In [1]:
"""
This example shows how to use the Mesh class in order to generate a
geometry similar to those that may define a lifting surface planform.
Y ^ B This geometry is positioned in space with two chords
| +---+ simulating the root and tip chords, using points
| / | A and B to store their respective leading edge
| / | b coordinates.
|/ |
+-------+----> With the parameters n and m, the grid density in the
A c X chordwise and spanwise directions will be defined.
"""
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.cm as cm
from vlm import Mesh
Geometry definition¶
In [2]:
# Parameters
c = 1 # root chord length
b = 10 # panel span length
n = 2 # number of panels chordwise
m = 3 # number of panels spanwise
# Wing
A = np.array([0, 0]) # root chord leading edge coordinates
B = np.array([c/2, b]) # tip chord leading edge coordinates
leading_edges_coord = [A, B]
chord_lengths = [c, c/2]
mesh = Mesh(leading_edges_coord, chord_lengths, n, m)
Points = mesh.points()
Panels = mesh.panels()
Printing and plotting¶
In [3]:
# Points of the mesh
print('\n Point | Coordinates ')
print('------------------------')
for p, i in zip(Points, range(len(Points))):
print(' %2s |' % i, np.round(p, 2))
# Mesh
plt.style.use('ggplot')
colors = plt.cm.Blues(np.linspace(0, 1, len(Panels) + 5))
for p, i in zip(Panels, range(len(Panels))):
col = colors[i + 4]
x = [p.P1[0], p.P2[0], p.P3[0], p.P4[0]]
y = [p.P1[1], p.P2[1], p.P3[1], p.P4[1]]
plt.fill(x, y, c=col, alpha=0.65)
plt.plot(x, y, c='w', lw=2)
centre = (p.P1 + p.P3) / 2
plt.text(centre[0], centre[1], i, color='k', fontsize=20)
for p in Points:
plt.plot(p[0], p[1], 'bo')
plt.show()
# Panels distribution
print('\n Panel | Chrd % | Span | Points coordinates')
print('------------------------------------------------')
for p, i in zip(Panels, range(len(Panels))):
print(' %3s | %4.1f | %6.2f | '
% (i, 100*p.chordwise_position, p.span),
np.round(p.P1, 2), np.round(p.P2, 2),
np.round(p.P3, 2), np.round(p.P4, 2))
Point | Coordinates ------------------------ 0 | [0 0] 1 | [0.17 3.33] 2 | [0.33 6.67] 3 | [ 0.5 10. ] 4 | [0.5 0. ] 5 | [0.58 3.33] 6 | [0.67 6.67] 7 | [ 0.75 10. ] 8 | [1. 0.] 9 | [1. 3.33] 10 | [1. 6.67] 11 | [ 1. 10.]
Panel | Chrd % | Span | Points coordinates
------------------------------------------------
0 | 25.0 | 3.33 | [0.5 0. ] [0 0] [0.17 3.33] [0.58 3.33]
1 | 25.0 | 3.33 | [0.58 3.33] [0.17 3.33] [0.33 6.67] [0.67 6.67]
2 | 25.0 | 3.33 | [0.67 6.67] [0.33 6.67] [ 0.5 10. ] [ 0.75 10. ]
3 | 75.0 | 3.33 | [1. 0.] [0.5 0. ] [0.58 3.33] [1. 3.33]
4 | 75.0 | 3.33 | [1. 3.33] [0.58 3.33] [0.67 6.67] [1. 6.67]
5 | 75.0 | 3.33 | [1. 6.67] [0.67 6.67] [ 0.75 10. ] [ 1. 10.]