"""Estimation of the optimal aerodynamics configuration for the aircraft in cruise condition."""
# This file is part of FAST-OAD_CS23 : A framework for rapid Overall Aircraft Design
# Copyright (C) 2022 ONERA & ISAE-SUPAERO
# FAST is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
import numpy as np
import fastoad.api as oad
from openmdao.core.explicitcomponent import ExplicitComponent
from ..constants import SUBMODEL_MAX_L_D
[docs]@oad.RegisterSubmodel(SUBMODEL_MAX_L_D, "fastga.submodel.aerodynamics.aircraft.l_d_max.legacy")
class ComputeLDMax(ExplicitComponent):
"""
Computes optimal CL/CD aerodynamic performance of the aircraft in cruise conditions.
"""
[docs] def setup(self):
self.add_input("data:aerodynamics:wing:cruise:CL0_clean", val=np.nan)
self.add_input("data:aerodynamics:wing:cruise:CL_alpha", val=np.nan, units="rad**-1")
self.add_input("data:aerodynamics:aircraft:cruise:CD0", val=np.nan)
self.add_input("data:aerodynamics:wing:cruise:induced_drag_coefficient", val=np.nan)
self.add_output("data:aerodynamics:aircraft:cruise:L_D_max")
self.add_output("data:aerodynamics:aircraft:cruise:optimal_CL")
self.add_output("data:aerodynamics:aircraft:cruise:optimal_CD")
self.add_output("data:aerodynamics:aircraft:cruise:optimal_alpha", units="deg")
self.declare_partials(
"data:aerodynamics:aircraft:cruise:optimal_CL",
[
"data:aerodynamics:aircraft:cruise:CD0",
"data:aerodynamics:wing:cruise:induced_drag_coefficient",
],
method="exact",
)
self.declare_partials(
"data:aerodynamics:aircraft:cruise:optimal_CD",
[
"data:aerodynamics:aircraft:cruise:CD0",
],
method="exact",
)
self.declare_partials(
"data:aerodynamics:aircraft:cruise:L_D_max",
[
"data:aerodynamics:aircraft:cruise:CD0",
"data:aerodynamics:wing:cruise:induced_drag_coefficient",
],
method="exact",
)
self.declare_partials(
"data:aerodynamics:aircraft:cruise:optimal_alpha",
[
"data:aerodynamics:aircraft:cruise:CD0",
"data:aerodynamics:wing:cruise:induced_drag_coefficient",
"data:aerodynamics:wing:cruise:CL_alpha",
"data:aerodynamics:wing:cruise:CL0_clean",
],
method="exact",
)
[docs] def compute(self, inputs, outputs, discrete_inputs=None, discrete_outputs=None):
# TODO: to be written with momentum equilibrium formula to consider htp drag
cl0_clean = inputs["data:aerodynamics:wing:cruise:CL0_clean"]
cl_alpha = inputs["data:aerodynamics:wing:cruise:CL_alpha"]
cd0 = inputs["data:aerodynamics:aircraft:cruise:CD0"]
coeff_k = inputs["data:aerodynamics:wing:cruise:induced_drag_coefficient"]
cl_opt = np.sqrt(cd0 / coeff_k)
alpha_opt = (cl_opt - cl0_clean) / cl_alpha * 180 / np.pi
cd_opt = cd0 + coeff_k * cl_opt**2
outputs["data:aerodynamics:aircraft:cruise:L_D_max"] = cl_opt / cd_opt
outputs["data:aerodynamics:aircraft:cruise:optimal_CL"] = cl_opt
outputs["data:aerodynamics:aircraft:cruise:optimal_CD"] = cd_opt
outputs["data:aerodynamics:aircraft:cruise:optimal_alpha"] = alpha_opt
[docs] def compute_partials(self, inputs, partials, discrete_inputs=None):
cl0_clean = inputs["data:aerodynamics:wing:cruise:CL0_clean"]
cl_alpha = inputs["data:aerodynamics:wing:cruise:CL_alpha"]
cd0 = inputs["data:aerodynamics:aircraft:cruise:CD0"]
coeff_k = inputs["data:aerodynamics:wing:cruise:induced_drag_coefficient"]
cl_opt = np.sqrt(cd0 / coeff_k)
d_cl_opt_d_cd0 = 0.5 * np.sqrt(1.0 / (coeff_k * cd0))
d_cl_opt_d_coeff_k = -0.5 * np.sqrt(cd0) * coeff_k**-1.5
partials[
"data:aerodynamics:aircraft:cruise:optimal_CL", "data:aerodynamics:aircraft:cruise:CD0"
] = d_cl_opt_d_cd0
partials[
"data:aerodynamics:aircraft:cruise:optimal_CL",
"data:aerodynamics:wing:cruise:induced_drag_coefficient",
] = d_cl_opt_d_coeff_k
partials[
"data:aerodynamics:aircraft:cruise:optimal_CD", "data:aerodynamics:aircraft:cruise:CD0"
] = 2.0
partials[
"data:aerodynamics:aircraft:cruise:L_D_max", "data:aerodynamics:aircraft:cruise:CD0"
] = -0.25 * coeff_k**-0.5 * cd0**-1.5
partials[
"data:aerodynamics:aircraft:cruise:L_D_max",
"data:aerodynamics:wing:cruise:induced_drag_coefficient",
] = -0.25 * coeff_k**-1.5 * cd0**-0.5
partials[
"data:aerodynamics:aircraft:cruise:optimal_alpha",
"data:aerodynamics:aircraft:cruise:CD0",
] = d_cl_opt_d_cd0 / cl_alpha * 180 / np.pi
partials[
"data:aerodynamics:aircraft:cruise:optimal_alpha",
"data:aerodynamics:wing:cruise:induced_drag_coefficient",
] = d_cl_opt_d_coeff_k / cl_alpha * 180 / np.pi
partials[
"data:aerodynamics:aircraft:cruise:optimal_alpha",
"data:aerodynamics:wing:cruise:CL0_clean",
] = -1.0 / cl_alpha * 180 / np.pi
partials[
"data:aerodynamics:aircraft:cruise:optimal_alpha",
"data:aerodynamics:wing:cruise:CL_alpha",
] = -(cl_opt - cl0_clean) / cl_alpha**2.0 * 180.0 / np.pi