def test_induced_velocity():
P1, P2 = np.array([1, 0]), np.array([0, 0])
P3, P4 = np.array([0, 1]), np.array([1, 1])
panel = Panel(P1, P2, P3, P4)
CP = panel.control_point()
calculated_induced_velocity = panel.induced_velocity(CP)
expected_induced_velocity = -0.7684680
assert_almost_equal(calculated_induced_velocity, expected_induced_velocity)
for i in range(0, n):
for j in range(0, m):
P1 = np.array([x[i + 1], y[j]])
P2 = np.array([x[i], y[j]])
P3 = np.array([x[i], y[j + 1]])
P4 = np.array([x[i + 1], y[j + 1]])
panel_pivot = Panel(P1, P2, P3, P4)
s = panel_pivot.area()
CP = panel_pivot.control_point()
# print(P1, P2, P3, P4)
print('---- Induced vel. on panel %s...' % k)
# print('area = ', s, 'control point = ', CP)
kk = 0
for ii in range(0, n):
for jj in range(0, m):
PP1 = np.array([x[ii + 1], y[jj]])
PP2 = np.array([x[ii], y[jj]])
PP3 = np.array([x[ii], y[jj + 1]])
PP4 = np.array([x[ii + 1], y[jj + 1]])
panel = Panel(PP1, PP2, PP3, PP4)
w = panel.induced_velocity(CP)
print(' ...by panel %s = %s' % (kk, w))
A[k, kk] = w
kk += 1
k += 1
np.set_printoptions(precision=4)
print()
print('Matrix A =')
print(A)
P3 = np.array([0, 0])
P4 = np.array([0, b / 2])
P5 = np.array([c, b / 2])
P6 = np.array([c, 0])
# Calculations
panel1 = Panel(P1, P2, P3, P6)
panel2 = Panel(P6, P3, P4, P5)
S1 = panel1.area()
S2 = panel2.area()
CP1 = panel1.control_point()
CP2 = panel2.control_point()
w11 = panel1.induced_velocity(CP1)
w12 = panel1.induced_velocity(CP2)
w22 = panel2.induced_velocity(CP2)
w21 = panel2.induced_velocity(CP1)
print('control point1 =', CP1, ' area1 =', '%4.3F' % S1)
print('control point2 =', CP2, ' area2 =', '%4.3F' % S2)
print('w11_induced =', '%4.3F' % w11, ' w12_induced =', '%4.3F' % w12)
print('w21_induced =', '%4.3F' % w21, ' w22_induced =', '%4.3F' % w22)
# Linear equation solving AX = Y
A = np.array([[w11, w12], [w21, w22]])
v1 = -V * np.sin(alpha)
v2 = -V * np.sin(alpha)
Y = np.array([[v1], [v2]])
X = np.linalg.solve(A, Y)