%
%  w06wing.m -- djm -- 09 feb 2010
%

figure(1);  clf;  hold on

ang = pi/6;

dphi = 0.02;  Lp = 10;
phi = -Lp:dphi:Lp;

psi_list = [(-7:-1) -0.01 0.01 (1:7)];

for psi = psi_list
    wf = phi + 1i*psi;

    %  bad branch 
    %zf = 0.5*( wf + ((wf.^2 - 4).^(1/2)) );

    zf = 0.5*( wf + ((wf-2).^(1/2) .* (wf+2).^(1/2)) );
    cf = exp(1i*ang)*zf;
    df = cf + (1./cf);
    ef = exp(-1i*ang)*df;
    
    plot(real(ef),imag(ef),'-');  hold on
end

plot([-2 2]*cos(ang),[2 -2]*sin(ang),'k','linewidth',2)

axis equal
axis([-5 5 -5 5])

title(['\bf flow past a flat wing'])
xlabel('\bf Re-axis')
ylabel('\bf Im-axis')