I'm trying to plot an airfoil from the formula as described on this wikipedia page. This Jupyter notebook can be viewed on this github page. %matplotlib inline import math import matplotlib.pyplot as pyplot def frange( start, stop, step ): yield start while start <= stop: start += step yield start #https://en.wikipedia.org/wiki/NACA_airfoil#Equation_for_a_cambered_4-digit_NACA_airfoil def camber_line( x, m, p, c ): if 0 <= x <= c * p: yc = m * (x / math.pow(p,2)) * (2 * p - (x / c)) #elif p * c <= x <= c: else: yc = m * ((c - x) / math.pow(1-p,2)) * (1 + (x / c) - 2 * p ) return yc def dyc_over_dx( x, m, p, c ): if 0 <= x <= c * p: dyc_dx = ((2 * m) / math.pow(p,2)) * (p - x / c) #elif p * c <= x <= c: else: dyc_dx = ((2 * m ) / math.pow(1-p,2)) * (p - x / c ) return dyc_dx def thickness( x, t, c ): term1 = 0.2969 * (math.sqrt(x/c)) term2 = -0.1260 * (x/c) term3 = -0.3516 * math.pow(x/c,2) term4 = 0.2843 * math.pow(x/c,3) term5 = -0.1015 * math.pow(x/c,4) return 5 * t * c * (term1 + term2 + term3 + term4 + term5) def naca4( m, p, t, c=1 ): for x in frange( 0, 1.0, 0.01 ): dyc_dx = dyc_over_dx( x, m, p, c ) th = math.atan( dyc_dx ) yt = thickness( x, t, c ) yc = camber_line( x, m, p, c ) xu = x - yt * math.sin(th) xl = x + yt * math.sin(th) yu = yc + yt * math.cos(th) yl = yc - yt * math.cos(th) yield (xu, yu), (xl, yl) #naca2412 m = 0.02 p = 0.4 t = 12 naca4points = naca4( m, p, t ) for (xu,yu),(xl,yl) in naca4points: pyplot.plot( xu, yu, 'r,') pyplot.plot( xl, yl, 'r,') pyplot.ylabel('y') pyplot.xlabel('x') pyplot.axis('equal') figure = pyplot.gcf() figure.set_size_inches(16,16,forward=True) The result looks like . I expected it to look more like . Questions: Why is the line not completely smooth? There seems to be a discontinuity where the beginning and end meet. Why does it not look like the diagram on wikipedia? How do I remove the extra loop at the trailing edge? How do I fix the chord so that it runs from 0.0 to 1.0? Continue reading...
