Source code for RCAIDE.Library.Mission.Segments.Descent.Constant_CAS_Constant_Rate

# RCAIDE/Library/Missions/Segments/Descent/Constant_CAS_Constant_Rate.py
# 
# 
# Created:  Jul 2023, M. Clarke 

# ----------------------------------------------------------------------------------------------------------------------  
#  IMPORT 
# ---------------------------------------------------------------------------------------------------------------------- 
# RCAIDE imports 
import RCAIDE
from RCAIDE.Framework.Core import Units

# package imports 
import numpy as np

# ----------------------------------------------------------------------------------------------------------------------  
#  Initialize Conditions
# ----------------------------------------------------------------------------------------------------------------------  


def initialize_conditions(segment):
    """
    Initializes conditions for constant calibrated airspeed descent at fixed rate

    Parameters
    ----------
    segment : Segment
        The mission segment being analyzed
            - descent_rate : float
                Rate of descent [m/s]
            - calibrated_air_speed : float
                Calibrated airspeed to maintain [m/s]
            - altitude_start : float
                Initial altitude [m]
            - altitude_end : float
                Final altitude [m]
            - sideslip_angle : float
                Aircraft sideslip angle [rad]
            - temperature_deviation : float
                Temperature offset from standard day [K]
            - state:
                numerics.dimensionless.control_points : array
                    Discretization points [-]
                conditions : Data
                    State conditions container
            - analyses:
                atmosphere : Model
                    Atmospheric model for property calculations
    
    Returns
    -------
    None

    Notes
    -----
    This function sets up the initial conditions for a descent segment with constant
    calibrated airspeed (CAS) and constant descent rate. It handles the conversion
    between CAS and true airspeed accounting for pressure and density variations
    with altitude. Updates segment conditions directly with velocity_vector [m/s], altitude [m],
    and position_vector [m].

    **Calculation Process**
        1. Discretize altitude profile
        2. Get atmospheric properties at each altitude
        3. Convert CAS to true airspeed using:
            - Pressure ratio (δ)
            - Compressibility effects
            - Equivalent airspeed (EAS) conversion
        4. Decompose velocity into components using:
            - Fixed descent rate
            - Sideslip angle
            - Computed true airspeed

    **Major Assumptions**
        * Constant calibrated airspeed
        * Constant descent rate
        * Standard atmosphere model with temperature deviation
        * Small angle approximations
        * Quasi-steady flight

    See Also
    --------
    RCAIDE.Framework.Mission.Segments
    RCAIDE.Library.Mission.Common.Update.atmosphere
    """       
    
    # unpack
    descent_rate = segment.descent_rate
    cas          = segment.calibrated_air_speed   
    alt0         = segment.altitude_start 
    altf         = segment.altitude_end
    beta         = segment.sideslip_angle
    t_nondim     = segment.state.numerics.dimensionless.control_points
    conditions   = segment.state.conditions  

    # check for initial altitude
    if alt0 is None:
        if not segment.state.initials: raise AttributeError('initial altitude not set')
        alt0 = -1.0 * segment.state.initials.conditions.frames.inertial.position_vector[-1,2]

    # discretize on altitude
    alt = t_nondim * (altf-alt0) + alt0
    
    # determine airspeed from calibrated airspeed
    RCAIDE.Library.Mission.Common.Update.atmosphere(segment) # get density for airspeed

    alt_data = segment.analyses.atmosphere.compute_values(alt,segment.temperature_deviation)
    density  = alt_data.density[:,0]  
    pressure = alt_data.pressure[:,0] 

    MSL_data  = segment.analyses.atmosphere.compute_values(0.0,segment.temperature_deviation)
    pressure0 = MSL_data.pressure[0]
    

    if cas is None:
        if not segment.state.initials: raise AttributeError('initial equivalent airspeed not set')
        air_speed =  np.linalg.norm(segment.state.initials.conditions.frames.inertial.velocity_vector[-1,:])    
    else:  
        kcas  = cas / Units.knots
        delta = pressure / pressure0 
    
        mach = 2.236*((((1+4.575e-7*kcas**2)**3.5-1)/delta + 1)**0.2857 - 1)**0.5
    
        qc  = pressure * ((1+0.2*mach**2)**3.5 - 1)
        eas = cas * (pressure/pressure0)**0.5*(((qc/pressure+1)**0.286-1)/((qc/pressure0+1)**0.286-1))**0.5
        
        air_speed = eas/np.sqrt(density/MSL_data.density[0])    
    
    # process velocity vector
    v_mag = air_speed
    v_z   = descent_rate # z points down
    v_xy  = np.sqrt( v_mag**2 - v_z**2 )
    v_x   = np.cos(beta)*v_xy
    v_y   = np.sin(beta)*v_xy
    
    # pack conditions    
    conditions.frames.inertial.velocity_vector[:,0] = v_x
    conditions.frames.inertial.velocity_vector[:,1] = v_y
    conditions.frames.inertial.velocity_vector[:,2] = v_z
    conditions.frames.inertial.position_vector[:,2] = -alt[:,0] # z points down
    conditions.freestream.altitude[:,0]             =  alt[:,0] # positive altitude in this context