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-79201.

Hi. First of all sorry for asking the same question again and again but I am really close to the solution (maybe not). I have 2 questions.

1) 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,den_cr.m,den_des.m,drag.m,drag_cr.m,drag_des.m,lift.m,lift_cr.m,lift_des.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]
x6 = W;
% 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 (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,x4);                         % Changing drag coefficient
   Cl = lift_cr(5249.3,x4);                          % Changing lift coefficient
   p = den_cr(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,x4);                         % Changing drag coefficient
   Cl = lift_cr(5249.3,x4);                          % Changing lift coefficient
   p = den_cr(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,x4);                         % Changing drag coefficient
   Cl = lift_cr(3608.9,x4);                          % Changing lift coefficient
   p = den_cr(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;                    %%% line 136 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%                     
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);

I got this error:

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-79201.

Error in Flight (line 136)
x(1,i)= x(1,i-1) + h * dx1dt;

dx1dt is the 1-by-79201 one there. Is it because I have set the output lenghts of aforementioned functions in seperate tabs as linspace(H1,H2,79201)? If yes what should I hange, if no what should I do? 79201 is the length of t. Before doing that I have faced with array size problems. I am open to better suggestions.

2) With these lines I've tried to state that altitude [x(3,i-1)] remains constant:

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

and to state descent:

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.    

Are they correct? If no, can you provide the corrected versions?

Thanks.

[Torsten]

Given a (6x1) vector of state variables and a scalar for the actual time, calculate the corresponding (9x1) vector [x4; x5; f;u1; u2; u3; C_D; Cl; p] and feed it into the formulae for dx1dt,dx2dt,dx3dt,dx4dt,dx5dt and dx6dt.

I don't understand why you are always creating arrays for x4,x5,f,u1,u2,u3,C_D,Cl and p in the if-clause. You need one value for each of these parameters dependent on the given (6x1) state vector [x1; x2; x3; x4; x5; x6] and the actual time t.

[Turgut Ataseven]

@Torsten Thanks for the response and patience.

Sorry but I have thought about your suggestions at this and previous questions but could not come up with a reasonable solution. Do you want me to use preallocations like:

x1 = zeros(1);
x2 = zeros(1);
...
Cl = zeros(1);
p = zeros(1);

If not (probably), can you give just one example on that? [x4; x5; f;u1; C_D; Cl; p] varies with altitude (x3) and I don't know how to state that without using arrays which gets the value from functions like this (79201 is the length(t)):

function [Vtas_cl] = Velocities(H1,H2)

%%%%%%%%%%%%    Constants %%%%%%%%%%%%%%%%%%%%%%%%%%
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 = linspace(H1,H2,79201);                  %%%%% Input %%%%%%%%%%%
Vnom_climb_jet = zeros(1, length(H_climb));
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]
% Output %%%%%%%%%%%%
end

end

[Torsten]

I mean:

Instead of setting

H_climb = linspace(H1,H2,79201);

in "Velocities", simply set

H_climb = x3

where x3 is your solution for the altitude at time t(i-1) (thus one single value).

This will return one single value for x4.

Same for the other deduced model variables x5, f, u1, u2, u3, C_D, Cl and p.