def test_results_under_84km():
h = np.array([52000,
60000,
84500
]) # m
expected_T = np.array([267.850,
245.450,
187.650
]) # K
expected_rho = np.array([7.6687e-4,
2.8832e-4,
7.3914e-6
]) # kg / m3
expected_a = np.array([328.2055,
314.1822,
274.7099,
]) # m/s
for ii, h_ in enumerate(h):
T, p, rho, a = atm(h_)
assert_almost_equal(T, expected_T[ii], decimal=3)
assert_almost_equal(rho, expected_rho[ii], decimal=4)
assert_almost_equal(a, expected_a[ii], decimal=2)
def test_results_under_51km():
h = np.array([47200,
49000,
51000
]) # m
expected_T = np.array([270.650,
270.650,
270.650
]) # K
expected_rho = np.array([0.0013919,
0.0011090,
0.00086160
]) # kg / m3
expected_a = np.array([329.9165,
329.9165,
329.9165
]) # m / s
for ii, h_ in enumerate(h):
T, p, rho, a = atm(h_)
assert_almost_equal(T, expected_T[ii], decimal=3)
assert_almost_equal(rho, expected_rho[ii], decimal=4)
assert_almost_equal(a, expected_a[ii], decimal=2)
def test_results_under_32km():
h = np.array([22100,
24000,
28800,
32000
]) # m
expected_T = np.array([218.750,
220.650,
225.450,
228.650
]) # K
expected_rho = np.array([0.062711,
0.046267,
0.021708,
0.013225
]) # kg / m3
expected_a = np.array([296.6020,
297.8873,
301.1100,
303.2394
]) # m/s
for ii, h_ in enumerate(h):
T, p, rho, a = atm(h_)
assert_almost_equal(T, expected_T[ii], decimal=3)
assert_almost_equal(rho, expected_rho[ii], decimal=4)
assert_almost_equal(a, expected_a[ii], decimal=2)
def test_results_under_71km():
h = np.array([51500,
60000,
71000
]) # m
expected_T = np.array([269.250,
245.450,
214.650
]) # K
expected_rho = np.array([0.00081298,
2.8832e-4,
6.4211e-5
]) # kg / m3
expected_a = np.array([329.0621,
314.1823,
293.8092
]) # m / s
for ii, h_ in enumerate(h):
T, p, rho, a = atm(h_)
assert_almost_equal(T, expected_T[ii], decimal=3)
assert_almost_equal(rho, expected_rho[ii], decimal=4)
assert_almost_equal(a, expected_a[ii], decimal=2)
def test_results_under_47km():
h = np.array([32200,
36000,
42000,
47000
]) # m
expected_T = np.array([229.210,
239.850,
256.650,
270.650
]) # K
expected_rho = np.array([0.012805,
0.0070344,
0.0028780,
0.0014275
]) # kg / m3
expected_a = np.array([303.6105,
310.5774,
321.2704,
329.9165
]) # m / s
for ii, h_ in enumerate(h):
T, p, rho, a = atm(h_)
assert_almost_equal(T, expected_T[ii], decimal=3)
assert_almost_equal(rho, expected_rho[ii], decimal=4)
assert_almost_equal(a, expected_a[ii], decimal=2)
def test_results_under_20km():
h = np.array([12000,
14200,
17500,
20000
]) # m
expected_T = np.array([216.650,
216.650,
216.650,
216.650,
]) # K
expected_rho = np.array([0.31083,
0.21971,
0.13058,
0.088035
]) # kg / m3
expected_a = np.array([295.1749,
295.1749,
295.1749,
295.1749,
])
for ii, h_ in enumerate(h):
T, p, rho, a = atm(h_)
assert_almost_equal(T, expected_T[ii], decimal=3)
assert_almost_equal(rho, expected_rho[ii], decimal=4)
assert_almost_equal(a, expected_a[ii], decimal=2)
def test_results_under_11km():
h = np.array([0.0,
50.0,
550.0,
6500.0,
10000.0,
11000.0
]) # m
expected_T = np.array([288.150,
287.825,
284.575,
245.900,
223.150,
216.650
]) # K
expected_rho = np.array([1.2250,
1.2191,
1.1616,
0.62384,
0.41271,
0.36392
]) # kg / m3
for ii, h_ in enumerate(h):
T, p, rho = atm(h_)
assert_almost_equal(T, expected_T[ii], decimal=3)
assert_almost_equal(rho, expected_rho[ii], decimal=4)
def test_stagnation_pressure():
# subsonic case
_, p, _, a = atm(11000)
tas = 240
p_stagnation_expected = 34952.7493849545
p_stagnation = stagnation_pressure(p, a, tas)
assert_almost_equal(p_stagnation, p_stagnation_expected)
# supersonic case
_, p, _, a = atm(11000)
tas = 400
p_stagnation_expected = 65521.299596290904
p_stagnation = stagnation_pressure(p, a, tas)
assert_almost_equal(p_stagnation, p_stagnation_expected)
def test_stagnation_pressure():
# subsonic case
_, p, _, a = atm(11000)
tas = 240
p_stagnation_expected = 34952.7493849545
p_stagnation = stagnation_pressure(p, a, tas)
assert_almost_equal(p_stagnation, p_stagnation_expected)
# supersonic case
_, p, _, a = atm(11000)
tas = 400
p_stagnation_expected = 65521.299596290904
p_stagnation = stagnation_pressure(p, a, tas)
assert_almost_equal(p_stagnation, p_stagnation_expected)
def test_results_under_51km():
h = np.array([47200, 49000, 51000]) # m
expected_T = np.array([270.650, 270.650, 270.650]) # K
expected_rho = np.array([0.0013919, 0.0011090, 0.00086160]) # kg / m3
for ii, h_ in enumerate(h):
T, p, rho = atm(h_)
assert_almost_equal(T, expected_T[ii], decimal=3)
assert_almost_equal(rho, expected_rho[ii], decimal=4)
def test_results_under_84km():
h = np.array([52000, 60000, 84500]) # m
expected_T = np.array([267.850, 245.450, 187.650]) # K
expected_rho = np.array([7.6687e-4, 2.8832e-4, 7.3914e-6]) # kg / m3
for ii, h_ in enumerate(h):
T, p, rho = atm(h_)
assert_almost_equal(T, expected_T[ii], decimal=3)
assert_almost_equal(rho, expected_rho[ii], decimal=4)
def test_results_under_71km():
h = np.array([51500, 60000, 71000]) # m
expected_T = np.array([269.250, 245.450, 214.650]) # K
expected_rho = np.array([0.00081298, 2.8832e-4, 6.4211e-5]) # kg / m3
for ii, h_ in enumerate(h):
T, p, rho = atm(h_)
assert_almost_equal(T, expected_T[ii], decimal=3)
assert_almost_equal(rho, expected_rho[ii], decimal=4)
def test_results_under_47km():
h = np.array([32200, 36000, 42000, 47000]) # m
expected_T = np.array([229.210, 239.850, 256.650, 270.650]) # K
expected_rho = np.array([0.012805, 0.0070344, 0.0028780,
0.0014275]) # kg / m3
for ii, h_ in enumerate(h):
T, p, rho = atm(h_)
assert_almost_equal(T, expected_T[ii], decimal=3)
assert_almost_equal(rho, expected_rho[ii], decimal=4)
def test_results_under_32km():
h = np.array([22100, 24000, 28800, 32000]) # m
expected_T = np.array([218.750, 220.650, 225.450, 228.650]) # K
expected_rho = np.array([0.062711, 0.046267, 0.021708,
0.013225]) # kg / m3
for ii, h_ in enumerate(h):
T, p, rho = atm(h_)
assert_almost_equal(T, expected_T[ii], decimal=3)
assert_almost_equal(rho, expected_rho[ii], decimal=4)
def test_results_under_11km():
h = np.array([0.0, 50.0, 550.0, 6500.0, 10000.0, 11000.0]) # m
expected_T = np.array(
[288.150, 287.825, 284.575, 245.900, 223.150, 216.650]) # K
expected_rho = np.array(
[1.2250, 1.2191, 1.1616, 0.62384, 0.41271, 0.36392]) # kg / m3
for ii, h_ in enumerate(h):
T, p, rho = atm(h_)
assert_almost_equal(T, expected_T[ii], decimal=3)
assert_almost_equal(rho, expected_rho[ii], decimal=4)
def test_sea_level():
h = 0.0 # m
expected_T = 288.15 # K
expected_p = 101325.0 # Pa
expected_rho = 1.2250 # kg / m3
T, p, rho = atm(h)
# Reads: "Assert if T equals expected_T"
assert_equal(T, expected_T)
assert_equal(p, expected_p)
assert_almost_equal(rho, expected_rho, decimal=4)
def test_sea_level():
h = 0.0 # m
expected_T = 288.15 # K
expected_p = 101325.0 # Pa
expected_rho = 1.2250 # kg / m3
T, p, rho = atm(h)
# Reads: "Assert if T equals expected_T"
assert_equal(T, expected_T)
assert_equal(p, expected_p)
assert_almost_equal(rho, expected_rho, decimal=4)
def test_results_under_20km():
h = np.array([12000, 14200, 17500, 20000]) # m
expected_T = np.array([
216.650,
216.650,
216.650,
216.650,
]) # K
expected_rho = np.array([0.31083, 0.21971, 0.13058, 0.088035]) # kg / m3
for ii, h_ in enumerate(h):
T, p, rho = atm(h_)
assert_almost_equal(T, expected_T[ii], decimal=3)
assert_almost_equal(rho, expected_rho[ii], decimal=4)
def test_results_under_11km():
h = np.array([0.0, 50.0, 550.0, 6500.0, 10000.0, 11000.0]) # m
expected_T = np.array(
[288.150, 287.825, 284.575, 245.900, 223.150, 216.650]) # K
expected_rho = np.array(
[1.2250, 1.2191, 1.1616, 0.62384, 0.41271, 0.36392]) # kg / m3
expected_a = np.array(
[340.4155, 340.2235, 338.2972, 314.4700, 299.5701, 295.1749]) # m / s
for ii, h_ in enumerate(h):
T, p, rho, a = atm(h_)
assert_almost_equal(T, expected_T[ii], decimal=3)
assert_almost_equal(rho, expected_rho[ii], decimal=4)
assert_almost_equal(a, expected_a[ii], decimal=2)
def func(trimmed_params, h, TAS, gamma, turn_rate, aircraft, dynamic_eqs):
"""Function to optimize
"""
alpha = trimmed_params[0]
beta = trimmed_params[1]
delta_e = trimmed_params[2]
delta_ail = trimmed_params[3]
delta_r = trimmed_params[4]
delta_t = trimmed_params[5]
if abs(turn_rate) < 1e-8:
phi = 0
else:
phi = turn_coord_cons(turn_rate, alpha, beta, TAS, gamma)
theta = rate_of_climb_cons(gamma, alpha, beta, phi)
# w = turn_rate * k_h
# k_h = sin(theta) i_b + sin(phi) * cos(theta) j_b + cos(theta) * sin(phi)
# w = p * i_b + q * j_b + r * k_b
p = - turn_rate * sin(theta)
q = turn_rate * sin(phi) * cos(theta)
r = turn_rate * cos(theta) * sin(phi)
ang_vel = np.array([p, q, r])
lin_vel = wind2body((TAS, 0, 0), alpha, beta)
# FIXME: This implied some changes in the aircraft model.
# psi angle does not influence the attitude of the aircraft for gravity
# force projection. So it is set to 0.
attitude = np.array([theta, phi, 0])
_, _, rho, _ = atm(h)
forces, moments = aircraft.get_forces_and_moments(TAS, rho, alpha, beta,
delta_e, 0, delta_ail,
delta_r, delta_t,
attitude)
mass, inertia = aircraft.mass_and_inertial_data()
vel = np.concatenate((lin_vel[:], ang_vel[:]))
output = dynamic_eqs(0, vel, mass, inertia, forces, moments)
return output
def func(trimmed_params, h, TAS, gamma, turn_rate, aircraft, dynamic_eqs):
"""Function to optimize
"""
alpha = trimmed_params[0]
beta = trimmed_params[1]
delta_e = trimmed_params[2]
delta_ail = trimmed_params[3]
delta_r = trimmed_params[4]
delta_t = trimmed_params[5]
if abs(turn_rate) < 1e-8:
phi = 0
else:
phi = turn_coord_cons(turn_rate, alpha, beta, TAS, gamma)
theta = rate_of_climb_cons(gamma, alpha, beta, phi)
# w = turn_rate * k_h
# k_h = sin(theta) i_b + sin(phi) * cos(theta) j_b + cos(theta) * sin(phi)
# w = p * i_b + q * j_b + r * k_b
p = -turn_rate * sin(theta)
q = turn_rate * sin(phi) * cos(theta)
r = turn_rate * cos(theta) * sin(phi)
ang_vel = np.array([p, q, r])
lin_vel = wind2body((TAS, 0, 0), alpha, beta)
# FIXME: This implied some changes in the aircraft model.
# psi angle does not influence the attitude of the aircraft for gravity
# force projection. So it is set to 0.
attitude = np.array([theta, phi, 0])
_, _, rho, _ = atm(h)
forces, moments = aircraft.get_forces_and_moments(TAS, rho, alpha, beta,
delta_e, 0, delta_ail,
delta_r, delta_t,
attitude)
mass, inertia = aircraft.mass_and_inertial_data()
vel = np.concatenate((lin_vel[:], ang_vel[:]))
output = dynamic_eqs(0, vel, mass, inertia, forces, moments)
return output
def test_cas2tas():
# sea level
cas = 275
tas_expected = 275
tas = cas2tas(cas, p_0, rho_0)
assert_almost_equal(tas, tas_expected)
# Test at 11000m
_, p, rho, _ = atm(11000)
cas = 162.03569680495048
tas_expected = 275
tas = cas2tas(cas, p, rho)
assert_almost_equal(tas, tas_expected)
def test_tas2cas():
# sea level
tas = 275
cas_expected = 275
cas = tas2cas(tas, p_0, rho_0)
assert_almost_equal(cas, cas_expected)
# Test at 11000m
_, p, rho, _ = atm(11000)
tas = 275
cas_expected = 162.03569680495048
cas = tas2cas(tas, p, rho)
assert_almost_equal(cas, cas_expected)
def test_eas2tas():
# sea level
eas = 149.88797172756003
tas_expected = 149.88797172756003
tas = eas2tas(eas, rho_0)
assert_almost_equal(tas, tas_expected)
# Test at 11000m
_, _, rho, _ = atm(11000)
eas = 149.88797172756003
tas_expected = 275
tas = eas2tas(eas, rho)
assert_almost_equal(tas, tas_expected)
def test_tas2eas():
# sea level
tas = 275
eas_expected = 275
eas = tas2eas(tas, rho_0)
assert_almost_equal(eas, eas_expected)
# Test at 11000m
_, _, rho, _ = atm(11000)
tas = 275
eas_expected = 149.88797172756003
eas = tas2eas(tas, rho)
assert_almost_equal(eas, eas_expected)
def test_eas2cas():
# sea level
eas = 275
cas_expected = 275
cas = eas2cas(eas, p_0, rho_0)
assert_almost_equal(cas, cas_expected)
# Test at 11000m
_, p, rho, _ = atm(11000)
eas = 149.88797172756003
cas_expected = 162.03569680495048
cas = eas2cas(eas, p, rho)
assert_almost_equal(cas, cas_expected)
def test_cas2eas():
# sea level
cas = 275
eas_expected = 275
eas = cas2eas(cas, p_0, rho_0)
assert_almost_equal(eas, eas_expected)
# Test at 11000m
_, p, rho, _ = atm(11000)
cas = 162.03569680495048
eas_expected = 149.88797172756003
eas = cas2eas(cas, p, rho)
assert_almost_equal(eas, eas_expected)
def test_results_under_11km():
h = np.array([0.0,
50.0,
550.0,
6500.0,
10000.0,
11000.0
]) # m
expected_T = np.array([288.150,
287.825,
284.575,
245.900,
223.150,
216.650
]) # K
expected_rho = np.array([1.2250,
1.2191,
1.1616,
0.62384,
0.41271,
0.36392
]) # kg / m3
expected_a = np.array([340.4155,
340.2235,
338.2972,
314.4700,
299.5701,
295.1749
]) # m / s
for ii, h_ in enumerate(h):
T, p, rho, a = atm(h_)
assert_almost_equal(T, expected_T[ii], decimal=3)
assert_almost_equal(rho, expected_rho[ii], decimal=4)
assert_almost_equal(a, expected_a[ii], decimal=2)
TAS = np.empty_like(time)
TAS[0] = TAS_
# Linear Momentum and Angular Momentum eqs.
equations = System(integrator='dopri5',
model='euler_flat_earth',
jac=False)
u, v, w = lin_vel
p, q, r = ang_vel
equations.set_initial_values(u, v, w,
p, q, r,
theta, phi, psi_0,
x_0, y_0, h)
_, _, rho, _ = atm(h)
# Define control vectors.
delta_e, delta_ail, delta_r, delta_t = control_vector
d_e = np.ones_like(time) * delta_e
d_e[np.where(time<2)] = delta_e * 1.30
d_e[np.where(time<1)] = delta_e * 0.70
d_a = np.ones_like(time) * delta_ail
d_r = np.ones_like(time) * delta_r
d_t = np.ones_like(time) * delta_t
attitude = theta, phi, psi_0
# Rename function to make it shorter
forces_and_moments = cessna_310.get_forces_and_moments
for ii, t in enumerate(time[1:]):
def test_altitude_is_out_of_range():
wrong_h = (-1.0, 84501) # m
for h in wrong_h:
with pytest.raises(ValueError):
atm(h)
def test_altitude_is_out_of_range(recwarn):
wrong_h = (-1.0, 84501) # m
for h in wrong_h:
with pytest.raises(ValueError):
atm(h)
