# 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 ...constants import SUBMODEL_CN_R_VT
[docs]@oad.RegisterSubmodel(
SUBMODEL_CN_R_VT, "fastga.submodel.aerodynamics.vertical_tail.cn_yaw_rate.legacy"
)
class ComputeCnYawRateVerticalTail(om.ExplicitComponent):
"""
Computation of the increase in yaw rate due to a yaw rate. The coefficient depends on the
angle of attack so the same remark as in ..compute_cy_yaw_rate. holds. The convention from
:cite:`roskampart6:1985` are used, meaning that for lateral derivative, the reference length
is the wing span. Another important point is that, for the derivative with respect to yaw and
roll, the rotation speed are made dimensionless by multiplying them by the wing span and
dividing them by 2 times the airspeed.
Based on :cite:`roskampart6:1985` section 10.2.8
"""
[docs] def initialize(self):
self.options.declare("low_speed_aero", default=False, types=bool)
[docs] def setup(self):
self.add_input("data:geometry:wing:span", val=np.nan, units="m")
self.add_input("data:geometry:wing:root:z", units="m", val=np.nan)
self.add_input(
"data:geometry:vertical_tail:MAC:at25percent:x:from_wingMAC25", units="m", val=np.nan
)
self.add_input("data:geometry:vertical_tail:MAC:z", units="m", val=np.nan)
self.add_input("data:geometry:fuselage:maximum_height", units="m", val=np.nan)
if self.options["low_speed_aero"]:
self.add_input(
"settings:aerodynamics:reference_flight_conditions:low_speed:AOA",
units="rad",
val=5.0 * np.pi / 180.0,
)
self.add_input(
"data:aerodynamics:vertical_tail:low_speed:Cy_beta", val=np.nan, units="rad**-1"
)
self.add_output("data:aerodynamics:vertical_tail:low_speed:Cn_r", units="rad**-1")
else:
self.add_input(
"settings:aerodynamics:reference_flight_conditions:cruise:AOA",
units="rad",
val=1.0 * np.pi / 180.0,
)
self.add_input(
"data:aerodynamics:vertical_tail:cruise:Cy_beta", val=np.nan, units="rad**-1"
)
self.add_output("data:aerodynamics:vertical_tail:cruise:Cn_r", units="rad**-1")
self.declare_partials(of="*", wrt="*", method="exact")
[docs] def compute(self, inputs, outputs, discrete_inputs=None, discrete_outputs=None):
z_v = (
inputs["data:geometry:wing:root:z"]
+ 0.5 * inputs["data:geometry:fuselage:maximum_height"]
+ inputs["data:geometry:vertical_tail:MAC:z"]
)
lp_vt = inputs["data:geometry:vertical_tail:MAC:at25percent:x:from_wingMAC25"]
wing_span = inputs["data:geometry:wing:span"]
if self.options["low_speed_aero"]:
aoa_ref = inputs["settings:aerodynamics:reference_flight_conditions:low_speed:AOA"]
cy_beta_vt = inputs["data:aerodynamics:vertical_tail:low_speed:Cy_beta"]
outputs["data:aerodynamics:vertical_tail:low_speed:Cn_r"] = (
2.0
* cy_beta_vt
* (lp_vt * np.cos(aoa_ref) + z_v * np.sin(aoa_ref)) ** 2.0
/ wing_span**2.0
)
else:
aoa_ref = inputs["settings:aerodynamics:reference_flight_conditions:cruise:AOA"]
cy_beta_vt = inputs["data:aerodynamics:vertical_tail:cruise:Cy_beta"]
outputs["data:aerodynamics:vertical_tail:cruise:Cn_r"] = (
2.0
* cy_beta_vt
* (lp_vt * np.cos(aoa_ref) + z_v * np.sin(aoa_ref)) ** 2.0
/ wing_span**2.0
)
[docs] def compute_partials(self, inputs, partials, discrete_inputs=None):
z_v = (
inputs["data:geometry:wing:root:z"]
+ 0.5 * inputs["data:geometry:fuselage:maximum_height"]
+ inputs["data:geometry:vertical_tail:MAC:z"]
)
lp_vt = inputs["data:geometry:vertical_tail:MAC:at25percent:x:from_wingMAC25"]
wing_span = inputs["data:geometry:wing:span"]
if self.options["low_speed_aero"]:
aoa_ref = inputs["settings:aerodynamics:reference_flight_conditions:low_speed:AOA"]
cy_beta_vt = inputs["data:aerodynamics:vertical_tail:low_speed:Cy_beta"]
partials[
"data:aerodynamics:vertical_tail:low_speed:Cn_r",
"data:aerodynamics:vertical_tail:low_speed:Cy_beta",
] = 2.0 * (lp_vt * np.cos(aoa_ref) + z_v * np.sin(aoa_ref)) ** 2.0 / wing_span**2.0
partials[
"data:aerodynamics:vertical_tail:low_speed:Cn_r",
"data:geometry:wing:root:z",
] = (
4.0
* cy_beta_vt
* (lp_vt * np.cos(aoa_ref) + z_v * np.sin(aoa_ref))
* np.sin(aoa_ref)
/ wing_span**2.0
)
partials[
"data:aerodynamics:vertical_tail:low_speed:Cn_r",
"data:geometry:fuselage:maximum_height",
] = (
2.0
* cy_beta_vt
* (lp_vt * np.cos(aoa_ref) + z_v * np.sin(aoa_ref))
* np.sin(aoa_ref)
/ wing_span**2.0
)
partials[
"data:aerodynamics:vertical_tail:low_speed:Cn_r",
"data:geometry:vertical_tail:MAC:z",
] = (
4.0
* cy_beta_vt
* (lp_vt * np.cos(aoa_ref) + z_v * np.sin(aoa_ref))
* np.sin(aoa_ref)
/ wing_span**2.0
)
partials[
"data:aerodynamics:vertical_tail:low_speed:Cn_r",
"data:geometry:vertical_tail:MAC:at25percent:x:from_wingMAC25",
] = (
4.0
* cy_beta_vt
* (lp_vt * np.cos(aoa_ref) + z_v * np.sin(aoa_ref))
* np.cos(aoa_ref)
/ wing_span**2.0
)
partials[
"data:aerodynamics:vertical_tail:low_speed:Cn_r",
"data:geometry:wing:span",
] = (
-4.0
* cy_beta_vt
* (lp_vt * np.cos(aoa_ref) + z_v * np.sin(aoa_ref)) ** 2.0
/ wing_span**3.0
)
partials[
"data:aerodynamics:vertical_tail:low_speed:Cn_r",
"settings:aerodynamics:reference_flight_conditions:low_speed:AOA",
] = (
4.0
* cy_beta_vt
* (lp_vt * np.cos(aoa_ref) + z_v * np.sin(aoa_ref))
* (-lp_vt * np.sin(aoa_ref) + z_v * np.cos(aoa_ref))
/ wing_span**2.0
)
else:
aoa_ref = inputs["settings:aerodynamics:reference_flight_conditions:cruise:AOA"]
cy_beta_vt = inputs["data:aerodynamics:vertical_tail:cruise:Cy_beta"]
partials[
"data:aerodynamics:vertical_tail:cruise:Cn_r",
"data:aerodynamics:vertical_tail:cruise:Cy_beta",
] = 2.0 * (lp_vt * np.cos(aoa_ref) + z_v * np.sin(aoa_ref)) ** 2.0 / wing_span**2.0
partials[
"data:aerodynamics:vertical_tail:cruise:Cn_r",
"data:geometry:wing:root:z",
] = (
4.0
* cy_beta_vt
* (lp_vt * np.cos(aoa_ref) + z_v * np.sin(aoa_ref))
* np.sin(aoa_ref)
/ wing_span**2.0
)
partials[
"data:aerodynamics:vertical_tail:cruise:Cn_r",
"data:geometry:fuselage:maximum_height",
] = (
2.0
* cy_beta_vt
* (lp_vt * np.cos(aoa_ref) + z_v * np.sin(aoa_ref))
* np.sin(aoa_ref)
/ wing_span**2.0
)
partials[
"data:aerodynamics:vertical_tail:cruise:Cn_r",
"data:geometry:vertical_tail:MAC:z",
] = (
4.0
* cy_beta_vt
* (lp_vt * np.cos(aoa_ref) + z_v * np.sin(aoa_ref))
* np.sin(aoa_ref)
/ wing_span**2.0
)
partials[
"data:aerodynamics:vertical_tail:cruise:Cn_r",
"data:geometry:vertical_tail:MAC:at25percent:x:from_wingMAC25",
] = (
4.0
* cy_beta_vt
* (lp_vt * np.cos(aoa_ref) + z_v * np.sin(aoa_ref))
* np.cos(aoa_ref)
/ wing_span**2.0
)
partials["data:aerodynamics:vertical_tail:cruise:Cn_r", "data:geometry:wing:span"] = (
-4.0
* cy_beta_vt
* (lp_vt * np.cos(aoa_ref) + z_v * np.sin(aoa_ref)) ** 2.0
/ wing_span**3.0
)
partials[
"data:aerodynamics:vertical_tail:cruise:Cn_r",
"settings:aerodynamics:reference_flight_conditions:cruise:AOA",
] = (
4.0
* cy_beta_vt
* (lp_vt * np.cos(aoa_ref) + z_v * np.sin(aoa_ref))
* (-lp_vt * np.sin(aoa_ref) + z_v * np.cos(aoa_ref))
/ wing_span**2.0
)