:orphan:

.. ****************************************************************************
.. CUI//REL TO USA ONLY
..
.. The Advanced Framework for Simulation, Integration, and Modeling (AFSIM)
..
.. The use, dissemination or disclosure of data in this file is subject to
.. limitation or restriction. See accompanying README and LICENSE for details.
.. ****************************************************************************

WSF_CHAFF_PARCEL
----------------

.. model:: chaff_parcel WSF_CHAFF_PARCEL

.. parsed-literal::

   chaff_parcel <name> :model:`WSF_CHAFF_PARCEL`
      # Geometric inputs
      bloom_diameter_ ...
      expansion_time_constant_ | bloom_time_constant_ ...

      # Kinematic inputs
      terminal_velocity_ ...
      deceleration_rate_ ...

      # Lifetime and debugging inputs
      expiration_time_ ...
      debug_ ...

      # Signal return (RCS) inputs
      `RCS Related Commands`_

   end_chaff_parcel

Overview
========

:model:`WSF_CHAFF_PARCEL` represents a chaff parcel or bundle dispensed from a system of ejectors composing a :model:`WSF_CHAFF_WEAPON`.
They are modeled as spheres, whose mean radial size is computed as an exponential growth according to the bloom equation:

.. math::
   R_{parcel} = 0.5D_{max}(1 - e^{-t_{fall}/\tau_{D}})

where :math:`D_{max}` is the bloom_diameter_, :math:`t_{fall}` is time since the parcel was ejected, and :math:`\tau_{D}` is the 
expansion_time_constant_.

A group of one or more parcels dropped with a call to script method :method:`WsfChaffWeapon.DropChaffCloud` together form a chaff cloud. 
When illuminated by RF energy, each parcel produces a return signal with a radar cross section defined by:

.. math::
   \sigma_{parcel} = \frac{A_{p}}{N}\Big[1 - e^{-(N\sigma_{max}/A_{p})}\Big]

where :math:`A_{p}` is the bistatic presented area of the cloud, :math:`N` is the number of parcels in the cloud, and :math:`\sigma_{max}`
is the maximum theoretical RCS of the dispersed parcel when its dipoles are widely spaced (i.e., no shielding effects). 

The bistatic presented area of the cloud accounts for parcel blooming and aspect angle dependency. It is the average of the areas 
presented to the transmitter and receiver, each of which uses aspect angle to compute a weighted RMS value of the cross-sectional areas of the cloud viewed
from the front and broad-side.

:math:`\sigma_{max}` can be a function of frequency and specified with the frequency_maximum_rcs_table_ command. If this table is not
specified, :math:`\sigma_{max}` is computed, assuming spot chaff with half-wave dipoles (all dipoles are cut to the same length 
:math:`L=\lambda/2`), as follows: 

.. math::
   \sigma_{max} = 0.15N_{d}\lambda^2

where :math:`N_{d}` is the number of chaff dipoles specified by the number_dipoles_ command, and :math:`\lambda` is the wavelength 
of the radar. (Ref: Schleher, Electronic Warfare in the Information Age)

.. note::

   Chaff parcels are removed from the simulation when they hit the ground, or have been falling for a maximum amount of time specified
   by expiration_time_, whichever comes first.

Commands
========

.. command:: bloom_diameter <length-value>

   Specifies the diameter to which the parcel blooms asymptotically, as time goes to infinity.

   **Default:** 10.0 meters

.. command:: expansion_time_constant <time-value>
.. command:: bloom_time_constant <time-value>

   Specifies the expansion time constant (:math:`\tau_{D}`) in the bloom equation above. The smaller the value, the faster the 
   parcel approaches its bloom_diameter_.

   **Default:** 0.75 sec

.. command:: terminal_velocity <speed-value>

   Free fall velocity of the parcel. Parcels are assumed to reach terminal velocity instantaneously upon ejection.

   **Default:** 1.0 m/s

.. command:: deceleration_rate <acceleration-value>

   The rate at which the parcel decelerates upon ejection. This should specify a positive value, giving the magnitude of the 
   acceleration vector that is aligned opposite the initial velocity vector.

   **Default:** 100.0 m/s^2

.. command:: expiration_time <time-value>

   The time at which the parcel will be removed from the simulation, after ejection, unless it hits the ground first.

   **Default:** 60.0 sec

.. command:: debug <boolean-value>

   If true, will print debugging information about parcel status to the console.

   **Default:** false

RCS Related Commands
====================

.. include:: chaff_parcel_rcs_commands.txt