A wind tunnel test conducted on an airfoil section yielded t

A wind tunnel test conducted on an airfoil section yielded the following data between the lift coefficient (Cl) and the angle of attack You are required to develop a suitable polynomial relationship between alpha and C_L and fit a curve to the data points by the least-squares method using (a) hand calculations and (b) Matlab programming The procedure of solution should be as follows: (a) Write a Matlab function to fit a quadratic equation to the data points. Create [A] and [b] given by (1) and use backslash operator x = A\\b to find a vector of unknowns {a_o a_1 a_2} (b) Use Matlab functions polyfit() and polyval(). Plot original data (from the table), function y(x) = a_0 + a1_x + a_2x2 with coefficients obtained in (a); and values obtained using polyval () at the same graph. (Don\'t forget to create a vector for the range [0 20]!). Explain the results.

Solution

a) Matlab Code

A = [1 0 0;1 4 16; 1 8 64];
b = [0.11;0.55;0.95];
x = A\\b

Output

x =

    0.1100
    0.1150
   -0.0013

b) Matlab Code

a = [0 4 8 12 16 20];
Cl = [0.11 0.55 0.95 1.40 1.71 1.38];
p = polyfit(a,Cl,3);
f = polyval(p,a);
plot(a,Cl,\'r\',a,f,\'b\');