps,1);
Izz = zeros(t_steps,1);
I = zeros(t_steps,3);
% Id = 1788.5;
Id = 1239.3*normrnd(1,.1^2);
Idz = 3.9*normrnd(1,.1^2);
If = zeros(t_steps,1);
Io = zeros(t_steps,1);
alpha = zeros(t_steps,3);
Idot = zeros(t_steps,1);
aoa = zeros(t_steps,1);
aoan = zeros(t_steps,1);
aoai = zeros(t_steps,4);
vrw = zeros(t_steps,3);
% vn = zeros(t_steps,1);
% vnx = zeros(t_steps,1);
% vnz = zeros(t_steps,1);
% vrwn = zeros(t_steps,2);
vrot = zeros(t_steps,3);
vrotx = zeros(t_steps,4);
vrotz = zeros(t_steps,4);
vrwrot = zeros(t_steps,4);
phirot = zeros(t_steps,4);
vwgturb = zeros(t_steps,3);
ts_turb = dt*(0:t_steps-1);
filt = fir1(64,0.5);
nu = randn(2,t_steps); % Need randn(t_steps) for one of the models
nuf = filter(filt,1,nu);
variance = 1.0;
for turbk = 1:1:2
scale = sqrt(variance)/std(nuf(turbk,:));
nufs(turbk,:) = scale*nuf(turbk,:);
end
vgust = zeros(t_steps,1);
j = zeros(t_steps,1);
iters = zeros(t_steps,1);
aoad = 4:2:20;
aoadd = [0.78,0.82,0.92,0.94,0.96,0.97,0.975,0.98,0.985];
aoadn = [0.6,0.63,0.66,0.68,0.72,0.73,0.74,0.75,0.76];
AF = zeros(t_steps,1);
NF = zeros(t_steps,1);
%% Simulate
i = 1;
for t = ti:dt:tf
if i>length(F)
% disp(i)
break
end
if t>tb
% cdv = mach_cd(:,7);
end
H = x(i,3);
Hs(i) = H;
z = x(i,3)-h;
zs(i) = z;
if H < 36152 && H >= 0
temp(i) = 59 - 0.00356*H;
tempr(i) = temp(i);
temp(i) = tempr(i)+(Temp0-tempr(1))*exp((Hs(1)-H)/kTemp);
P(i) = 2116*((temp(i)+459.67)/518.6)^5.256;
Pr(i) = P(i);
P(i) = Pr(i)+(P0-Pr(1))*exp((Hs(1)-H)/kTemp);
elseif H >= 36152 && H < 82854
temp(i) = -70;
tempr(i) = temp(i);
temp(i) = tempr(i)+(Temp0-tempr(1))*exp((Hs(1)-H)/kTemp);
P(i) = 473.1*exp(1)^(1.73-0.000048*H);
Pr(i) = P(i);
P(i) = Pr(i)+(P0-Pr(1))*exp((Hs(1)-H)/kTemp);
else
temp(i) = -205.05+0.00164*H;
tempr(i) = temp(i);
temp(i) = tempr(i)+(Temp0-tempr(1))*exp((Hs(1)-H)/kTemp);
P(i) = 51.97*((temp(i)+459.67)/389.98)^-11.388;
Pr(i) = P(i);
P(i) = Pr(i)+(P0-Pr(1))*exp((Hs(1)-H)/kTemp);
end
hr(i) = hr0;
rhod(i) = P(i)/(R*(temp(i)+459.67));
rho(i) = rhod(i)*(1+hr(i))/(1+1.609*hr(i));
% if dist(i)>RL-Rl+cg(i)
% if H<6560
% vwg(i,1) = (ustar(i)/k*log((H/3.28-dref/3.28)/(z1/3.28)))*3.28;
% %ustar(i+1) = k*(vwg(i,1)-vwg(i-1,1))/log(((x(i,2)-h)-dref)/((x(i-1,2)-h)-dref));
% %vwg(i,1) = vwgx;
% elseif H>=6560
% vwg(i,1) = vwg(i-1,1)*(H/(x(i-1,2)-h))^(1/7);
% %break
% end
% end
if x(i,3) == h
vwg(i,1) = vwgx;
elseif z<=hv % Implement geostrophic patterns at z > hv
if atm_stability == 1
vwg(i,1) = ustar(i)/k*(log(z/z1)+z/LMBL-z/hv*(z/2/LMBL));
elseif atm_stability == 2
vwg(i,1) = ustar(i)/k*(log(z/z1)+4.7*z/Lv*(1-z/2/hv)+z/LMBL-z/hv*(z/2/LMBL));
elseif atm_stability == 3
vx = (1-12*z/Lv)^(1/3);
fzl = 1.5*log((1+vx+vx^2)/3)-sqrt(3)*atan((1+2*vx)/sqrt(3))+pi/sqrt(3);
vwg(i,1) = ustar(i)/k*(log(z/z1)-fzl+z/LMBL-z/hv*(z/2/LMBL));
end
if v(i,3)>=0
dpdx(i) = vwg(i,1)*rho(i)*fv;
dpdxi = i;
end
elseif z>hv
if vwgx == 0
dpdx(i) = 0;
else
dpdx(i) = ((P(i)/P(i-1)+1)/2)*dpdx(i-1);
% dpdx(i) = dpdx(i-1);
% dpdx(i) = d(P(i)/P(i-1))*dpdx(i-1);
end
vwg(i,1) = dpdx(i)/fv/rho(i);
end
%g = (glat-3.086*(10^(-6))*(x(i,2)/3.28))*3.28;
g = GM/(re+H)^2;
m = w(i)/g;
if z >= 9 && z <= 11 % or 12 or 13
vwg10 = vwg(i,1);
end
if z >= 19 && z <= 21 % or 22 or 23
vwg20 = vwg(i,1);
end
if turb ~= 0 && z > 21
if z>=21 && z<=1000
Lw(i) = z;
Lu(i) = z/(0.177+0.000823*z)^1.2;
sigw(i) = 0.1*vwg20;
sigu(i) = sigw(i)/(0.177+0.000823*z)^0.4;
elseif z>=2000
Lw(i) = 1750;
Lu(i) = 1750;
if turb == 1 % Change to the high altitude chart later
sigw(i) = 5;
elseif turb == 2
sigw(i) = 10;
elseif turb == 3
sigw(i) = 15;
end
sigu(i) = sigw(i);
elseif z>1000 && z<2000
Lw(i) = 1000+(z-1000)*750/1000;
Lu(i) = Lw(i);
if turb == 1 % Change to the high altitude chart later
sigw(i) = 0.1*vwg20+(z-1000)*(5-0.1*vwg20)/1000;
elseif turb == 2
sigw(i) = 0.1*vwg20+(z-1000)*(10-0.1*vwg20)/1000;
elseif turb == 3
sigw(i) = 0.1*vwg20+(z-1000)*(15-0.1*vwg20)/1000;
end
sigu(i) = sigw(i);
end
% Gun(i,:) = sigu(i)*sqrt(2*Lu(i)/pi/s(i))*[0 1];
% Gud(i,:) = [Lu(i)/s(i) 1];
% [AuT(i),BuT(i),CuT(i),DuT(i)] = tf2ss(Gun(i,:),Gud(i,:));
% vwgturb(i,1) = CuT(i)*xTurb(i)+DuT(i)*nufs(i,1);
% xTurb(i+1) = AuT(i)*xTurb(i)+BuT(i)*nufs(i,1);
% % vwgturb(i,1) = mean(filter(Gun(i,:),Gud(i,:),nufs(:,i)));
% Gwn(i,:) = sigw(i)*sqrt(2*Lw(i)/pi/s(i))*[2*sqrt(3)*Lw(i)/s(i) 1];
% Gwd(i,:) = [4*(Lw(i)^2)/(s(i)^2) 4*Lw(i)/(s(i)) 1];
% [AwT,BwT,CwT,DwT] = tf2ss(Gwn(i,:),Gwd(i,:));
% vwgturb(i,2) = CwT*zTurb(i,:).'+DwT*nufs(i,2);
% zTurb(i+1,:) = AwT*zTurb(i,:).'+BwT*nufs(i,2);
% % vwgturb(i,2) = mean(filter(Gwn(i,:),Gwd(i,:),nufs(:,i)));
vwgturb(i+1,1) = (1-s(i)*(dt/100)/Lu(i))*vwgturb(i,1)+...
sqrt(2*s(i)*(dt/100)/Lu(i))*sigu(i)/std(nufs(1,:))*nufs(1,i);
vwgturb(i+1,2) = (1-s(i)*(dt/100)/Lu(i))*vwgturb(i,2)+...
sqrt(2*s(i)*(dt/100)/Lu(i))*sigw(i)/std(nufs(2,:))*nufs(2,i);
vwgturb(i+1,3) = 0;
vwg(i,:) = vwg(i,:) + vwgturb(i,:);
end
if t >= tgust && t <= tgust+dtgust+2*dtrise
if t <= tgust+dtrise
if dtrise == 0
vgust(i) = gust;
else
vgust(i) = gust/2*(1-cos(pi*(t-tgust)/dtrise));
end
elseif t <= tgust+dtrise+dtgust
vgust(i) = gust;
else
if dtrise == 0
vgust(i) = gust;
else
vgust(i) = gust/2*(1-cos(pi*(t-tgust-dtgust)/dtrise));
end
end
else
vgust(i) = 0;
end
vwg(i,1) = vwg(i,1) + vgust(i);
% vwg(i,1) = vwgx;
vwg(i,2) = vwgy;
%vrw(i) = ((vx(i)-vwg)^2+vz(i)^2)^(1/2);
vrw(i,:) = v(i,:)-vwg(i,:);
aoacm(i) = acos(dot((vrw(i,:)/norm(vrw(i,:))),rA(:,i)));
if v(i,3)<0
aoacm(i) = 0;
end
vs(i) = (gamma*R*(temp(i)+459.69))^(1/2);
% mach(i) = round(norm(v(i,:))/vs(i),2);
mach(i) = norm(vrw(i,:))/vs(i);
if mach(i)>0.9 && mach(i)<1.1
beta = sqrt(1-0.9^2);
CNaf = CNa(1,4)/beta;
% CNaf = 2*pi*Afin*((Afe/2)/Aref)/(2+sqrt(4+beta*Afin/cos(thetaLE)));
elseif mach(i) <= 0.9
beta = sqrt(1-mach(i)^2);
CNaf = CNa(1,4)/beta;
% CNaf = 2*pi*Afin*((Afe/2)/Aref)/(2+sqrt(4+beta*Afin/cos(thetaLE)));
else
beta = sqrt(mach(i)^2-1);
CNaf = CNa(1,4)/beta;
% C3 = (gamma*mach(i)^4+(mach(i)^2-2)^2)/(2*(mach(i)^2-1)^1.5);
% Aprime = 2*ft/3/vs(i);
% CNaf = 4/beta*(1-(1-C3*Aprime)/2/beta/Afin);
% CNaf = K_wb*(Sfin/Aref)*CNaf;
nosebodyCNa = msCNa*mach(i) + bsCNa;
CNan = 0.2*mach(i) + 2.03;
CNab = nosebodyCNa - CNan;
end
betas(i) = beta;
if mach(i)>1.1 && mach(i)<1.15
% beta = sqrt(mach(i)^2-1);
end
% CNaf = CNa(1,4)*beta;
if abs(aoacm(i))<20*pi/180 && mach(i)<1.2
CNab = 4*K/pi*Ap/(d/12)^2*abs(aoacm(i));
elseif mach(i)<1.2
CNab = 4*K/pi*Ap/(d/12)^2*20*pi/180;
end
%CNa = CNan+CNat+CNaf+CNab;
% if mach(i)<1.2
CNa(i,:) = [CNa(1,1)/beta,CNab/beta,CNa(1,3)/beta,CNaf];
% else
% CNa(i,:) = [CNan,CNab,CNa(1,3)/beta,CNaf];
% end
% CNa(i,:) = [CNa(1,1),CNab,CNa(1,3),CNa(1,4)];
% CNa(i,:) = [CNa(1,1)/beta,CNab/beta,CNa(1,3)/beta,CNaf];
%CP8(i) = sum(CNa(i,:).*CPi(1,:))/sum(CNa(i,:));
% CPi(i,:) = CPi(1,:)/beta;
if mach(i)>0.5
CPi(i,4) = CPi(1,4)+(CPiFM2-CPiFM0)/(2-0.5)*(mach(i)-0.5);
else
CPi(i,4) = CPi(1,4);
end
CPi(i,1:3) = CPi(1,1:3);
% CPi(i,:) = CPi(1,:);
% CP8(i) = sum(abs(CNa(i,:)).*CPi(i,:))/sum(abs(CNa(i,:))); % Why abs?
CP8(i) = sum(CNa(i,:).*CPi(i,:))/sum(CNa(i,:))*Ecp;
% CP(i) = CP8(i);
% CPb(i) = sum(CNa(i,1:3).*CPi(i,1:3))/sum(CNa(i,1:3));
% CP8(i) = CP8(i)+sin(abs(aoa(i)))*(CPcut-CP(i));
%CP8(i) = CP8(i)/beta;
if CP8(i)>Rl
CP8(i)=Rl;
elseif CP8(i)<0
CP8(i)=0;
end
if t>tb
Tt(i) = 0;
end
if i==2
% Tt(i) = 2*max(Tt);
end
if t<=tb
% tA(1:3,i) = [cos(tma(2)),0,sin(tma(2));0,1,0;-sin(tma(2)),0,cos(tma(2))]*...
% [1,0,0;0,cos(tma(1)),-sin(tma(1));0,sin(tma(1)),cos(tma(1))]*rA(:,i);
tAe(1:3,i) = rA(:,i)*cos(tma(1))+pA(:,i)*(dot(pA(:,i),rA(:,i)))*(1-cos(tma(1)))+...
cross(rA(:,i),pA(:,i))*sin(tma(1));
tA(1:3,i) = tAe(:,i)*cos(tma(2))+yA(:,i)*(dot(yA(:,i),tAe(:,i)))*(1-cos(tma(2)))+...
cross(tAe(:,i),yA(:,i))*sin(tma(2));
% tA(2,i) = -tA(2,i);
% tA(3,i) = sqrt(1-tA(2,i)^2-tA(1,i)^2);
% T(i,:) = (Tt(i) + (P(1)-P(i))*(pi*(dnoz/2/12)^2))*transpose(rA(:,i));
% T(i,:) = (Tt(i) + (P(1)-P(i))*(pi*(dnoz/2/12)^2))*sqrt(1-tA(2,i)^2-tA(1,i)^2)*...
% transpose(tA(:,i));
T(i,:) = (Tt(i) + (P(1)-P(i))*(pi*(dnoz/2/12)^2))*transpose(tA(:,i));
% yoyo = [cos(tma(2)),-sin(tma(2)),0;sin(tma(2)),cos(tma(2)),0;0,0,1]*...
% %[cos(tma(1)),0,sin(tma(1));0,1,0;-sin(tma(1)),0,cos(tma(1))]*...
% [1,0,0;0,cos(tma(1)),-sin(tma(1));0,sin(tma(1)),cos(tma(1))];
end
% Tx(i) = -Tt(i)*sin(p(i));
% Tz(i) = Tt(i)*cos(p(i));
Tr(i,1:3) = cross(rA(:,i),cross(rA(:,i),T(i,:)));
Tr(i,1) = -Tr(i,1);
% Tr(i,1:2) = -Tr(i,1:2);
% T(i,:) = T(i,:)+Tr(i,:);
% wfr(i) = norm(T(i,:))/Isp;
if t>=tb
w(i) = dw;
Tt(i) = 0;
end
wfr(i) = Tt(i)/Isp;
w(i+1) = w(i) - wfr(i)*dt;
wfrf(i) = wfr(i)/(OF+1);
wf(i+1) = wf(i) - wfrf(i)*dt;
wfro(i) = wfrf(i)*OF;
wo(i+1) = wo(i) - wfro(i)*dt;
lf(i+1) = (wf(i+1)/g)/(pi*rtank^2*df);
lo(i+1) = (wo(i+1)/g)/(pi*rtank^2*dox);
xfuel = xfuel0 + lfi - lf(i);
xox = xox0 + loi - lo(i);
cgf(i+1) = xfuel + lf(i)/2;
cgo(i+1) = xox + lo(i)/2;
if t<tb
cg(i) = (cgd*dw + cgf(i)*wf(i) + cgo(i)*wo(i))/(w(i))*Ecg;
else
cg(i) = cgd*Ecg;
cg(i+1) = cgd*Ecg; %To cover blind spots
end
if v(i,3) >=0 && dist(i)>RL
stab(i) = (CP8(i)-cg(i))/(d/12);
end
vrwi(i,:) = vrw(i,:);
if norm(omega(i,:)) == 0
vrot(i,:) = [0,0,0];
else
vrot(i,:) = abs(CP8(i)-cg(i))*sin(acos(dot(rA(:,i),omega(i,:)/...
norm(omega(i,:)))))*transpose(cross(rA(:,i),omega(i,:)))/...
norm(cross(rA(:,i),omega(i,:)/norm(omega(i,:))));
end
vrw(i,:) = vrw(i,:)+vrot(i,:);
aoa(i) = acos(dot((vrw(i,:)/norm(vrw(i,:))),rA(:,i)));
if v(i,3)<0
aoa(i) = 0;
end
vhat(i,:) = vrw(i,:)/norm(vrw(i,:));
% if norm(omega(i,:)) == 0
% vrotb(i,:) = [0,0,0];
% vrotf(i,:) = [0,0,0];
% else
vrotb(i,:) = vrw(i,:)+vrot(i,:)/abs(CP8(i)-cg(i))*(cgi(2)-cg(i));
vrotf(i,:) = vrw(i,:)+vrot(i,:)/abs(CP8(i)-cg(i))*(cgi(4)-cg(i));
% end
% vrot(i,:) = (cgi(:)-cg(i))*omega(i);
% vrotx(i,:) = vrot(i,:)*cos(p(i));
% vrotz(i,:) = vrot(i,:)*sin(p(i));
% vrwrot(i,:) = ((vrotx(i,:)+vrw(i,1)).^2+(vrotz(i,:)+vrw(i,2)).^2).^0.5;
mach(i) = norm(vrw(i,:))/vs(i);
j(i) = mach(i)*100;
% if mach(i) == 0
% cd(i) = cdv(1);
% else
% cd(i) = cdv(floor(j(i)));
% end
temp(i) = temp(i)+459.67;
mu(i) = mu0*((temp0+198.72)/(temp(i)+198.72))*(temp(i)/temp0)^1.5;
Rnc(i,1) = rho(i)*norm(vrotb(i,:))*Lc(1)/mu(i)*(1+0.0283*mach(i)-0.043*mach(i)^2+...
0.2107*mach(i)^3-0.03829*mach(i)^4+0.002709*mach(i)^5);
Rnc(i,2) = rho(i)*norm(vrotf(i,:))*Lc(2)/mu(i)*(1+0.0283*mach(i)-0.043*mach(i)^2+...
0.2107*mach(i)^3-0.03829*mach(i)^4+0.002709*mach(i)^5);
Rnc(i,3) = rho(i)*norm(vrw(i,:))*Lc(3)/mu(i)*(1+0.0283*mach(i)-0.043*mach(i)^2+...
0.2107*mach(i)^3-0.03829*mach(i)^4+0.002709*mach(i)^5);
Rnc(i,4) = rho(i)*norm(vrw(i,:))*Lc(4)/mu(i)*(1+0.0283*mach(i)-0.043*mach(i)^2+...
0.2107*mach(i)^3-0.03829*mach(i)^4+0.002709*mach(i)^5);
% B(i,1) = Rec*(0.074./Re(i,1)^.2-1.328/sqrt(Re(i,1)));
% B(i,2) = Rec*(0.074./Re(i,2)^.2-1.328/sqrt(Re(i,2)));
% for j = 1:2
% if Rnc(i,j)<=Rec
% Cf(i,j) = 1.328/sqrt(Rnc(i,j));
% else
% Cf(i,j) = 0.074/Rnc(i,j)^.2 - B(i,j)/Rnc(i,j);
% end
% end
Cfi(i,:) = 0.037036*Rnc(i,:).^(-0.155079);
Cf(i,:) = Cfi(i,:)*(1+0.00798*mach(i)-0.1813*mach(i)^2+0.0632*mach(i)^3-...
0.00933*mach(i)^4+0.000549*mach(i)^5);
CfiT(i,:) = (1.89+1.62*log10(Lc(:)/0.00025)).^(-2.5);
CfT(i,:) = CfiT(i,:)/(1+0.2044*mach(i)^2);
if Cf(i,1)<=CfT(i,1)
Cf(i,1) = CfT(i,1);
end
if Cf(i,2)<=CfT(i,2)
Cf(i,2) = CfT(i,2);
end
if Cf(i,3)<=CfT(i,3)
Cf(i,3) = CfT(i,3);
end
if Cf(i,4)<=CfT(i,4)
Cf(i,4) = CfT(i,4);
end
SB = pi*(d/12)*Rl*0.8;
CDfb(i) = Cf(i,1)*(1+60/(Lc(1)/(d/12))^3+0.0025*Lc(1)/(d/12))*4*SB/pi/(d/12)^2;
Rn(i) = rho(i)*norm(vrotf(i,:))*Lc(2)/mu(i);
Cfg(i) = Cf(i,2)*(log10(Rn(i)))^2.6/(tr^2-1)*(tr^2*(log10(Rn(i)*tr))^(-2.6)-...
(log10(Rn(i)))^(-2.6)+0.5646*(tr^2*(log10(Rn(i)*tr))^(-3.6)-...
(log10(Rn(i)))^(-3.6)));
CDff(i) = Cfg(i)*(1+60*(Tf/Cr)^4+0.8*(1+5*(Cr*0.3/Cr)^2)*(Tf/Cr))*4*n*Afe2/pi/(d/12)^2;
X = (mach(i)-machD)/(machF-machD);
f(i) = -8.3474*X^5+24.543*X^4-24.946*X^3+8.6321*X^2+1.1195*X;
if mach(i)<=machF && mach(i)>=machD
CDt(i) = dCDmax*f(i);
CDs(i) = 0;
dCDpro(i) = 0.01*f(i);
elseif mach(i) > machF
CDt(i) = 0;
% CDs(i) = dCDmax;
CDs(i) = dCDmax-0.1*abs(machF-mach(i));
dCDpro(i) = 0.01;
else
CDt(i) = 0;
CDs(i) = 0;
dCDpro(i) = 0;
end
Cfpro(i) = 0.8151*Cf(i,3)*((aPro/12)/Lc(3))^(-0.1243);
if Apro > 0
CDfpro(i) = Cfpro(i)*(1+1.798*(sqrt(Apro)/Lc(3))^1.5)*4*Spro/pi/(d/12)^2;
CDfpro(i) = CDfpro(i)+dCDpro(i);
else
CDfpro(i) = 0;
end
%CDfpro(i) = 0;
Cfll(i) = 0.8151*Cf(i,4)*((aLL/12)/Lll)^(-0.1243);
CDll(i) = Cfll(i)*(1+1.798*(sqrt(All)/Lc(4))^1.5)*4*Sll/pi/(d/12)^2;
CDll(i) = CDll(i)+dCDpro(i);
if mach(i)<0.78
Ke(i) = 0.00038;
elseif mach(i)>=0.78 && mach(i)<=1.04
Ke(i) = -0.4501*mach(i)^4+1.5954*mach(i)^3-2.1062*mach(i)^2+1.2288*mach(i)-0.26717;
elseif mach(i)>1.04
Ke(i) = 0.0002*mach(i)^2-0.0012*mach(i)+0.0018;
else
% error('mach number fail');
end
CDfe(i) = Ke(i)*4*((SB+Afe2)+4*S*(Cr+Ct))/pi/(d/12)^2;
CDfe(i) = 0;
% CDfe(i) = 0.5*CDfe(i);
CDf(i) = CDfb(i)+1.04*CDff(i)+1.04*CDfpro(i)+CDfe(i)+1.04*CDll(i);
% CDf(i) = CDf(i)/beta;
if mach(i) <= 0.6 && t<tb
CDf6 = CDfb(i)+1.04*CDff(i)+1.04*CDfpro(i)+CDfe(i)+1.04*CDll(i);
CDb6 = Kb*((dr/(d/12))^nb)/sqrt(CDf6);
end
if mach(i)<=0.6
CDb(i) = Kb*((dr/(d/12))^nb)/sqrt(CDf(i));
elseif mach(i)>0.6
if mach(i)<=1
fb(i) = 1+215.8*(mach(i)-0.6)^6;
elseif mach(i)<=2
fb(i) = 2.0881*(mach(i)-1)^3-3.7938*(mach(i)-1)^2+1.4618*(mach(i)-1)+1.883917;
elseif mach(i)>2
fb(i) = 0.297*(mach(i)-1)^3-0.7937*(mach(i)-1)^2-0.1115*(mach(i)-1)+1.64006;
end
CDb(i) = CDb6*fb(i);
end
if t<=tb
% CDb(i) = CDb(i)*0.8;
% CDb(i) = 0;
end