def scattering_factor(elevation_angle):
"""
Calculates a scattering factor (a factor that gives losses due to atmospheric scattering at low elevation angles).
Source: AeroSandbox/studies/SolarPanelScattering
:param elevation_angle: Angle between the horizon and the sun [degrees]
:return: Fraction of the light that is not lost to scattering.
"""
elevation_angle = np.clip(elevation_angle, 0, 90)
theta = 90 - elevation_angle # Angle between panel normal and the sun, in degrees
# # Model 1
# c = (
# 0.27891510500505767300438719757949,
# -0.015994330894744987481281839336589,
# -19.707332432605799255043166340329,
# -0.66260979582573353852126274432521
# )
# scattering_factor = c[0] + c[3] * theta_rad + cas.exp(
# c[1] * (
# cas.tan(theta_rad) + c[2] * theta_rad
# )
# )
# Model 2
c = (
-0.04636,
-0.3171
)
scattering_factor = np.exp(
c[0] * (
np.tand(theta * 0.999) + c[1] * np.radians(theta)
)
)
# # Model 3
# p1 = -21.74
# p2 = 282.6
# p3 = -1538
# p4 = 1786
# q1 = -923.2
# q2 = 1456
# x = theta_rad
# scattering_factor = ((p1*x**3 + p2*x**2 + p3*x + p4) /
# (x**2 + q1*x + q2))
# Keep this:
# scattering_factor = cas.fmin(cas.fmax(scattering_factor, 0), 1)
return scattering_factor
def CL_over_Cl(aspect_ratio: float,
mach: float = 0.,
sweep: float = 0.) -> float:
"""
Returns the ratio of 3D lift coefficient (with compressibility) to 2D lift coefficient (incompressible).
:param aspect_ratio: Aspect ratio
:param mach: Mach number
:param sweep: Sweep angle [deg]
:return:
"""
beta = np.where(1 - mach**2 >= 0, np.fmax(1 - mach**2, 0)**0.5, 0)
# return aspect_ratio / (aspect_ratio + 2) # Equivalent to equation in Drela's FVA in incompressible, 2*pi*alpha limit.
# return aspect_ratio / (2 + cas.sqrt(4 + aspect_ratio ** 2)) # more theoretically sound at low aspect_ratio
eta = 0.95
return aspect_ratio / (2 + np.sqrt(4 + (aspect_ratio * beta / eta)**2 *
(1 + (np.tand(sweep) / beta)**2))
) # From Raymer, Sect. 12.4.1; citing DATCOM
def CL_over_Cl(
aspect_ratio: float,
mach: float = 0.,
sweep: float = 0.,
Cl_is_compressible: bool = True
) -> float:
"""
Returns the ratio of 3D lift coefficient (with compressibility) to the 2D lift coefficient.
Specifically: CL_3D / CL_2D
Args:
aspect_ratio: The aspect ratio of the wing.
mach: The freestream Mach number.
sweep: The sweep of the wing, in degrees. To be most accurate, this should be the sweep at the locus of
thickest points along the wing.
Cl_is_compressible: This flag indicates whether the 2D airfoil data already has compressibility effects
modeled.
For example:
* If this flag is True, this function returns: CL_3D / CL_2D, where CL_2D is the sectional lift
coefficient based on the local profile at the freestream mach number.
* If this flag is False, this function returns: CL_3D / CL_2D_at_mach_zero, where CL_2D_... is the
sectional lift coefficient based on the local profile at mach zero.
For most accurate results, set this flag to True, and then model profile characteristics separately.
"""
prandtl_glauert_beta_squared_ideal = 1 - mach ** 2
# beta_squared = 1 - mach ** 2
beta_squared = np.softmax(
prandtl_glauert_beta_squared_ideal,
-prandtl_glauert_beta_squared_ideal,
hardness=3.0
)
### Alternate formulations
# CL_ratio = aspect_ratio / (aspect_ratio + 2) # Equivalent to equation in Drela's FVA in incompressible, 2*pi*alpha limit.
# CL_ratio = aspect_ratio / (2 + np.sqrt(4 + aspect_ratio ** 2)) # more theoretically sound at low aspect_ratio
### Formulation from Raymer, Sect. 12.4.1; citing DATCOM.
# Comparison to experiment suggests this is the most accurate.
# Symbolically simplified to remove the PG singularity.
eta = 0.95
CL_ratio = aspect_ratio / (
2 + (
4 + (aspect_ratio ** 2 * beta_squared / eta ** 2) + (np.tand(sweep) * aspect_ratio / eta) ** 2
) ** 0.5
)
if Cl_is_compressible:
CL_ratio = CL_ratio * beta_squared ** 0.5
return CL_ratio