The surface of many airfoils can be described with an equation of the form tc 0.

Question

The surface of many airfoils can be described with an equation of the form tc 0.2 where t is the maximum thickness as a fraction of the chord length c (e.g. tmax-ct). Given that c = 1m and t = 0.2m, the following values for y have been measured for a particular airfoil x(m) y(m) Determine the constants ao, ai , a2, , a4- 0.15 0.85 0.35 0.09914 write a system of five equations and five unknowns, and use MATLAB to solve the equations. 0.5 0.7 0.08909 0.08823 0.06107 0.03421 What is the value of ao? 0.1025 O 0.2969 0.2861 O-0.3526 O-0.1258

Explanation / Answer

ANS:

CODE:

%start the   script

Clc

C=1;

T=0.2;

Y= [0.08909 0.09914 0.08823 0.06107 0.03421];

X= [0.15 0.35 0.5 0.7 0.85];

For I =1:1:5;

J=1;

A (I, j) =sqrt ((x (I))/c);

J=j+1;

A (I, j) =(x (I))/c;

J=j+1;

A (I, j) = ((x (i))/c) ^2;

J=j+1;

A (I, j) = ((x (i))/c) ^3;

J=j+1;

A (I, j) = ((x (I))/c) ^4;

End

A

X=Inv (A)*transpose(y);

For k=0:1:4

Fprintf(‘a% d=%3.3f ’,k ,x(k+1))

End

Output

A=

0.3873    0.1500   0.0225   0.0034   0.0005

0.5916    0.3500   0.1225   0.0429   0.0150

0.7071    0.5000   0.2500   0.1250   0.0625

0.8367    0.7000   0.4900   0.3430   0.2401

0.990      0.8500   0.7225   0.6141   0.5220

A0=0.297

A1=-0.126

A2=-0.353

A3=0.286

A4=-0.103

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