The surface of many airfoils can be described with an equation of the form y = m

Question

The surface of many airfoils can be described with an equation of the form y = minus plus tc/0.2 {a_0 squareroot x/c + a_1(x/c) + a_2(X/c)^2 + a_3(x/C)^3 + a_4(x/c)^4] where t is the maximum thickness as a fraction of the chord length c (e.g., t_max = ct). Given that c = 1 m and t = 0.2 m, the following values for y have been measured for a particular airfoil: Determine the constants a_0, a_1 a_2, a_3, and a_4. (Write a system of five equations and five unknowns, and use MATLAB to solve the equations.) An epicycloid is a curve (shown partly in the figure) obtained by tracing a point on a circle that rolls around a fixed circle. The parametric equation of a cycloid is given by: x = 13 cos(t) - 2cos(6.5t) y = 13 sin(t) - 2sin(6.5t)Plot the cycloid for 0 lessthanorequalto t lessthanorequalto 4 pi

Explanation / Answer

P22)

%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

Mat lab 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

P23)

%Assigning t

T= [0:0.01:4*pi];

X= (13*cos (t))-(2*cos (6.5*t));

Y= (13*sin (t))-(2*sin (6.5*t));

Plot(x, y)

Xlabel (‘x’)

Ylabel (‘y’)

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