I wish to limit plotting a point on a single line and not anywhere else on the graph (just on the line) with every input

for M1 = 1:1:5

m = m+1;

%================================

% theta-beta-M relation

%================================

Nr = ((M1^2)*((sin(beta_range)).^2))-1;

Dr = ((gamma+(cos(2*beta_range)))*M1^2)+2;

theta = atan(2*cot(beta_range).*Nr./Dr);

%================================

% max. theta for a M1

%================================

% For a given mach number, theta max flow deflection angle for which an

% attached shock is possible.

% max theta for the Mach No.

a(m) = max(theta);

% find the beta for max. theta

b(m) = beta_range(find(theta==a(m)));

plot(theta,beta_range,'-b')

hold on

end

% Mach number downstream of a strong shock will always be sub-sonic

plot(a,b,'-r','Linewidth',1.5)

xlabel('\theta')

ylabel('\beta')

axis([0 42*pi/180 0 pi/2])

% Flow Deflection angle theta Comes from geometry in radian

Theta_r1 = 0.261;

% Flow Deflection angle in degrees

for M1 = 5

Theta_1 = Theta_r1*(180/pi);

fprintf('Flow Deflection angle = %0.2f°\n', Theta_1);

end

% Shock wave angle in radians

beta_r1 = interp1(theta,beta_range,Theta_r1)

% Shock wave angle in radians

Beta_1 = beta_r1*(180/pi);

fprintf('Shock wave angle = %0.2f°\n', Beta_1);

if Theta_r1 < a(m)

fprintf('Weak Shock wave')

else

fprintf('Strong Shock wave')

end

plot (Theta_r1,beta_r1, 'o')

%This is a standard Theta-Beta-Mach Number plot

%The plot this code will generated will have 4 curved lines. Each represents Mach number M1. Outermost being Mach 5. With every input value of theta_r1, I wish to limit plotting the point only on Mach 5 line.

Thanks in advance.

[VBBV]

It seems you are converting the Theta and Beta values to degrees which produces out of bound values of the chart and makes it invisible.

m = 0;
% change these range values for different curve 
beta_range = linspace(0,pi/2,100);
gamma = 1.4;
for M1                = 1:1:5
    m                 = m+1;
    %================================
    %     theta-beta-M relation
    %================================
    Nr                = ((M1^2)*((sin(beta_range)).^2))-1;    
    
    Dr                = ((gamma+(cos(2*beta_range)))*M1^2)+2;
    
    theta             = atan(2*cot(beta_range).*Nr./Dr);
    %================================
    %      max. theta for a M1
    %================================
    % For a given mach number, theta max flow deflection angle for which an
    % attached shock is possible.
    % max theta for the Mach No.
    a(m)              = max(theta);                   
    
    % find the beta for max. theta
    b(m)              = beta_range(find(theta==a(m)));     
    
    plot(theta,beta_range,'-b')
    
    hold on
end
xlabel('\theta')
ylabel('\beta')
axis([0 42*pi/180 0 pi/2])

% Mach number downstream of a strong shock will always be sub-sonic
plot(a,b,'-r','Linewidth',1.5)
hold on
% Flow Deflection angle theta Comes from geometry in radian
Theta_r1              = 0.261;
% Flow Deflection angle in degrees

if isequal(M1, 5)
        Theta_1               = Theta_r1;
        fprintf('Flow Deflection angle =  %0.2f°\n', Theta_1);
        % Shock wave angle in radians
        beta_r1               = interp1(theta,beta_range,Theta_r1)
        % Shock wave angle in radians
        Beta_1                = beta_r1;
        fprintf('Shock wave angle =  %0.2f°\n', Beta_1);
        if Theta_r1 < max(a)
            fprintf('Weak Shock wave')
        else
            fprintf('Strong Shock wave')
        end 
        % put this line insdie the condition for Mach number = 5
        plot (Theta_r1,Beta_1, 'ro','MarkerFaceColor','r')
end

Flow Deflection angle =  0.26°

beta_r1 = 0.4237

Shock wave angle =  0.42°

Weak Shock wave

xlim([0 pi/4]); ylim([0 pi/2])

Answer 1

[VBBV]

for M1                = 1:1:5
    m                 = m+1;
    %================================
    %     theta-beta-M relation
    %================================
    Nr                = ((M1^2)*((sin(beta_range)).^2))-1;    
    
    Dr                = ((gamma+(cos(2*beta_range)))*M1^2)+2;
    
    theta             = atan(2*cot(beta_range).*Nr./Dr);
    %================================
    %      max. theta for a M1
    %================================
    % For a given mach number, theta max flow deflection angle for which an
    % attached shock is possible.
    % max theta for the Mach No.
    a(m)              = max(theta);                   
    
    % find the beta for max. theta
    b(m)              = beta_range(find(theta==a(m)));     
    
    plot(theta,beta_range,'-b')
    
    hold on
end
% Mach number downstream of a strong shock will always be sub-sonic
plot(a,b,'-r','Linewidth',1.5)
xlabel('\theta')
ylabel('\beta')
axis([0 42*pi/180 0 pi/2])
% Flow Deflection angle theta Comes from geometry in radian
Theta_r1              = 0.261;
% Flow Deflection angle in degrees

hold on
if isequal(M1, 5)
        Theta_1               = Theta_r1*(180/pi);
        fprintf('Flow Deflection angle =  %0.2f°\n', Theta_1);
        % Shock wave angle in radians
        beta_r1               = interp1(theta,beta_range,Theta_r1)
        % Shock wave angle in radians
        Beta_1                = beta_r1*(180/pi);
        fprintf('Shock wave angle =  %0.2f°\n', Beta_1);
        if Theta_r1 < a(m)
            fprintf('Weak Shock wave')
        else
            fprintf('Strong Shock wave')
        end 
        % put this line insdie the condition for Mach number = 5
        plot (Theta_1,Beta_1, 'o')
end

put this line insdie the condition for Mach number = 5

plot (Theta_r1,beta_r1, 'o')

[Dean]

I used your input but it did not work. May I did not explain it better. Allow me to try again, this is the figure that my code generates, has a red line line that connects all the maximum theta values for each mach number. For mach 5 (outermost curve). When I input the the of certain theta angle. I want matlab to plot a point below the maximum theta angle line for output of the corresonding beta value suggesting a weak shock wave. Everything about the red line gives a strong shock wave.

[VBBV]

It will plot exactly on the outer curve if you use the code which i gave earlier, See the example demonstration below plotted not for a maximum theta angle

m = 0;
% change these range values for different curve 
beta_range = linspace(0,pi/2,100);
gamma = 1.4;
for M1                = 1:1:5
    m                 = m+1;
    %================================
    %     theta-beta-M relation
    %================================
    Nr                = ((M1^2)*((sin(beta_range)).^2))-1;    
    
    Dr                = ((gamma+(cos(2*beta_range)))*M1^2)+2;
    
    theta             = atan(2*cot(beta_range).*Nr./Dr);
    %================================
    %      max. theta for a M1
    %================================
    % For a given mach number, theta max flow deflection angle for which an
    % attached shock is possible.
    % max theta for the Mach No.
    a(m)              = max(theta);                   
    
    % find the beta for max. theta
    b(m)              = beta_range(find(theta==a(m)));     
    
    plot(theta,beta_range,'-b')
    
    hold on
end
xlabel('\theta')
ylabel('\beta')
axis([0 42*pi/180 0 pi/2])

% Mach number downstream of a strong shock will always be sub-sonic
%plot(a,b,'-r','Linewidth',1.5)
hold on
% Flow Deflection angle theta Comes from geometry in radian
Theta_r1              = 0.161;
% Flow Deflection angle in degrees

if isequal(M1, 5)
        Theta_1               = Theta_r1;
        fprintf('Flow Deflection angle =  %0.2f°\n', Theta_1);
        % Shock wave angle in radians
        beta_r1               = interp1(theta,beta_range,Theta_r1)
        % Shock wave angle in radians
        Beta_1                = beta_r1;
        fprintf('Shock wave angle =  %0.2f°\n', Beta_1);
        if Theta_r1 < max(a)
            fprintf('Weak Shock wave')
        else
            fprintf('Strong Shock wave')
        end 
        % put this line insdie the condition for Mach number = 5
        plot (Theta_r1,Beta_1, 'ro','MarkerFaceColor','r')
end

Flow Deflection angle =  0.16°

beta_r1 = 0.3258

Shock wave angle =  0.33°

Weak Shock wave

xlim([0 pi/4]); ylim([0 pi/2])