def fuselage_base_drag_coefficient(mach: float) -> float:
"""
A fit for the fuselage base drag coefficient of a cylindrical fuselage, as described in:
MIL-HDBK-762: DESIGN OF AERODYNAMICALLY STABILIZED FREE ROCKETS:
* Section 5-5.3.1 Body-of-Revolution Base Drag, Rocket Jet Plume-Off
* Figure 5-140: Effects of Mach Number and Reynolds Number on Base Pressure
Fits in /studies/FuselageBaseDragCoefficient
Args:
mach: Mach number [-]
Returns: Fuselage base drag coefficient
"""
m = mach
p = {
'a': 0.18024110740341143,
'center_sup': -0.21737019935624047,
'm_trans': 0.9985447737532848,
'pc_sub': 0.15922582283573747,
'pc_sup': 0.04698820458826384,
'scale_sup': 0.34978926411193456,
'trans_str': 9.999987483414937
}
return np.blend(
p["trans_str"] * (m - p["m_trans"]), p["pc_sup"] +
p["a"] * np.exp(-(p["scale_sup"] * (m - p["center_sup"]))**2),
p["pc_sub"])
def CM_function(alpha, Re, mach=0, deflection=0):
alpha = np.mod(alpha + 180,
360) - 180 # Keep alpha in the valid range.
CM_attached = CM_attached_interpolator({
"alpha": alpha,
"ln_Re": np.log(Re),
})
CM_separated = CM_separated_interpolator(alpha)
return np.blend(separation_parameter(alpha, Re), CM_separated,
CM_attached)
def CD_function(alpha, Re, mach=0, deflection=0):
alpha = np.mod(alpha + 180,
360) - 180 # Keep alpha in the valid range.
log10_CD_attached = log10_CD_attached_interpolator({
"alpha":
alpha,
"ln_Re":
np.log(Re),
})
log10_CD_separated = log10_CD_separated_interpolator(alpha)
return 10**np.blend(
separation_parameter(alpha, Re),
log10_CD_separated,
log10_CD_attached,
)
def approximate_CD_wave(
mach,
mach_crit,
CD_wave_at_fully_supersonic,
):
"""
An approximate relation for computing transonic wave drag, based on an object's Mach number.
Considered reasonably valid from Mach 0 up to around Mach 2 or 3-ish.
Methodology is a combination of:
* The methodology described in Raymer, "Aircraft Design: A Conceptual Approach", Section 12.5.10 Transonic Parasite Drag (pg. 449 in Ed. 2)
and
* The methodology described in W.H. Mason's Configuration Aerodynamics, Chapter 7. Transonic Aerodynamics of Airfoils and Wings.
Args:
mach: Mach number at the operating point to be evaluated
mach_crit: Critical mach number, a function of the body geometry
CD_wave_at_fully_supersonic: The wave drag coefficient of the body at the speed that it first goes (
effectively) fully supersonic.
Here, that is taken to mean at the Mach 1.2 case.
This value should probably be derived using something similar to a Sears-Haack relation for the body in
question, with a markup depending on geometry smoothness.
The CD_wave predicted by this function will match this value exactly at M=1.2 and M=1.05.
The peak CD_wave that is predicted is ~1.23 * this value, which occurs at M=1.10.
In the high-Mach limit, this function asymptotes at 0.80 * this value, as empirically stated by Raymer.
However, this model is only approximate and is likely not valid for high-supersonic flows.
Returns: The approximate wave drag coefficient at the specified Mach number.
The reference area is whatever the reference area used in the `CD_wave_at_fully_supersonic` parameter is.
"""
mach_crit_max = 1 - (0.1 / 80)**(1 / 3)
mach_crit = -np.softmax(-mach_crit, -mach_crit_max, hardness=50)
### The following approximate relation is derived in W.H. Mason, "Configuration Aerodynamics", Chapter 7. Transonic Aerodynamics of Airfoils and Wings.
### Equation 7-8 on Page 7-19.
### This is in turn based on Lock's proposed empirically-derived shape of the drag rise, from Hilton, W.F., High Speed Aerodynamics, Longmans, Green & Co., London, 1952, pp. 47-49
mach_dd = mach_crit + (0.1 / 80)**(1 / 3)
### Model drag sections and cutoffs:
return CD_wave_at_fully_supersonic * np.where(
mach < mach_crit,
0,
np.where(
mach < mach_dd,
20 * (mach - mach_crit)**4,
np.where(
mach < 1.05,
cubic_hermite_patch(mach,
x_a=mach_dd,
x_b=1.05,
f_a=20 * (0.1 / 80)**(4 / 3),
f_b=1,
dfdx_a=0.1,
dfdx_b=10),
np.where(mach < 1.2,
cubic_hermite_patch(mach,
x_a=1.05,
x_b=1.2,
f_a=1,
f_b=1,
dfdx_a=10,
dfdx_b=-4),
np.blend(
switch=4 * 2 * (mach - 1.2) / (1.2 - 0.8),
value_switch_high=0.8,
value_switch_low=1.2,
)
# 0.8 + 0.2 * np.exp(20 * (1.2 - mach))
))))
def model(m, p):
return np.blend(
p["trans_str"] * (m - p["m_trans"]), p["pc_sup"] +
p["a"] * np.exp(-(p["scale_sup"] * (m - p["center_sup"]))**2),
p["pc_sub"])
def model(m, p):
return np.blend(
p["trans_str"] * (m - p["trans"]),
p["cd_sup"] + np.exp(p["a_sup"] + p["s_sup"] * (m - p["trans"])),
p["cd_sub"] + np.exp(p["a_sub"] + p["s_sub"] * (m - p["trans"])))
def Cd_cylinder(Re_D: float,
mach: float = 0.,
include_mach_effects=True,
subcritical_only=False) -> float:
"""
Returns the drag coefficient of a cylinder in crossflow as a function of its Reynolds number and Mach.
Args:
Re_D: Reynolds number, referenced to diameter
mach: Mach number
include_mach_effects: If this is set False, it assumes Mach = 0, which simplifies the computation.
subcritical_only: Determines whether the model models purely subcritical (Re < 300k) cylinder flows. Useful, since
this model is now convex and can be more well-behaved.
Returns:
# TODO rework this function to use tanh blending, which will mitigate overflows
"""
##### Do the viscous part of the computation
csigc = 5.5766722118597247
csigh = 23.7460859935990563
csub0 = -0.6989492360435040
csub1 = 1.0465189382830078
csub2 = 0.7044228755898569
csub3 = 0.0846501115443938
csup0 = -0.0823564417206403
csupc = 6.8020230357616764
csuph = 9.9999999999999787
csupscl = -0.4570690347113859
x = np.log10(np.abs(Re_D) + 1e-16)
if subcritical_only:
Cd_mach_0 = 10**(csub0 * x + csub1) + csub2 + csub3 * x
else:
log10_Cd = (
(np.log10(10**(csub0 * x + csub1) + csub2 + csub3 * x)) *
(1 - 1 / (1 + np.exp(-csigh * (x - csigc)))) +
(csup0 + csupscl / csuph * np.log(np.exp(csuph *
(csupc - x)) + 1)) *
(1 / (1 + np.exp(-csigh * (x - csigc)))))
Cd_mach_0 = 10**log10_Cd
##### Do the compressible part of the computation
if include_mach_effects:
m = mach
p = {
'a_sub': 0.03458900259594298,
'a_sup': -0.7129528087049688,
'cd_sub': 1.163206940186374,
'cd_sup': 1.2899213533122527,
's_sub': 3.436601777569716,
's_sup': -1.37123096976983,
'trans': 1.022819211244295,
'trans_str': 19.017600596069848
}
Cd_over_Cd_mach_0 = np.blend(
p["trans_str"] *
(m - p["trans"]), p["cd_sup"] + np.exp(p["a_sup"] + p["s_sup"] *
(m - p["trans"])),
p["cd_sub"] + np.exp(p["a_sub"] + p["s_sub"] *
(m - p["trans"]))) / 1.1940010047391572
Cd = Cd_mach_0 * Cd_over_Cd_mach_0
else:
Cd = Cd_mach_0
return Cd