to plot alpha(a) vs diameter(D) in the given problem. where A = l*sin(b), B = l*cos(b), C = ( h + 0.5*D )*sin (b) − 0.5*D*tan(b) and E = ( h + 0.5*D)*cos(b) − 0.5*D.

Given equation is A*sin(a)*cos(a) + B*sin(a)*sin(a) − C*cos(a) − E*sin(a) = 0 Also l = 89in., h = 49in. and b= 11.5(angle in degree).

we have to plot alpha(a) vs Diameter(D) using Newton's method where D varies from 30 - 100 inches with a step of 10 inch. plz reply soon.

[KSSV]

Where is D in the given equation? Also what have you attempted for your Home Work?

[Rahul Joshi]

%% initial conditions

l = 89;

h = 49;

b1 = 11.5;

D = 30:10:100;

a = 33;

maxIter = 10;

tola = 1e-6;

%% define function

for j = 1:1:8

A = l*sind(b1);

B = l*cosd(b1);

C = ((h+0.5*D)*sind(b1)) - (0.5*D*tand(b1));

E = ((h+0.5*D)*cosd(b1)) - (0.5*D);

for i = 1:maxIter

f = (A*sind(a)*cosd(a) + B*sind(a)*sind(a) - C*cosd(a) - E*sind(a));

df = (A*cosd(2*a) + B*sind(2*a) + C*sind(a) - E*cosd(a));

a = a - f/df;

end

end

Here is the code I tried. I am beginner at MATLAB code writing so please keep it simple.

[Cris LaPierre]

MATLAB Onramp

[Rahul Joshi]

Thank you for the link..

Answer 1

[Alan Stevens]

Try replacing D within the j-loop by D(j). Also add something like alpha(j) = a after the end of the i-loop (but inside the j-loop). Then you can plot D vs alpha.

I think you will need to increase your value of maxIter to get a converged solution.

You might also think of using a while loop, instead of the i-loop, with an error calculation in order to compare the error to your tola value (which is currently unused).

[Rahul Joshi]

Thank you for the help, these all things I did with some other modification but I couldnt get rid of the error value. Its not coming below tola value. Can u suggest any point?

[Alan Stevens]

How about:

%% initial conditions
l = 89;
h = 49;
b1 = 11.5;
D = 30:10:100;
a = 33;
maxIter = 1000;
tola = 1e-6;
err = 1;
%% define function
for j = 1:1:8
    
    A = l*sind(b1);
    B = l*cosd(b1);
    C = ((h+0.5*D(j))*sind(b1)) - (0.5*D(j)*tand(b1));
    E = ((h+0.5*D(j))*cosd(b1)) - (0.5*D(j));
    its = 0;
    err = 1;
    while err>tola && its<maxIter
        its = its+1;
        aold = a;
        f = (A*sind(a)*cosd(a) + B*sind(a)*sind(a) - C*cosd(a) - E*sind(a));
        df = (A*cosd(2*a) + B*sind(2*a) + C*sind(a) - E*cosd(a));
        a = a - f/df;
        err = abs(a - aold);
    end
    if its==maxIter, disp(j), end
    alpha(j) = a;
end

plot(D,alpha),grid
xlabel('D'), ylabel('alpha')