# 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_CY_BETA_VT
[docs]@oad.RegisterSubmodel(
SUBMODEL_CY_BETA_VT, "fastga.submodel.aerodynamics.vertical_tail.side_force_beta.legacy"
)
class ComputeCyBetaVerticalTail(om.ExplicitComponent):
"""
Class to compute the contribution of the vertical tail to the side force coefficient due to
sideslip.
Based on :cite:`roskampart6:1985` section 10.2.4.1
"""
[docs] def initialize(self):
self.options.declare("low_speed_aero", default=False, types=bool)
[docs] def setup(self):
self.add_input("data:geometry:wing:area", val=np.nan, units="m**2")
self.add_input("data:geometry:wing:aspect_ratio", val=np.nan)
self.add_input("data:geometry:wing:sweep_25", val=np.nan, units="rad")
self.add_input("data:geometry:wing:root:z", val=np.nan, units="m")
self.add_input("data:geometry:vertical_tail:area", val=np.nan, units="m**2")
self.add_input("data:geometry:vertical_tail:span", val=np.nan, units="m")
self.add_input("data:geometry:fuselage:maximum_height", val=np.nan, units="m")
self.add_input("data:geometry:fuselage:average_depth", val=np.nan, units="m")
self.add_input("data:aerodynamics:vertical_tail:efficiency", val=0.95)
if self.options["low_speed_aero"]:
self.add_input(
"data:aerodynamics:vertical_tail:low_speed:CL_alpha", val=np.nan, units="rad**-1"
)
self.add_output("data:aerodynamics:vertical_tail:low_speed:Cy_beta", units="rad**-1")
else:
self.add_input(
"data:aerodynamics:vertical_tail:cruise:CL_alpha", val=np.nan, units="rad**-1"
)
self.add_output("data:aerodynamics:vertical_tail:cruise:Cy_beta", 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_area = inputs["data:geometry:wing:area"]
wing_sweep_25 = inputs["data:geometry:wing:sweep_25"]
z_w = inputs["data:geometry:wing:root:z"]
z_f = inputs["data:geometry:fuselage:maximum_height"]
vt_area = inputs["data:geometry:vertical_tail:area"]
vt_span = inputs["data:geometry:vertical_tail:span"]
avg_fus_depth = inputs["data:geometry:fuselage:average_depth"]
eta_v = inputs["data:aerodynamics:vertical_tail:efficiency"]
if self.options["low_speed_aero"]:
cl_alpha_vt = inputs["data:aerodynamics:vertical_tail:low_speed:CL_alpha"]
else:
cl_alpha_vt = inputs["data:aerodynamics:vertical_tail:cruise:CL_alpha"]
if vt_span / avg_fus_depth < 2.0:
k_v = 0.75
elif vt_span / avg_fus_depth < 3.5:
k_v = 0.418 + 0.166 * vt_span / avg_fus_depth
else:
k_v = 1.0
k_sigma = (
0.724
+ 0.4 * z_w / z_f
+ 0.009 * wing_ar
+ 3.06 / (1.0 + np.cos(wing_sweep_25)) * vt_area / wing_area
)
cy_beta_vt = -k_v * cl_alpha_vt * k_sigma * eta_v * vt_area / wing_area
if self.options["low_speed_aero"]:
outputs["data:aerodynamics:vertical_tail:low_speed:Cy_beta"] = cy_beta_vt
else:
outputs["data:aerodynamics:vertical_tail:cruise:Cy_beta"] = cy_beta_vt
[docs] def compute_partials(self, inputs, partials, discrete_inputs=None):
wing_ar = inputs["data:geometry:wing:aspect_ratio"]
wing_area = inputs["data:geometry:wing:area"]
wing_sweep_25 = inputs["data:geometry:wing:sweep_25"]
z_w = inputs["data:geometry:wing:root:z"]
z_f = inputs["data:geometry:fuselage:maximum_height"]
vt_area = inputs["data:geometry:vertical_tail:area"]
vt_span = inputs["data:geometry:vertical_tail:span"]
avg_fus_depth = inputs["data:geometry:fuselage:average_depth"]
eta_v = inputs["data:aerodynamics:vertical_tail:efficiency"]
if self.options["low_speed_aero"]:
cl_alpha_vt = inputs["data:aerodynamics:vertical_tail:low_speed:CL_alpha"]
else:
cl_alpha_vt = inputs["data:aerodynamics:vertical_tail:cruise:CL_alpha"]
if vt_span / avg_fus_depth < 2.0:
k_v = 0.75
d_k_v_d_span = 0.0
d_k_v_d_hf = 0.0
elif vt_span / avg_fus_depth < 3.5:
k_v = 0.418 + 0.166 * vt_span / avg_fus_depth
d_k_v_d_span = 0.166
d_k_v_d_hf = -0.166 * vt_span / avg_fus_depth**2.0
else:
k_v = 1.0
d_k_v_d_span = 0.0
d_k_v_d_hf = 0.0
k_sigma = (
0.724
+ 0.4 * z_w / z_f
+ 0.009 * wing_ar
+ 3.06 / (1.0 + np.cos(wing_sweep_25)) * vt_area / wing_area
)
d_k_sigma_d_z_w = 0.4 / z_f
d_k_sigma_d_z_f = -0.4 * z_w / z_f**2.0
d_k_sigma_d_wing_ar = 0.009
d_k_sigma_d_sweep_25 = (
3.06
* np.sin(wing_sweep_25)
/ (1.0 + np.cos(wing_sweep_25)) ** 2.0
* vt_area
/ wing_area
)
d_k_sigma_d_wing_area = -3.06 / (1.0 + np.cos(wing_sweep_25)) * vt_area / wing_area**2.0
d_k_sigma_d_vt_area = 3.06 / (1.0 + np.cos(wing_sweep_25)) / wing_area
if self.options["low_speed_aero"]:
partials[
"data:aerodynamics:vertical_tail:low_speed:Cy_beta",
"data:geometry:wing:aspect_ratio",
] = -k_v * cl_alpha_vt * d_k_sigma_d_wing_ar * eta_v * vt_area / wing_area
partials[
"data:aerodynamics:vertical_tail:low_speed:Cy_beta",
"data:geometry:wing:area",
] = (
-k_v
* cl_alpha_vt
* eta_v
* (d_k_sigma_d_wing_area * vt_area / wing_area - k_sigma * vt_area / wing_area**2.0)
)
partials[
"data:aerodynamics:vertical_tail:low_speed:Cy_beta",
"data:geometry:wing:sweep_25",
] = -k_v * cl_alpha_vt * d_k_sigma_d_sweep_25 * eta_v * vt_area / wing_area
partials[
"data:aerodynamics:vertical_tail:low_speed:Cy_beta", "data:geometry:wing:root:z"
] = -k_v * cl_alpha_vt * d_k_sigma_d_z_w * eta_v * vt_area / wing_area
partials[
"data:aerodynamics:vertical_tail:low_speed:Cy_beta",
"data:geometry:fuselage:maximum_height",
] = -k_v * cl_alpha_vt * d_k_sigma_d_z_f * eta_v * vt_area / wing_area
partials[
"data:aerodynamics:vertical_tail:low_speed:Cy_beta",
"data:aerodynamics:vertical_tail:efficiency",
] = -k_v * cl_alpha_vt * k_sigma * vt_area / wing_area
partials[
"data:aerodynamics:vertical_tail:low_speed:Cy_beta",
"data:aerodynamics:vertical_tail:low_speed:CL_alpha",
] = -k_v * k_sigma * eta_v * vt_area / wing_area
partials[
"data:aerodynamics:vertical_tail:low_speed:Cy_beta",
"data:geometry:vertical_tail:area",
] = (
-k_v
* cl_alpha_vt
* eta_v
* (d_k_sigma_d_vt_area * vt_area / wing_area + k_sigma / wing_area)
)
partials[
"data:aerodynamics:vertical_tail:low_speed:Cy_beta",
"data:geometry:vertical_tail:span",
] = cl_alpha_vt * eta_v * k_sigma * vt_area / wing_area * d_k_v_d_span
partials[
"data:aerodynamics:vertical_tail:low_speed:Cy_beta",
"data:geometry:fuselage:average_depth",
] = cl_alpha_vt * eta_v * k_sigma * vt_area / wing_area * d_k_v_d_hf
else:
partials[
"data:aerodynamics:vertical_tail:cruise:Cy_beta",
"data:geometry:wing:aspect_ratio",
] = -k_v * cl_alpha_vt * d_k_sigma_d_wing_ar * eta_v * vt_area / wing_area
partials[
"data:aerodynamics:vertical_tail:cruise:Cy_beta",
"data:geometry:wing:area",
] = (
-k_v
* cl_alpha_vt
* eta_v
* (d_k_sigma_d_wing_area * vt_area / wing_area - k_sigma * vt_area / wing_area**2.0)
)
partials[
"data:aerodynamics:vertical_tail:cruise:Cy_beta",
"data:geometry:wing:sweep_25",
] = -k_v * cl_alpha_vt * d_k_sigma_d_sweep_25 * eta_v * vt_area / wing_area
partials[
"data:aerodynamics:vertical_tail:cruise:Cy_beta", "data:geometry:wing:root:z"
] = -k_v * cl_alpha_vt * d_k_sigma_d_z_w * eta_v * vt_area / wing_area
partials[
"data:aerodynamics:vertical_tail:cruise:Cy_beta",
"data:geometry:fuselage:maximum_height",
] = -k_v * cl_alpha_vt * d_k_sigma_d_z_f * eta_v * vt_area / wing_area
partials[
"data:aerodynamics:vertical_tail:cruise:Cy_beta",
"data:aerodynamics:vertical_tail:efficiency",
] = -k_v * cl_alpha_vt * k_sigma * vt_area / wing_area
partials[
"data:aerodynamics:vertical_tail:cruise:Cy_beta",
"data:aerodynamics:vertical_tail:cruise:CL_alpha",
] = -k_v * k_sigma * eta_v * vt_area / wing_area
partials[
"data:aerodynamics:vertical_tail:cruise:Cy_beta",
"data:geometry:vertical_tail:area",
] = (
-k_v
* cl_alpha_vt
* eta_v
* (d_k_sigma_d_vt_area * vt_area / wing_area + k_sigma / wing_area)
)
partials[
"data:aerodynamics:vertical_tail:cruise:Cy_beta",
"data:geometry:vertical_tail:span",
] = cl_alpha_vt * eta_v * k_sigma * vt_area / wing_area * d_k_v_d_span
partials[
"data:aerodynamics:vertical_tail:cruise:Cy_beta",
"data:geometry:fuselage:average_depth",
] = cl_alpha_vt * eta_v * k_sigma * vt_area / wing_area * d_k_v_d_hf