Return to airfoil.dem CVS log

Up to [local] / OpenXM_contrib / gnuplot / demo

Annotation of OpenXM_contrib/gnuplot/demo/airfoil.dem, Revision 1.1.1.2

1.1       maekawa     1: #
1.1.1.2 ! maekawa     2: # $Id: airfoil.dem,v 1.1.1.1.2.1 1999/10/11 13:17:35 lhecking Exp $
1.1       maekawa     3: #
                      4: # This demo shows how to use bezier splines to define NACA four
                      5: # series airfoils and complex variables to define Joukowski
                      6: # Airfoils.  It will be expanded after overplotting in implemented
                      7: # to plot Coefficient of Pressure as well.
                      8: #              Alex Woo, Dec. 1992
                      9: #
                     10: # The definitions below follows: "Bezier presentation of airfoils",
                     11: # by Wolfgang Boehm, Computer Aided Geometric Design 4 (1987) pp 17-22.
                     12: #
                     13: #                              Gershon Elber, Nov. 1992
                     14: #
                     15: # m = percent camber
                     16: # p = percent chord with maximum camber
                     17: pause 0  "NACA four series airfoils by bezier splines"
                     18: pause 0  "Will add pressure distribution later with Overplotting"
                     19: mm = 0.6
                     20: # NACA6xxx
                     21: thick = 0.09
                     22: # nine percent  NACAxx09
                     23: pp = 0.4
                     24: # NACAx4xx
                     25: # Combined this implies NACA6409 airfoil
                     26: #
                     27: # Airfoil thickness function.
                     28: #
                     29: set xlabel "NACA6409 -- 9% thick, 40% max camber, 6% camber"
                     30: x0 = 0.0
                     31: y0 = 0.0
                     32: x1 = 0.0
                     33: y1 = 0.18556
                     34: x2 = 0.03571
                     35: y2 = 0.34863
                     36: x3 = 0.10714
                     37: y3 = 0.48919
                     38: x4 = 0.21429
                     39: y4 = 0.58214
                     40: x5 = 0.35714
                     41: y5 = 0.55724
                     42: x6 = 0.53571
                     43: y6 = 0.44992
                     44: x7 = 0.75000
                     45: y7 = 0.30281
                     46: x8 = 1.00000
                     47: y8 = 0.01050
                     48: #
                     49: # Directly defining the order 8 Bezier basis function for a faster evaluation.
                     50: #
                     51: bez_d4_i0(x) =     (1 - x)**4
                     52: bez_d4_i1(x) = 4 * (1 - x)**3 * x
                     53: bez_d4_i2(x) = 6 * (1 - x)**2 * x**2
                     54: bez_d4_i3(x) = 4 * (1 - x)**1 * x**3
                     55: bez_d4_i4(x) =                  x**4
                     56:
                     57: bez_d8_i0(x) =      (1 - x)**8
                     58: bez_d8_i1(x) =  8 * (1 - x)**7 * x
                     59: bez_d8_i2(x) = 28 * (1 - x)**6 * x**2
                     60: bez_d8_i3(x) = 56 * (1 - x)**5 * x**3
                     61: bez_d8_i4(x) = 70 * (1 - x)**4 * x**4
                     62: bez_d8_i5(x) = 56 * (1 - x)**3 * x**5
                     63: bez_d8_i6(x) = 28 * (1 - x)**2 * x**6
                     64: bez_d8_i7(x) =  8 * (1 - x)    * x**7
                     65: bez_d8_i8(x) =                   x**8
                     66:
                     67:
                     68: m0 = 0.0
                     69: m1 = 0.1
                     70: m2 = 0.1
                     71: m3 = 0.1
                     72: m4 = 0.0
                     73: mean_y(t) = m0 * mm * bez_d4_i0(t) + \
                     74:            m1 * mm * bez_d4_i1(t) + \
                     75:            m2 * mm * bez_d4_i2(t) + \
                     76:            m3 * mm * bez_d4_i3(t) + \
                     77:            m4 * mm * bez_d4_i4(t)
                     78:
                     79: p0 = 0.0
                     80: p1 = pp / 2
                     81: p2 = pp
                     82: p3 = (pp + 1) / 2
                     83: p4 = 1.0
                     84: mean_x(t) = p0 * bez_d4_i0(t) + \
                     85:            p1 * bez_d4_i1(t) + \
                     86:            p2 * bez_d4_i2(t) + \
                     87:            p3 * bez_d4_i3(t) + \
                     88:            p4 * bez_d4_i4(t)
                     89:
                     90: z_x(x) = x0 * bez_d8_i0(x) + x1 * bez_d8_i1(x) + x2 * bez_d8_i2(x) + \
                     91:         x3 * bez_d8_i3(x) + x4 * bez_d8_i4(x) + x5 * bez_d8_i5(x) + \
                     92:         x6 * bez_d8_i6(x) + x7 * bez_d8_i7(x) + x8 * bez_d8_i8(x)
                     93:
                     94: z_y(x, tk) = \
                     95:    y0 * tk * bez_d8_i0(x) + y1 * tk * bez_d8_i1(x) + y2 * tk * bez_d8_i2(x) + \
                     96:    y3 * tk * bez_d8_i3(x) + y4 * tk * bez_d8_i4(x) + y5 * tk * bez_d8_i5(x) + \
                     97:    y6 * tk * bez_d8_i6(x) + y7 * tk * bez_d8_i7(x) + y8 * tk * bez_d8_i8(x)
                     98:
                     99: #
                    100: # Given t value between zero and one, the airfoild curve is defined as
                    101: #
                    102: #                      c(t) = mean(t1(t)) +/- z(t2(t)) n(t1(t)),
                    103: #
                    104: # where n is the unit normal to the mean line. See the above paper for more.
                    105: #
                    106: # Unfortunately, the parametrization of c(t) is not the same for mean(t1)
                    107: # and z(t2). The mean line (and its normal) can assume linear function t1 = t,
                    108: #                                                     -1
                    109: # but the thickness z_y is, in fact, a function of z_x  (t). Since it is
                    110: # not obvious how to compute this inverse function analytically, we instead
                    111: # replace t in c(t) equation above by z_x(t) to get:
                    112: #
                    113: #                      c(z_x(t)) = mean(z_x(t)) +/- z(t) n(z_x(t)),
                    114: #
                    115: # and compute and display this instead. Note we also ignore n(t) and assumes
                    116: # n(t) is constant in the y direction,
                    117: #
                    118:
                    119: airfoil_y1(t, thick) = mean_y(z_x(t)) + z_y(t, thick)
                    120: airfoil_y2(t, thick) = mean_y(z_x(t)) - z_y(t, thick)
                    121: airfoil_y(t) = mean_y(z_x(t))
                    122: airfoil_x(t) = mean_x(z_x(t))
                    123: set nogrid
                    124: set nozero
                    125: set parametric
                    126: set xrange [-0.1:1.1]
                    127: set yrange [-0.1:.7]
                    128: set trange [ 0.0:1.0]
                    129: set title "NACA6409 Airfoil"
                    130: plot airfoil_x(t), airfoil_y(t) title "mean line" w l 2, \
                    131:      airfoil_x(t), airfoil_y1(t, thick) title "upper surface" w l 1, \
                    132:      airfoil_x(t), airfoil_y2(t, thick) title "lower surface" w l 1
                    133: pause -1 "Press Return"
                    134: mm = 0.0
                    135: pp = .5
                    136: thick = .12
                    137: set title "NACA0012 Airfoil"
                    138: set xlabel "12% thick, no camber -- classical test case"
                    139: plot airfoil_x(t), airfoil_y(t) title "mean line" w l 2, \
                    140:      airfoil_x(t), airfoil_y1(t, thick) title "upper surface" w l 1, \
                    141:      airfoil_x(t), airfoil_y2(t, thick) title "lower surface" w l 1
                    142: pause -1 "Press Return"
                    143: set title ""
                    144: set xlab ""
1.1.1.2 ! maekawa   145: set key box
1.1       maekawa   146: set parametric
                    147: set samples 100
                    148: set isosamples 10
                    149: set data style lines
                    150: set function style lines
                    151: pause 0  "Joukowski Airfoil using Complex Variables"
                    152: set title "Joukowski Airfoil using Complex Variables" 0,0
                    153: set time
                    154: set yrange [-.2 : 1.8]
                    155: set trange [0: 2*pi]
                    156: set xrange [-.6:.6]
                    157: zeta(t) = -eps + (a+eps)*exp(t*{0,1})
                    158: eta(t) = zeta(t) + a*a/zeta(t)
                    159: eps = 0.06
                    160: a =.250
                    161: set xlabel "eps = 0.06 real"
                    162: plot real(eta(t)),imag(eta(t))
                    163: pause -1 "Press Return"
                    164: eps = 0.06*{1,-1}
                    165: set xlabel "eps = 0.06 + i0.06"
                    166: plot real(eta(t)),imag(eta(t))
                    167: pause -1 "Press Return"
1.1.1.2 ! maekawa   168: reset