Numerical integration of a subfunction

Hello,

I'm trying to do a numerical integration of a function (which is defined in another function), and I'm getting some errors, what I get wrong here ? Thanks. Nimrod Daniel.

function [C_l]=lift_coefficient(a,b)
% the function calculates the lift coeeficient  of a wing

if nargin<2 %default input
%wing parameters:   
h=1.4;
t=2.1;
chord=8.6;

%defining camber-line paramets:
a=h/t^2; % a before normalization
a=a/chord;
b=(1-2*t)/(t^2); % b before normalization
b=b/chord;
end;

C_l=quad(@camber,x,-0.9999,0.9999) %numerical integration of f

function f=camber(x)
      y_c=a/2*(1-x.^2)/(2+b*(x+1)); %camber-line function
      dyc_dx=diff(y_c,x,1)% first derivative of y_c
      f=-2*sqrt((1+x)/(1-x))*dyc_dx % integrand
end

end

[Nimrod Daniel]

I solved the problem in another approach. I had the points on the function, so I implemented the trapezoidal rule, though I'd like to know what I should have fixed in the code (more cleaner now).

function [C_l]=lift_coefficient(a,b) % the function calculates the lift coeeficient of a wing's cross-sections %inputs - vectors a and b are defining the cross-sectional parameters

if nargin<2 a=[0.3 0.5 0.7]; b=[-0.7 -0.8 -0.9]; end;

C_l=quad(@camber,-0.9999,0.9999) %numerical integration of f

function f=camber(x) y_c=a./2*(1-x.^2)./(2+b.*(x+1)); %camber-line function dyc_dx=diff(y_c,x)% first derivative of y_c f=-2*sqrt((1+x)./(1-x))*dyc_dx % integrand end

end

Answer 1

[Patrik Ek]

Where does the error occur? Also I see a number of errors, that you have done. Firstly, you need to use points before all the operators that may want to do a pointwise multiplication of two vectors. This since quad will recursively input a vector to the function.

Secondly, matlab uses simpsons quadraure in quad, it is not a symbolic operation. This means that the variable x is not necessary in the function call of quad, which is why the syntax is only

quad(@fun,a,b) You can check this up on the internet.

Good luck and please accept the answer if this solves the issue! BR/ Patrik