How to iterate an equation to solve for missing variable

So I need to run a loop that inserts a value into a variable inside an equation until the equation equals a known amount.

Known amount: Thrust Coefficient (CT) = 0.0071

Equation: CT = ((1/2)*sigma*a)*(((1/3)*theta)-((1/2)*sqrt(CT/2)))

Non-working code:

close all; clear all; clc;

CT = 0.0071;
sigma = 0.0850;
a = 6;

theta = 0:360;
for i = theta
    CT(i) = ((1/2)*sigma*a)*(((1/3)*theta)-((1/2)*sqrt(CT/2)));
        if CT(i) == CT
            break
        end
end

Answer 1

[Joseph Wilson]

So there are a couple problems here:

1) the for loop can't start at zero so change to

for i = 1:length(theta) solves that

2) CT will try to override itself so need a new variable: change made after 3)

3) theta needs to be indexed in the equation to use only a single value so equation is then:

CT_test(i) = ((1/2)*sigma*a)*(((1/3)*theta(i))-((1/2)*sqrt(CT/2)));

4) you have CT in your equation... not sure if you need to do a little more algebra to solve that to the left side or not...

5) your step values of theta once it starts working are too large to find a solution

theta = 0:0.001:360

6) your if statement has no room for error so change to:

if abs(CT_test(i)-CT) < 0.00001

break

end

final solution:

close all; clear all; clc;

CT = 0.0071;

sigma = 0.0850;

a = 6;

theta = 0:0.001:360;

for i = 1:length(theta)

CT_test(i) = ((1/2)*sigma*a)*(((1/3)*theta(i))-((1/2)*sqrt(CT/2)));

if abs(CT_test(i)-CT) < 0.00001

break

end

end

[Terry Poole]

Thanks a bunch!

Worked perfectly.

I knew it was something small but I've been staring at this code for so many hours now that my brain just isn't functioning properly.