def __call__(self, conditions):
""" process vehicle to setup geometry, condititon and configuration
Inputs:
conditions - DataDict() of aerodynamic conditions
results - DataDict() of
Outputs:
Assumptions:
"""
# unpack
configuration = self.configuration
geometry = self.geometry
stability_model = self.stability_model
q = conditions.freestream.dynamic_pressure
Sref = geometry.reference_area
mach = conditions.freestream.mach_number
velocity = conditions.freestream.velocity
density = conditions.freestream.density
Span = geometry.wings['main_wing'].spans.projected
mac = geometry.wings['main_wing'].chords.mean_aerodynamic
aero = conditions.aerodynamics
# set up data structures
static_stability = Data()
dynamic_stability = Data()
# Calculate CL_alpha
if not conditions.has_key('lift_curve_slope'):
conditions.lift_curve_slope = datcom(geometry.wings['main_wing'],
mach)
# Calculate change in downwash with respect to change in angle of attack
for surf in geometry.wings:
sref = surf.areas.reference
span = (surf.aspect_ratio * sref)**0.5
surf.CL_alpha = datcom(surf, mach)
surf.ep_alpha = Supporting_Functions.ep_alpha(
surf.CL_alpha, sref, span)
# Static Stability Methods
static_stability.cm_alpha = taw_cmalpha(geometry, mach, conditions,
configuration)
static_stability.cn_beta = taw_cnbeta(geometry, conditions,
configuration)
# Dynamic Stability
if np.count_nonzero(
configuration.mass_properties.moments_of_inertia.tensor) > 0:
# Dynamic Stability Approximation Methods - valid for non-zero I tensor
# Derivative of yawing moment with respect to the rate of yaw
cDw = aero.drag_breakdown.parasite[
'main_wing'].parasite_drag_coefficient # Might not be the correct value
l_v = geometry.wings['vertical_stabilizer'].origin[
0] + geometry.wings['vertical_stabilizer'].aerodynamic_center[
0] - geometry.wings['main_wing'].origin[
0] - geometry.wings['main_wing'].aerodynamic_center[0]
dynamic_stability.cn_r = Supporting_Functions.cn_r(
cDw, geometry.wings['vertical_stabilizer'].areas.reference,
Sref, l_v, span,
geometry.wings['vertical_stabilizer'].dynamic_pressure_ratio,
geometry.wings['vertical_stabilizer'].CL_alpha)
# Derivative of rolling moment with respect to roll rate
dynamic_stability.cl_p = 0 # Need to see if there is a low fidelity way to calculate cl_p
# Derivative of roll rate with respect to sideslip (dihedral effect)
dynamic_stability.cl_beta = 0 # Need to see if there is a low fidelity way to calculate cl_beta
# Derivative of pitching moment with respect to pitch rate
l_t = geometry.wings['horizontal_stabilizer'].origin[
0] + geometry.wings['horizontal_stabilizer'].aerodynamic_center[
0] - geometry.wings['main_wing'].origin[
0] - geometry.wings['main_wing'].aerodynamic_center[
0] #Need to check this is the length of the horizontal tail moment arm
dynamic_stability.cm_q = Supporting_Functions.cm_q(
conditions.lift_curve_slope, l_t,
mac) # Need to check Cm_i versus Cm_alpha
# Derivative of pitching rate with respect to d(alpha)/d(t)
dynamic_stability.cm_alpha_dot = Supporting_Functions.cm_alphadot(
static_stability.cm_alpha,
geometry.wings['horizontal_stabilizer'].ep_alpha, l_t,
mac) # Need to check Cm_i versus Cm_alpha
# Derivative of Z-axis force with respect to angle of attack
dynamic_stability.cz_alpha = Supporting_Functions.cz_alpha(
aero.drag_coefficient, conditions.lift_curve_slope)
stability_model.dutch_roll = Approximations.dutch_roll(
velocity, static_stability.cn_beta, Sref, density, Span,
configuration.mass_properties.moments_of_inertia.tensor[2][2],
dynamic_stability.cn_r)
if dynamic_stability.cl_p != 0:
stability_model.roll_tau = Approximations.roll(
configuration.mass_properties.momen[2][2], Sref, density,
velocity, Span, dynamic_stability.cl_p)
dynamic_stability.cy_phi = Supporting_Functions.cy_phi(
aero.lift_coefficient)
dynamic_stability.cl_r = Supporting_Functions.cl_r(
aero.lift_coefficient) # Will need to be changed
stability_model.spiral_tau = Approximations.spiral(
conditions.weights.total_mass, velocity, density, Sref,
dynamic_stability.cl_p, static_stability.cn_beta,
dynamic_stability.cy_phi, dynamic_stability.cl_beta,
dynamic_stability.cn_r, dynamic_stability.cl_r)
stability_model.short_period = Approximations.short_period(
velocity, density, Sref, mac, dynamic_stability.cm_q,
dynamic_stability.cz_alpha, conditions.weights.total_mass,
static_stability.cm_alpha,
configuration.mass_properties.moments_of_inertia.tensor[1][1],
dynamic_stability.cm_alpha_dot)
stability_model.phugoid = Approximations.phugoid(
conditions.freestream.gravity, conditions.freestream.velocity,
aero.drag_coefficient, aero.lift_coefficient)
# Dynamic Stability Full Linearized Methods
if aero.has_key(
'cy_beta'
) and dynamic_stability.cl_p != 0 and dynamic_stability.cl_beta != 0:
theta = conditions.frames.wind.body_rotations[:, 1]
dynamic_stability.cy_beta = aero.cy_beta
dynamic_stability.cl_psi = Supporting_Functions.cy_psi(
aero.lift_coefficient, theta)
dynamic_stability.cL_u = 0
dynamic_stability.cz_u = Supporting_Functions.cz_u(
aero.lift_coefficient, velocity, dynamic_stability.cL_u)
dynamic_stability.cz_alpha_dot = Supporting_Functions.cz_alphadot(
static_stability.cm_alpha,
geometry.wings['horizontal_stabilizer'].ep_alpha)
dynamic_stability.cz_q = Supporting_Functions.cz_q(
static_stability.cm_alpha)
dynamic_stability.cx_u = Supporting_Functions.cx_u(
aero.drag_coefficient)
dynamic_stability.cx_alpha = Supporting_Functions.cx_alpha(
aero.lift_coefficient, conditions.lift_curve_slope)
lateral_directional = Full_Linearized_Equations.lateral_directional(
velocity, static_stability.cn_beta, Sref, density, Span,
configuration.mass_properties.moments_of_inertia.tensor[2]
[2], dynamic_stability.cn_r,
configuration.mass_properties.Moments_Of_Inertia.tensor[0]
[0], dynamic_stability.cl_p,
configuration.mass_properties.moments_of_inertia.tensor[0]
[2], dynamic_stability.cl_r, dynamic_stability.cl_beta,
dynamic_stability.cn_p, dynamic_stability.cy_phi,
dynamic_stability.cy_psi, dynamic_stability.cy_beta,
conditions.weights.total_mass)
longitudinal = Full_Linearized_Equations.longitudinal(
velocity, density, Sref, mac, dynamic_stability.cm_q,
dynamic_stability.cz_alpha, conditions.weights.total_mass,
static_stability.cm_alpha,
configuration.mass_properties.moments_of_inertia.tensor[1]
[1], dynamic_stability.cm_alpha_dot,
dynamic_stability.cz_u, dynamic_stability.cz_alpha_dot,
dynamic_stability.cz_q, -aero.lift_coefficient, theta,
dynamic_stability.cx_u, dynamic_stability.cx_alpha)
stability_model.dutch_roll.natural_frequency = lateral_directional.dutch_natural_frequency
stability_model.dutch_roll.damping_ratio = lateral_directional.dutch_damping_ratio
stability_model.spiral_tau = lateral_directional.spiral_tau
stability_model.roll_tau = lateral_directional.roll_tau
stability_model.short_period.natural_frequency = longitudinal.short_natural_frequency
stability_model.short_period.damping_ratio = longitudinal.short_damping_ratio
stability_model.phugoid.natural_frequency = longitudinal.phugoid_natural_frequency
stability_model.phugoid.damping_ratio = longitudinal.phugoid_damping_ratio
# pack results
results = Data()
results.static = static_stability
results.dynamic = dynamic_stability
return results
def main():
# Taken from Blakelock
#Lateral/Directional Inputs
velocity = 440 * (Units['ft/sec']) # Flight Velocity
Cn_Beta = 0.096 # Yawing moment coefficient due to sideslip
S_gross_w = 2400 * (Units['ft**2']) # Wing reference area
density = 0.002378 * (Units['slugs/ft**3']) # Sea level density
span = 130 * Units.ft # Span of the aircraft
mass = 5900 * Units.slugs # mass of the aircraft
I_x = 1.995 * 10**6 * (Units['slugs*ft**2']) # Moment of Inertia in x-axis
I_z = 4.2 * 10**6 * (Units['slugs*ft**2']) # Moment of Inertia in z-axis
Cn_r = -0.107 # Yawing moment coefficient due to yawing velocity
Cl_p = -0.38 # Rolling moment coefficient due to the rolling velocity
Cy_phi = 0.344 # Side force coefficient due to aircraft roll
Cl_Beta = -0.057 # Rolling moment coefficient due to to sideslip
Cl_r = 0.086 # Rolling moment coefficient due to the yawing velocity (usually evaluated analytically)
J_xz = 0 # Assumed
Cn_p = -0.0228
Cy_psi = 0
Cy_Beta = -0.6
mass = 5900 * Units.slugs # mass of the aircraft
dutch_roll=Approximations.dutch_roll(velocity, Cn_Beta, S_gross_w, density, span, I_z, Cn_r)
roll_tau = Approximations.roll(I_x, S_gross_w, density, velocity, span, Cl_p)
spiral_tau = Approximations.spiral(mass, velocity, density, S_gross_w, Cl_p, Cn_Beta, Cy_phi, Cl_Beta, Cn_r, Cl_r)
lateral_directional = Full_Linearized_Equations.lateral_directional(velocity, Cn_Beta, S_gross_w, density, span, I_z, Cn_r, I_x, Cl_p, J_xz, Cl_r, Cl_Beta, Cn_p, Cy_phi, Cy_psi, Cy_Beta, mass)
# Longitudinal Inputs
mass= 5800 * Units.slugs # mass of the aircraft
velocity = 600 * (Units['ft/sec']) # Flight Velocity
mac = 20.2 * Units.ft # mean aerodynamic chord
Cm_q = -11.4 # Change in pitching moment coefficient due to pitching velocity
CL = 0.74 # Coefficient of Lift
CD = 0.044 # Coefficient of Drag
CL_alpha = 4.42 # Change in aircraft lift due to change in angle of attack
Cz_alpha = -4.46
SM = -0.14 # static margin
Cm_alpha = SM * CL_alpha
Cm_alpha_dot = -3.27
Iy = 2.62 * 10**6 * (Units['slugs*ft**2']) # Moment of Inertia in y-axis
density = 0.000585 * (Units['slugs/ft**3']) # 40,000 ft density
g = 9.8 # gravitational constant
Cz_u = -2*CL # change in Z force with respect to change in forward velocity
Cm_alpha_dot = -3.27
Cz_q = -3.94
Cw = -CL
Theta = 0
Cx_u = -2*CD
Cx_alpha = 0.392
Cz_alpha_dot = -1.13
short_period = Approximations.short_period(velocity, density, S_gross_w, mac, Cm_q, Cz_alpha, mass, Cm_alpha, Iy, Cm_alpha_dot)
phugoid = Approximations.phugoid(g, velocity, CD, CL)
longitudinal = Full_Linearized_Equations.longitudinal(velocity, density, S_gross_w, mac, Cm_q, Cz_alpha, mass, Cm_alpha, Iy, Cm_alpha_dot, Cz_u, Cz_alpha_dot, Cz_q, Cw, Theta, Cx_u, Cx_alpha)
# Expected Values
Blakelock = Data()
Blakelock.longitudinal_short_zeta = 0.352
Blakelock.longitudinal_short_w_n = 1.145
Blakelock.longitudinal_phugoid_zeta = 0.032
Blakelock.longitudinal_phugoid_w_n = 0.073
Blakelock.short_period_short_w_n = 1.15
Blakelock.short_period_short_zeta = 0.35
Blakelock.phugoid_phugoid_w_n = 0.0765
Blakelock.phugoid_phugoid_zeta = 0.042
Blakelock.lateral_directional_dutch_w_n = 1.345
Blakelock.lateral_directional_dutch_zeta = 0.14
Blakelock.lateral_directional_spiral_tau = 1/0.004
Blakelock.lateral_directional_roll_tau = -1/2.09
Blakelock.dutch_roll_dutch_w_n = 1.28
Blakelock.dutch_roll_dutch_zeta = 0.114
Blakelock.spiral_tau = 1./0.0042
Blakelock.roll_tau = -0.493
# Calculating error percentage
error = Data()
error.longitudinal_short_zeta = (Blakelock.longitudinal_short_zeta - longitudinal.short_damping_ratio) / Blakelock.longitudinal_short_zeta
error.longitudinal_short_w_n = (Blakelock.longitudinal_short_w_n - longitudinal.short_natural_frequency) / Blakelock.longitudinal_short_w_n
error.longitudinal_phugoid_zeta = (Blakelock.longitudinal_phugoid_zeta - longitudinal.phugoid_damping_ratio) / Blakelock.longitudinal_phugoid_zeta
error.longitudinal_phugoid_w_n = (Blakelock.longitudinal_phugoid_w_n - longitudinal.phugoid_natural_frequency) / Blakelock.longitudinal_phugoid_w_n
error.short_period_w_n = (Blakelock.short_period_short_w_n - short_period.natural_frequency) / Blakelock.short_period_short_w_n
error.short_period_short_zeta = (Blakelock.short_period_short_zeta - short_period.damping_ratio) / Blakelock.short_period_short_zeta
error.phugoid_phugoid_w_n = (Blakelock.phugoid_phugoid_w_n - phugoid.natural_frequency) / Blakelock.phugoid_phugoid_w_n
error.phugoid_phugoid_zeta = (Blakelock.phugoid_phugoid_zeta - phugoid.damping_ratio) / Blakelock.phugoid_phugoid_zeta
error.lateral_directional_dutch_w_n = (Blakelock.lateral_directional_dutch_w_n - lateral_directional.dutch_natural_frequency) / Blakelock.lateral_directional_dutch_w_n
error.lateral_directional_dutch_zeta = (Blakelock.lateral_directional_dutch_zeta - lateral_directional.dutch_damping_ratio) / Blakelock.lateral_directional_dutch_zeta
error.lateral_directional_spiral_tau = (Blakelock.lateral_directional_spiral_tau - lateral_directional.spiral_tau) / Blakelock.lateral_directional_spiral_tau
error.lateral_directional_roll_tau = (Blakelock.lateral_directional_roll_tau - lateral_directional.roll_tau) / Blakelock.lateral_directional_roll_tau
error.dutch_roll_dutch_w_n = (Blakelock.dutch_roll_dutch_w_n - dutch_roll.natural_frequency) / Blakelock.dutch_roll_dutch_w_n
error.dutch_roll_dutch_zeta = (Blakelock.dutch_roll_dutch_zeta - dutch_roll.damping_ratio) / Blakelock.dutch_roll_dutch_zeta
error.spiral_tau = (Blakelock.spiral_tau - spiral_tau) / Blakelock.spiral_tau
error.roll_tau = (Blakelock.roll_tau - roll_tau) / Blakelock.roll_tau
print error
for k,v in error.items():
assert(np.abs(v)<0.08)
return
def __call__(self,conditions):
""" process vehicle to setup geometry, condititon and configuration
Inputs:
conditions - DataDict() of aerodynamic conditions
results - DataDict() of
Outputs:
Assumptions:
"""
# unpack
configuration = self.configuration
geometry = self.geometry
q = conditions.freestream.dynamic_pressure
Sref = geometry.reference_area
mach = conditions.freestream.mach_number
velocity = conditions.freestream.velocity
density = conditions.freestream.density
Span = geometry.Wings['Main Wing'].span
mac = geometry.Wings['Main Wing'].chord_mac
aero = conditions.aerodynamics
# Calculate CL_alpha
if not conditions.has_key('lift_curve_slope'):
conditions.lift_curve_slope = (datcom(geometry.Wings['Main Wing'],mach))
# Calculate change in downwash with respect to change in angle of attack
for surf in geometry.Wings:
e = surf.e
sref = surf.sref
span = (surf.ar * sref ) ** 0.5
surf.CL_alpha = datcom(surf,mach)
surf.ep_alpha = Supporting_Functions.ep_alpha(surf.CL_alpha, sref, span, e)
# Static Stability Methods
aero.cm_alpha = taw_cmalpha(geometry,mach,conditions,configuration)
aero.cn_beta = taw_cnbeta(geometry,conditions,configuration)
if np.count_nonzero(configuration.mass_props.I_cg) > 0:
# Dynamic Stability Approximation Methods
if not aero.has_key('cn_r'):
cDw = aero.drag_breakdown.parasite['Main Wing'].parasite_drag_coefficient # Might not be the correct value
l_v = geometry.Wings['Vertical Stabilizer'].origin[0] + geometry.Wings['Vertical Stabilizer'].aero_center[0] - geometry.Wings['Main Wing'].origin[0] - geometry.Wings['Main Wing'].aero_center[0]
aero.cn_r = Supporting_Functions.cn_r(cDw, geometry.Wings['Vertical Stabilizer'].sref, Sref, l_v, span, geometry.Wings['Vertical Stabilizer'].eta, geometry.Wings['Vertical Stabilizer'].CL_alpha)
if not aero.has_key('cl_p'):
aero.cl_p = 0 # Need to see if there is a low fidelity way to calculate cl_p
if not aero.has_key('cl_beta'):
aero.cl_beta = 0 # Need to see if there is a low fidelity way to calculate cl_beta
l_t = geometry.Wings['Horizontal Stabilizer'].origin[0] + geometry.Wings['Horizontal Stabilizer'].aero_center[0] - geometry.Wings['Main Wing'].origin[0] - geometry.Wings['Main Wing'].aero_center[0] #Need to check this is the length of the horizontal tail moment arm
if not aero.has_key('cm_q'):
aero.cm_q = Supporting_Functions.cm_q(conditions.lift_curve_slope, l_t,mac) # Need to check Cm_i versus Cm_alpha
if not aero.has_key('cm_alpha_dot'):
aero.cm_alpha_dot = Supporting_Functions.cm_alphadot(aero.cm_alpha, geometry.Wings['Horizontal Stabilizer'].ep_alpha, l_t, mac) # Need to check Cm_i versus Cm_alpha
if not aero.has_key('cz_alpha'):
aero.cz_alpha = Supporting_Functions.cz_alpha(aero.drag_coefficient,conditions.lift_curve_slope)
conditions.dutch_roll = Approximations.dutch_roll(velocity, aero.cn_beta, Sref, density, Span, configuration.mass_props.I_cg[2][2], aero.cn_r)
if aero.cl_p != 0:
roll_tau = Approximations.roll(configuration.mass_props.I_cg[2][2], Sref, density, velocity, Span, aero.cl_p)
if aero.cl_beta != 0:
aero.cy_phi = Supporting_Functions.cy_phi(aero.lift_coefficient)
aero.cl_r = Supporting_Functions.cl_r( aero.lift_coefficient) # Will need to be changed
spiral_tau = Approximations.spiral(conditions.weights.total_mass, velocity, density, Sref, aero.cl_p, aero.cn_beta, aero.cy_phi, aero.cl_beta, aero.cn_r, aero.cl_r)
conditions.short_period = Approximations.short_period(velocity, density, Sref, mac, aero.cm_q, aero.cz_alpha, conditions.weights.total_mass, aero.cm_alpha, configuration.mass_props.I_cg[1][1], aero.cm_alpha_dot)
conditions.phugoid = Approximations.phugoid(conditions.freestream.gravity, conditions.freestream.velocity, aero.drag_coefficient, aero.lift_coefficient)
# Dynamic Stability Full Linearized Methods
if aero.has_key('cy_beta') and aero.cl_p != 0 and aero.cl_beta != 0:
if not aero.has_key('cy_psi'):
theta = conditions.frames.wind.body_rotations[:,1]
aero.cl_psi = Supporting_Functions.cy_psi(aero.lift_coefficient, theta)
if not aero.has_key('cz_u'):
if not aero.has_key('cL_u'):
aero.cL_u = 0
aero.cz_u = Supporting_Functions.cz_u(aero.lift_coefficient,velocity,aero.cL_u)
if not aero.has_key('cz_alpha_dot'):
aero.cz_alpha_dot = Supporting_Functions.cz_alphadot(aero.cm_alpha, geometry.Wings['Horizontal Stabilizer'].ep_alpha)
if not aero.has_key('cz_q'):
aero.cz_q = Supporting_Functions.cz_q(aero.cm_alpha)
if not aero.has_key('cx_u'):
aero.cx_u = Supporting_Functions.cx_u(aero.drag_coefficient)
if not aero.has_key('cx_alpha'):
aero.cx_alpha = Supporting_Functions.cx_alpha(aero.lift_coefficient, conditions.lift_curve_slope)
lateral_directional = Full_Linearized_Equations.lateral_directional(velocity, aero.cn_beta , Sref, density, Span, configuration.mass_props.I_cg[2][2], aero.cn_r, configuration.mass_props.I_cg[0][0], aero.cl_p, configuration.mass_props.I_cg[0][2], aero.cl_r, aero.cl_beta, aero.cn_p, aero.cy_phi, aero.cy_psi, aero.cy_beta, conditions.weights.total_mass)
longitudinal = Full_Linearized_Equations.longitudinal(velocity, density, Sref, mac, aero.cm_q, aero.cz_alpha, conditions.weights.total_mass, aero.cm_alpha, configuration.mass_props.I_cg[1][1], aero.cm_alpha_dot, aero.cz_u, aero.cz_alpha_dot, aero.cz_q, -aero.lift_coefficient, theta, aero.cx_u, aero.cx_alpha)
return
def __call__(self, conditions):
""" Process vehicle to setup geometry, condititon and configuration
Assumptions:
None
Source:
N/A
Inputs:
conditions - DataDict() of aerodynamic conditions
results - DataDict() of moment coeffients and stability and body axis derivatives
Outputs:
None
Properties Used:
self.geometry
"""
# unpack
configuration = self.configuration
geometry = self.geometry
q = conditions.freestream.dynamic_pressure
Sref = geometry.reference_area
mach = conditions.freestream.mach_number
velocity = conditions.freestream.velocity
density = conditions.freestream.density
Span = geometry.wings['main_wing'].spans.projected
mac = geometry.wings['main_wing'].chords.mean_aerodynamic
aero = conditions.aerodynamics
# set up data structures
stability = Data()
stability.static = Data()
stability.dynamic = Data()
# Calculate CL_alpha
conditions.lift_curve_slope = datcom(geometry.wings['main_wing'], mach)
# Calculate change in downwash with respect to change in angle of attack
for surf in geometry.wings:
sref = surf.areas.reference
span = (surf.aspect_ratio * sref)**0.5
surf.CL_alpha = datcom(surf, mach)
surf.ep_alpha = Supporting_Functions.ep_alpha(
surf.CL_alpha, sref, span)
# Static Stability Methods
stability.static.Cm_alpha, stability.static.Cm0, stability.static.CM = taw_cmalpha(
geometry, mach, conditions, configuration)
if 'vertical_stabilizer' in geometry.wings:
stability.static.Cn_beta = taw_cnbeta(geometry, conditions,
configuration)
else:
stability.static.Cn_beta = np.zeros_like(mach)
# calculate the static margin
stability.static.static_margin = -stability.static.Cm_alpha / conditions.lift_curve_slope
# Dynamic Stability
if np.count_nonzero(
configuration.mass_properties.moments_of_inertia.tensor) > 0:
# Dynamic Stability Approximation Methods - valid for non-zero I tensor
# Derivative of yawing moment with respect to the rate of yaw
cDw = aero.drag_breakdown.parasite[
'main_wing'].parasite_drag_coefficient # Might not be the correct value
l_v = geometry.wings['vertical_stabilizer'].origin[
0] + geometry.wings['vertical_stabilizer'].aerodynamic_center[
0] - geometry.wings['main_wing'].origin[
0] - geometry.wings['main_wing'].aerodynamic_center[0]
stability.static.Cn_r = Supporting_Functions.cn_r(
cDw, geometry.wings['vertical_stabilizer'].areas.reference,
Sref, l_v, span,
geometry.wings['vertical_stabilizer'].dynamic_pressure_ratio,
geometry.wings['vertical_stabilizer'].CL_alpha)
# Derivative of rolling moment with respect to roll rate
stability.static.Cl_p = Supporting_Functions.cl_p(
conditions.lift_curve_slope, geometry)
# Derivative of roll rate with respect to sideslip (dihedral effect)
if 'dihedral' in geometry.wings['main_wing']:
stability.static.Cl_beta = Supporting_Functions.cl_beta(
geometry, stability.static.Cl_p)
else:
stability.static.Cl_beta = np.zeros(1)
stability.static.Cy_beta = 0
# Derivative of pitching moment with respect to pitch rate
l_t = geometry.wings['horizontal_stabilizer'].origin[
0] + geometry.wings['horizontal_stabilizer'].aerodynamic_center[
0] - geometry.wings['main_wing'].origin[
0] - geometry.wings['main_wing'].aerodynamic_center[
0] #Need to check this is the length of the horizontal tail moment arm
stability.static.Cm_q = Supporting_Functions.cm_q(
conditions.lift_curve_slope, l_t,
mac) # Need to check Cm_i versus Cm_alpha
# Derivative of pitching rate with respect to d(alpha)/d(t)
stability.static.Cm_alpha_dot = Supporting_Functions.cm_alphadot(
stability.static.Cm_alpha,
geometry.wings['horizontal_stabilizer'].ep_alpha, l_t,
mac) # Need to check Cm_i versus Cm_alpha
# Derivative of Z-axis force with respect to angle of attack
stability.static.Cz_alpha = Supporting_Functions.cz_alpha(
aero.drag_coefficient, conditions.lift_curve_slope)
dutch_roll = Approximations.dutch_roll(
velocity, stability.static.Cn_beta, Sref, density, Span,
configuration.mass_properties.moments_of_inertia.tensor[2][2],
stability.static.Cn_r)
stability.dynamic.dutchRollFreqHz = dutch_roll.natural_frequency
stability.dynamic.dutchRollDamping = dutch_roll.damping_ratio
if stability.static.Cl_p.all() != 0:
stability.dynamic.rollSubsistenceTimeConstant = Approximations.roll(
configuration.mass_properties.moments_of_inertia.tensor[2]
[2], Sref, density, velocity, Span, stability.static.Cl_p)
stability.static.Cy_phi = Supporting_Functions.cy_phi(
aero.lift_coefficient)
stability.static.Cl_r = Supporting_Functions.cl_r(
aero.lift_coefficient) # Will need to be changed
stability.dynamic.spiralSubsistenceTimeConstant = Approximations.spiral(conditions.weights.total_mass, velocity, density, Sref, stability.static.Cl_p, stability.static.Cn_beta, stability.static.Cy_phi,\
stability.static.Cl_beta, stability.static.Cn_r, stability.static.Cl_r)
short_period_res = Approximations.short_period(velocity, density, Sref, mac, stability.static.Cm_q, stability.static.Cz_alpha, conditions.weights.total_mass, stability.static.Cm_alpha,\
configuration.mass_properties.moments_of_inertia.tensor[1][1], stability.static.Cm_alpha_dot)
stability.dynamic.shortPeriodFreqHz = short_period_res.natural_frequency
stability.dynamic.shortPeriodDamp = short_period_res.damping_ratio
phugoid_res = Approximations.phugoid(
conditions.freestream.gravity, conditions.freestream.velocity,
aero.drag_coefficient, aero.lift_coefficient)
stability.dynamic.phugoidFreqHz = phugoid_res.natural_frequency
stability.dynamic.phugoidDamp = phugoid_res.damping_ratio
# Dynamic Stability Full Linearized Methods
if stability.static.Cy_beta != 0 and stability.static.Cl_p.all(
) != 0 and stability.static.Cl_beta.all() != 0:
theta = conditions.frames.wind.body_rotations[:, 1]
stability.static.Cy_psi = Supporting_Functions.cy_psi(
aero.lift_coefficient, theta)
stability.static.CL_u = 0
stability.static.Cz_u = Supporting_Functions.cz_u(
aero.lift_coefficient, velocity, stability.static.cL_u)
stability.static.Cz_alpha_dot = Supporting_Functions.cz_alphadot(
stability.static.Cm_alpha,
geometry.wings['horizontal_stabilizer'].ep_alpha)
stability.static.Cz_q = Supporting_Functions.cz_q(
stability.static.Cm_alpha)
stability.static.Cx_u = Supporting_Functions.cx_u(
aero.drag_coefficient)
stability.static.Cx_alpha = Supporting_Functions.cx_alpha(
aero.lift_coefficient, conditions.lift_curve_slope)
lateral_directional = Full_Linearized_Equations.lateral_directional(velocity, stability.static.cn_beta , Sref, density, Span, configuration.mass_properties.moments_of_inertia.tensor[2][2], stability.static.Cn_r,\
configuration.mass_properties.moments_of_inertia.tensor[0][0], stability.static.Cl_p, configuration.mass_properties.moments_of_inertia.tensor[0][2], stability.static.Cl_r, stability.static.Cl_beta,\
stability.static.Cn_p, stability.static.Cy_phi, stability.static.Cy_psi, stability.static.Cy_beta, conditions.weights.total_mass)
longitudinal = Full_Linearized_Equations.longitudinal(velocity, density, Sref, mac, stability.static.Cm_q, stability.static.Cz_alpha, conditions.weights.total_mass, stability.static.Cm_alpha, \
configuration.mass_properties.moments_of_inertia.tensor[1][1], stability.static.Cm_alpha_dot, stability.static.Cz_u, stability.static.Cz_alpha_dot, stability.static.Cz_q, -aero.lift_coefficient,\
theta, stability.static.Cx_u, stability.static.Cx_alpha)
stability.dynamic.dutchRollFreqHz = lateral_directional.dutch_natural_frequency
stability.dynamic.dutchRollDamping = lateral_directional.dutch_damping_ratio
stability.dynamic.spiralSubsistenceTimeConstant = lateral_directional.spiral_tau
stability.dynamic.rollSubsistenceTimeConstant = lateral_directional.roll_tau
stability.dynamic.shortPeriodFreqHz = longitudinal.short_natural_frequency
stability.dynamic.shortPeriodDamp = longitudinal.short_damping_ratio
stability.dynamic.phugoidFreqHz = longitudinal.phugoid_natural_frequency
stability.dynamic.phugoidDamp = longitudinal.phugoid_damping_ratio
# pack results
results = Data()
results = stability
return results
def __call__(self,conditions):
""" process vehicle to setup geometry, condititon and configuration
Inputs:
conditions - DataDict() of aerodynamic conditions
results - DataDict() of
Outputs:
Assumptions:
"""
# unpack
configuration = self.configuration
geometry = self.geometry
stability_model = self.stability_model
q = conditions.freestream.dynamic_pressure
Sref = geometry.reference_area
mach = conditions.freestream.mach_number
velocity = conditions.freestream.velocity
density = conditions.freestream.density
Span = geometry.wings['main_wing'].spans.projected
mac = geometry.wings['main_wing'].chords.mean_aerodynamic
aero = conditions.aerodynamics
# set up data structures
static_stability = Data()
dynamic_stability = Data()
# Calculate CL_alpha
if not conditions.has_key('lift_curve_slope'):
conditions.lift_curve_slope = datcom(geometry.wings['main_wing'],mach)
# Calculate change in downwash with respect to change in angle of attack
for surf in geometry.wings:
sref = surf.areas.reference
span = (surf.aspect_ratio * sref ) ** 0.5
surf.CL_alpha = datcom(surf,mach)
surf.ep_alpha = Supporting_Functions.ep_alpha(surf.CL_alpha, sref, span)
# Static Stability Methods
static_stability.cm_alpha = taw_cmalpha(geometry,mach,conditions,configuration)
static_stability.cn_beta = taw_cnbeta(geometry,conditions,configuration)
# Dynamic Stability
if np.count_nonzero(configuration.mass_properties.moments_of_inertia.tensor) > 0:
# Dynamic Stability Approximation Methods - valid for non-zero I tensor
# Derivative of yawing moment with respect to the rate of yaw
cDw = aero.drag_breakdown.parasite['main_wing'].parasite_drag_coefficient # Might not be the correct value
l_v = geometry.wings['vertical_stabilizer'].origin[0] + geometry.wings['vertical_stabilizer'].aerodynamic_center[0] - geometry.wings['main_wing'].origin[0] - geometry.wings['main_wing'].aerodynamic_center[0]
dynamic_stability.cn_r = Supporting_Functions.cn_r(cDw, geometry.wings['vertical_stabilizer'].areas.reference, Sref, l_v, span, geometry.wings['vertical_stabilizer'].dynamic_pressure_ratio, geometry.wings['vertical_stabilizer'].CL_alpha)
# Derivative of rolling moment with respect to roll rate
dynamic_stability.cl_p = 0 # Need to see if there is a low fidelity way to calculate cl_p
# Derivative of roll rate with respect to sideslip (dihedral effect)
dynamic_stability.cl_beta = 0 # Need to see if there is a low fidelity way to calculate cl_beta
# Derivative of pitching moment with respect to pitch rate
l_t = geometry.wings['horizontal_stabilizer'].origin[0] + geometry.wings['horizontal_stabilizer'].aerodynamic_center[0] - geometry.wings['main_wing'].origin[0] - geometry.wings['main_wing'].aerodynamic_center[0] #Need to check this is the length of the horizontal tail moment arm
dynamic_stability.cm_q = Supporting_Functions.cm_q(conditions.lift_curve_slope, l_t,mac) # Need to check Cm_i versus Cm_alpha
# Derivative of pitching rate with respect to d(alpha)/d(t)
dynamic_stability.cm_alpha_dot = Supporting_Functions.cm_alphadot(static_stability.cm_alpha, geometry.wings['horizontal_stabilizer'].ep_alpha, l_t, mac) # Need to check Cm_i versus Cm_alpha
# Derivative of Z-axis force with respect to angle of attack
dynamic_stability.cz_alpha = Supporting_Functions.cz_alpha(aero.drag_coefficient,conditions.lift_curve_slope)
stability_model.dutch_roll = Approximations.dutch_roll(velocity, static_stability.cn_beta, Sref, density, Span, configuration.mass_properties.moments_of_inertia.tensor[2][2], dynamic_stability.cn_r)
if dynamic_stability.cl_p != 0:
stability_model.roll_tau = Approximations.roll(configuration.mass_properties.momen[2][2], Sref, density, velocity, Span, dynamic_stability.cl_p)
dynamic_stability.cy_phi = Supporting_Functions.cy_phi(aero.lift_coefficient)
dynamic_stability.cl_r = Supporting_Functions.cl_r( aero.lift_coefficient) # Will need to be changed
stability_model.spiral_tau = Approximations.spiral(conditions.weights.total_mass, velocity, density, Sref, dynamic_stability.cl_p, static_stability.cn_beta, dynamic_stability.cy_phi, dynamic_stability.cl_beta, dynamic_stability.cn_r, dynamic_stability.cl_r)
stability_model.short_period = Approximations.short_period(velocity, density, Sref, mac, dynamic_stability.cm_q, dynamic_stability.cz_alpha, conditions.weights.total_mass, static_stability.cm_alpha, configuration.mass_properties.moments_of_inertia.tensor[1][1], dynamic_stability.cm_alpha_dot)
stability_model.phugoid = Approximations.phugoid(conditions.freestream.gravity, conditions.freestream.velocity, aero.drag_coefficient, aero.lift_coefficient)
# Dynamic Stability Full Linearized Methods
if aero.has_key('cy_beta') and dynamic_stability.cl_p != 0 and dynamic_stability.cl_beta != 0:
theta = conditions.frames.wind.body_rotations[:,1]
dynamic_stability.cy_beta = aero.cy_beta
dynamic_stability.cl_psi = Supporting_Functions.cy_psi(aero.lift_coefficient, theta)
dynamic_stability.cL_u = 0
dynamic_stability.cz_u = Supporting_Functions.cz_u(aero.lift_coefficient,velocity,dynamic_stability.cL_u)
dynamic_stability.cz_alpha_dot = Supporting_Functions.cz_alphadot(static_stability.cm_alpha, geometry.wings['horizontal_stabilizer'].ep_alpha)
dynamic_stability.cz_q = Supporting_Functions.cz_q(static_stability.cm_alpha)
dynamic_stability.cx_u = Supporting_Functions.cx_u(aero.drag_coefficient)
dynamic_stability.cx_alpha = Supporting_Functions.cx_alpha(aero.lift_coefficient, conditions.lift_curve_slope)
lateral_directional = Full_Linearized_Equations.lateral_directional(velocity, static_stability.cn_beta , Sref, density, Span, configuration.mass_properties.moments_of_inertia.tensor[2][2], dynamic_stability.cn_r, configuration.mass_properties.Moments_Of_Inertia.tensor[0][0], dynamic_stability.cl_p, configuration.mass_properties.moments_of_inertia.tensor[0][2], dynamic_stability.cl_r, dynamic_stability.cl_beta, dynamic_stability.cn_p, dynamic_stability.cy_phi, dynamic_stability.cy_psi, dynamic_stability.cy_beta, conditions.weights.total_mass)
longitudinal = Full_Linearized_Equations.longitudinal(velocity, density, Sref, mac, dynamic_stability.cm_q, dynamic_stability.cz_alpha, conditions.weights.total_mass, static_stability.cm_alpha, configuration.mass_properties.moments_of_inertia.tensor[1][1], dynamic_stability.cm_alpha_dot, dynamic_stability.cz_u, dynamic_stability.cz_alpha_dot, dynamic_stability.cz_q, -aero.lift_coefficient, theta, dynamic_stability.cx_u, dynamic_stability.cx_alpha)
stability_model.dutch_roll.natural_frequency = lateral_directional.dutch_natural_frequency
stability_model.dutch_roll.damping_ratio = lateral_directional.dutch_damping_ratio
stability_model.spiral_tau = lateral_directional.spiral_tau
stability_model.roll_tau = lateral_directional.roll_tau
stability_model.short_period.natural_frequency = longitudinal.short_natural_frequency
stability_model.short_period.damping_ratio = longitudinal.short_damping_ratio
stability_model.phugoid.natural_frequency = longitudinal.phugoid_natural_frequency
stability_model.phugoid.damping_ratio = longitudinal.phugoid_damping_ratio
# pack results
results = Data()
results.static = static_stability
results.dynamic = dynamic_stability
return results
def __call__(self, conditions):
""" process vehicle to setup geometry, condititon and configuration
Inputs:
conditions - DataDict() of aerodynamic conditions
results - DataDict() of
Outputs:
Assumptions:
"""
# unpack
configuration = self.configuration
geometry = self.geometry
stability_model = self.stability_model
q = conditions.freestream.dynamic_pressure
Sref = geometry.reference_area
mach = conditions.freestream.mach_number
velocity = conditions.freestream.velocity
density = conditions.freestream.density
Span = geometry.wings['Main Wing'].spans.projected
mac = geometry.wings['Main Wing'].chords.mean_aerodynamic
aero = conditions.aerodynamics
# Calculate CL_alpha
if not conditions.has_key('lift_curve_slope'):
conditions.lift_curve_slope = datcom(geometry.wings['Main Wing'],
mach)
# Calculate change in downwash with respect to change in angle of attack
for surf in geometry.wings:
e = surf.span_efficiency
sref = surf.areas.reference
span = (surf.aspect_ratio * sref)**0.5
surf.CL_alpha = datcom(surf, mach)
surf.ep_alpha = Supporting_Functions.ep_alpha(
surf.CL_alpha, sref, span, e)
# Static Stability Methods
aero.cm_alpha = taw_cmalpha(geometry, mach, conditions, configuration)
aero.cn_beta = taw_cnbeta(geometry, conditions, configuration)
if np.count_nonzero(
configuration.mass_properties.moments_of_inertia.tensor) > 0:
# Dynamic Stability Approximation Methods
if not aero.has_key('cn_r'):
cDw = aero.drag_breakdown.parasite[
'Main Wing'].parasite_drag_coefficient # Might not be the correct value
l_v = geometry.wings['Vertical Stabilizer'].origin[
0] + geometry.wings[
'Vertical Stabilizer'].aerodynamic_center[
0] - geometry.wings['Main Wing'].origin[
0] - geometry.wings[
'Main Wing'].aerodynamic_center[0]
aero.cn_r = Supporting_Functions.cn_r(
cDw, geometry.wings['Vertical Stabilizer'].areas.reference,
Sref, l_v, span, geometry.wings['Vertical Stabilizer'].eta,
geometry.wings['Vertical Stabilizer'].CL_alpha)
if not aero.has_key('cl_p'):
aero.cl_p = 0 # Need to see if there is a low fidelity way to calculate cl_p
if not aero.has_key('cl_beta'):
aero.cl_beta = 0 # Need to see if there is a low fidelity way to calculate cl_beta
l_t = geometry.wings['Horizontal Stabilizer'].origin[
0] + geometry.wings['Horizontal Stabilizer'].aerodynamic_center[
0] - geometry.wings['Main Wing'].origin[
0] - geometry.wings['Main Wing'].aerodynamic_center[
0] #Need to check this is the length of the horizontal tail moment arm
if not aero.has_key('cm_q'):
aero.cm_q = Supporting_Functions.cm_q(
conditions.lift_curve_slope, l_t,
mac) # Need to check Cm_i versus Cm_alpha
if not aero.has_key('cm_alpha_dot'):
aero.cm_alpha_dot = Supporting_Functions.cm_alphadot(
aero.cm_alpha,
geometry.wings['Horizontal Stabilizer'].ep_alpha, l_t,
mac) # Need to check Cm_i versus Cm_alpha
if not aero.has_key('cz_alpha'):
aero.cz_alpha = Supporting_Functions.cz_alpha(
aero.drag_coefficient, conditions.lift_curve_slope)
stability_model.dutch_roll = Approximations.dutch_roll(
velocity, aero.cn_beta, Sref, density, Span,
configuration.mass_properties.moments_of_inertia.tensor[2][2],
aero.cn_r)
if aero.cl_p != 0:
stability_model.roll_tau = Approximations.roll(
configuration.mass_properties.momen[2][2], Sref, density,
velocity, Span, aero.cl_p)
if aero.cl_beta != 0:
aero.cy_phi = Supporting_Functions.cy_phi(
aero.lift_coefficient)
aero.cl_r = Supporting_Functions.cl_r(
aero.lift_coefficient) # Will need to be changed
stability_model.spiral_tau = Approximations.spiral(
conditions.weights.total_mass, velocity, density, Sref,
aero.cl_p, aero.cn_beta, aero.cy_phi, aero.cl_beta,
aero.cn_r, aero.cl_r)
stability_model.short_period = Approximations.short_period(
velocity, density, Sref, mac, aero.cm_q, aero.cz_alpha,
conditions.weights.total_mass, aero.cm_alpha,
configuration.mass_properties.moments_of_inertia.tensor[1][1],
aero.cm_alpha_dot)
stability_model.phugoid = Approximations.phugoid(
conditions.freestream.gravity, conditions.freestream.velocity,
aero.drag_coefficient, aero.lift_coefficient)
# Dynamic Stability Full Linearized Methods
if aero.has_key(
'cy_beta') and aero.cl_p != 0 and aero.cl_beta != 0:
if not aero.has_key('cy_psi'):
theta = conditions.frames.wind.body_rotations[:, 1]
aero.cl_psi = Supporting_Functions.cy_psi(
aero.lift_coefficient, theta)
if not aero.has_key('cz_u'):
if not aero.has_key('cL_u'):
aero.cL_u = 0
aero.cz_u = Supporting_Functions.cz_u(
aero.lift_coefficient, velocity, aero.cL_u)
if not aero.has_key('cz_alpha_dot'):
aero.cz_alpha_dot = Supporting_Functions.cz_alphadot(
aero.cm_alpha,
geometry.wings['Horizontal Stabilizer'].ep_alpha)
if not aero.has_key('cz_q'):
aero.cz_q = Supporting_Functions.cz_q(aero.cm_alpha)
if not aero.has_key('cx_u'):
aero.cx_u = Supporting_Functions.cx_u(
aero.drag_coefficient)
if not aero.has_key('cx_alpha'):
aero.cx_alpha = Supporting_Functions.cx_alpha(
aero.lift_coefficient, conditions.lift_curve_slope)
lateral_directional = Full_Linearized_Equations.lateral_directional(
velocity, aero.cn_beta, Sref, density, Span,
configuration.mass_properties.moments_of_inertia.tensor[2]
[2], aero.cn_r,
configuration.mass_properties.Moments_Of_Inertia.tensor[0]
[0], aero.cl_p,
configuration.mass_properties.moments_of_inertia.tensor[0]
[2], aero.cl_r, aero.cl_beta, aero.cn_p, aero.cy_phi,
aero.cy_psi, aero.cy_beta, conditions.weights.total_mass)
longitudinal = Full_Linearized_Equations.longitudinal(
velocity, density, Sref, mac, aero.cm_q, aero.cz_alpha,
conditions.weights.total_mass, aero.cm_alpha,
configuration.mass_properties.moments_of_inertia.tensor[1]
[1], aero.cm_alpha_dot, aero.cz_u, aero.cz_alpha_dot,
aero.cz_q, -aero.lift_coefficient, theta, aero.cx_u,
aero.cx_alpha)
stability_model.dutch_roll.natural_frequency = lateral_directional.dutch_natural_frequency
stability_model.dutch_roll.damping_ratio = lateral_directional.dutch_damping_ratio
stability_model.spiral_tau = lateral_directional.spiral_tau
stability_model.roll_tau = lateral_directional.roll_tau
stability_model.short_period.natural_frequency = longitudinal.short_natural_frequency
stability_model.short_period.damping_ratio = longitudinal.short_damping_ratio
stability_model.phugoid.natural_frequency = longitudinal.phugoid_natural_frequency
stability_model.phugoid.damping_ratio = longitudinal.phugoid_damping_ratio
return
