Source code for RCAIDE.Library.Methods.Stability.Vortex_Lattice_Method.compute_neutral_point
# RCAIDE/Library/Methods/Stability/Vortex_Lattice_Method/compute_neutral_point.py
#
# ----------------------------------------------------------------------------------------------------------------------
# IMPORT
# ----------------------------------------------------------------------------------------------------------------------
# RCAIDE imports
import RCAIDE
from RCAIDE.Library.Methods.Aerodynamics.Vortex_Lattice_Method.VLM import VLM
from copy import deepcopy
# package imports
import numpy as np
from scipy.optimize import minimize
# ----------------------------------------------------------------------------------------------------------------------
# compute_neutral_point
# ----------------------------------------------------------------------------------------------------------------------
[docs]
def compute_neutral_point(stability, vehicle):
"""
Computes the neutral point of an aircraft using Vortex Lattice Method optimization.
Parameters
----------
stability : RCAIDE.Framework.Analyses.Stability
Stability analysis object containing:
- vehicle : RCAIDE.Library.Components.Vehicle
Vehicle object with geometry and mass properties
- settings : RCAIDE.Framework.Analyses.Stability.Settings
Stability analysis settings
- training : Data
Training data for analysis
- angle_of_attack : numpy.ndarray
Array of angle of attack values [radians]
- Mach : numpy.ndarray
Array of Mach numbers [unitless]
Returns
-------
None
The neutral point is stored in vehicle.neutral_point
Notes
-----
This function computes the neutral point of an aircraft by finding the center
of gravity location where the pitching moment coefficient derivative with respect
to angle of attack is zero. It uses an optimization approach with the Vortex
Lattice Method to evaluate aerodynamic characteristics. It specifically uses the
Scipy SLSQP solver.
**Major Assumptions**
* Linear aerodynamics within the analysis range
* Control surfaces are removed for clean configuration analysis
* Vortex Lattice Method accurately represents the aerodynamics
* Small angle approximations apply
**Theory**
The neutral point is defined as the center of gravity location where:
:math:`\\frac{\\partial C_M}{\\partial \\alpha} = 0`
**Definitions**
'Neutral Point'
Center of gravity location where the aircraft has neutral static stability (i.e. Cm_alpha = 0).
"""
settings = stability.settings
AoA = np.array([stability.training.angle_of_attack[2],stability.training.angle_of_attack[3]])
Mach = np.array([stability.training.Mach[0]])
len_Mach = len(Mach)
len_AoA = len(AoA)
AoAs = np.atleast_2d(np.tile(AoA,len_Mach).T.flatten()).T
Machs = np.atleast_2d(np.repeat(Mach,len_AoA)).T
conditions = RCAIDE.Framework.Mission.Common.Results()
conditions.freestream.mach_number = Machs
conditions.freestream.velocity = np.ones_like(Machs) * 1e-6
conditions.aerodynamics.angles.alpha = np.ones_like(Machs)*AoAs
# --------------------------------------------------------------------------------------------------------------
# Neutral Point
# --------------------------------------------------------------------------------------------------------------
clean_wing_vehicle_np = deepcopy(vehicle) # Double check this is correct
for wing in clean_wing_vehicle_np.wings:
wing.control_surfaces = []
# use center of gravity as inital guess
cg = vehicle.mass_properties.center_of_gravity[0][0]
bnds = [[0, 100]]
sol = minimize(neutral_point_objective, [cg], args=(conditions,settings,clean_wing_vehicle_np,Mach,AoA) , method='SLSQP', bounds=bnds, tol=1e-4)
vehicle.neutral_point = sol.x[0]
return
[docs]
def neutral_point_objective(cg_location,conditions,settings,clean_wing_vehicle_np,Mach,AoA):
"""
Objective function for neutral point optimization.
Parameters
----------
cg_location : list
Center of gravity location [m]
conditions : RCAIDE.Framework.Mission.Common.Results
Flight conditions for VLM analysis
settings : RCAIDE.Framework.Analyses.Stability.Settings
Stability analysis settings
clean_wing_vehicle_np : RCAIDE.Library.Components.Vehicle
Clean wing vehicle configuration (no control surfaces)
Mach : numpy.ndarray
Array of Mach numbers [unitless]
AoA : numpy.ndarray
Array of angle of attack values [radians]
Returns
-------
float
Absolute value of pitching moment coefficient derivative with respect to angle of attack
Notes
-----
This function serves as the objective function for the neutral point optimization.
It updates the vehicle center of gravity, runs VLM analysis, and computes the
pitching moment coefficient derivative to minimize.
**Major Assumptions**
* VLM analysis is valid for the given conditions
* Pitching moment coefficient varies linearly with angle of attack
* Clean wing configuration represents the neutral point condition
"""
len_Mach = len(Mach)
len_AoA = len(AoA)
# update neutral point
clean_wing_vehicle_np.mass_properties.center_of_gravity[0][0] = cg_location[0]
# run VLM
VLM_results = VLM(conditions,settings,clean_wing_vehicle_np)
AoA = conditions.aerodynamics.angles.alpha
CM_res = VLM_results.CM
CM = np.reshape(CM_res,(len_Mach,len_AoA)).T
# compute dCM_dalpha
dCM_dalpha = ( CM[1, 0] - CM[0, 0]) /( AoA[1] - AoA[0])
# find abs
return abs(dCM_dalpha)
