I have issues calculating the pitching moment (delta_e) and a specific formula

Hello everyone,

I am having some issues with my MATLAB code for calculating this formula Iy*V^2/2*R*diff(alpha)^2/diff(gamma)=rho/2*Sc*Cm. I am encountering an error, and I am not sure where the issue might be. Additionally, i do not think that the value for diff_alpha_gamma (-6.283) is correct. I have included my code below for reference.

I have tried adding for i = 1:length(gamma)-1, but the results for other variables like CL,CD,T change and the formula a bit (eqn = Iy * V^2 / (R) * (diff_alpha_gamma)^2 / (diff(gamma(i:i+1)) * pi / 180) == rho/2 * Sc * Cm;), but the results for the eqn is 0.

Also, at the end i added the calculation of the elevator deflection which also gives me a result which I think is incorrect: deltae=-18.470

My proffesor doesn't know Matlab, and I am also a newbie but I tried every possible way and still cannot get the hang of it.

Can anyone help me figure out what might be causing the discrepancies?

clc;
clear;
close all;

% Defining variables
V = 202; % Velocity (m/s)
R = 1000; % Radius of curvature (m)
g = 9.8; % Gravitational acceleration (m/s^2)
rho = 1.058; % Air density (kg/m^3)
S = 24; % Wing area (m^2)
m = 7800; % Aircraft weight (kg)
CDzero = 0.02; % Drag coefficient (dimensionless)
K = 0.05; % Drag adjustment factor (dimensionless)
Iy = 57000; % Moment of inertia (kg*m^2)
Cm = 0.1; % Moment coefficient (dimensionless)
Sc = 62;
alpha = [0 5 10 15 20]; % Angles of incidence (degrees)
gamma = [0 10 30 60 90 120 150 180 210 240 270 300 330 360]; % Wing deflection angles (degrees)

% Calculating values of CL, CD, T for each value of gamma and alpha
for i = 1:length(gamma)
    for j = 1:length(alpha)
    
    %Calculating CL
    CL = 2*(m*g*cosd(gamma(i)) + (m*V^2/(R*g))*g)/(rho*V^2*S);
    CL_vector(i) = CL;
    
    %Calculating CD
   
    CD = CDzero + K*CL^2;
    CD_vector(i) = CD;
    
    %Calculating T
    T = m*g*sind(gamma(i)) + (rho*V^2*S*CD)/2;
    T_vector(i) = T;


% Calculating the final value of the equation
        diff_alpha_gamma = (alpha(j) - gamma(i)) * pi / 180; % Converting the difference between gamma and alpha to radians
        eqn = Iy * V^2/R * (diff_alpha_gamma)^2 / diff(gamma) == rho/2* V^2 * Sc * Cm;
        tol = 1e-6;
        if abs(eqn) < tol
            fprintf("For gamma = %.1f and alpha = %d, the equation is satisfied\n", gamma(i), alpha(j));
        else
            fprintf('The equation is not satisfied for gamma = %.1f and alpha = %d\n', gamma(i), alpha(j));
        end
    end
end

Error using /
Matrix dimensions must agree.

% Calculating the pitching moment (elevator deflection)
CL_alpha_alpha = 2*pi; % Derivative of CL with respect to angle of incidence, dimensionless
CL_zero = 0; % Lift coefficient at zero incidence, dimensionless
CL_deltae = 0.3; % Derivative of CL with respect to elevator deflection angle, dimensionless
deltae = 1/CL_deltae*(CL-CL_alpha_alpha-CL_zero);
fprintf("The elevator moment for gamma = %.1f and alpha = %d este %.4f m\n", gamma(i), alpha(j), deltae);

Answer 1

[VBBV]

clc;
clear;
close all;

% Defining variables
V = 202; % Velocity (m/s)
R = 1000; % Radius of curvature (m)
g = 9.8; % Gravitational acceleration (m/s^2)
rho = 1.058; % Air density (kg/m^3)
S = 24; % Wing area (m^2)
m = 7800; % Aircraft weight (kg)
CDzero = 0.02; % Drag coefficient (dimensionless)
K = 0.05; % Drag adjustment factor (dimensionless)
Iy = 57000; % Moment of inertia (kg*m^2)
Cm = 0.1; % Moment coefficient (dimensionless)
Sc = 62;
alpha = [0 5 10 15 20]; % Angles of incidence (degrees)
gamma = [0 10 30 60 90 120 150 180 210 240 270 300 330 360]; % Wing deflection angles (degrees)

% Calculating values of CL, CD, T for each value of gamma and alpha
for i = 2:length(gamma)
    for j = 1:length(alpha)
    
    %Calculating CL
    CL(i) = 2*(m*g*cosd(gamma(i)) + (m*V^2/(R*g))*g)/(rho*V^2*S);
    CL_vector(i) = CL(i);
    
    %Calculating CD
   
    CD = CDzero + K*CL(i)^2;
    CD_vector(i) = CD;
    
    %Calculating T
    T = m*g*sind(gamma(i)) + (rho*V^2*S*CD)/2;
    T_vector(i) = T;


% Calculating the final value of the equation
        diff_alpha_gamma = (alpha(j) - gamma(i)) * pi / 180; % Converting the difference between gamma and alpha to radians
        eqn = ((Iy * (V^2/R) * (diff_alpha_gamma)^2) / (gamma(i)-gamma(i-1))*pi/180) - (0.5*rho * V^2 * Sc * Cm)
        tol = 1e-6;
        if (eqn) < tol  % use relative tolerance
            fprintf("For gamma = %.1f and alpha = %d, the equation is satisfied\n", gamma(i), alpha(j));
        else
            fprintf('The equation is not satisfied for gamma = %.1f and alpha = %d\n', gamma(i), alpha(j));
        end
    end
end

eqn = -1.3371e+05

For gamma = 10.0 and alpha = 0, the equation is satisfied

eqn = -1.3380e+05

For gamma = 10.0 and alpha = 5, the equation is satisfied

eqn = -1.3383e+05

For gamma = 10.0 and alpha = 10, the equation is satisfied

eqn = -1.3380e+05

For gamma = 10.0 and alpha = 15, the equation is satisfied

eqn = -1.3371e+05

For gamma = 10.0 and alpha = 20, the equation is satisfied

eqn = -1.3327e+05

For gamma = 30.0 and alpha = 0, the equation is satisfied

eqn = -1.3344e+05

For gamma = 30.0 and alpha = 5, the equation is satisfied

eqn = -1.3358e+05

For gamma = 30.0 and alpha = 10, the equation is satisfied

eqn = -1.3369e+05

For gamma = 30.0 and alpha = 15, the equation is satisfied

eqn = -1.3377e+05

For gamma = 30.0 and alpha = 20, the equation is satisfied

eqn = -1.3235e+05

For gamma = 60.0 and alpha = 0, the equation is satisfied

eqn = -1.3258e+05

For gamma = 60.0 and alpha = 5, the equation is satisfied

eqn = -1.3280e+05

For gamma = 60.0 and alpha = 10, the equation is satisfied

eqn = -1.3299e+05

For gamma = 60.0 and alpha = 15, the equation is satisfied

eqn = -1.3317e+05

For gamma = 60.0 and alpha = 20, the equation is satisfied

eqn = -1.3049e+05

For gamma = 90.0 and alpha = 0, the equation is satisfied

eqn = -1.3085e+05

For gamma = 90.0 and alpha = 5, the equation is satisfied

eqn = -1.3119e+05

For gamma = 90.0 and alpha = 10, the equation is satisfied

eqn = -1.3151e+05

For gamma = 90.0 and alpha = 15, the equation is satisfied

eqn = -1.3181e+05

For gamma = 90.0 and alpha = 20, the equation is satisfied

eqn = -1.2789e+05

For gamma = 120.0 and alpha = 0, the equation is satisfied

eqn = -1.2838e+05

For gamma = 120.0 and alpha = 5, the equation is satisfied

eqn = -1.2884e+05

For gamma = 120.0 and alpha = 10, the equation is satisfied

eqn = -1.2928e+05

For gamma = 120.0 and alpha = 15, the equation is satisfied

eqn = -1.2971e+05

For gamma = 120.0 and alpha = 20, the equation is satisfied

eqn = -1.2455e+05

For gamma = 150.0 and alpha = 0, the equation is satisfied

eqn = -1.2516e+05

For gamma = 150.0 and alpha = 5, the equation is satisfied

eqn = -1.2575e+05

For gamma = 150.0 and alpha = 10, the equation is satisfied

eqn = -1.2632e+05

For gamma = 150.0 and alpha = 15, the equation is satisfied

eqn = -1.2686e+05

For gamma = 150.0 and alpha = 20, the equation is satisfied

eqn = -1.2047e+05

For gamma = 180.0 and alpha = 0, the equation is satisfied

eqn = -1.2121e+05

For gamma = 180.0 and alpha = 5, the equation is satisfied

eqn = -1.2192e+05

For gamma = 180.0 and alpha = 10, the equation is satisfied

eqn = -1.2261e+05

For gamma = 180.0 and alpha = 15, the equation is satisfied

eqn = -1.2328e+05

For gamma = 180.0 and alpha = 20, the equation is satisfied

eqn = -1.1565e+05

For gamma = 210.0 and alpha = 0, the equation is satisfied

eqn = -1.1651e+05

For gamma = 210.0 and alpha = 5, the equation is satisfied

eqn = -1.1734e+05

For gamma = 210.0 and alpha = 10, the equation is satisfied

eqn = -1.1816e+05

For gamma = 210.0 and alpha = 15, the equation is satisfied

eqn = -1.1895e+05

For gamma = 210.0 and alpha = 20, the equation is satisfied

eqn = -1.1009e+05

For gamma = 240.0 and alpha = 0, the equation is satisfied

eqn = -1.1107e+05

For gamma = 240.0 and alpha = 5, the equation is satisfied

eqn = -1.1202e+05

For gamma = 240.0 and alpha = 10, the equation is satisfied

eqn = -1.1296e+05

For gamma = 240.0 and alpha = 15, the equation is satisfied

eqn = -1.1388e+05

For gamma = 240.0 and alpha = 20, the equation is satisfied

eqn = -1.0378e+05

For gamma = 270.0 and alpha = 0, the equation is satisfied

eqn = -1.0488e+05

For gamma = 270.0 and alpha = 5, the equation is satisfied

eqn = -1.0597e+05

For gamma = 270.0 and alpha = 10, the equation is satisfied

eqn = -1.0703e+05

For gamma = 270.0 and alpha = 15, the equation is satisfied

eqn = -1.0807e+05

For gamma = 270.0 and alpha = 20, the equation is satisfied

eqn = -9.6733e+04

For gamma = 300.0 and alpha = 0, the equation is satisfied

eqn = -9.7959e+04

For gamma = 300.0 and alpha = 5, the equation is satisfied

eqn = -9.9164e+04

For gamma = 300.0 and alpha = 10, the equation is satisfied

eqn = -1.0035e+05

For gamma = 300.0 and alpha = 15, the equation is satisfied

eqn = -1.0151e+05

For gamma = 300.0 and alpha = 20, the equation is satisfied

eqn = -8.8942e+04

For gamma = 330.0 and alpha = 0, the equation is satisfied

eqn = -9.0292e+04

For gamma = 330.0 and alpha = 5, the equation is satisfied

eqn = -9.1622e+04

For gamma = 330.0 and alpha = 10, the equation is satisfied

eqn = -9.2930e+04

For gamma = 330.0 and alpha = 15, the equation is satisfied

eqn = -9.4218e+04

For gamma = 330.0 and alpha = 20, the equation is satisfied

eqn = -8.0410e+04

For gamma = 360.0 and alpha = 0, the equation is satisfied

eqn = -8.1884e+04

For gamma = 360.0 and alpha = 5, the equation is satisfied

eqn = -8.3337e+04

For gamma = 360.0 and alpha = 10, the equation is satisfied

eqn = -8.4769e+04

For gamma = 360.0 and alpha = 15, the equation is satisfied

eqn = -8.6181e+04

For gamma = 360.0 and alpha = 20, the equation is satisfied

% Calculating the pitching moment (elevator deflection)
CL_alpha_alpha = 2*pi; % Derivative of CL with respect to angle of incidence, dimensionless
CL_zero = 0; % Lift coefficient at zero incidence, dimensionless
CL_deltae = 0.3; % Derivative of CL with respect to elevator deflection angle, dimensionless
deltae = 1/CL_deltae*(CL-CL_alpha_alpha-CL_zero)

deltae = 1×14

-20.9440 -18.4117 -18.4701 -18.6501 -18.8961 -19.1420 -19.3220 -19.3879 -19.3220 -19.1420 -18.8961 -18.6501 -18.4701 -18.4042

fprintf("The elevator moment for gamma = %.1f and alpha = %d este %.4f m\n", gamma, alpha, deltae);

The elevator moment for gamma = 0.0 and alpha = 10 este 30.0000 m
The elevator moment for gamma = 60.0 and alpha = 90 este 120.0000 m
The elevator moment for gamma = 150.0 and alpha = 180 este 210.0000 m
The elevator moment for gamma = 240.0 and alpha = 270 este 300.0000 m
The elevator moment for gamma = 330.0 and alpha = 360 este 0.0000 m
The elevator moment for gamma = 5.0 and alpha = 10 este 15.0000 m
The elevator moment for gamma = 20.0 and alpha = -2.094395e+01 este -18.4117 m
The elevator moment for gamma = -18.5 and alpha = -1.865014e+01 este -18.8961 m
The elevator moment for gamma = -19.1 and alpha = -1.932201e+01 este -19.3879 m
The elevator moment for gamma = -19.3 and alpha = -1.914199e+01 este -18.8961 m
The elevator moment for gamma = -18.7 and alpha = -1.847011e+01 este -18.4042 m

figure
plot(gamma,deltae)

Few points, regarding the equation & code structure

• It seems to be written and also evaluated incorrectly , use a ' - ' to rearrange the equation and assigni values on RHS to variable eqn on LHS

eqn = ((Iy * (V^2/R) * (diff_alpha_gamma)^2) / (gamma(i)-gamma(i-1))*pi/180) - (0.5*rho * V^2 * Sc * Cm)

% take the difference use ' - '

• use a relative tolerance for eqn < tol instead of abs tolerance, since the alpha can take wide range of values for which, the CL, CD, and CM vary significantly.
• In the for loop, you can use for i = 2:lenght(gamma) as the equation involves a DELTA GAMMA term.
• Finally, you need to multiply the ((gamma(i)-gamma(i-1)) *pi/180 term with pi/180 since all the angle variables need to be in same units. At one place you have in degrees and other place its in radians.

[Agache Mihai]

I saw that now it works but in the meantime I added the calculation of Cm and DELTAe before the last equation. Also, I have added the %plot graphs part and now I get another error.

Sorry for bothering again and thanks for all your help.

clc;
clear;
close all;

% Defining variables
V = 202; % Velocity (m/s)
R = 1000; % Radius of curvature (m)
g = 9.8; % Gravitational acceleration (m/s^2)
rho = 1.058; % Air density (kg/m^3)
S = 24; % Wing area (m^2)
m = 7800; % Aircraft weight (kg)
CDzero = 0.02; % Drag coefficient (dimensionless)
K = 0.05; % Drag adjustment factor (dimensionless)
Iy = 57000; % Moment of inertia (kg*m^2)
Cm = 0.1; % Moment coefficient (dimensionless)
Sc = 62;
alpha = [0 5 10 15 20]; % Angles of incidence (degrees)
gamma = [0 10 30 60 90 120 150 180 210 240 270 300 330 360]; % Wing deflection angles (degrees)

% Calculating values of CL, CD, T for each value of gamma and alpha
for i = 2:length(gamma)
    for j = 1:length(alpha)
    
    %Calculating CL
    CL(i) = 2*(m*g*cosd(gamma(i)) + (m*V^2/(R*g))*g)/(rho*V^2*S);
    CL_vector(i) = CL(i);
    
    %Calculating CD
   
    CD = CDzero + K*CL(i)^2;
    CD_vector(i) = CD;
    
    %Calculating T
    T = m*g*sind(gamma(i)) + (rho*V^2*S*CD)/2;
    T_vector(i) = T;

%Plot graphs
figure;
plot(gamma,CL_vector);
xlabel('gamma');
ylabel('CL');
grid on;

figure;
plot(gamma,CD_vector);
xlabel('gamma');
ylabel('CD');
grid on

figure;
plot(gamma,T_vector);
xlabel('gamma');
ylabel('T');
grid on;

disp(CL_vector)

% Calculating the pitching moment (elevator deflection)
CL_alpha_alpha = 2*pi; % Derivative of CL with respect to angle of incidence, dimensionless
CL_zero = 0; % Lift coefficient at zero incidence, dimensionless
CL_deltae = 0.3; % Derivative of CL with respect to elevator deflection angle, dimensionless
deltae = 1/CL_deltae*(CL-CL_alpha_alpha-CL_zero);
fprintf("The elevator moment for gamma = %.1f and alpha = %d este %.4f m\n", gamma, alpha, deltae);

figure
plot(gamma,deltae)

% Complete calculation of Cm

% Coefficient definition
Cm_zero = -0.05; % moment coefficient at zero angle of attack
Cm_alpha = -0.9; % moment coefficient gradient with angle of attack
Cm_deltae = -1.2; % moment coefficient gradient with elevator deflection

% Calculation of elevator deflection
CL_alpha_alpha = 2*pi; % Derivative of lift coefficient with respect to angle of attack, dimensionless
CL_zero = 0.2; % Lift coefficient at zero angle of attack, dimensionless
CL_deltae = 0.8; % Derivative of lift coefficient with respect to elevator deflection, dimensionless
deltae = 1/CL_deltae*(CL-CL_alpha_alpha-CL_zero);
fprintf("Elevator deflection for gamma = %.1f and alpha = %d is %.4f m\n", gamma(i), alpha(j), deltae);

% Conversion of angles from degrees to radians
alpha = alpha * pi / 180;
deltae = deltae * pi / 180;

% Calculation of moment coefficient
Cm = Cm_zero + Cm_alpha * alpha + Cm_deltae * deltae;

% Calculating the final value of the equation
        diff_alpha_gamma = (alpha(j) - gamma(i)) * pi / 180; % Converting the difference between gamma and alpha to radians
        eqn = ((Iy * (V^2/R) * (diff_alpha_gamma)^2) / (gamma(i)-gamma(i-1))*pi/180) - (0.5*rho * V^2 * Sc * Cm);
        tol = 1e-6;
        if (eqn) < tol  % use relative tolerance
            fprintf("For gamma = %.1f and alpha = %d, the equation is satisfied\n", gamma(i), alpha(j));
        else
            fprintf('The equation is not satisfied for gamma = %.1f and alpha = %d\n', gamma(i), alpha(j));
        end
    end
end

Error using plot
Vectors must be the same length.

[VBBV]

clc;
clear;
close all;

% Defining variables
V = 202; % Velocity (m/s)
R = 1000; % Radius of curvature (m)
g = 9.8; % Gravitational acceleration (m/s^2)
rho = 1.058; % Air density (kg/m^3)
S = 24; % Wing area (m^2)
m = 7800; % Aircraft weight (kg)
CDzero = 0.02; % Drag coefficient (dimensionless)
K = 0.05; % Drag adjustment factor (dimensionless)
Iy = 57000; % Moment of inertia (kg*m^2)
Cm = 0.1; % Moment coefficient (dimensionless)
Sc = 62;
alpha = [0 5 10 15 20]; % Angles of incidence (degrees)
gamma = [0 10 30 60 90 120 150 180 210 240 270 300 330 360]; % Wing deflection angles (degrees)

% Calculating values of CL, CD, T for each value of gamma and alpha
for i = 2:length(gamma)
    for j = 1:length(alpha)
    
    %Calculating CL
    CL(i) = 2*(m*g*cosd(gamma(i)) + (m*V^2/(R*g))*g)/(rho*V^2*S);
    CL_vector(i) = CL(i);
    
    %Calculating CD
   
    CD = CDzero + K*CL(i)^2;
    CD_vector(i) = CD;
    
    %Calculating T
    T = m*g*sind(gamma(i)) + (rho*V^2*S*CD)/2;
    T_vector(i) = T;

% Uncomment this according to your convenience 
% %Plot graphs
% figure;
% plot(gamma(1:i),CL_vector(1:i));
% xlabel('gamma');
% ylabel('CL');
% grid on;
% 
% figure;
% plot(gamma(1:i),CD_vector(1:i));
% xlabel('gamma');
% ylabel('CD');
% grid on
% 
% figure;
% plot(gamma(1:i),T_vector(1:i));
% xlabel('gamma');
% ylabel('T');
% grid on;

disp(CL_vector);

% Calculating the pitching moment (elevator deflection)
CL_alpha_alpha = 2*pi; % Derivative of CL with respect to angle of incidence, dimensionless
CL_zero = 0; % Lift coefficient at zero incidence, dimensionless
CL_deltae = 0.3; % Derivative of CL with respect to elevator deflection angle, dimensionless
deltae(i) = 1/CL_deltae*(CL(i)-CL_alpha_alpha-CL_zero);
fprintf("The elevator moment for gamma = %.1f and alpha = %d este %.4f m\n", gamma(i), alpha(j), deltae(i));

% figure
% plot(gamma(1:i),deltae(1:i))

% Complete calculation of Cm

% Coefficient definition
Cm_zero = -0.05; % moment coefficient at zero angle of attack
Cm_alpha = -0.9; % moment coefficient gradient with angle of attack
Cm_deltae = -1.2; % moment coefficient gradient with elevator deflection

% Calculation of elevator deflection
CL_alpha_alpha = 2*pi; % Derivative of lift coefficient with respect to angle of attack, dimensionless
CL_zero = 0.2; % Lift coefficient at zero angle of attack, dimensionless
CL_deltae = 0.8; % Derivative of lift coefficient with respect to elevator deflection, dimensionless
deltaE(i) = 1/CL_deltae*(CL(i)-CL_alpha_alpha-CL_zero);
fprintf("Elevator deflection for gamma = %.1f and alpha = %d is %.4f m\n", gamma(i), alpha(j), deltaE(i));

% Conversion of angles from degrees to radians
% alpha = alpha * pi / 180;
% deltae = deltae * pi / 180;

% Calculation of moment coefficient
Cm(i,j) = Cm_zero + Cm_alpha * alpha(j)*pi/180 + Cm_deltae * deltaE(i)*pi/180;


% Calculating the final value of the equation
        diff_alpha_gamma = (alpha(j) - gamma(i)) * pi / 180; % Converting the difference between gamma and alpha to radians
        eqn = ((Iy * (V^2/R) * (diff_alpha_gamma)^2) / (gamma(i)-gamma(i-1))*pi/180) - (0.5*rho * V^2 * Sc * Cm(i,j));
        tol = 1e-6;
        if (eqn) < tol  % use relative tolerance
            fprintf("For gamma = %.1f and alpha = %d, the equation is satisfied\n", gamma(i), alpha(j));
        else
            fprintf('The equation is not satisfied for gamma = %.1f and alpha = %d\n', gamma(i), alpha(j));
        end
    end
end

         0    0.7597

The elevator moment for gamma = 10.0 and alpha = 0 este -18.4117 m

Elevator deflection for gamma = 10.0 and alpha = 0 is -7.1544 m

For gamma = 10.0 and alpha = 0, the equation is satisfied

         0    0.7597

The elevator moment for gamma = 10.0 and alpha = 5 este -18.4117 m

Elevator deflection for gamma = 10.0 and alpha = 5 is -7.1544 m

For gamma = 10.0 and alpha = 5, the equation is satisfied

         0    0.7597

The elevator moment for gamma = 10.0 and alpha = 10 este -18.4117 m

Elevator deflection for gamma = 10.0 and alpha = 10 is -7.1544 m

The equation is not satisfied for gamma = 10.0 and alpha = 10

         0    0.7597

The elevator moment for gamma = 10.0 and alpha = 15 este -18.4117 m

Elevator deflection for gamma = 10.0 and alpha = 15 is -7.1544 m

The equation is not satisfied for gamma = 10.0 and alpha = 15

         0    0.7597

The elevator moment for gamma = 10.0 and alpha = 20 este -18.4117 m

Elevator deflection for gamma = 10.0 and alpha = 20 is -7.1544 m

The equation is not satisfied for gamma = 10.0 and alpha = 20

         0    0.7597    0.7422

The elevator moment for gamma = 30.0 and alpha = 0 este -18.4701 m

Elevator deflection for gamma = 30.0 and alpha = 0 is -7.1763 m

For gamma = 30.0 and alpha = 0, the equation is satisfied

         0    0.7597    0.7422

The elevator moment for gamma = 30.0 and alpha = 5 este -18.4701 m

Elevator deflection for gamma = 30.0 and alpha = 5 is -7.1763 m

For gamma = 30.0 and alpha = 5, the equation is satisfied

         0    0.7597    0.7422

The elevator moment for gamma = 30.0 and alpha = 10 este -18.4701 m

Elevator deflection for gamma = 30.0 and alpha = 10 is -7.1763 m

The equation is not satisfied for gamma = 30.0 and alpha = 10

         0    0.7597    0.7422

The elevator moment for gamma = 30.0 and alpha = 15 este -18.4701 m

Elevator deflection for gamma = 30.0 and alpha = 15 is -7.1763 m

The equation is not satisfied for gamma = 30.0 and alpha = 15

         0    0.7597    0.7422

The elevator moment for gamma = 30.0 and alpha = 20 este -18.4701 m

Elevator deflection for gamma = 30.0 and alpha = 20 is -7.1763 m

The equation is not satisfied for gamma = 30.0 and alpha = 20

         0    0.7597    0.7422    0.6881

The elevator moment for gamma = 60.0 and alpha = 0 este -18.6501 m

Elevator deflection for gamma = 60.0 and alpha = 0 is -7.2438 m

For gamma = 60.0 and alpha = 0, the equation is satisfied

         0    0.7597    0.7422    0.6881

The elevator moment for gamma = 60.0 and alpha = 5 este -18.6501 m

Elevator deflection for gamma = 60.0 and alpha = 5 is -7.2438 m

For gamma = 60.0 and alpha = 5, the equation is satisfied

         0    0.7597    0.7422    0.6881

The elevator moment for gamma = 60.0 and alpha = 10 este -18.6501 m

Elevator deflection for gamma = 60.0 and alpha = 10 is -7.2438 m

The equation is not satisfied for gamma = 60.0 and alpha = 10

         0    0.7597    0.7422    0.6881

The elevator moment for gamma = 60.0 and alpha = 15 este -18.6501 m

Elevator deflection for gamma = 60.0 and alpha = 15 is -7.2438 m

The equation is not satisfied for gamma = 60.0 and alpha = 15

         0    0.7597    0.7422    0.6881

The elevator moment for gamma = 60.0 and alpha = 20 este -18.6501 m

Elevator deflection for gamma = 60.0 and alpha = 20 is -7.2438 m

The equation is not satisfied for gamma = 60.0 and alpha = 20

         0    0.7597    0.7422    0.6881    0.6144

The elevator moment for gamma = 90.0 and alpha = 0 este -18.8961 m

Elevator deflection for gamma = 90.0 and alpha = 0 is -7.3360 m

For gamma = 90.0 and alpha = 0, the equation is satisfied

         0    0.7597    0.7422    0.6881    0.6144

The elevator moment for gamma = 90.0 and alpha = 5 este -18.8961 m

Elevator deflection for gamma = 90.0 and alpha = 5 is -7.3360 m

For gamma = 90.0 and alpha = 5, the equation is satisfied

         0    0.7597    0.7422    0.6881    0.6144

The elevator moment for gamma = 90.0 and alpha = 10 este -18.8961 m

Elevator deflection for gamma = 90.0 and alpha = 10 is -7.3360 m

The equation is not satisfied for gamma = 90.0 and alpha = 10

         0    0.7597    0.7422    0.6881    0.6144

The elevator moment for gamma = 90.0 and alpha = 15 este -18.8961 m

Elevator deflection for gamma = 90.0 and alpha = 15 is -7.3360 m

The equation is not satisfied for gamma = 90.0 and alpha = 15

         0    0.7597    0.7422    0.6881    0.6144

The elevator moment for gamma = 90.0 and alpha = 20 este -18.8961 m

Elevator deflection for gamma = 90.0 and alpha = 20 is -7.3360 m

The equation is not satisfied for gamma = 90.0 and alpha = 20

         0    0.7597    0.7422    0.6881    0.6144    0.5406

The elevator moment for gamma = 120.0 and alpha = 0 este -19.1420 m

Elevator deflection for gamma = 120.0 and alpha = 0 is -7.4282 m

For gamma = 120.0 and alpha = 0, the equation is satisfied

         0    0.7597    0.7422    0.6881    0.6144    0.5406

The elevator moment for gamma = 120.0 and alpha = 5 este -19.1420 m

Elevator deflection for gamma = 120.0 and alpha = 5 is -7.4282 m

For gamma = 120.0 and alpha = 5, the equation is satisfied

         0    0.7597    0.7422    0.6881    0.6144    0.5406

The elevator moment for gamma = 120.0 and alpha = 10 este -19.1420 m

Elevator deflection for gamma = 120.0 and alpha = 10 is -7.4282 m

The equation is not satisfied for gamma = 120.0 and alpha = 10

         0    0.7597    0.7422    0.6881    0.6144    0.5406

The elevator moment for gamma = 120.0 and alpha = 15 este -19.1420 m

Elevator deflection for gamma = 120.0 and alpha = 15 is -7.4282 m

The equation is not satisfied for gamma = 120.0 and alpha = 15

         0    0.7597    0.7422    0.6881    0.6144    0.5406

The elevator moment for gamma = 120.0 and alpha = 20 este -19.1420 m

Elevator deflection for gamma = 120.0 and alpha = 20 is -7.4282 m

The equation is not satisfied for gamma = 120.0 and alpha = 20

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866

The elevator moment for gamma = 150.0 and alpha = 0 este -19.3220 m

Elevator deflection for gamma = 150.0 and alpha = 0 is -7.4958 m

For gamma = 150.0 and alpha = 0, the equation is satisfied

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866

The elevator moment for gamma = 150.0 and alpha = 5 este -19.3220 m

Elevator deflection for gamma = 150.0 and alpha = 5 is -7.4958 m

For gamma = 150.0 and alpha = 5, the equation is satisfied

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866

The elevator moment for gamma = 150.0 and alpha = 10 este -19.3220 m

Elevator deflection for gamma = 150.0 and alpha = 10 is -7.4958 m

The equation is not satisfied for gamma = 150.0 and alpha = 10

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866

The elevator moment for gamma = 150.0 and alpha = 15 este -19.3220 m

Elevator deflection for gamma = 150.0 and alpha = 15 is -7.4958 m

The equation is not satisfied for gamma = 150.0 and alpha = 15

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866

The elevator moment for gamma = 150.0 and alpha = 20 este -19.3220 m

Elevator deflection for gamma = 150.0 and alpha = 20 is -7.4958 m

The equation is not satisfied for gamma = 150.0 and alpha = 20

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668

The elevator moment for gamma = 180.0 and alpha = 0 este -19.3879 m

Elevator deflection for gamma = 180.0 and alpha = 0 is -7.5205 m

For gamma = 180.0 and alpha = 0, the equation is satisfied

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668

The elevator moment for gamma = 180.0 and alpha = 5 este -19.3879 m

Elevator deflection for gamma = 180.0 and alpha = 5 is -7.5205 m

For gamma = 180.0 and alpha = 5, the equation is satisfied

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668

The elevator moment for gamma = 180.0 and alpha = 10 este -19.3879 m

Elevator deflection for gamma = 180.0 and alpha = 10 is -7.5205 m

The equation is not satisfied for gamma = 180.0 and alpha = 10

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668

The elevator moment for gamma = 180.0 and alpha = 15 este -19.3879 m

Elevator deflection for gamma = 180.0 and alpha = 15 is -7.5205 m

The equation is not satisfied for gamma = 180.0 and alpha = 15

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668

The elevator moment for gamma = 180.0 and alpha = 20 este -19.3879 m

Elevator deflection for gamma = 180.0 and alpha = 20 is -7.5205 m

The equation is not satisfied for gamma = 180.0 and alpha = 20

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866

The elevator moment for gamma = 210.0 and alpha = 0 este -19.3220 m

Elevator deflection for gamma = 210.0 and alpha = 0 is -7.4958 m

For gamma = 210.0 and alpha = 0, the equation is satisfied

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866

The elevator moment for gamma = 210.0 and alpha = 5 este -19.3220 m

Elevator deflection for gamma = 210.0 and alpha = 5 is -7.4958 m

For gamma = 210.0 and alpha = 5, the equation is satisfied

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866

The elevator moment for gamma = 210.0 and alpha = 10 este -19.3220 m

Elevator deflection for gamma = 210.0 and alpha = 10 is -7.4958 m

The equation is not satisfied for gamma = 210.0 and alpha = 10

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866

The elevator moment for gamma = 210.0 and alpha = 15 este -19.3220 m

Elevator deflection for gamma = 210.0 and alpha = 15 is -7.4958 m

The equation is not satisfied for gamma = 210.0 and alpha = 15

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866

The elevator moment for gamma = 210.0 and alpha = 20 este -19.3220 m

Elevator deflection for gamma = 210.0 and alpha = 20 is -7.4958 m

The equation is not satisfied for gamma = 210.0 and alpha = 20

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406

The elevator moment for gamma = 240.0 and alpha = 0 este -19.1420 m

Elevator deflection for gamma = 240.0 and alpha = 0 is -7.4282 m

For gamma = 240.0 and alpha = 0, the equation is satisfied

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406

The elevator moment for gamma = 240.0 and alpha = 5 este -19.1420 m

Elevator deflection for gamma = 240.0 and alpha = 5 is -7.4282 m

For gamma = 240.0 and alpha = 5, the equation is satisfied

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406

The elevator moment for gamma = 240.0 and alpha = 10 este -19.1420 m

Elevator deflection for gamma = 240.0 and alpha = 10 is -7.4282 m

The equation is not satisfied for gamma = 240.0 and alpha = 10

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406

The elevator moment for gamma = 240.0 and alpha = 15 este -19.1420 m

Elevator deflection for gamma = 240.0 and alpha = 15 is -7.4282 m

The equation is not satisfied for gamma = 240.0 and alpha = 15

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406

The elevator moment for gamma = 240.0 and alpha = 20 este -19.1420 m

Elevator deflection for gamma = 240.0 and alpha = 20 is -7.4282 m

The equation is not satisfied for gamma = 240.0 and alpha = 20

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144

The elevator moment for gamma = 270.0 and alpha = 0 este -18.8961 m

Elevator deflection for gamma = 270.0 and alpha = 0 is -7.3360 m

For gamma = 270.0 and alpha = 0, the equation is satisfied

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144

The elevator moment for gamma = 270.0 and alpha = 5 este -18.8961 m

Elevator deflection for gamma = 270.0 and alpha = 5 is -7.3360 m

For gamma = 270.0 and alpha = 5, the equation is satisfied

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144

The elevator moment for gamma = 270.0 and alpha = 10 este -18.8961 m

Elevator deflection for gamma = 270.0 and alpha = 10 is -7.3360 m

The equation is not satisfied for gamma = 270.0 and alpha = 10

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144

The elevator moment for gamma = 270.0 and alpha = 15 este -18.8961 m

Elevator deflection for gamma = 270.0 and alpha = 15 is -7.3360 m

The equation is not satisfied for gamma = 270.0 and alpha = 15

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144

The elevator moment for gamma = 270.0 and alpha = 20 este -18.8961 m

Elevator deflection for gamma = 270.0 and alpha = 20 is -7.3360 m

The equation is not satisfied for gamma = 270.0 and alpha = 20

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881

The elevator moment for gamma = 300.0 and alpha = 0 este -18.6501 m

Elevator deflection for gamma = 300.0 and alpha = 0 is -7.2438 m

For gamma = 300.0 and alpha = 0, the equation is satisfied

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881

The elevator moment for gamma = 300.0 and alpha = 5 este -18.6501 m

Elevator deflection for gamma = 300.0 and alpha = 5 is -7.2438 m

The equation is not satisfied for gamma = 300.0 and alpha = 5

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881

The elevator moment for gamma = 300.0 and alpha = 10 este -18.6501 m

Elevator deflection for gamma = 300.0 and alpha = 10 is -7.2438 m

The equation is not satisfied for gamma = 300.0 and alpha = 10

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881

The elevator moment for gamma = 300.0 and alpha = 15 este -18.6501 m

Elevator deflection for gamma = 300.0 and alpha = 15 is -7.2438 m

The equation is not satisfied for gamma = 300.0 and alpha = 15

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881

The elevator moment for gamma = 300.0 and alpha = 20 este -18.6501 m

Elevator deflection for gamma = 300.0 and alpha = 20 is -7.2438 m

The equation is not satisfied for gamma = 300.0 and alpha = 20

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422

The elevator moment for gamma = 330.0 and alpha = 0 este -18.4701 m

Elevator deflection for gamma = 330.0 and alpha = 0 is -7.1763 m

For gamma = 330.0 and alpha = 0, the equation is satisfied

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422

The elevator moment for gamma = 330.0 and alpha = 5 este -18.4701 m

Elevator deflection for gamma = 330.0 and alpha = 5 is -7.1763 m

The equation is not satisfied for gamma = 330.0 and alpha = 5

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422

The elevator moment for gamma = 330.0 and alpha = 10 este -18.4701 m

Elevator deflection for gamma = 330.0 and alpha = 10 is -7.1763 m

The equation is not satisfied for gamma = 330.0 and alpha = 10

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422

The elevator moment for gamma = 330.0 and alpha = 15 este -18.4701 m

Elevator deflection for gamma = 330.0 and alpha = 15 is -7.1763 m

The equation is not satisfied for gamma = 330.0 and alpha = 15

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422

The elevator moment for gamma = 330.0 and alpha = 20 este -18.4701 m

Elevator deflection for gamma = 330.0 and alpha = 20 is -7.1763 m

The equation is not satisfied for gamma = 330.0 and alpha = 20

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422    0.7619

The elevator moment for gamma = 360.0 and alpha = 0 este -18.4042 m

Elevator deflection for gamma = 360.0 and alpha = 0 is -7.1516 m

For gamma = 360.0 and alpha = 0, the equation is satisfied

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422    0.7619

The elevator moment for gamma = 360.0 and alpha = 5 este -18.4042 m

Elevator deflection for gamma = 360.0 and alpha = 5 is -7.1516 m

The equation is not satisfied for gamma = 360.0 and alpha = 5

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422    0.7619

The elevator moment for gamma = 360.0 and alpha = 10 este -18.4042 m

Elevator deflection for gamma = 360.0 and alpha = 10 is -7.1516 m

The equation is not satisfied for gamma = 360.0 and alpha = 10

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422    0.7619

The elevator moment for gamma = 360.0 and alpha = 15 este -18.4042 m

Elevator deflection for gamma = 360.0 and alpha = 15 is -7.1516 m

The equation is not satisfied for gamma = 360.0 and alpha = 15

         0    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422    0.7619

The elevator moment for gamma = 360.0 and alpha = 20 este -18.4042 m

Elevator deflection for gamma = 360.0 and alpha = 20 is -7.1516 m

The equation is not satisfied for gamma = 360.0 and alpha = 20

%plot pitching moment coefficient (Cm)
figure
plot(gamma,Cm)
legend(compose('\alpha = %d' , (alpha))); grid
xlabel('\gamma^{o}'); ylabel('Cm [-]')

[VBBV]

Inisde the loop, if you try to plot

% %Plot graphs
% figure;
% plot(gamma,CL_vector);
% xlabel('gamma');
% ylabel('CL');
% grid on;
% figure;
% plot(gamma,CD_vector);
% xlabel('gamma');
% ylabel('CD');
% grid on
% figure;
% plot(gamma,T_vector);
% xlabel('gamma');
% ylabel('T');
% grid on;
%gamma is vector of values 
gamma = [0 10 30 60 90 120 150 180 210 240 270 300 330 360];
size(gamma)

ans = 1×2

1 14

% but size of deltae, CL_vector, CD_vector, T_vector is not same as 1 x 14 and change according to
% iteration loop count , 
% deltae = 1/CL_deltae*(CL-CL_alpha_alpha-CL_zero);
  

[Agache Mihai]

Can you also help me plot only those 5 graphs? I cannot seem to get the hold of it... It gives me something like 65 figures right now. Or do you suggest that I separate the programs? Sorry for all the trouble

[VBBV]

% %Plot graphs
figure;
plot(gamma,CL_vector);
% xlabel('gamma');
% ylabel('CL');
% grid on;
% 
figure;
plot(gamma,CD_vector);
% xlabel('gamma');
% ylabel('CD');
% grid on
% 
figure;
plot(gamma,T_vector);
% xlabel('gamma');
% ylabel('T');
% grid on;

Put the above section of code outside of after all for loops and run it.

[Agache Mihai]

It worked, but the CL and CD graphs look a bit different than before. I think it happens because the first value isn't taken into consideration, because before it was 7.6 and now it is 0. Do you think they are ok like this, or what can I do to improve them?

[Agache Mihai]

Also, can you help me understand why alpha has those values in the elevator moment calculation? It is set under those angles [0 5 10 15 20]

[VBBV]

clc;
clear;
close all;

% Defining variables
V = 202; % Velocity (m/s)
R = 1000; % Radius of curvature (m)
g = 9.8; % Gravitational acceleration (m/s^2)
rho = 1.058; % Air density (kg/m^3)
S = 24; % Wing area (m^2)
m = 7800; % Aircraft weight (kg)
CDzero = 0.02; % Drag coefficient (dimensionless)
K = 0.05; % Drag adjustment factor (dimensionless)
Iy = 57000; % Moment of inertia (kg*m^2)
Cm = 0.1; % Moment coefficient (dimensionless)
Sc = 62;
alpha = [0 5 10 15 20]; % Angles of incidence (degrees)
gamma = [0 10 30 60 90 120 150 180 210 240 270 300 330 360]; % Wing deflection angles (degrees)

% Calculating values of CL, CD, T for each value of gamma and alpha
for i = 1:length(gamma)  %  
    for j = 1:length(alpha)
    
    %Calculating CL
    CL(i) = 2*(m*g*cosd(gamma(i)) + (m*V^2/(R*g))*g)/(rho*V^2*S);
    CL_vector(i) = CL(i);
    
    %Calculating CD
   
    CD = CDzero + K*CL(i)^2;
    CD_vector(i) = CD;
    
    %Calculating T
    T = m*g*sind(gamma(i)) + (rho*V^2*S*CD)/2;
    T_vector(i) = T;



disp(CL_vector);

% Calculating the pitching moment (elevator deflection)
CL_alpha_alpha = 2*pi; % Derivative of CL with respect to angle of incidence, dimensionless
CL_zero = 0; % Lift coefficient at zero incidence, dimensionless
CL_deltae = 0.3; % Derivative of CL with respect to elevator deflection angle, dimensionless
deltae(i) = 1/CL_deltae*(CL(i)-CL_alpha_alpha-CL_zero);
fprintf("The elevator moment for gamma = %.1f and alpha = %d este %.4f m\n", gamma(i), alpha(j), deltae(i));


% Complete calculation of Cm

% Coefficient definition
Cm_zero = -0.05; % moment coefficient at zero angle of attack
Cm_alpha = -0.9; % moment coefficient gradient with angle of attack
Cm_deltae = -1.2; % moment coefficient gradient with elevator deflection

% Calculation of elevator deflection
CL_alpha_alpha = 2*pi; % Derivative of lift coefficient with respect to angle of attack, dimensionless
CL_zero = 0.2; % Lift coefficient at zero angle of attack, dimensionless
CL_deltae = 0.8; % Derivative of lift coefficient with respect to elevator deflection, dimensionless
deltaE(i) = 1/CL_deltae*(CL(i)-CL_alpha_alpha-CL_zero);
fprintf("Elevator deflection for gamma = %.1f and alpha = %d is %.4f m\n", gamma(i), alpha(j), deltaE(i));

% Conversion of angles from degrees to radians
% alpha = alpha * pi / 180;
% deltae = deltae * pi / 180;

% Calculation of moment coefficient
Cm(i,j) = Cm_zero + Cm_alpha * alpha(j)*pi/180 + Cm_deltae * deltaE(i)*pi/180;


% Calculating the final value of the equation
        diff_alpha_gamma = (alpha(j) - gamma(i)) * pi / 180; % Converting the difference between gamma and alpha to radians
%         eqn = ((Iy * (V^2/R) * (diff_alpha_gamma)^2) / (gamma(i+1)-gamma(i))*pi/180) - (0.5*rho * V^2 * Sc * Cm(i,j));
        eqn = ((Iy * (V^2/R) * (diff_alpha_gamma)^2) ./ gradient(gamma)*pi/180) - (0.5*rho * V^2 * Sc * Cm(i,j));
        tol = 1e-6;
        if (eqn) < tol  % use relative tolerance
            fprintf("For gamma = %.1f and alpha = %d, the equation is satisfied\n", gamma(i), alpha(j));
        else
            fprintf('The equation is not satisfied for gamma = %.1f and alpha = %d\n', gamma(i), alpha(j));
        end
    end
end

    0.7619

The elevator moment for gamma = 0.0 and alpha = 0 este -18.4042 m

Elevator deflection for gamma = 0.0 and alpha = 0 is -7.1516 m

For gamma = 0.0 and alpha = 0, the equation is satisfied

    0.7619

The elevator moment for gamma = 0.0 and alpha = 5 este -18.4042 m

Elevator deflection for gamma = 0.0 and alpha = 5 is -7.1516 m

For gamma = 0.0 and alpha = 5, the equation is satisfied

    0.7619

The elevator moment for gamma = 0.0 and alpha = 10 este -18.4042 m

Elevator deflection for gamma = 0.0 and alpha = 10 is -7.1516 m

The equation is not satisfied for gamma = 0.0 and alpha = 10

    0.7619

The elevator moment for gamma = 0.0 and alpha = 15 este -18.4042 m

Elevator deflection for gamma = 0.0 and alpha = 15 is -7.1516 m

The equation is not satisfied for gamma = 0.0 and alpha = 15

    0.7619

The elevator moment for gamma = 0.0 and alpha = 20 este -18.4042 m

Elevator deflection for gamma = 0.0 and alpha = 20 is -7.1516 m

The equation is not satisfied for gamma = 0.0 and alpha = 20

    0.7619    0.7597

The elevator moment for gamma = 10.0 and alpha = 0 este -18.4117 m

Elevator deflection for gamma = 10.0 and alpha = 0 is -7.1544 m

For gamma = 10.0 and alpha = 0, the equation is satisfied

    0.7619    0.7597

The elevator moment for gamma = 10.0 and alpha = 5 este -18.4117 m

Elevator deflection for gamma = 10.0 and alpha = 5 is -7.1544 m

For gamma = 10.0 and alpha = 5, the equation is satisfied

    0.7619    0.7597

The elevator moment for gamma = 10.0 and alpha = 10 este -18.4117 m

Elevator deflection for gamma = 10.0 and alpha = 10 is -7.1544 m

The equation is not satisfied for gamma = 10.0 and alpha = 10

    0.7619    0.7597

The elevator moment for gamma = 10.0 and alpha = 15 este -18.4117 m

Elevator deflection for gamma = 10.0 and alpha = 15 is -7.1544 m

The equation is not satisfied for gamma = 10.0 and alpha = 15

    0.7619    0.7597

The elevator moment for gamma = 10.0 and alpha = 20 este -18.4117 m

Elevator deflection for gamma = 10.0 and alpha = 20 is -7.1544 m

The equation is not satisfied for gamma = 10.0 and alpha = 20

    0.7619    0.7597    0.7422

The elevator moment for gamma = 30.0 and alpha = 0 este -18.4701 m

Elevator deflection for gamma = 30.0 and alpha = 0 is -7.1763 m

For gamma = 30.0 and alpha = 0, the equation is satisfied

    0.7619    0.7597    0.7422

The elevator moment for gamma = 30.0 and alpha = 5 este -18.4701 m

Elevator deflection for gamma = 30.0 and alpha = 5 is -7.1763 m

For gamma = 30.0 and alpha = 5, the equation is satisfied

    0.7619    0.7597    0.7422

The elevator moment for gamma = 30.0 and alpha = 10 este -18.4701 m

Elevator deflection for gamma = 30.0 and alpha = 10 is -7.1763 m

The equation is not satisfied for gamma = 30.0 and alpha = 10

    0.7619    0.7597    0.7422

The elevator moment for gamma = 30.0 and alpha = 15 este -18.4701 m

Elevator deflection for gamma = 30.0 and alpha = 15 is -7.1763 m

The equation is not satisfied for gamma = 30.0 and alpha = 15

    0.7619    0.7597    0.7422

The elevator moment for gamma = 30.0 and alpha = 20 este -18.4701 m

Elevator deflection for gamma = 30.0 and alpha = 20 is -7.1763 m

The equation is not satisfied for gamma = 30.0 and alpha = 20

    0.7619    0.7597    0.7422    0.6881

The elevator moment for gamma = 60.0 and alpha = 0 este -18.6501 m

Elevator deflection for gamma = 60.0 and alpha = 0 is -7.2438 m

For gamma = 60.0 and alpha = 0, the equation is satisfied

    0.7619    0.7597    0.7422    0.6881

The elevator moment for gamma = 60.0 and alpha = 5 este -18.6501 m

Elevator deflection for gamma = 60.0 and alpha = 5 is -7.2438 m

For gamma = 60.0 and alpha = 5, the equation is satisfied

    0.7619    0.7597    0.7422    0.6881

The elevator moment for gamma = 60.0 and alpha = 10 este -18.6501 m

Elevator deflection for gamma = 60.0 and alpha = 10 is -7.2438 m

The equation is not satisfied for gamma = 60.0 and alpha = 10

    0.7619    0.7597    0.7422    0.6881

The elevator moment for gamma = 60.0 and alpha = 15 este -18.6501 m

Elevator deflection for gamma = 60.0 and alpha = 15 is -7.2438 m

The equation is not satisfied for gamma = 60.0 and alpha = 15

    0.7619    0.7597    0.7422    0.6881

The elevator moment for gamma = 60.0 and alpha = 20 este -18.6501 m

Elevator deflection for gamma = 60.0 and alpha = 20 is -7.2438 m

The equation is not satisfied for gamma = 60.0 and alpha = 20

    0.7619    0.7597    0.7422    0.6881    0.6144

The elevator moment for gamma = 90.0 and alpha = 0 este -18.8961 m

Elevator deflection for gamma = 90.0 and alpha = 0 is -7.3360 m

For gamma = 90.0 and alpha = 0, the equation is satisfied

    0.7619    0.7597    0.7422    0.6881    0.6144

The elevator moment for gamma = 90.0 and alpha = 5 este -18.8961 m

Elevator deflection for gamma = 90.0 and alpha = 5 is -7.3360 m

For gamma = 90.0 and alpha = 5, the equation is satisfied

    0.7619    0.7597    0.7422    0.6881    0.6144

The elevator moment for gamma = 90.0 and alpha = 10 este -18.8961 m

Elevator deflection for gamma = 90.0 and alpha = 10 is -7.3360 m

The equation is not satisfied for gamma = 90.0 and alpha = 10

    0.7619    0.7597    0.7422    0.6881    0.6144

The elevator moment for gamma = 90.0 and alpha = 15 este -18.8961 m

Elevator deflection for gamma = 90.0 and alpha = 15 is -7.3360 m

The equation is not satisfied for gamma = 90.0 and alpha = 15

    0.7619    0.7597    0.7422    0.6881    0.6144

The elevator moment for gamma = 90.0 and alpha = 20 este -18.8961 m

Elevator deflection for gamma = 90.0 and alpha = 20 is -7.3360 m

The equation is not satisfied for gamma = 90.0 and alpha = 20

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406

The elevator moment for gamma = 120.0 and alpha = 0 este -19.1420 m

Elevator deflection for gamma = 120.0 and alpha = 0 is -7.4282 m

For gamma = 120.0 and alpha = 0, the equation is satisfied

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406

The elevator moment for gamma = 120.0 and alpha = 5 este -19.1420 m

Elevator deflection for gamma = 120.0 and alpha = 5 is -7.4282 m

For gamma = 120.0 and alpha = 5, the equation is satisfied

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406

The elevator moment for gamma = 120.0 and alpha = 10 este -19.1420 m

Elevator deflection for gamma = 120.0 and alpha = 10 is -7.4282 m

The equation is not satisfied for gamma = 120.0 and alpha = 10

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406

The elevator moment for gamma = 120.0 and alpha = 15 este -19.1420 m

Elevator deflection for gamma = 120.0 and alpha = 15 is -7.4282 m

The equation is not satisfied for gamma = 120.0 and alpha = 15

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406

The elevator moment for gamma = 120.0 and alpha = 20 este -19.1420 m

Elevator deflection for gamma = 120.0 and alpha = 20 is -7.4282 m

The equation is not satisfied for gamma = 120.0 and alpha = 20

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866

The elevator moment for gamma = 150.0 and alpha = 0 este -19.3220 m

Elevator deflection for gamma = 150.0 and alpha = 0 is -7.4958 m

For gamma = 150.0 and alpha = 0, the equation is satisfied

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866

The elevator moment for gamma = 150.0 and alpha = 5 este -19.3220 m

Elevator deflection for gamma = 150.0 and alpha = 5 is -7.4958 m

For gamma = 150.0 and alpha = 5, the equation is satisfied

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866

The elevator moment for gamma = 150.0 and alpha = 10 este -19.3220 m

Elevator deflection for gamma = 150.0 and alpha = 10 is -7.4958 m

The equation is not satisfied for gamma = 150.0 and alpha = 10

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866

The elevator moment for gamma = 150.0 and alpha = 15 este -19.3220 m

Elevator deflection for gamma = 150.0 and alpha = 15 is -7.4958 m

The equation is not satisfied for gamma = 150.0 and alpha = 15

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866

The elevator moment for gamma = 150.0 and alpha = 20 este -19.3220 m

Elevator deflection for gamma = 150.0 and alpha = 20 is -7.4958 m

The equation is not satisfied for gamma = 150.0 and alpha = 20

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668

The elevator moment for gamma = 180.0 and alpha = 0 este -19.3879 m

Elevator deflection for gamma = 180.0 and alpha = 0 is -7.5205 m

For gamma = 180.0 and alpha = 0, the equation is satisfied

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668

The elevator moment for gamma = 180.0 and alpha = 5 este -19.3879 m

Elevator deflection for gamma = 180.0 and alpha = 5 is -7.5205 m

For gamma = 180.0 and alpha = 5, the equation is satisfied

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668

The elevator moment for gamma = 180.0 and alpha = 10 este -19.3879 m

Elevator deflection for gamma = 180.0 and alpha = 10 is -7.5205 m

The equation is not satisfied for gamma = 180.0 and alpha = 10

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668

The elevator moment for gamma = 180.0 and alpha = 15 este -19.3879 m

Elevator deflection for gamma = 180.0 and alpha = 15 is -7.5205 m

The equation is not satisfied for gamma = 180.0 and alpha = 15

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668

The elevator moment for gamma = 180.0 and alpha = 20 este -19.3879 m

Elevator deflection for gamma = 180.0 and alpha = 20 is -7.5205 m

The equation is not satisfied for gamma = 180.0 and alpha = 20

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866

The elevator moment for gamma = 210.0 and alpha = 0 este -19.3220 m

Elevator deflection for gamma = 210.0 and alpha = 0 is -7.4958 m

For gamma = 210.0 and alpha = 0, the equation is satisfied

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866

The elevator moment for gamma = 210.0 and alpha = 5 este -19.3220 m

Elevator deflection for gamma = 210.0 and alpha = 5 is -7.4958 m

The equation is not satisfied for gamma = 210.0 and alpha = 5

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866

The elevator moment for gamma = 210.0 and alpha = 10 este -19.3220 m

Elevator deflection for gamma = 210.0 and alpha = 10 is -7.4958 m

The equation is not satisfied for gamma = 210.0 and alpha = 10

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866

The elevator moment for gamma = 210.0 and alpha = 15 este -19.3220 m

Elevator deflection for gamma = 210.0 and alpha = 15 is -7.4958 m

The equation is not satisfied for gamma = 210.0 and alpha = 15

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866

The elevator moment for gamma = 210.0 and alpha = 20 este -19.3220 m

Elevator deflection for gamma = 210.0 and alpha = 20 is -7.4958 m

The equation is not satisfied for gamma = 210.0 and alpha = 20

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406

The elevator moment for gamma = 240.0 and alpha = 0 este -19.1420 m

Elevator deflection for gamma = 240.0 and alpha = 0 is -7.4282 m

For gamma = 240.0 and alpha = 0, the equation is satisfied

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406

The elevator moment for gamma = 240.0 and alpha = 5 este -19.1420 m

Elevator deflection for gamma = 240.0 and alpha = 5 is -7.4282 m

The equation is not satisfied for gamma = 240.0 and alpha = 5

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406

The elevator moment for gamma = 240.0 and alpha = 10 este -19.1420 m

Elevator deflection for gamma = 240.0 and alpha = 10 is -7.4282 m

The equation is not satisfied for gamma = 240.0 and alpha = 10

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406

The elevator moment for gamma = 240.0 and alpha = 15 este -19.1420 m

Elevator deflection for gamma = 240.0 and alpha = 15 is -7.4282 m

The equation is not satisfied for gamma = 240.0 and alpha = 15

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406

The elevator moment for gamma = 240.0 and alpha = 20 este -19.1420 m

Elevator deflection for gamma = 240.0 and alpha = 20 is -7.4282 m

The equation is not satisfied for gamma = 240.0 and alpha = 20

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144

The elevator moment for gamma = 270.0 and alpha = 0 este -18.8961 m

Elevator deflection for gamma = 270.0 and alpha = 0 is -7.3360 m

For gamma = 270.0 and alpha = 0, the equation is satisfied

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144

The elevator moment for gamma = 270.0 and alpha = 5 este -18.8961 m

Elevator deflection for gamma = 270.0 and alpha = 5 is -7.3360 m

The equation is not satisfied for gamma = 270.0 and alpha = 5

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144

The elevator moment for gamma = 270.0 and alpha = 10 este -18.8961 m

Elevator deflection for gamma = 270.0 and alpha = 10 is -7.3360 m

The equation is not satisfied for gamma = 270.0 and alpha = 10

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144

The elevator moment for gamma = 270.0 and alpha = 15 este -18.8961 m

Elevator deflection for gamma = 270.0 and alpha = 15 is -7.3360 m

The equation is not satisfied for gamma = 270.0 and alpha = 15

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144

The elevator moment for gamma = 270.0 and alpha = 20 este -18.8961 m

Elevator deflection for gamma = 270.0 and alpha = 20 is -7.3360 m

The equation is not satisfied for gamma = 270.0 and alpha = 20

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881

The elevator moment for gamma = 300.0 and alpha = 0 este -18.6501 m

Elevator deflection for gamma = 300.0 and alpha = 0 is -7.2438 m

For gamma = 300.0 and alpha = 0, the equation is satisfied

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881

The elevator moment for gamma = 300.0 and alpha = 5 este -18.6501 m

Elevator deflection for gamma = 300.0 and alpha = 5 is -7.2438 m

The equation is not satisfied for gamma = 300.0 and alpha = 5

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881

The elevator moment for gamma = 300.0 and alpha = 10 este -18.6501 m

Elevator deflection for gamma = 300.0 and alpha = 10 is -7.2438 m

The equation is not satisfied for gamma = 300.0 and alpha = 10

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881

The elevator moment for gamma = 300.0 and alpha = 15 este -18.6501 m

Elevator deflection for gamma = 300.0 and alpha = 15 is -7.2438 m

The equation is not satisfied for gamma = 300.0 and alpha = 15

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881

The elevator moment for gamma = 300.0 and alpha = 20 este -18.6501 m

Elevator deflection for gamma = 300.0 and alpha = 20 is -7.2438 m

The equation is not satisfied for gamma = 300.0 and alpha = 20

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422

The elevator moment for gamma = 330.0 and alpha = 0 este -18.4701 m

Elevator deflection for gamma = 330.0 and alpha = 0 is -7.1763 m

The equation is not satisfied for gamma = 330.0 and alpha = 0

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422

The elevator moment for gamma = 330.0 and alpha = 5 este -18.4701 m

Elevator deflection for gamma = 330.0 and alpha = 5 is -7.1763 m

The equation is not satisfied for gamma = 330.0 and alpha = 5

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422

The elevator moment for gamma = 330.0 and alpha = 10 este -18.4701 m

Elevator deflection for gamma = 330.0 and alpha = 10 is -7.1763 m

The equation is not satisfied for gamma = 330.0 and alpha = 10

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422

The elevator moment for gamma = 330.0 and alpha = 15 este -18.4701 m

Elevator deflection for gamma = 330.0 and alpha = 15 is -7.1763 m

The equation is not satisfied for gamma = 330.0 and alpha = 15

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422

The elevator moment for gamma = 330.0 and alpha = 20 este -18.4701 m

Elevator deflection for gamma = 330.0 and alpha = 20 is -7.1763 m

The equation is not satisfied for gamma = 330.0 and alpha = 20

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422    0.7619

The elevator moment for gamma = 360.0 and alpha = 0 este -18.4042 m

Elevator deflection for gamma = 360.0 and alpha = 0 is -7.1516 m

The equation is not satisfied for gamma = 360.0 and alpha = 0

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422    0.7619

The elevator moment for gamma = 360.0 and alpha = 5 este -18.4042 m

Elevator deflection for gamma = 360.0 and alpha = 5 is -7.1516 m

The equation is not satisfied for gamma = 360.0 and alpha = 5

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422    0.7619

The elevator moment for gamma = 360.0 and alpha = 10 este -18.4042 m

Elevator deflection for gamma = 360.0 and alpha = 10 is -7.1516 m

The equation is not satisfied for gamma = 360.0 and alpha = 10

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422    0.7619

The elevator moment for gamma = 360.0 and alpha = 15 este -18.4042 m

Elevator deflection for gamma = 360.0 and alpha = 15 is -7.1516 m

The equation is not satisfied for gamma = 360.0 and alpha = 15

    0.7619    0.7597    0.7422    0.6881    0.6144    0.5406    0.4866    0.4668    0.4866    0.5406    0.6144    0.6881    0.7422    0.7619

The elevator moment for gamma = 360.0 and alpha = 20 este -18.4042 m

Elevator deflection for gamma = 360.0 and alpha = 20 is -7.1516 m

The equation is not satisfied for gamma = 360.0 and alpha = 20

%plot pitching moment coefficient (Cm)
figure
plot(gamma,Cm)
legend(compose('\alpha = %d' , (alpha))); grid
xlabel('\gamma^{o}'); ylabel('Cm [-]')

% Uncomment this according to your convenience 
%Plot graphs
figure;
plot(gamma,CL_vector);
xlabel('gamma');
ylabel('CL');
grid on;

figure;
plot(gamma,CD_vector);
xlabel('gamma');
ylabel('CD');
grid on

figure;
plot(gamma,T_vector);
xlabel('gamma');
ylabel('T');
grid on;

In the below line

eqn = ((Iy * (V^2/R) * (diff_alpha_gamma)^2) ./ gradient(gamma)*pi/180) - (0.5*rho * V^2 * Sc * Cm(i,j));

you can use gradient function as shwon and change the for loop as

for i = 1:length(gamma)

Regarding the second point, you are probably using a different index for alpha , since alpha vector is accessed using loop index j

fprintf("The elevator moment for gamma = %.1f and alpha = %d este %.4f m\n", gamma(i), alpha(j), deltae(i));
                                                                         %  ^^ use i  ^^ use j   ^^ use i