Ep 12 - About Elliptical wing & Solidworks

The Matlab script

clc
clear
N = 9; % (number of segments - 1)
S = 25; % m^2
AR = 8; % Aspect ratio
lambda = 0.6; % Taper ratio
alpha_twist = -1; % Twist angle (deg)
i_w = 2; % wing setting angle (deg)
a_2d = 6.3; % lift curve slope (1/rad)
alpha_0 = -1.5; % zero-lift angle of attack (deg)
b = sqrt(AR*S); % wing span (m)
MAC = S/b; % Mean Aerodynamic Chord (m)
Croot = (1.5*(1+lambda)*MAC)/(1+lambda+lambda^2); % root chord (m)
theta = pi/(2*N):pi/(2*N):pi/2;
alpha = i_w+alpha_twist:-alpha_twist/(N-1):i_w;
% segment’s angle of attack
z = (b/2)*cos(theta);
c = Croot * (1 - (1-lambda)*cos(theta)); % Mean Aerodynamics
Chord at each segment (m)
mu = c * a_2d / (4 * b);
LHS = mu .* (alpha-alpha_0)/57.3; % Left Hand Side
% Solving N equations to find coefficients A(i):
for i=1:N
for j=1:N
B(i,j) = sin((2*j-1) * theta(i)) * (1 + (mu(i) * (2*j-1)) /
sin(theta(i)));
end
end
A=B\transpose(LHS);
for i = 1:N
sum1(i) = 0;
sum2(i) = 0;
for j = 1 : N
sum1(i) = sum1(i) + (2*j-1) * A(j)*sin((2*j-1)*theta(i));
sum2(i) = sum2(i) + A(j)*sin((2*j-1)*theta(i));
end
end
CL = 4*b*sum2 ./ c;
CL1=[0 CL(1) CL(2) CL(3) CL(4) CL(5) CL(6) CL(7) CL(8) CL(9)];
y_s=[b/2 z(1) z(2) z(3) z(4) z(5) z(6) z(7) z(8) z(9)];
plot(y_s,CL1,’-o’)
grid
title(‘Lift distribution’)
xlabel(‘Semi-span location (m)’)
ylabel (‘Lift coefficient’)
CL_wing = pi * AR * A(1)