#!/usr/local/bin/gnuplot -persist # set terminal svg size 600,400 dynamic enhanced font 'arial,10' mousing name "airfoil_4" butt dashlength 1.0 # set output 'airfoil.4.svg' set dummy t, y set key fixed right top vertical Right noreverse enhanced autotitle box lt black linewidth 1.000 dashtype solid set parametric set style data lines set title "Joukowski Airfoil using Complex Variables" set timestamp "%a %b %d %H:%M:%S %Y" set trange [ 0.00000 : 6.28319 ] noreverse nowriteback set xlabel "eps = 0.06 + i0.06" set xrange [ -0.600000 : 0.600000 ] noreverse nowriteback set x2range [ * : * ] noreverse writeback set yrange [ -0.200000 : 1.80000 ] noreverse nowriteback set y2range [ * : * ] noreverse writeback set zrange [ * : * ] noreverse writeback set cbrange [ * : * ] noreverse writeback set rrange [ * : * ] noreverse writeback set colorbox vertical origin screen 0.9, 0.2 size screen 0.05, 0.6 front noinvert bdefault bez_d4_i0(x) = (1 - x)**4 bez_d4_i1(x) = 4 * (1 - x)**3 * x bez_d4_i2(x) = 6 * (1 - x)**2 * x**2 bez_d4_i3(x) = 4 * (1 - x)**1 * x**3 bez_d4_i4(x) = x**4 bez_d8_i0(x) = (1 - x)**8 bez_d8_i1(x) = 8 * (1 - x)**7 * x bez_d8_i2(x) = 28 * (1 - x)**6 * x**2 bez_d8_i3(x) = 56 * (1 - x)**5 * x**3 bez_d8_i4(x) = 70 * (1 - x)**4 * x**4 bez_d8_i5(x) = 56 * (1 - x)**3 * x**5 bez_d8_i6(x) = 28 * (1 - x)**2 * x**6 bez_d8_i7(x) = 8 * (1 - x) * x**7 bez_d8_i8(x) = x**8 mean_y(t) = m0 * mm * bez_d4_i0(t) + m1 * mm * bez_d4_i1(t) + m2 * mm * bez_d4_i2(t) + m3 * mm * bez_d4_i3(t) + m4 * mm * bez_d4_i4(t) mean_x(t) = p0 * bez_d4_i0(t) + p1 * bez_d4_i1(t) + p2 * bez_d4_i2(t) + p3 * bez_d4_i3(t) + p4 * bez_d4_i4(t) z_x(x) = x0 * bez_d8_i0(x) + x1 * bez_d8_i1(x) + x2 * bez_d8_i2(x) + x3 * bez_d8_i3(x) + x4 * bez_d8_i4(x) + x5 * bez_d8_i5(x) + x6 * bez_d8_i6(x) + x7 * bez_d8_i7(x) + x8 * bez_d8_i8(x) z_y(x, tk) = y0 * tk * bez_d8_i0(x) + y1 * tk * bez_d8_i1(x) + y2 * tk * bez_d8_i2(x) + y3 * tk * bez_d8_i3(x) + y4 * tk * bez_d8_i4(x) + y5 * tk * bez_d8_i5(x) + y6 * tk * bez_d8_i6(x) + y7 * tk * bez_d8_i7(x) + y8 * tk * bez_d8_i8(x) airfoil_y1(t, thick) = mean_y(z_x(t)) + z_y(t, thick) airfoil_y2(t, thick) = mean_y(z_x(t)) - z_y(t, thick) airfoil_y(t) = mean_y(z_x(t)) airfoil_x(t) = mean_x(z_x(t)) zeta(t) = -eps + (a+eps)*exp(t*{0,1}) eta(t) = zeta(t) + a*a/zeta(t) NO_ANIMATION = 1 mm = 0.0 thick = 0.12 pp = 0.5 x0 = 0.0 y0 = 0.0 x1 = 0.0 y1 = 0.18556 x2 = 0.03571 y2 = 0.34863 x3 = 0.10714 y3 = 0.48919 x4 = 0.21429 y4 = 0.58214 x5 = 0.35714 y5 = 0.55724 x6 = 0.53571 y6 = 0.44992 x7 = 0.75 y7 = 0.30281 x8 = 1.0 y8 = 0.0105 m0 = 0.0 m1 = 0.1 m2 = 0.1 m3 = 0.1 m4 = 0.0 p0 = 0.0 p1 = 0.2 p2 = 0.4 p3 = 0.7 p4 = 1.0 eps = {0.06, -0.06} a = 0.25 plot real(eta(t)),imag(eta(t))