Utilizing the Euler Method

Hi. First of all sorry for asking a huge question.I need a guide to utilize the Euler Method. I am having troubles with the sizes of variables.

This code tries to solve 6 ODEs with 6 state variables [horizontal position (x1 and x2), altitude (x3), the true airspeed (x4), the heading angle (x5) and the mass of the aircraft (x6)] and 3 control inputs [engine thrust (u1), the bank angle (u2) and the flight path angle (u3)] by using Euler's method. Different flight maneuvers are performed for the specified time intervals.

Velocities.m, Cruise_Vel.m, Des_Vel.m, Thr_cl.m, Thr_cr.m, Thr_des.m, fuel_cl.m, fuel_cr.m, fuel_des.m,den.m,drag.m,drag_cr.m,lift.m,lift_cr.m are functions in seperate tabs. Code in the main file (Flight.m) is:

% Climb from h1=1100 [m] to h2=1600 [m] with α=5 flight path angle.
% Perform cruise flight for t=60 minutes.
% Turn with β=30 bank angle until heading is changed by η=270◦.
% Descent from h2=1600 [m] to h1=1100 [m] with ζ=4◦ flight path angle.
% Complete a 360◦ turn (loiter) at level flight.
% Descent to h3=800 [m] with κ=4.5◦ flight path angle.

% Aircraft Properties

W = .44225E+06;                             % .44225E+03 tons = .44225E+06 kg 
S = .51097E+03;                             % Surface Area [m^2]
g0 = 9.80665;                               % Gravitational acceleration [m/s2]

% solving 1st order ODE using numerical methods 

t0=0;           
tend=3960;
h=0.05; 
N=(tend-t0)/h;
t=t0:h:tend; 

x = zeros(6,length(t));

% Initial conditions

x(:,1)=[0;0;3608.92;1.0e+02 * 1.161544478045788;0;W];



for i=2:length(t)
      
if and (t(i-1) > 0,t(i-1)<=60) % Climb from h1=1100 [m] to h2=1600 [m] with α=5 flight path angle.
   x3 = 3608.9:5249.3;                               % Changing altitude [m] -> [ft]
   x4 = Velocities(3608.9,5249.3);                   % Changing speed [m/s]
   x5 = 0;                                           % Changing head angle [deg]
   f = fuel_cl(3608.9,5249.3);                       % Changing fuel flow [kg/min] 
   
   u1 = Thr_cl(3608.9,5249.3);                       % Changing thrust [N]
   u2 = 0;                                           % Changing bank angle [deg]
   u3 = 5;                                           % Changing flight path angle [deg]
   V_ver = x4*sin(u3);                               % Changing vertical speed [m/s]
   C_D = drag(3608.9,5249.3,x4);                     % Changing drag coefficient
   Cl = lift(3608.9,5249.3,x4);                      % Changing lift coefficient
   p = den(3608.9,5249.3);                           % Changing density [kg/m3]                              


elseif and (t(i-1) >60,t(i-1)<=3660) % Perform cruise flight for t=60 minutes.
   x3 = 5249.3;                                      % Changing altitude [m] -> [ft]
   x4 = Cruise_Vel(5249.3);                          % Changing speed [m/s]
   x5 = 0;                                           % Changing head angle [deg]
   f = fuel_cr(5249.3);                              % Changing fuel flow [kg/min] 
   
   u1 = Thr_cr(5249.3);                              % Changing thrust [N]
   u2 = 0;                                           % Changing bank angle [deg]
   u3 = 0;                                           % Changing flight path angle [deg]
   V_ver = x4*sin(u3);                               % Changing vertical speed [m/s]
   C_D = drag_cr(5249.3,5249.3,x4);                  % Changing drag coefficient
   Cl = lift_cr(5249.3,5249.3,x4);                   % Changing lift coefficient
   p = den(5249.3,5249.3);                           % Changing density [kg/m3]


elseif and (t (i-1)>3660,t(i-1)<=3720) % Turn with β=30 bank angle until heading is changed by η=270◦.
   x3 = 5249.3;                                      % Changing altitude [m] -> [ft]
   x4 = Cruise_Vel(5249.3);                          % Changing speed [m/s]
   x5 = 0:30:270;                                    % Changing head angle [deg]
   f = fuel_cr(5249.3);                              % Changing fuel flow [kg/min] 
   
   u1 = Thr_cr(5249.3);                              % Changing thrust [N]
   u2 = 30;                                          % Changing bank angle [deg]
   u3 = 0;                                           % Changing flight path angle [deg]
   V_ver = x4*sin(u3);                               % Changing vertical speed [m/s]
   C_D = drag_cr(5249.3,5249.3,x4);                  % Changing drag coefficient
   Cl = lift_cr(5249.3,5249.3,x4);                   % Changing lift coefficient
   p = den(5249.3,5249.3);                           % Changing density [kg/m3]

elseif and (t(i-1) >3720,t(i-1)<=3780) % Descent from h2=1600 [m] to h1=1100 [m] with ζ=4◦ flight path angle.
   x3 = 5249.3:3608.9;                               % Changing altitude [m] -> [ft]
   x4 = Des_Vel(5249.3,3608.9);                      % Changing speed [m/s]
   x5 = 270;                                         % Changing head angle [deg]
   f = fuel_des(5249.3,3608.9);                      % Changing fuel flow [kg/min] 
   
   u1 = Thr_des(5249.3,3608.9);                      % Changing thrust [N]
   u2 = 0;                                           % Changing bank angle [deg]
   u3 = 4;                                           % Changing flight path angle [deg]
   V_ver = x4*sin(u3);                               % Changing vertical speed [m/s]
   C_D = drag(5249.3,3608.9,x4);                     % Changing drag coefficient
   Cl = lift(5249.3,3608.9,x4);                      % Changing lift coefficient
   p = den(5249.3,3608.9);                           % Changing density [kg/m3]


elseif and (t (i-1)>3780,t(i-1)<=3900) % Complete a 360◦ turn (loiter) at level flight.
   x3 = 3608.9;                                      % Changing altitude [m] -> [ft]
   x4 = Cruise_Vel(3608.9);                          % Changing speed [m/s]
   lon = [270 300 360 60 120 180 240 270];
   x5 = wrapTo360(lon);                              % Changing head angle [deg]
   f = fuel_cr(3608.9);                              % Changing fuel flow [kg/min] 
   
   u1 = Thr_cr(3608.9);                              % Changing thrust [N] 
   u2 = 0;                                           % Changing bank angle [deg]
   u3 = 0;                                           % Changing flight path angle [deg]
   V_ver = x4*sin(u3);                               % Changing vertical speed [m/s]
   C_D = drag_cr(3608.9,3608.9,x4);                  % Changing drag coefficient
   Cl = lift_cr(3608.9,3608.9,x4);                   % Changing lift coefficient
   p = den(3608.9,3608.9);                           % Changing density [kg/m3]


elseif and (t(i-1) >3900,t(i-1)<=3960) % Descent to h3=800 [m] with κ=4.5◦ flight path angle.
   x3 = 3608.9:2624.67;                              % Changing altitude [m] -> [ft]
   x4 = Des_Vel(3608.9,2624.67);                     % Changing speed [m/s] 
   x5 = 270;                                         % Changing head angle [deg]
   f = fuel_des(3608.9,2624.67);                     % Changing fuel flow [kg/min] 
   
   u1 = Thr_des(3608.9,2624.67);                     % Changing thrust [N] 
   u2 = 0;                                           % Changing bank angle [deg]
   u3 = 4.5;                                         % Changing flight path angle [deg]
   V_ver = x4*sin(u3);                               % Changing vertical speed [m/s]
   C_D = drag(3608.9,2624.67,x4);                    % Changing drag coefficient
   Cl = lift(3608.9,2624.67,x4);                     % Changing lift coefficient
   p = den(3608.9,2624.67);                          % Changing density [kg/m3]
end

dx1dt = x4 .* cos(x5) .* cos(u3);       
dx2dt = x4 .* sin(x5) .* cos(u3);       
dx3dt = x4 .* sin(u3);               
dx4dt = -C_D.*S.*p.*(x4.^2)./(2.*x6)-g0.*sin(u3)+u1./x6; 
dx5dt = -Cl.*S.*p.*x4./(2.*x6).*sin(u2);
dx6dt = -f;

x(1,i)= x(1,i-1) + h * dx1dt;                         % line 129 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
x(2,i)= x(2,i-1) + h * dx2dt;
x(3,i)= x(3,i-1) + h * dx3dt;
x(4,i)= x(4,i-1) + h * dx4dt;
x(5,i)= x(5,i-1) + h * dx5dt;
x(6,i)= x(6,i-1) + h * dx6dt;
end

tot=cell2mat(f);                % Total fuel consumption during mission [kg/min]
Tot_fuel=sum(tot);

figure(1)
plot3(x1(:),x2(:),x3(:));       % 3D position graph

figure(2)
plot(t,x4(:));                  % Vtas − Time graph

figure(3)
plot(t,V_ver(:));               % V_vertical − Time graph

figure(4)
plot(t,x5(:));                  % Heading − Time graph

figure(5)
plot(t,x6(:));                  % Mass − Time graph

figure(6)
plot(t,u1(:));                  % Thrust − Time graph

figure(7)
plot(t,u2(:));                  % Bank Angle − Time graph

figure(8)
plot(t,u3(:));                  % Flight Path Angle − Time graph

fprintf('Total fuel consumption during mission is %.2f [kg]',Tot_fuel*tend/60);

Aforementioned functions in seperate tabs gets altitude interval as input and outputs the answer. Here is some of them:

function [Vtas_cl] = Velocities(H1,H2)

Vcl_1 = 335;             % Standard calibrated airspeed [kt]
Vcl_2 = 172.3;           % Standard calibrated airspeed [kt] -> [m/s] (To find the  Mach transition altitude)
Vcl_2_in_knots = 335;    % Standard calibrated airspeed [kt] (To find the result in knots, if altitude is between 10,000 ft and Mach transition altitude)
M_cl  = 0.86;            % Standard calibrated airspeed [kt]

K = 1.4;                 % Adiabatic index of air
R = 287.05287;           % Real gas constant for air [m2/(K·s2)]
Bt = - 0.0065;           % ISA temperature gradient with altitude below the tropopause [K/m]
T0 = 288.15;             % Standard atmospheric temperature at MSL [K]
g0 = 9.80665;            % Gravitational acceleration [m/s2]
a0= 340.294;             % Speed of Sound [m/s]

Vd_CL1 = 5;              % Climb speed increment below 1500 ft (jet)
Vd_CL2 = 10;             % Climb speed increment below 3000 ft (jet)
Vd_CL3 = 30;             % Climb speed increment below 4000 ft (jet)
Vd_CL4 = 60;             % Climb speed increment below 5000 ft (jet)
Vd_CL5 = 80;             % Climb speed increment below 6000 ft (jet)

CV_min = 1.3;            % Minimum speed coefficient 
Vstall_TO = .14200E+03;  % Stall speed at take-off [KCAS]

CAS_climb  = Vcl_2;   
Mach_climb = M_cl;
delta_trans = (((1+((K-1)/2)*(CAS_climb/a0)^2)^(K/(K-1)))-1)/(((1+(K-1)/2*Mach_climb^2)^(K/(K-1)))-1);    % Pressure ratio at the transition altitude

teta_trans = delta_trans ^ (-Bt*R/g0);      % Temperature ratio at the transition altitude

H_p_trans_climb = (1000/0.348/6.5)*(T0*(1-teta_trans));   %  Transition altitude for climb [ft]

H_climb = H1:H2;
for k1 = 1:length(H_climb)
    
    if (0<=H_climb(k1)&&H_climb(k1)<1500)
Vnom_climb_jet(k1) = CV_min * Vstall_TO + Vd_CL1;

elseif (1500<=H_climb(k1)&&H_climb(k1)<3000)
        Vnom_climb_jet(k1) = CV_min * Vstall_TO + Vd_CL2;
        
elseif (3000<=H_climb(k1)&&H_climb(k1)<4000)
        Vnom_climb_jet (k1)= CV_min * Vstall_TO + Vd_CL3; 
        
elseif (4000<=H_climb(k1)&&H_climb(k1)<5000)
        Vnom_climb_jet (k1)= CV_min * Vstall_TO + Vd_CL4;
        
elseif (5000<=H_climb(k1)&&H_climb(k1)<6000)
        Vnom_climb_jet(k1) = CV_min * Vstall_TO + Vd_CL5;
        
elseif (6000<=H_climb(k1)&&H_climb(k1)<10000)
        Vnom_climb_jet (k1)= min(Vcl_1,250);
        
elseif (10000<=H_climb(k1)&&H_climb(k1)<=H_p_trans_climb)
        Vnom_climb_jet(k1) = Vcl_2_in_knots;
        
elseif (H_p_trans_climb<H_climb(k1))
        Vnom_climb_jet(k1) = M_cl;
    end

Vcas_cl(k1) = Vnom_climb_jet(k1)* 0.514;   % [kn] -> [m/s]


H_climb (k1)= H_climb(k1) * 0.3048;         % [feet] -> [m]
K = 1.4;                                    % Adiabatic index of air
R = 287.05287;                              % Real gas constant for air [m2/(K·s2)]
Bt = - 0.0065;                              % ISA temperature gradient with altitude below the tropopause [K/m]
deltaT = 0;                                 % Value of the real temperature T in ISA conditions [K]
T0 = 288.15;                                % Standard atmospheric temperature at MSL [K]
P0 = 101325;                                % Standard atmospheric pressure at MSL [Pa]
g0 = 9.80665;                               % Gravitational acceleration [m/s2]
p0 = 1.225;                                 % Standard atmospheric density at MSL [kg/m3]
visc = (K-1)./K;

T(k1) = T0 + deltaT + Bt * H_climb(k1);         % Temperature [K]
P (k1)= P0*((T(k1)-deltaT)/T0).^((-g0)/(Bt*R));     % Pressure [Pa]
p (k1)= P(k1) ./ (R*T(k1));                             % Density [kg/m^3]
Vtas_cl(k1) = (2*P(k1)/visc/p(k1)*((1 + P0/P(k1)*((1 + visc*p0*Vcas_cl(k1)*Vcas_cl(k1)/2/P0).^(1/visc)-1)).^(visc)-1)).^(1/2); % True Air Speed [m/s]
end

end

Another one:

function [Thr_jet_climb_ISA] = Thr_cl(H1,H2)

H_climb = H1:H2;               % Climb altitude range [m] -> [ft]
for k3 = 1:length(H_climb)
C_Tc_1 = .75979E+06;
C_Tc_2 = .52423E+05;
C_Tc_3 = .40968E-10;

Thr_jet_climb_ISA(k3) = C_Tc_1* (1-(H_climb(k3)/C_Tc_2)+C_Tc_3*H_climb(k3).^2);     % Maximum climb and take-off thrust for jet engine [N] 
end
end

And the ones with the single altitude input:

function [Vtas_cr] = Cruise_Vel(H_cruise)  
Vcr_1 = 320;             % Standard calibrated airspeed [kt]
Vcr_2 = 164.62;          % Standard calibrated airspeed [kt] -> [m/s] (To find the  Mach transition altitude)
Vcr_2_in_knots = 320;    % Standard calibrated airspeed [kt] (To find the result in knots, if altitude is between 10,000 ft and Mach transition altitude)
M_cr  = 0.84;            % Standard calibrated airspeed [kt]

K = 1.4;                 % Adiabatic index of air
R = 287.05287;           % Real gas constant for air [m2/(K·s2)]
Bt = - 0.0065;           % ISA temperature gradient with altitude below the tropopause [K/m]
T0 = 288.15;             % Standard atmospheric temperature at MSL [K]
g0 = 9.80665;            % Gravitational acceleration [m/s2]
a0= 340.294;             % Speed of Sound [m/s]
deltaT = 0;                                 % Value of the real temperature T in ISA conditions [K]
T0 = 288.15;                                % Standard atmospheric temperature at MSL [K]
P0 = 101325;                                % Standard atmospheric pressure at MSL [Pa]
g0 = 9.80665;                               % Gravitational acceleration [m/s2]
p0 = 1.225;                                 % Standard atmospheric density at MSL [kg/m3]
visc = (K-1)./K;

CAS_cruise  = Vcr_2;   
Mach_cruise = M_cr;
delta_trans = (((1+((K-1)/2)*(CAS_cruise/a0)^2)^(K/(K-1)))-1)/(((1+(K-1)/2*Mach_cruise^2)^(K/(K-1)))-1);    % Pressure ratio at the transition altitude

teta_trans = delta_trans ^ (-Bt*R/g0);      % Temperature ratio at the transition altitude

H_p_trans_cruise = (1000/0.348/6.5)*(T0*(1-teta_trans));   %  Transition altitude for cruise [ft]
                         

if (0<=H_cruise&&H_cruise<=2999)
Vnom_cruise_jet = min(Vcr_1,170);

elseif (3000<=H_cruise&&H_cruise<=5999)
        Vnom_cruise_jet = min(Vcr_1,220);
        
elseif (6000<=H_cruise&&H_cruise<=13999)
        Vnom_cruise_jet = min(Vcr_1,250);
        
elseif (14000<=H_cruise&&H_cruise<=H_p_trans_cruise)
        Vnom_cruise_jet = Vcr_2_in_knots;
 
elseif (H_p_trans_cruise < H_cruise)
        Vnom_cruise_jet = M_cr;
end

Vcas_cr = Vnom_cruise_jet * 0.514;          % [knots] -> [m/s]

H_cruise = H_cruise * 0.3048;               % [feet] -> [m]

T = T0 + deltaT + Bt * H_cruise;            % Temperature [K]
P = P0*((T-deltaT)/T0).^((-g0)/(Bt*R));     % Pressure [Pa]
p = P ./ (R*T);                             % Density [kg/m^3]
Vtas_cr = (2*P/visc/p*((1 + P0/P*((1 + visc*p0*Vcas_cr*Vcas_cr/2/P0).^(1/visc)-1)).^(visc)-1)).^(1/2); % True Air Speed [m/s]
end

Another single-input function:

function [Thr_cra] = Thr_cr(H_cruise)

W = .44225E+06;                             % .44225E+03 tons = .44225E+06 kg 
S = .51097E+03;                             % Surface Area [m^2]

Vcr_1 = 320;             % Standard calibrated airspeed [kt]
Vcr_2 = 164.62;          % Standard calibrated airspeed [kt] -> [m/s] (To find the  Mach transition altitude)
Vcr_2_in_knots = 320;    % Standard calibrated airspeed [kt] (To find the result in knots, if altitude is between 10,000 ft and Mach transition altitude)
M_cr  = 0.84;            % Standard calibrated airspeed [kt]

K = 1.4;                 % Adiabatic index of air
R = 287.05287;           % Real gas constant for air [m2/(K·s2)]
Bt = - 0.0065;           % ISA temperature gradient with altitude below the tropopause [K/m]
T0 = 288.15;             % Standard atmospheric temperature at MSL [K]
g0 = 9.80665;            % Gravitational acceleration [m/s2]
a0= 340.294;             % Speed of Sound [m/s]
deltaT = 0;                                 % Value of the real temperature T in ISA conditions [K]
T0 = 288.15;                                % Standard atmospheric temperature at MSL [K]
P0 = 101325;                                % Standard atmospheric pressure at MSL [Pa]
g0 = 9.80665;                               % Gravitational acceleration [m/s2]
p0 = 1.225;                                 % Standard atmospheric density at MSL [kg/m3]
visc = (K-1)./K;

CAS_cruise  = Vcr_2;   
Mach_cruise = M_cr;
delta_trans = (((1+((K-1)/2)*(CAS_cruise/a0)^2)^(K/(K-1)))-1)/(((1+(K-1)/2*Mach_cruise^2)^(K/(K-1)))-1);    % Pressure ratio at the transition altitude

teta_trans = delta_trans ^ (-Bt*R/g0);      % Temperature ratio at the transition altitude

H_p_trans_cruise = (1000/0.348/6.5)*(T0*(1-teta_trans));   %  Transition altitude for cruise [ft]
                         

if (0<=H_cruise&&H_cruise<=2999)
Vnom_cruise_jet = min(Vcr_1,170);

elseif (3000<=H_cruise&&H_cruise<=5999)
        Vnom_cruise_jet = min(Vcr_1,220);
        
elseif (6000<=H_cruise&&H_cruise<=13999)
        Vnom_cruise_jet = min(Vcr_1,250);
        
elseif (14000<=H_cruise&&H_cruise<=H_p_trans_cruise)
        Vnom_cruise_jet = Vcr_2_in_knots;
 
elseif (H_p_trans_cruise < H_cruise)
        Vnom_cruise_jet = M_cr;
end

Vcas_cr = Vnom_cruise_jet * 0.514;          % [knots] -> [m/s]

H_cruise = H_cruise * 0.3048;               % [feet] -> [m]

T = T0 + deltaT + Bt * H_cruise;            % Temperature [K]
P = P0*((T-deltaT)/T0).^((-g0)/(Bt*R));     % Pressure [Pa]
p = P ./ (R*T);                             % Density [kg/m^3]
Vtas_cr = (2*P/visc/p*((1 + P0/P*((1 + visc*p0*Vcas_cr*Vcas_cr/2/P0).^(1/visc)-1)).^(visc)-1)).^(1/2); % True Air Speed [m/s]

Cl = 2*W / (p*Vtas_cr*Vtas_cr*S);                 % Lift coefficient
C_D0cr = .25669E-01;
C_D2cr = .39082E-01;
C_D = C_D0cr + C_D2cr * (Cl).^2;                  % Drag Coefficient
D = 1/2 * p * Vtas_cr* Vtas_cr * S * C_D;         % Drag Force [N]

Thr_cra = D;                                      % Cruise drag (Thrust) [N]
end

The rest is like the above ones, they get either one or two altitude inputs.

When I run the code, this error message displays:

>> Flight
Unable to perform assignment because the size of the left side is 1-by-1 and the size of the right side is 1-by-1641.

Error in Flight (line 129)
x(1,i)= x(1,i-1) + h * dx1dt;

The reason why it says right side is 1-by-1641 is because in the first if-else, x4 is defined as:

x4 = Velocities(3608.9,5249.3);                   % Changing speed [m/s]

A guide on what to do would be really helpful to me. If you want to analyse the code: https://drive.google.com/drive/folders/1RtM_XMuhQs2voZFXOnoFAgtkxMI3nKFt?usp=sharing

Thanks.

[Stephen23]

@Turgut Ataseven: so much code makes your question very hard to follow and understand.

Rather than showing all code in the question, consider uploading it by clicking the paperclip button.

Answer 1

[Torsten]

In the if-statement in Flight.m, set x3 to x(3,i-1) and calculate the other variables x4,x5,f,u1,u2,u3,V_ver,C_D,Cl and p only for this single value, not for the complete range (mostly 3608.9:5249.3).

[Turgut Ataseven]

Nice approach. Here is what I did.

x = zeros(6,length(t));
x1 = zeros(1,length(t));
x2 = zeros(1,length(t));
x3 = zeros(1,length(t));
x4 = zeros(1,length(t));
x5 = zeros(1,length(t));
x6 = zeros(1,length(t));
u1 = zeros(1,length(t));
u2 = zeros(1,length(t));
u3 = zeros(1,length(t));
C_D= zeros(1,length(t));
p = zeros(1,length(t));
Cl = zeros(1,length(t));
f = zeros(1,length(t));
% Initial conditions

x(:,1)=[0;0;3608.92;1.0e+02 * 1.161544478045788;0;W];



for i=2:length(t)
      
if and (x(3,i-1) > 3608.92,x(3,i-1)<=5249.3)         % Climb from h1=1100 [m] to h2=1600 [m] with α=5 flight path angle.
   t =0:60;
   x4 = Velocities(3608.9,5249.3);                   % Changing speed [m/s]
   x5 = 0;                                           % Changing head angle [deg]
   f = fuel_cl(3608.9,5249.3);                       % Changing fuel flow [kg/min] 
   
   u1 = Thr_cl(3608.9,5249.3);                       % Changing thrust [N]
   u2 = 0;                                           % Changing bank angle [deg]
   u3 = 5;                                           % Changing flight path angle [deg]
   V_ver = x4*sin(u3);                               % Changing vertical speed [m/s]
   C_D = drag(3608.9,5249.3,x4);                     % Changing drag coefficient
   Cl = lift(3608.9,5249.3,x4);                      % Changing lift coefficient
   p = den(3608.9,5249.3);                           % Changing density [kg/m3]                              


elseif and (x(3,i-1) > 5249.3,x(3,i-1)<=5249.3) % Perform cruise flight for t=60 minutes.
   for t=60:3660
   
   x4 = Cruise_Vel(5249.3);                          % Changing speed [m/s]
   x5 = 0;                                           % Changing head angle [deg]
   f = fuel_cr(5249.3);                              % Changing fuel flow [kg/min] 
   
   u1 = Thr_cr(5249.3);                              % Changing thrust [N]
   u2 = 0;                                           % Changing bank angle [deg]
   u3 = 0;                                           % Changing flight path angle [deg]
   V_ver = x4*sin(u3);                               % Changing vertical speed [m/s]
   C_D = drag_cr(5249.3,5249.3,x4);                  % Changing drag coefficient
   Cl = lift_cr(5249.3,5249.3,x4);                   % Changing lift coefficient
   p = den(5249.3,5249.3);                           % Changing density [kg/m3]
   end

    % Turn with β=30 bank angle until heading is changed by η=270◦.
   for t=3660:3720
   x4 = Cruise_Vel(5249.3);                          % Changing speed [m/s]
   x5 = 0:30:270;                                    % Changing head angle [deg]
   f = fuel_cr(5249.3);                              % Changing fuel flow [kg/min] 
   
   u1 = Thr_cr(5249.3);                              % Changing thrust [N]
   u2 = 30;                                          % Changing bank angle [deg]
   u3 = 0;                                           % Changing flight path angle [deg]
   V_ver = x4*sin(u3);                               % Changing vertical speed [m/s]
   C_D = drag_cr(5249.3,5249.3,x4);                  % Changing drag coefficient
   Cl = lift_cr(5249.3,5249.3,x4);                   % Changing lift coefficient
   p = den(5249.3,5249.3);                           % Changing density [kg/m3]
   end
elseif and (x(3,i-1) < 5249.3,x(3,i-1)>=3608.9) % Descent from h2=1600 [m] to h1=1100 [m] with ζ=4◦ flight path angle.
   t=3720:3780;
   
   x4 = Des_Vel(5249.3,3608.9);                      % Changing speed [m/s]
   x5 = 270;                                         % Changing head angle [deg]
   f = fuel_des(5249.3,3608.9);                      % Changing fuel flow [kg/min] 
   
   u1 = Thr_des(5249.3,3608.9);                      % Changing thrust [N]
   u2 = 0;                                           % Changing bank angle [deg]
   u3 = 4;                                           % Changing flight path angle [deg]
   V_ver = x4*sin(u3);                               % Changing vertical speed [m/s]
   C_D = drag_des(5249.3,3608.9,x4);                 % Changing drag coefficient
   Cl = lift_des(5249.3,3608.9,x4);                  % Changing lift coefficient
   p = den_des(5249.3,3608.9);                       % Changing density [kg/m3]


elseif and (x(3,i-1) < 3608.9,x(3,i-1)>=3608.9)      % Complete a 360◦ turn (loiter) at level flight.
   t = 3780:3900;
   
   x4 = Cruise_Vel(3608.9);                          % Changing speed [m/s]
   lon = [270 300 360 60 120 180 240 270];
   x5 = wrapTo360(lon);                              % Changing head angle [deg]
   f = fuel_cr(3608.9);                              % Changing fuel flow [kg/min] 
   
   u1 = Thr_cr(3608.9);                              % Changing thrust [N] 
   u2 = 0;                                           % Changing bank angle [deg]
   u3 = 0;                                           % Changing flight path angle [deg]
   V_ver = x4*sin(u3);                               % Changing vertical speed [m/s]
   C_D = drag_cr(3608.9,3608.9,x4);                  % Changing drag coefficient
   Cl = lift_cr(3608.9,3608.9,x4);                   % Changing lift coefficient
   p = den(3608.9,3608.9);                           % Changing density [kg/m3]


elseif and (x(3,i-1) < 3608.9,x(3,i-1)>=2624.67) % Descent to h3=800 [m] with κ=4.5◦ flight path angle.
   t=3900:3960;
   
   x4 = Des_Vel(3608.9,2624.67);                     % Changing speed [m/s] 
   x5 = 270;                                         % Changing head angle [deg]
   f = fuel_des(3608.9,2624.67);                     % Changing fuel flow [kg/min] 
   
   u1 = Thr_des(3608.9,2624.67);                     % Changing thrust [N] 
   u2 = 0;                                           % Changing bank angle [deg]
   u3 = 4.5;                                         % Changing flight path angle [deg]
   V_ver = x4*sin(u3);                               % Changing vertical speed [m/s]
   C_D = drag_des(3608.9,2624.67,x4);                % Changing drag coefficient
   Cl = lift_des(3608.9,2624.67,x4);                 % Changing lift coefficient
   p = den_des(3608.9,2624.67);                      % Changing density [kg/m3]
else
    fprintf("A problem occured.");
end

dx1dt = x4 .* cos(x5) .* cos(u3);       
dx2dt = x4 .* sin(x5) .* cos(u3);       
dx3dt = x4 .* sin(u3);               
dx4dt = -C_D.*S.*p.*(x4.^2)./(2.*x6)-g0.*sin(u3)+u1./x6; 
dx5dt = -Cl.*S.*p.*x4./(2.*x6).*sin(u2);
dx6dt = -f;

x(1,i)= x(1,i-1) + h * dx1dt;                         
x(2,i)= x(2,i-1) + h * dx2dt;
x(3,i)= x(3,i-1) + h * dx3dt;
x(4,i)= x(4,i-1) + h * dx4dt;
x(5,i)= x(5,i-1) + h * dx5dt;
x(6,i)= x(6,i-1) + h * dx6dt;
end

With these statements I've tried to state that altitude is constant. Is there a better way to do it?

elseif and (x(3,i-1) > 5249.3,x(3,i-1)<=5249.3) % Perform cruise flight for t=60 minutes.
    

and

    elseif and (x(3,i-1) < 3608.9,x(3,i-1)>=3608.9)      % Complete a 360◦ turn (loiter) at level flight.

Answer 2

[Burhan Burak AKMAN]

Change your code like this. May be work.

x(1,i)= x(1,i-1) + h * dx1dt(1,i-1);                         % line 129 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
x(2,i)= x(2,i-1) + h * dx2dt(1,i-1);
x(3,i)= x(3,i-1) + h * dx3dt(1,i-1);
x(4,i)= x(4,i-1) + h * dx4dt(1,i-1);
x(5,i)= x(5,i-1) + h * dx5dt(1,i-1);
x(6,i)= x(6,i-1) + h * dx6dt(1,i-1);