How do I get a real, decimal answer from my equation instead of an empty array?

Hi, I am struggling to get a real, decimal answer for the equation used below in my code. It keeps returning an empty array. Please let me know where I am going wrong. Thank you in advance.

% Parameters
syms x1
width = 1; % meters
nozzle = 0.05; % meters
cstress = 0.6 * 10^6; % Pa
force = 6.43 * 10^3; % N (converted over 1m width)

% Design criteria
crushing = force / cstress;

% Variable area
% Area 1   
A1 = width * 2 * nozzle;
% Area 2 with variables
cent_height1 = x1-(7*nozzle/3); 
angle1 = atan(cent_height1/(0.5*width))

angle1 = 

vertical_dist1 = nozzle/(cos(angle1));
A2 = (width/2)*(cent_height1+vertical_dist1);
A3 = 0.5*(width/2)*(cent_height1);
% Total Area
A = A1 + A2 - 2*(A3);

% Solve for x1
eqn1 = crushing == A

eqn1 = 

value1 = solve(eqn1, x1);
finalvalue1 = max(real(value1));
finalvalue1 = max(double(finalvalue1), 3*nozzle);
fprintf('x2: %.6f m \n', finalvalue1);

x2:  m 

[Rik]

It isn't immediately obvious to me that there is a solution (and the lack of formatting isn't helping).

How did you verify there is one?

[Dyuman Joshi]

FYI - Wolfram Alpha also gives output as (no solutions exist) for eqn1.

643/60000 = sqrt((2*x-7/30)^2+1)/40 + 1/10

[Alan Stevens]

Plot the right-hand side of eqn1 against x1. You will see that its minimum value is larger than that of the left-hand side, hence no solution.

Answer 1

[Nipun]

Hi Ruby,

I understand that you are trying to solve an equation using MATLAB solve functionality with no output.

On closely inspecting your input equations, I see that no solution exists for the system. The value of constant crushing as output by MATLAB:

0.0107

Additionally, if you plot A against x1, it has a minima at 7/60 with value 0.1250 . Hence, there is no intersection point for crushing and A. Therefore, no solution exists for eqn1

Hope this helps.

Regards,

Nipun