"""Estimation of the vertical tail profile drag."""
# 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_CD0_VT
[docs]@oad.RegisterSubmodel(SUBMODEL_CD0_VT, "fastga.submodel.aerodynamics.vertical_tail.cd0.legacy")
class Cd0VerticalTail(ExplicitComponent):
"""
Profile drag estimation for the vertical tail
Based on : Gudmundsson, Snorri. General aviation aircraft design: Applied Methods and
Procedures. Butterworth-Heinemann, 2013.
And :
Raymer, Daniel. Aircraft design: a conceptual approach. American Institute of Aeronautics and
Astronautics, Inc., 2012.
"""
[docs] def initialize(self):
self.options.declare("low_speed_aero", default=False, types=bool)
[docs] def setup(self):
self.add_input("data:geometry:vertical_tail:tip:chord", val=np.nan, units="m")
self.add_input("data:geometry:vertical_tail:root:chord", val=np.nan, units="m")
self.add_input("data:geometry:vertical_tail:sweep_25", val=np.nan, units="rad")
self.add_input("data:geometry:vertical_tail:wet_area", val=np.nan, units="m**2")
self.add_input("data:geometry:wing:area", val=np.nan, units="m**2")
self.add_input("data:geometry:vertical_tail:thickness_ratio", val=np.nan)
self.add_input("data:geometry:vertical_tail:max_thickness:x_ratio", val=0.3)
if self.options["low_speed_aero"]:
self.add_input("data:aerodynamics:low_speed:mach", val=np.nan)
self.add_input("data:aerodynamics:low_speed:unit_reynolds", val=np.nan, units="m**-1")
self.add_output("data:aerodynamics:vertical_tail:low_speed:CD0")
self.declare_partials("*", "*", method="exact")
else:
self.add_input("data:aerodynamics:cruise:mach", val=np.nan)
self.add_input("data:aerodynamics:cruise:unit_reynolds", val=np.nan, units="m**-1")
self.add_output("data:aerodynamics:vertical_tail:cruise:CD0")
self.declare_partials("*", "*", method="exact")
[docs] def compute(self, inputs, outputs, discrete_inputs=None, discrete_outputs=None):
tip_chord = inputs["data:geometry:vertical_tail:tip:chord"]
root_chord = inputs["data:geometry:vertical_tail:root:chord"]
sweep_25_vt = inputs["data:geometry:vertical_tail:sweep_25"]
wet_area_vt = inputs["data:geometry:vertical_tail:wet_area"]
wing_area = inputs["data:geometry:wing:area"]
thickness = inputs["data:geometry:vertical_tail:thickness_ratio"]
x_t_max = inputs["data:geometry:vertical_tail:max_thickness:x_ratio"]
if self.options["low_speed_aero"]:
mach = inputs["data:aerodynamics:low_speed:mach"]
unit_reynolds = inputs["data:aerodynamics:low_speed:unit_reynolds"]
else:
mach = inputs["data:aerodynamics:cruise:mach"]
unit_reynolds = inputs["data:aerodynamics:cruise:unit_reynolds"]
# Root: 50% NLF
x_trans = 0.5
x0_turbulent = 36.9 * x_trans**0.625 * (1 / (unit_reynolds * root_chord)) ** 0.375
cf_root = (
0.074 / (unit_reynolds * root_chord) ** 0.2 * (1 - (x_trans - x0_turbulent)) ** 0.8
)
# Tip: 50% NLF
x_trans = 0.5
x0_turbulent = 36.9 * x_trans**0.625 * (1 / (unit_reynolds * tip_chord)) ** 0.375
cf_tip = 0.074 / (unit_reynolds * tip_chord) ** 0.2 * (1 - (x_trans - x0_turbulent)) ** 0.8
# Global
cf_vt = (cf_root + cf_tip) * 0.5
form_factor = 1 + 0.6 / x_t_max * thickness + 100 * thickness**4
form_factor = form_factor * 1.05 # Due to hinged elevator (Raymer)
if mach > 0.2:
form_factor = form_factor * 1.34 * mach**0.18 * (np.cos(sweep_25_vt)) ** 0.28
interference_factor = 1.05
cd0 = form_factor * interference_factor * cf_vt * wet_area_vt / wing_area
if self.options["low_speed_aero"]:
outputs["data:aerodynamics:vertical_tail:low_speed:CD0"] = cd0
else:
outputs["data:aerodynamics:vertical_tail:cruise:CD0"] = cd0
[docs] def compute_partials(self, inputs, partials, discrete_inputs=None):
tip_chord = inputs["data:geometry:vertical_tail:tip:chord"]
root_chord = inputs["data:geometry:vertical_tail:root:chord"]
sweep_25_vt = inputs["data:geometry:vertical_tail:sweep_25"]
wet_area_vt = inputs["data:geometry:vertical_tail:wet_area"]
wing_area = inputs["data:geometry:wing:area"]
thickness = inputs["data:geometry:vertical_tail:thickness_ratio"]
x_t_max = inputs["data:geometry:vertical_tail:max_thickness:x_ratio"]
if self.options["low_speed_aero"]:
mach = inputs["data:aerodynamics:low_speed:mach"]
unit_reynolds = inputs["data:aerodynamics:low_speed:unit_reynolds"]
else:
mach = inputs["data:aerodynamics:cruise:mach"]
unit_reynolds = inputs["data:aerodynamics:cruise:unit_reynolds"]
x_trans = 0.5
# Tip
reynolds_tip = unit_reynolds * tip_chord
x0_tip = 36.9 * x_trans**0.625 * reynolds_tip**-0.375
d_x0_tip_d_unit_re = (
-0.375 * 36.9 * x_trans**0.625 * tip_chord**-0.375 * unit_reynolds**-1.375
)
d_x0_tip_d_tip_chord = (
-0.375 * 36.9 * x_trans**0.625 * unit_reynolds**-0.375 * tip_chord**-1.375
)
cf_vt_tip = 0.074 * reynolds_tip**-0.2 * (1.0 - (x_trans - x0_tip)) ** 0.8
d_cf_vt_tip_d_unit_re = (
-0.2 * 0.074 * tip_chord**-0.2 * unit_reynolds**-1.2 * (1.0 - (x_trans - x0_tip)) ** 0.8
) + 0.074 * reynolds_tip**-0.2 * 0.8 * (
1.0 - (x_trans - x0_tip)
) ** -0.2 * d_x0_tip_d_unit_re
d_cf_vt_tip_d_chord_tip = (
-0.2 * 0.074 * unit_reynolds**-0.2 * tip_chord**-1.2 * (1.0 - (x_trans - x0_tip)) ** 0.8
) + 0.074 * reynolds_tip**-0.2 * 0.8 * (
1.0 - (x_trans - x0_tip)
) ** -0.2 * d_x0_tip_d_tip_chord
# Root
reynolds_root = unit_reynolds * root_chord
x_trans = 0.5
x0_root = 36.9 * x_trans**0.625 * reynolds_root**-0.375
d_x0_root_d_unit_re = (
-0.375 * 36.9 * x_trans**0.625 * root_chord**-0.375 * unit_reynolds**-1.375
)
d_x0_root_d_root_chord = (
-0.375 * 36.9 * x_trans**0.625 * unit_reynolds**-0.375 * root_chord**-1.375
)
cf_vt_root = 0.074 * reynolds_root**-0.2 * (1.0 - (x_trans - x0_root)) ** 0.8
d_cf_vt_root_d_unit_re = (
-0.2
* 0.074
* root_chord**-0.2
* unit_reynolds**-1.2
* (1.0 - (x_trans - x0_root)) ** 0.8
) + 0.074 * reynolds_root**-0.2 * 0.8 * (
1.0 - (x_trans - x0_root)
) ** -0.2 * d_x0_root_d_unit_re
d_cf_vt_root_d_chord_root = (
-0.2
* 0.074
* unit_reynolds**-0.2
* root_chord**-1.2
* (1.0 - (x_trans - x0_root)) ** 0.8
) + 0.074 * reynolds_root**-0.2 * 0.8 * (
1.0 - (x_trans - x0_root)
) ** -0.2 * d_x0_root_d_root_chord
cf_vt = (cf_vt_root + cf_vt_tip) * 0.5
d_cf_vt_d_unit_re = 0.5 * (d_cf_vt_root_d_unit_re + d_cf_vt_tip_d_unit_re)
d_cf_vt_d_chord_tip = 0.5 * d_cf_vt_tip_d_chord_tip
c_cf_vt_d_chord_root = 0.5 * d_cf_vt_root_d_chord_root
form_factor = 1.05 * (1 + 0.6 / x_t_max * thickness + 100 * thickness**4.0)
d_ff_d_location = -1.05 * 0.6 / x_t_max**2.0 * thickness
d_ff_d_thickness = 1.05 * (0.6 / x_t_max + 4.0 * 100 * thickness**3.0)
if mach > 0.2:
mach_correction = 1.34 * mach**0.18 * (np.cos(sweep_25_vt)) ** 0.28
d_mach_correction_d_mach = 0.18 * 1.34 * mach**-0.82 * (np.cos(sweep_25_vt)) ** 0.28
d_mach_correction_d_sweep = (
-0.28 * 1.34 * mach**0.18 * (np.cos(sweep_25_vt)) ** -0.72 * np.sin(sweep_25_vt)
)
else:
mach_correction = 1.0
d_mach_correction_d_mach = 0.0
d_mach_correction_d_sweep = 0.0
interference_factor = 1.05
if self.options["low_speed_aero"]:
partials[
"data:aerodynamics:vertical_tail:low_speed:CD0",
"data:geometry:vertical_tail:tip:chord",
] = (
form_factor
* mach_correction
* interference_factor
* d_cf_vt_d_chord_tip
* wet_area_vt
/ wing_area
)
partials[
"data:aerodynamics:vertical_tail:low_speed:CD0",
"data:geometry:vertical_tail:root:chord",
] = (
form_factor
* mach_correction
* interference_factor
* c_cf_vt_d_chord_root
* wet_area_vt
/ wing_area
)
partials[
"data:aerodynamics:vertical_tail:low_speed:CD0",
"data:geometry:vertical_tail:sweep_25",
] = (
form_factor
* d_mach_correction_d_sweep
* interference_factor
* cf_vt
* wet_area_vt
/ wing_area
)
partials[
"data:aerodynamics:vertical_tail:low_speed:CD0",
"data:geometry:vertical_tail:wet_area",
] = form_factor * mach_correction * interference_factor * cf_vt / wing_area
partials["data:aerodynamics:vertical_tail:low_speed:CD0", "data:geometry:wing:area"] = (
-form_factor
* mach_correction
* interference_factor
* cf_vt
* wet_area_vt
/ wing_area**2.0
)
partials[
"data:aerodynamics:vertical_tail:low_speed:CD0",
"data:geometry:vertical_tail:thickness_ratio",
] = (
d_ff_d_thickness
* mach_correction
* interference_factor
* cf_vt
* wet_area_vt
/ wing_area
)
partials[
"data:aerodynamics:vertical_tail:low_speed:CD0",
"data:geometry:vertical_tail:max_thickness:x_ratio",
] = (
d_ff_d_location
* mach_correction
* interference_factor
* cf_vt
* wet_area_vt
/ wing_area
)
partials[
"data:aerodynamics:vertical_tail:low_speed:CD0", "data:aerodynamics:low_speed:mach"
] = (
form_factor
* d_mach_correction_d_mach
* interference_factor
* cf_vt
* wet_area_vt
/ wing_area
)
partials[
"data:aerodynamics:vertical_tail:low_speed:CD0",
"data:aerodynamics:low_speed:unit_reynolds",
] = (
form_factor
* mach_correction
* interference_factor
* d_cf_vt_d_unit_re
* wet_area_vt
/ wing_area
)
else:
partials[
"data:aerodynamics:vertical_tail:cruise:CD0",
"data:geometry:vertical_tail:tip:chord",
] = (
form_factor
* mach_correction
* interference_factor
* d_cf_vt_d_chord_tip
* wet_area_vt
/ wing_area
)
partials[
"data:aerodynamics:vertical_tail:cruise:CD0",
"data:geometry:vertical_tail:root:chord",
] = (
form_factor
* mach_correction
* interference_factor
* c_cf_vt_d_chord_root
* wet_area_vt
/ wing_area
)
partials[
"data:aerodynamics:vertical_tail:cruise:CD0",
"data:geometry:vertical_tail:sweep_25",
] = (
form_factor
* d_mach_correction_d_sweep
* interference_factor
* cf_vt
* wet_area_vt
/ wing_area
)
partials[
"data:aerodynamics:vertical_tail:cruise:CD0",
"data:geometry:vertical_tail:wet_area",
] = form_factor * mach_correction * interference_factor * cf_vt / wing_area
partials["data:aerodynamics:vertical_tail:cruise:CD0", "data:geometry:wing:area"] = (
-form_factor
* mach_correction
* interference_factor
* cf_vt
* wet_area_vt
/ wing_area**2.0
)
partials[
"data:aerodynamics:vertical_tail:cruise:CD0",
"data:geometry:vertical_tail:thickness_ratio",
] = (
d_ff_d_thickness
* mach_correction
* interference_factor
* cf_vt
* wet_area_vt
/ wing_area
)
partials[
"data:aerodynamics:vertical_tail:cruise:CD0",
"data:geometry:vertical_tail:max_thickness:x_ratio",
] = (
d_ff_d_location
* mach_correction
* interference_factor
* cf_vt
* wet_area_vt
/ wing_area
)
partials[
"data:aerodynamics:vertical_tail:cruise:CD0", "data:aerodynamics:cruise:mach"
] = (
form_factor
* d_mach_correction_d_mach
* interference_factor
* cf_vt
* wet_area_vt
/ wing_area
)
partials[
"data:aerodynamics:vertical_tail:cruise:CD0",
"data:aerodynamics:cruise:unit_reynolds",
] = (
form_factor
* mach_correction
* interference_factor
* d_cf_vt_d_unit_re
* wet_area_vt
/ wing_area
)