:orphan:

.. ****************************************************************************
.. CUI
..
.. 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_PIECEWISE_EXPONENTIAL_ATMOSPHERE
------------------------------------

**Script Type:** :class:`WsfPiecewiseExponentialAtmosphere`.

.. model:: atmosphere_model WSF_PIECEWISE_EXPONENTIAL_ATMOSPHERE

   .. parsed-literal::

      atmosphere_model <name> :model:`WSF_PIECEWISE_EXPONENTIAL_ATMOSPHERE`
         ... `Common Atmosphere Commands`_ ...
      end_atmosphere_model

Overview
========

The :model:`WSF_PIECEWISE_EXPONENTIAL_ATMOSPHERE` models the atmospheric density
using a series of exponential profiles for different altitude ranges. In each
range the profile takes the form:

:math:`\rho(h) = \rho_0 \exp{\left[-\frac{h - h_0}{H}\right]}`,

where :math:`H` is a scale height, :math:`h_0` is the altitude at which the
segment begins, and :math:`\rho_0` is the density of the model at that
altitude. The values of these constants can be found in Vallado's
*Fundamentals of Astrodynamics and Application*, Fourth Edition, in Table 8-4
on page 567, and are reproduced below. The values are chosen so that the
resulting density is continuous at the segment boundaries.

+-------------------------------+-----------------------------+-------------------------------------------------+
| :math:`h_0` [:math:`\rm{km}`] | :math:`H` [:math:`\rm{km}`] | :math:`\rho_0` [:math:`\rm{kg} \cdot \rm{m}^3`] |
+===============================+=============================+=================================================+
|    0.0                        |   7.294                     | 1.225e0                                         |
+-------------------------------+-----------------------------+-------------------------------------------------+
|   25.0                        |   6.349                     | 3.899e-2                                        |
+-------------------------------+-----------------------------+-------------------------------------------------+
|   30.0                        |   6.682                     | 1.774e-2                                        |
+-------------------------------+-----------------------------+-------------------------------------------------+
|   40.0                        |   7.554                     | 3.972e-3                                        |
+-------------------------------+-----------------------------+-------------------------------------------------+
|   50.0                        |   8.382                     | 1.057e-3                                        |
+-------------------------------+-----------------------------+-------------------------------------------------+
|   60.0                        |   7.714                     | 3.206e-4                                        |
+-------------------------------+-----------------------------+-------------------------------------------------+
|   70.0                        |   6.549                     | 8.770e-5                                        |
+-------------------------------+-----------------------------+-------------------------------------------------+
|   80.0                        |   5.799                     | 1.905e-5                                        |
+-------------------------------+-----------------------------+-------------------------------------------------+
|   90.0                        |   5.382                     | 3.396e-6                                        |
+-------------------------------+-----------------------------+-------------------------------------------------+
|  100.0                        |   5.877                     | 5.297e-7                                        |
+-------------------------------+-----------------------------+-------------------------------------------------+
|  110.0                        |   7.263                     | 9.661e-8                                        |
+-------------------------------+-----------------------------+-------------------------------------------------+
|  120.0                        |   9.473                     | 2.438e-8                                        |
+-------------------------------+-----------------------------+-------------------------------------------------+
|  130.0                        |  12.636                     | 8.484e-9                                        |
+-------------------------------+-----------------------------+-------------------------------------------------+
|  140.0                        |  16.149                     | 3.845e-9                                        |
+-------------------------------+-----------------------------+-------------------------------------------------+
|  150.0                        |  22.523                     | 2.070e-9                                        |
+-------------------------------+-----------------------------+-------------------------------------------------+
|  180.0                        |  29.740                     | 5.464e-10                                       |
+-------------------------------+-----------------------------+-------------------------------------------------+
|  200.0                        |  37.105                     | 2.789e-10                                       |
+-------------------------------+-----------------------------+-------------------------------------------------+
|  250.0                        |  45.546                     | 7.248e-11                                       |
+-------------------------------+-----------------------------+-------------------------------------------------+
|  300.0                        |  53.628                     | 2.418e-11                                       |
+-------------------------------+-----------------------------+-------------------------------------------------+
|  350.0                        |  53.298                     | 9.518e-12                                       |
+-------------------------------+-----------------------------+-------------------------------------------------+
|  400.0                        |  58.515                     | 3.725e-12                                       |
+-------------------------------+-----------------------------+-------------------------------------------------+
|  450.0                        |  60.828                     | 1.585e-12                                       |
+-------------------------------+-----------------------------+-------------------------------------------------+
|  500.0                        |  63.822                     | 6.967e-13                                       |
+-------------------------------+-----------------------------+-------------------------------------------------+
|  600.0                        |  71.835                     | 1.454e-13                                       |
+-------------------------------+-----------------------------+-------------------------------------------------+
|  700.0                        |  88.667                     | 3.614e-14                                       |
+-------------------------------+-----------------------------+-------------------------------------------------+
|  800.0                        | 124.64                      | 1.170e-14                                       |
+-------------------------------+-----------------------------+-------------------------------------------------+
|  900.0                        | 181.05                      | 5.245e-15                                       |
+-------------------------------+-----------------------------+-------------------------------------------------+
| 1000.0                        | 268.00                      | 3.019e-15                                       |
+-------------------------------+-----------------------------+-------------------------------------------------+

.. include:: common_atmosphere_commands.txt