# 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 openmdao.api as om
import fastoad.api as oad
from fastga.models.aerodynamics.constants import SUBMODEL_CL_Q_WING
[docs]@oad.RegisterSubmodel(
SUBMODEL_CL_Q_WING, "fastga.submodel.aerodynamics.wing.cl_pitch_velocity.legacy"
)
class ComputeCLPitchVelocityWing(om.ExplicitComponent):
"""
Computation of the contribution of the wing to the increase in lift due to a pitch velocity.
The convention from :cite:`roskampart6:1985` are used, meaning that, for the derivative with
respect to a pitch rate, this rate is made dimensionless by multiplying it by the MAC and
dividing it by 2 times the airspeed. The reference point for the CG was taken to be equal to
the wing quarter chord to match what is taken for other coefficient. If another reference
point is to be used, this coefficient should be multiplied by (1.0 + 4.0 * x_w / l0_wing)
with x_w the distance between CG and wing quarter chord, negative when CG is in front of the
wing quarter chord.
Based on :cite:`roskampart6:1985` section 10.2.7
"""
[docs] def initialize(self):
self.options.declare("low_speed_aero", default=False, types=bool)
[docs] def setup(self):
self.add_input("data:geometry:wing:aspect_ratio", val=np.nan)
self.add_input("data:geometry:wing:sweep_25", val=np.nan, units="rad")
if self.options["low_speed_aero"]:
self.add_input("data:aerodynamics:wing:low_speed:CL_alpha", val=np.nan, units="rad**-1")
self.add_input("data:aerodynamics:low_speed:mach", val=np.nan)
self.add_output("data:aerodynamics:wing:low_speed:CL_q", units="rad**-1")
else:
self.add_input("data:aerodynamics:wing:cruise:CL_alpha", val=np.nan, units="rad**-1")
self.add_input("data:aerodynamics:cruise:mach", val=np.nan)
self.add_output("data:aerodynamics:wing:cruise:CL_q", units="rad**-1")
self.declare_partials(of="*", wrt="*", method="exact")
[docs] def compute(self, inputs, outputs, discrete_inputs=None, discrete_outputs=None):
wing_ar = inputs["data:geometry:wing:aspect_ratio"]
wing_sweep_25 = inputs["data:geometry:wing:sweep_25"]
if self.options["low_speed_aero"]:
cl_alpha_w = inputs["data:aerodynamics:wing:low_speed:CL_alpha"]
mach = inputs["data:aerodynamics:low_speed:mach"]
else:
cl_alpha_w = inputs["data:aerodynamics:wing:cruise:CL_alpha"]
mach = inputs["data:aerodynamics:cruise:mach"]
# At Mach number = 0.0, simplified with respect to the formula in Roskam see the reason
# in the class docstring
cl_q_wing_0 = 0.5 * cl_alpha_w
b_coeff = np.sqrt(1.0 - mach**2.0 * np.cos(wing_sweep_25) ** 2.0)
cl_q_wing = (
(wing_ar + 2.0 * np.cos(wing_sweep_25))
/ (wing_ar * b_coeff + 2.0 * np.cos(wing_sweep_25))
* cl_q_wing_0
)
if self.options["low_speed_aero"]:
outputs["data:aerodynamics:wing:low_speed:CL_q"] = cl_q_wing
else:
outputs["data:aerodynamics:wing:cruise:CL_q"] = cl_q_wing
[docs] def compute_partials(self, inputs, partials, discrete_inputs=None):
wing_ar = inputs["data:geometry:wing:aspect_ratio"]
wing_sweep_25 = inputs["data:geometry:wing:sweep_25"]
if self.options["low_speed_aero"]:
cl_alpha_w = inputs["data:aerodynamics:wing:low_speed:CL_alpha"]
mach = inputs["data:aerodynamics:low_speed:mach"]
else:
cl_alpha_w = inputs["data:aerodynamics:wing:cruise:CL_alpha"]
mach = inputs["data:aerodynamics:cruise:mach"]
# At Mach number = 0.0
cl_q_wing_0 = 0.5 * cl_alpha_w
b_coeff = np.sqrt(1.0 - mach**2.0 * np.cos(wing_sweep_25) ** 2.0)
d_b_coeff_d_mach = (
-2.0
* mach
* np.cos(wing_sweep_25) ** 2.0
/ (2.0 * np.sqrt(1.0 - mach**2.0 * np.cos(wing_sweep_25) ** 2.0))
)
d_b_coeff_d_sweep = (
2.0
* mach**2.0
* np.cos(wing_sweep_25)
* np.sin(wing_sweep_25)
/ (2.0 * np.sqrt(1.0 - mach**2.0 * np.cos(wing_sweep_25) ** 2.0))
)
if self.options["low_speed_aero"]:
partials["data:aerodynamics:wing:low_speed:CL_q", "data:geometry:wing:aspect_ratio"] = (
(1.0 - b_coeff)
* 2.0
* np.cos(wing_sweep_25)
/ (wing_ar * b_coeff + 2.0 * np.cos(wing_sweep_25)) ** 2.0
* cl_q_wing_0
)
partials["data:aerodynamics:wing:low_speed:CL_q", "data:geometry:wing:sweep_25"] = (
(
2.0 * wing_ar * np.sin(wing_sweep_25) * (1.0 - b_coeff)
- wing_ar * d_b_coeff_d_sweep * (wing_ar + 2.0 * np.cos(wing_sweep_25))
)
/ (wing_ar * b_coeff + 2.0 * np.cos(wing_sweep_25)) ** 2.0
* cl_q_wing_0
)
# We're mostly gonna be at sweep_25 = 0.0 so the derivative will be null when
# computed explicitly but not with finite difference, was tested with a different
# sweep_25 and it works
partials[
"data:aerodynamics:wing:low_speed:CL_q", "data:aerodynamics:wing:low_speed:CL_alpha"
] = (
(wing_ar + 2.0 * np.cos(wing_sweep_25))
/ (wing_ar * b_coeff + 2.0 * np.cos(wing_sweep_25))
* 0.5
)
partials[
"data:aerodynamics:wing:low_speed:CL_q", "data:aerodynamics:low_speed:mach"
] = (
-wing_ar
* (wing_ar + 2.0 * np.cos(wing_sweep_25))
* cl_q_wing_0
/ (wing_ar * b_coeff + 2.0 * np.cos(wing_sweep_25)) ** 2.0
) * d_b_coeff_d_mach
else:
partials["data:aerodynamics:wing:cruise:CL_q", "data:geometry:wing:aspect_ratio"] = (
(1.0 - b_coeff)
* 2.0
* np.cos(wing_sweep_25)
/ (wing_ar * b_coeff + 2.0 * np.cos(wing_sweep_25)) ** 2.0
* cl_q_wing_0
)
partials["data:aerodynamics:wing:cruise:CL_q", "data:geometry:wing:sweep_25"] = (
(
2.0 * wing_ar * np.sin(wing_sweep_25) * (1.0 - b_coeff)
- wing_ar * d_b_coeff_d_sweep * (wing_ar + 2.0 * np.cos(wing_sweep_25))
)
/ (wing_ar * b_coeff + 2.0 * np.cos(wing_sweep_25)) ** 2.0
* cl_q_wing_0
)
partials[
"data:aerodynamics:wing:cruise:CL_q", "data:aerodynamics:wing:cruise:CL_alpha"
] = (
(wing_ar + 2.0 * np.cos(wing_sweep_25))
/ (wing_ar * b_coeff + 2.0 * np.cos(wing_sweep_25))
* 0.5
)
partials["data:aerodynamics:wing:cruise:CL_q", "data:aerodynamics:cruise:mach"] = (
-wing_ar
* (wing_ar + 2.0 * np.cos(wing_sweep_25))
* cl_q_wing_0
/ (wing_ar * b_coeff + 2.0 * np.cos(wing_sweep_25)) ** 2.0
) * d_b_coeff_d_mach