def test(self):
"""
This is an opt problem that tests the wingbox model with wave drag and the fuel vol constraint
"""
# Create a dictionary to store options about the surface
mesh_dict = {
'num_y': 7,
'num_x': 2,
'wing_type': 'CRM',
'symmetry': True,
'num_twist_cp': 6,
'chord_cos_spacing': 0,
'span_cos_spacing': 0,
}
mesh, twist_cp = generate_mesh(mesh_dict)
surf_dict = {
# Wing definition
'name':
'wing', # name of the surface
'type':
'aerostruct',
'symmetry':
True, # if true, model one half of wing
# reflected across the plane y = 0
'S_ref_type':
'wetted', # how we compute the wing area,
# can be 'wetted' or 'projected'
'fem_model_type':
'wingbox',
'spar_thickness_cp':
np.array([0.004, 0.005, 0.005, 0.008, 0.008, 0.01]), # [m]
'skin_thickness_cp':
np.array([0.005, 0.01, 0.015, 0.020, 0.025, 0.026]),
'twist_cp':
np.array([4., 5., 8., 8., 8., 9.]),
'mesh':
mesh,
'num_x':
mesh.shape[0],
'num_y':
mesh.shape[1],
'data_x_upper':
upper_x,
'data_x_lower':
lower_x,
'data_y_upper':
upper_y,
'data_y_lower':
lower_y,
'strength_factor_for_upper_skin':
1.,
# Aerodynamic performance of the lifting surface at
# an angle of attack of 0 (alpha=0).
# These CL0 and CD0 values are added to the CL and CD
# obtained from aerodynamic analysis of the surface to get
# the total CL and CD.
# These CL0 and CD0 values do not vary wrt alpha.
'CL0':
0.0, # CL of the surface at alpha=0
'CD0':
0.0078, # CD of the surface at alpha=0
# Airfoil properties for viscous drag calculation
'k_lam':
0.05, # percentage of chord with laminar
# flow, used for viscous drag
't_over_c_cp':
np.array([0.08, 0.08, 0.08, 0.10, 0.10, 0.08]),
'original_wingbox_airfoil_t_over_c':
0.12,
'c_max_t':
.38, # chordwise location of maximum thickness
'with_viscous':
True,
'with_wave':
True, # if true, compute wave drag
# Structural values are based on aluminum 7075
'E':
73.1e9, # [Pa] Young's modulus
'G': (
73.1e9 / 2 / 1.33
), # [Pa] shear modulus (calculated using E and the Poisson's ratio here)
'yield': (420.e6 / 1.5), # [Pa] allowable yield stress
'mrho':
2.78e3, # [kg/m^3] material density
'strength_factor_for_upper_skin':
1.0, # the yield stress is multiplied by this factor for the upper skin
# 'fem_origin' : 0.35, # normalized chordwise location of the spar
'wing_weight_ratio':
1.25,
'struct_weight_relief':
True,
# Constraints
'exact_failure_constraint':
False, # if false, use KS function
'fuel_density':
803.,
'Wf_reserve':
15000.,
}
surfaces = [surf_dict]
# Create the problem and assign the model group
prob = Problem()
# Add problem information as an independent variables component
indep_var_comp = IndepVarComp()
indep_var_comp.add_output('v', val=.85 * 295.07, units='m/s')
indep_var_comp.add_output('alpha', val=0., units='deg')
indep_var_comp.add_output('M', val=0.85)
indep_var_comp.add_output('re',
val=0.348 * 295.07 * .85 * 1. /
(1.43 * 1e-5),
units='1/m')
indep_var_comp.add_output('rho', val=0.348, units='kg/m**3')
indep_var_comp.add_output('CT', val=0.53 / 3600, units='1/s')
indep_var_comp.add_output('R', val=14.307e6, units='m')
indep_var_comp.add_output('W0',
val=(143000 - 2.5 * 11600 + 34000) + 15000,
units='kg')
indep_var_comp.add_output('a', val=295.07, units='m/s')
indep_var_comp.add_output('load_factor', val=1.)
indep_var_comp.add_output('empty_cg', val=np.zeros((3)), units='m')
prob.model.add_subsystem('prob_vars', indep_var_comp, promotes=['*'])
# Loop over each surface in the surfaces list
for surface in surfaces:
# Get the surface name and create a group to contain components
# only for this surface
name = surface['name']
aerostruct_group = Aerostruct(surface=surface)
# Add tmp_group to the problem with the name of the surface.
prob.model.add_subsystem(name, aerostruct_group)
# Loop through and add a certain number of aero points
for i in range(1):
point_name = 'AS_point_{}'.format(i)
# Connect the parameters within the model for each aero point
# Create the aero point group and add it to the model
AS_point = AerostructPoint(surfaces=surfaces)
prob.model.add_subsystem(point_name, AS_point)
# Connect flow properties to the analysis point
prob.model.connect('v', point_name + '.v')
prob.model.connect('alpha', point_name + '.alpha')
prob.model.connect('M', point_name + '.M')
prob.model.connect('re', point_name + '.re')
prob.model.connect('rho', point_name + '.rho')
prob.model.connect('CT', point_name + '.CT')
prob.model.connect('R', point_name + '.R')
prob.model.connect('W0', point_name + '.W0')
prob.model.connect('a', point_name + '.a')
prob.model.connect('empty_cg', point_name + '.empty_cg')
prob.model.connect('load_factor', point_name + '.load_factor')
for surface in surfaces:
prob.model.connect('load_factor', name + '.load_factor')
com_name = point_name + '.' + name + '_perf.'
prob.model.connect(name + '.K',
point_name + '.coupled.' + name + '.K')
# Connect aerodyamic mesh to coupled group mesh
prob.model.connect(name + '.mesh',
point_name + '.coupled.' + name + '.mesh')
prob.model.connect(
name + '.element_weights',
point_name + '.coupled.' + name + '.element_weights')
prob.model.connect(name + '.nodes',
point_name + '.coupled.' + name + '.nodes')
# Connect performance calculation variables
prob.model.connect(name + '.nodes', com_name + 'nodes')
prob.model.connect(
name + '.cg_location',
point_name + '.' + 'total_perf.' + name + '_cg_location')
prob.model.connect(
name + '.structural_weight', point_name + '.' +
'total_perf.' + name + '_structural_weight')
# Connect wingbox properties to von Mises stress calcs
prob.model.connect(name + '.Qz', com_name + 'Qz')
prob.model.connect(name + '.Iz', com_name + 'Iz')
prob.model.connect(name + '.J', com_name + 'J')
prob.model.connect(name + '.A_enc', com_name + 'A_enc')
prob.model.connect(name + '.htop', com_name + 'htop')
prob.model.connect(name + '.hbottom', com_name + 'hbottom')
prob.model.connect(name + '.hfront', com_name + 'hfront')
prob.model.connect(name + '.hrear', com_name + 'hrear')
prob.model.connect(name + '.spar_thickness',
com_name + 'spar_thickness')
prob.model.connect(name + '.skin_thickness',
com_name + 'skin_thickness')
prob.model.connect(name + '.t_over_c', com_name + 't_over_c')
#=======================================================================================
# Here we add the fuel volume constraint componenet to the model
#=======================================================================================
prob.model.add_subsystem('fuel_vol_delta',
WingboxFuelVolDelta(surface=surface))
prob.model.connect('AS_point_0.fuelburn',
'fuel_vol_delta.fuelburn')
prob.model.connect('wing.nodes', 'fuel_vol_delta.nodes')
prob.model.connect('wing.A_int', 'fuel_vol_delta.A_int')
#=======================================================================================
#=======================================================================================
from openmdao.api import ScipyOptimizeDriver
prob.driver = ScipyOptimizeDriver()
prob.driver.options['tol'] = 1e-9
# from openmdao.api import pyOptSparseDriver
# prob.driver = pyOptSparseDriver()
# prob.driver.add_recorder(SqliteRecorder("cases.sql"))
# prob.driver.options['optimizer'] = "SNOPT"
# prob.driver.opt_settings['Major optimality tolerance'] = 1e-6
# prob.driver.opt_settings['Major feasibility tolerance'] = 1e-8
# prob.driver.opt_settings['Major iterations limit'] = 200
prob.model.add_objective('AS_point_0.fuelburn', scaler=1e-5)
prob.model.add_design_var('wing.twist_cp',
lower=-15.,
upper=15.,
scaler=0.1)
prob.model.add_design_var('wing.spar_thickness_cp',
lower=0.003,
upper=0.1,
scaler=1e2)
prob.model.add_design_var('wing.skin_thickness_cp',
lower=0.003,
upper=0.1,
scaler=1e2)
prob.model.add_design_var('wing.geometry.t_over_c_cp',
lower=0.07,
upper=0.2,
scaler=10.)
prob.model.add_constraint('AS_point_0.total_perf.CL', equals=0.5)
prob.model.add_constraint('AS_point_0.wing_perf.failure', upper=0.)
#=======================================================================================
# Here we add the fuel volume constraint
#=======================================================================================
prob.model.add_constraint('fuel_vol_delta.fuel_vol_delta', lower=0.)
#=======================================================================================
#=======================================================================================
# Set up the problem
prob.setup()
# from openmdao.api import view_model
# view_model(prob)
prob.run_driver()
# prob.check_partials(form='central', compact_print=True)
# print(prob['AS_point_0.fuelburn'][0])
# print(prob['wing.structural_weight'][0]/1.25)
assert_rel_error(self, prob['AS_point_0.fuelburn'][0], 85033.119351,
1e-5)
assert_rel_error(self, prob['wing.structural_weight'][0] / 1.25,
185666.261281, 1e-5)
prob.model.connect(name + '.A_enc', com_name + 'A_enc')
prob.model.connect(name + '.htop', com_name + 'htop')
prob.model.connect(name + '.hbottom', com_name + 'hbottom')
prob.model.connect(name + '.hfront', com_name + 'hfront')
prob.model.connect(name + '.hrear', com_name + 'hrear')
prob.model.connect(name + '.spar_thickness',
com_name + 'spar_thickness')
prob.model.connect(name + '.t_over_c', com_name + 't_over_c')
prob.model.connect('alpha', 'AS_point_0' + '.alpha')
prob.model.connect('alpha_maneuver', 'AS_point_1' + '.alpha')
# Here we add the fuel volume constraint componenet to the model
prob.model.add_subsystem('fuel_vol_delta',
WingboxFuelVolDelta(surface=surface))
prob.model.connect('wing.struct_setup.fuel_vols', 'fuel_vol_delta.fuel_vols')
prob.model.connect('AS_point_0.fuelburn', 'fuel_vol_delta.fuelburn')
if surf_dict['distributed_fuel_weight']:
prob.model.connect('wing.struct_setup.fuel_vols',
'AS_point_0.coupled.wing.struct_states.fuel_vols')
prob.model.connect('fuel_mass',
'AS_point_0.coupled.wing.struct_states.fuel_mass')
prob.model.connect('wing.struct_setup.fuel_vols',
'AS_point_1.coupled.wing.struct_states.fuel_vols')
prob.model.connect('fuel_mass',
'AS_point_1.coupled.wing.struct_states.fuel_mass')
comp = ExecComp('fuel_diff = (fuel_mass - fuelburn) / fuelburn', units='kg')
prob.model.connect(name + '.t_over_c', com_name + 't_over_c')
coupled_name = point_name + '.coupled.' + name
prob.model.connect('point_masses', coupled_name + '.point_masses')
prob.model.connect('point_mass_locations', coupled_name + '.point_mass_locations')
#docs checkpoint 17
prob.model.connect('alpha', 'AS_point_0' + '.alpha')
prob.model.connect('alpha_maneuver', 'AS_point_1' + '.alpha')
#docs checkpoint 18
# Here we add the fuel volume constraint componenet to the model
prob.model.add_subsystem('fuel_vol_delta', WingboxFuelVolDelta(surface=surface))
prob.model.connect('wing.struct_setup.fuel_vols', 'fuel_vol_delta.fuel_vols')
prob.model.connect('AS_point_0.fuelburn', 'fuel_vol_delta.fuelburn')
if surf_dict['distributed_fuel_weight']:
prob.model.connect('wing.struct_setup.fuel_vols', 'AS_point_0.coupled.wing.struct_states.fuel_vols')
prob.model.connect('fuel_mass', 'AS_point_0.coupled.wing.struct_states.fuel_mass')
prob.model.connect('wing.struct_setup.fuel_vols', 'AS_point_1.coupled.wing.struct_states.fuel_vols')
prob.model.connect('fuel_mass', 'AS_point_1.coupled.wing.struct_states.fuel_mass')
#docs checkpoint 19
comp = om.ExecComp('fuel_diff = (fuel_mass - fuelburn) / fuelburn', units='kg')
prob.model.add_subsystem('fuel_diff', comp,
promotes_inputs=['fuel_mass'],
def test(self):
# Create a dictionary to store options about the surface
mesh_dict = {
'num_y': 7,
'num_x': 3,
'wing_type': 'uCRM_based',
'symmetry': True,
'chord_cos_spacing': 0,
'span_cos_spacing': 0,
'num_twist_cp': 6,
}
mesh, twist_cp = generate_mesh(mesh_dict)
surf_dict = {
# Wing definition
'name':
'wing', # name of the surface
'symmetry':
True, # if true, model one half of wing
'S_ref_type':
'wetted', # how we compute the wing area,
# can be 'wetted' or 'projected'
'mesh':
mesh,
'twist_cp':
np.array([4., 5., 8., 8., 8., 9.]),
'fem_model_type':
'wingbox',
'data_x_upper':
upper_x,
'data_x_lower':
lower_x,
'data_y_upper':
upper_y,
'data_y_lower':
lower_y,
'spar_thickness_cp':
np.array([0.004, 0.005, 0.005, 0.008, 0.008, 0.01]), # [m]
'skin_thickness_cp':
np.array([0.005, 0.01, 0.015, 0.020, 0.025, 0.026]),
'original_wingbox_airfoil_t_over_c':
0.12,
# Aerodynamic deltas.
# These CL0 and CD0 values are added to the CL and CD
# obtained from aerodynamic analysis of the surface to get
# the total CL and CD.
# These CL0 and CD0 values do not vary wrt alpha.
# They can be used to account for things that are not included, such as contributions from the fuselage, nacelles, tail surfaces, etc.
'CL0':
0.0,
'CD0':
0.0078,
'with_viscous':
True, # if true, compute viscous drag
'with_wave':
True, # if true, compute wave drag
# Airfoil properties for viscous drag calculation
'k_lam':
0.05, # percentage of chord with laminar
# flow, used for viscous drag
'c_max_t':
.38, # chordwise location of maximum thickness
't_over_c_cp':
np.array([0.08, 0.08, 0.08, 0.10, 0.10, 0.08]),
# Structural values are based on aluminum 7075
'E':
73.1e9, # [Pa] Young's modulus
'G': (
73.1e9 / 2 / 1.33
), # [Pa] shear modulus (calculated using E and the Poisson's ratio here)
'yield': (420.e6 / 1.5), # [Pa] allowable yield stress
'mrho':
2.78e3, # [kg/m^3] material density
'strength_factor_for_upper_skin':
1.0, # the yield stress is multiplied by this factor for the upper skin
'wing_weight_ratio':
1.25,
'exact_failure_constraint':
False, # if false, use KS function
'struct_weight_relief':
True,
'distributed_fuel_weight':
True,
'fuel_density':
803., # [kg/m^3] fuel density (only needed if the fuel-in-wing volume constraint is used)
'Wf_reserve':
15000., # [kg] reserve fuel mass
}
surfaces = [surf_dict]
# Create the problem and assign the model group
prob = Problem()
# Add problem information as an independent variables component
indep_var_comp = IndepVarComp()
indep_var_comp.add_output('v',
val=np.array([.85 * 295.07, .64 * 340.294]),
units='m/s')
indep_var_comp.add_output('alpha', val=0., units='deg')
indep_var_comp.add_output('alpha_maneuver', val=0., units='deg')
indep_var_comp.add_output('Mach_number', val=np.array([0.85, 0.64]))
indep_var_comp.add_output('re',val=np.array([0.348*295.07*.85*1./(1.43*1e-5), \
1.225*340.294*.64*1./(1.81206*1e-5)]), units='1/m')
indep_var_comp.add_output('rho',
val=np.array([0.348, 1.225]),
units='kg/m**3')
indep_var_comp.add_output('CT', val=0.53 / 3600, units='1/s')
indep_var_comp.add_output('R', val=14.307e6, units='m')
indep_var_comp.add_output('W0',
val=148000 + surf_dict['Wf_reserve'],
units='kg')
indep_var_comp.add_output('speed_of_sound',
val=np.array([295.07, 340.294]),
units='m/s')
indep_var_comp.add_output('load_factor', val=np.array([1., 2.5]))
indep_var_comp.add_output('empty_cg', val=np.zeros((3)), units='m')
indep_var_comp.add_output('fuel_mass', val=10000., units='kg')
prob.model.add_subsystem('prob_vars', indep_var_comp, promotes=['*'])
# Loop over each surface in the surfaces list
for surface in surfaces:
# Get the surface name and create a group to contain components
# only for this surface
name = surface['name']
aerostruct_group = AerostructGeometry(surface=surface)
# Add group to the problem with the name of the surface.
prob.model.add_subsystem(name, aerostruct_group)
# Loop through and add a certain number of aerostruct points
for i in range(2):
point_name = 'AS_point_{}'.format(i)
# Connect the parameters within the model for each aerostruct point
# Create the aero point group and add it to the model
AS_point = AerostructPoint(surfaces=surfaces,
internally_connect_fuelburn=False)
prob.model.add_subsystem(point_name, AS_point)
# Connect flow properties to the analysis point
prob.model.connect('v', point_name + '.v', src_indices=[i])
prob.model.connect('Mach_number',
point_name + '.Mach_number',
src_indices=[i])
prob.model.connect('re', point_name + '.re', src_indices=[i])
prob.model.connect('rho', point_name + '.rho', src_indices=[i])
prob.model.connect('CT', point_name + '.CT')
prob.model.connect('R', point_name + '.R')
prob.model.connect('W0', point_name + '.W0')
prob.model.connect('speed_of_sound',
point_name + '.speed_of_sound',
src_indices=[i])
prob.model.connect('empty_cg', point_name + '.empty_cg')
prob.model.connect('load_factor',
point_name + '.load_factor',
src_indices=[i])
prob.model.connect('fuel_mass',
point_name + '.total_perf.L_equals_W.fuelburn')
prob.model.connect('fuel_mass',
point_name + '.total_perf.CG.fuelburn')
for surface in surfaces:
name = surface['name']
if surf_dict['distributed_fuel_weight']:
prob.model.connect('load_factor',
point_name + '.coupled.load_factor',
src_indices=[i])
com_name = point_name + '.' + name + '_perf.'
prob.model.connect(
name + '.local_stiff_transformed', point_name +
'.coupled.' + name + '.local_stiff_transformed')
prob.model.connect(name + '.nodes',
point_name + '.coupled.' + name + '.nodes')
# Connect aerodyamic mesh to coupled group mesh
prob.model.connect(name + '.mesh',
point_name + '.coupled.' + name + '.mesh')
if surf_dict['struct_weight_relief']:
prob.model.connect(
name + '.element_mass',
point_name + '.coupled.' + name + '.element_mass')
# Connect performance calculation variables
prob.model.connect(name + '.nodes', com_name + 'nodes')
prob.model.connect(
name + '.cg_location',
point_name + '.' + 'total_perf.' + name + '_cg_location')
prob.model.connect(
name + '.structural_mass', point_name + '.' +
'total_perf.' + name + '_structural_mass')
# Connect wingbox properties to von Mises stress calcs
prob.model.connect(name + '.Qz', com_name + 'Qz')
prob.model.connect(name + '.J', com_name + 'J')
prob.model.connect(name + '.A_enc', com_name + 'A_enc')
prob.model.connect(name + '.htop', com_name + 'htop')
prob.model.connect(name + '.hbottom', com_name + 'hbottom')
prob.model.connect(name + '.hfront', com_name + 'hfront')
prob.model.connect(name + '.hrear', com_name + 'hrear')
prob.model.connect(name + '.spar_thickness',
com_name + 'spar_thickness')
prob.model.connect(name + '.t_over_c', com_name + 't_over_c')
prob.model.connect('alpha', 'AS_point_0' + '.alpha')
prob.model.connect('alpha_maneuver', 'AS_point_1' + '.alpha')
# Here we add the fuel volume constraint componenet to the model
prob.model.add_subsystem('fuel_vol_delta',
WingboxFuelVolDelta(surface=surface))
prob.model.connect('wing.struct_setup.fuel_vols',
'fuel_vol_delta.fuel_vols')
prob.model.connect('AS_point_0.fuelburn', 'fuel_vol_delta.fuelburn')
if surf_dict['distributed_fuel_weight']:
prob.model.connect(
'wing.struct_setup.fuel_vols',
'AS_point_0.coupled.wing.struct_states.fuel_vols')
prob.model.connect(
'fuel_mass', 'AS_point_0.coupled.wing.struct_states.fuel_mass')
prob.model.connect(
'wing.struct_setup.fuel_vols',
'AS_point_1.coupled.wing.struct_states.fuel_vols')
prob.model.connect(
'fuel_mass', 'AS_point_1.coupled.wing.struct_states.fuel_mass')
comp = ExecComp('fuel_diff = (fuel_mass - fuelburn) / fuelburn')
prob.model.add_subsystem('fuel_diff',
comp,
promotes_inputs=['fuel_mass'],
promotes_outputs=['fuel_diff'])
prob.model.connect('AS_point_0.fuelburn', 'fuel_diff.fuelburn')
## Use these settings if you do not have pyOptSparse or SNOPT
prob.driver = ScipyOptimizeDriver()
prob.driver.options['optimizer'] = 'SLSQP'
prob.driver.options['tol'] = 1e-8
recorder = SqliteRecorder("unit_test.db")
prob.driver.add_recorder(recorder)
# We could also just use prob.driver.recording_options['includes']=['*'] here, but for large meshes the database file becomes extremely large. So we just select the variables we need.
prob.driver.recording_options['includes'] = [
'alpha',
'rho',
'v',
'cg',
'AS_point_1.cg',
'AS_point_0.cg',
'AS_point_0.coupled.wing_loads.loads',
'AS_point_1.coupled.wing_loads.loads',
'AS_point_0.coupled.wing.normals',
'AS_point_1.coupled.wing.normals',
'AS_point_0.coupled.wing.widths',
'AS_point_1.coupled.wing.widths',
'AS_point_0.coupled.aero_states.wing_sec_forces',
'AS_point_1.coupled.aero_states.wing_sec_forces',
'AS_point_0.wing_perf.CL1',
'AS_point_1.wing_perf.CL1',
'AS_point_0.coupled.wing.S_ref',
'AS_point_1.coupled.wing.S_ref',
'wing.geometry.twist',
'wing.mesh',
'wing.skin_thickness',
'wing.spar_thickness',
'wing.t_over_c',
'wing.structural_mass',
'AS_point_0.wing_perf.vonmises',
'AS_point_1.wing_perf.vonmises',
'AS_point_0.coupled.wing.def_mesh',
'AS_point_1.coupled.wing.def_mesh',
]
prob.driver.recording_options['record_objectives'] = True
prob.driver.recording_options['record_constraints'] = True
prob.driver.recording_options['record_desvars'] = True
prob.driver.recording_options['record_inputs'] = True
prob.model.add_objective('AS_point_0.fuelburn', scaler=1e-5)
prob.model.add_design_var('wing.twist_cp',
lower=-15.,
upper=15.,
scaler=0.1)
prob.model.add_design_var('wing.spar_thickness_cp',
lower=0.003,
upper=0.1,
scaler=1e2)
prob.model.add_design_var('wing.skin_thickness_cp',
lower=0.003,
upper=0.1,
scaler=1e2)
prob.model.add_design_var('wing.geometry.t_over_c_cp',
lower=0.07,
upper=0.2,
scaler=10.)
prob.model.add_design_var('fuel_mass',
lower=0.,
upper=2e5,
scaler=1e-5)
prob.model.add_design_var('alpha_maneuver', lower=-15., upper=15)
prob.model.add_constraint('AS_point_0.CL', equals=0.5)
prob.model.add_constraint('AS_point_1.L_equals_W', equals=0.)
prob.model.add_constraint('AS_point_1.wing_perf.failure', upper=0.)
prob.model.add_constraint('fuel_vol_delta.fuel_vol_delta', lower=0.)
prob.model.add_constraint('fuel_diff', equals=0.)
# Set up the problem
prob.setup()
prob.run_driver()
# print(prob['AS_point_0.fuelburn'][0])
# print(prob['wing.structural_mass'][0]/surf_dict['wing_weight_ratio'])
# print(prob['wing.geometry.t_over_c_cp'])
assert_rel_error(self, prob['AS_point_0.fuelburn'][0], 101937.827384,
1e-5)
assert_rel_error(
self,
prob['wing.structural_mass'][0] / surf_dict['wing_weight_ratio'],
36539.6437566, 1e-5)
assert_rel_error(
self, prob['wing.geometry.t_over_c_cp'],
np.array([
0.10247881, 0.08207636, 0.11114547, 0.13114547, 0.10207636,
0.09365598
]), 1e-5)
