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How to iterate an equation to solve for missing variable

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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

Respuesta aceptada

Joseph Wilson
Joseph Wilson el 4 de Feb. de 2021
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
  1 comentario
Terry Poole
Terry Poole el 4 de Feb. de 2021
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.

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