Wish to use output of the first iteration in a loop as an input in the second iteration of the loop

tic

M1 = 5;

Altitude = 28000;

gamma = 1.4;

Theta = 8;

[Beta] = betacalling(M1);

%Assume Beta is = [17 21 32];

for i = 1:M1

for j = 1:Beta

Mn1s1 = M1.*sin(Beta.*(pi./180));

M2 = (1./sind(Beta-Theta)).*sqrt((1+((gamma-1)./2).*(M1.^2).*(sind...

(Beta).^2))./((gamma*(M1.^2).*(sind(Beta).^2)-(gamma-1)./2)));

end

end

toc

First time it runs the calculation I want it to use 1st Beta value and M1 as 5. Second time it runs the calculation, I want it to use Beta value of 21 and M2 value instead of M1. And similarly for the third time as.

Can you please help me with this kind of a for loop.

Thank you.

Answer 1

[Dyuman Joshi]

%Values
M1             = 5;
Altitude       = 28000;
gamma          = 1.4;
Theta          = 8;

%[Beta]         = betacalling(M1);

Beta = [17 21 32];
%Preallocate M2 to store the values of each iteration
M2 = zeros(size(Beta));

for j = 1:numel(Beta)
Mn1s1 = M1.*sin(Beta(j).*(pi./180));
%M2 value corresponding to value in Beta
M2(j)    = (1./sind(Beta(j)-Theta)).*sqrt((1+((gamma-1)./2).*(M1.^2).*(sind...
              (Beta(j)).^2))./((gamma*(M1.^2).*(sind(Beta(j)).^2)-(gamma-1)./2)));
%Assign M2 value i.e. M2(j) obtained to M1, to be used for next iteration
M1 = M2(j);
end

Beta

Beta = 1×3

17 21 32

M2

M2 = 1×3

4.5708 2.9221 1.6832

[Dean]

Thank you so much. If how do I take it one step ahead if I wish to on every iteration use Beta value from the function that I used above. The value of Beta depends on Fixed value of

Theta = [ 8 10 18];

and M,M2,M3

Below is the Beta calling function:

function [Beta] = betacalling(M1)

n = 0;

gamma = 1.4;

Theta = 8;

for i = Theta

theta = Theta*pi/180;

mu = asin(1/M1);

c = tan(mu)^2;

a = ((gamma-1)/2+(gamma+1)*c/2)*tan(theta);

b = ((gamma+1)/2+(gamma+3)*c/2)*tan(theta);

d = sqrt(4.*(1-3.*a.*b).^3./((27.*a.^2.*c+9.*a.*b-2).^2)-1);

Beta = atan((b+9.*a.*c)./(2.*(1-3.*a.*b))-(d.*(27.*a.^2.*c+9.*a.*b-2))./...

(6.*a.*(1-3.*a.*b)).*tan(n.*pi./3+1./3.*atan(1./d))).*180/pi;

end

[Dyuman Joshi]

Just to make it clear, we start from M1 = 5, find the corresponding Beta value from this function. Use the beta value to find M and then continue to cycle.

This is what you want to do, right?

[Dean]

Yes starting with M1 = 5, theta = 8, finding corresponding Beta and M2 value.

In the second iteration

uses: M2, Theta2 = 10, finds corresponding Beta2 and M3 value

and in the third iteration

use M4, Theta3 = Theta1+Theta2, finds corresponding Beta3 and M4 value

If easier then having theta = linspace(8,18,1) %to have more than 3 inputs for theta if required

I hope this clears things up.

[Dean]

I am currently as you can see calling Beta from a different .m file for modularisation. But we can have it in a single script too.

[Dyuman Joshi]

Which values do you want to store? All values of M and Beta?

"If easier then having theta = linspace(8,18,1) %to have more than 3 inputs for theta if required"

I did not understand this statement.

[Dean]

Yes all value of M, Beta and Mn1s1. They will be used in more code that i have not mentioned here.

[Dean]

"If easier then having theta = linspace(8,18,1) %to have more than 3 inputs for theta if required"

sorry. this is just to consider having more than 3 more values of theta. More than 8, 10, 18.

[Dyuman Joshi]

Running for more than 4 iterations give complex values for variables.

%Number of iterations to do
N = 4;

%Values
Altitude       = 28000;
gamma          = 1.4;
Theta          = [8 10 zeros(1,N-2)];

M1 = [5 zeros(1,N)];
Mn1s1 = zeros(1,N);
Beta = zeros(1,N);

for k = 1:N
    if k>2
        Theta(k) = Theta(k-1) + Theta(k-2);
    end
    %Beta value from the function
    Beta(k) = betacalling(M1(k),Theta(k));
    
    Mn1s1(k) = M1(k).*sind(Beta(k));
    
    %Next value of M1
    M1(k+1)    = (1./sind(Beta(k)-Theta(k))).*sqrt((1+((gamma-1)./2).*(M1(k).^2).*(sind...
              (Beta(k)).^2))./((gamma*(M1(k).^2).*(sind(Beta(k)).^2)-(gamma-1)./2)));
    
end

M1

M1 = 1×5

5.0000 4.1972 3.4319 2.3803 1.0481

Beta

Beta = 1×4

17.5700 21.5460 32.7167 60.6327

Mn1s1

Mn1s1 = 1×4

1.5094 1.5414 1.8549 2.0744

Theta

Theta = 1×4

8 10 18 28

function Beta = betacalling(M1,theta)
    n=0;
    gamma = 1.4;

    %All operations in degrees
    mu             = asind(1/M1);
    c              = tand(mu)^2;
    a              = ((gamma-1)/2+(gamma+1)*c/2)*tand(theta);
    b              = ((gamma+1)/2+(gamma+3)*c/2)*tand(theta);
    d              = sqrt(4.*(1-3.*a.*b).^3./((27.*a.^2.*c+9.*a.*b-2).^2)-1);
    Beta           = atand((b+9.*a.*c)./(2.*(1-3.*a.*b))-(d.*(27.*a.^2.*c+9.*a.*b-2))./...
                     (6.*a.*(1-3.*a.*b)).*tan(n.*pi./3+1./3.*atan(1./d)));
end