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16 changes: 8 additions & 8 deletions contributing/contributing.html
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Expand Up @@ -1055,21 +1055,21 @@ <h2>Notebook Creation<a class="headerlink" href="#notebook-creation" title="Perm
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| of &#39;&lt;variable&gt;&#39; | wrt &#39;&lt;variable&gt;&#39; | calc mag. | check mag. | a(cal-chk) | r(cal-chk) | error desc |
+=================+==================+=============+=============+=============+=============+============+
| &#39;check&#39; | &#39;theta&#39; | 1.3553e+03 | 1.3553e+03 | 8.5285e-14 | 6.2926e-17 | |
| &#39;check&#39; | &#39;theta&#39; | 3.8466e+02 | 3.8466e+02 | 1.1459e-13 | 2.9789e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;check&#39; | &#39;v&#39; | 2.6810e+01 | 2.6810e+01 | 4.9651e-16 | 1.8520e-17 | |
| &#39;check&#39; | &#39;v&#39; | 9.4537e+00 | 9.4537e+00 | 4.4409e-16 | 4.6975e-17 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;theta&#39; | 9.4844e+00 | 9.4844e+00 | 1.0175e-15 | 1.0729e-16 | |
| &#39;vdot&#39; | &#39;theta&#39; | 1.3367e+01 | 1.3367e+01 | 4.9651e-16 | 3.7144e-17 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;v&#39; | 0.0000e+00 | 0.0000e+00 | 0.0000e+00 | nan | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;theta&#39; | 7.2359e+00 | 7.2359e+00 | 4.9651e-16 | 6.8617e-17 | |
| &#39;xdot&#39; | &#39;theta&#39; | 1.0083e+01 | 1.0083e+01 | 1.5394e-15 | 1.5267e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;v&#39; | 9.6714e-01 | 9.6714e-01 | 1.2413e-16 | 1.2834e-16 | |
| &#39;xdot&#39; | &#39;v&#39; | 1.3631e+00 | 1.3631e+00 | 0.0000e+00 | 0.0000e+00 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;theta&#39; | 4.2930e+00 | 4.2930e+00 | 9.0195e-16 | 2.1010e-16 | |
| &#39;ydot&#39; | &#39;theta&#39; | 7.5441e+00 | 7.5441e+00 | 2.2888e-16 | 3.0339e-17 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;v&#39; | 2.0161e+00 | 2.0161e+00 | 0.0000e+00 | 0.0000e+00 | |
| &#39;ydot&#39; | &#39;v&#39; | 1.7726e+00 | 1.7726e+00 | 1.9230e-16 | 1.0848e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+

##################################################################
Expand All @@ -1078,7 +1078,7 @@ <h2>Notebook Creation<a class="headerlink" href="#notebook-creation" title="Perm
+-----------------+------------------+-------------+-------------+-------------+-------------+
| of &#39;&lt;variable&gt;&#39; | wrt &#39;&lt;variable&gt;&#39; | calc mag. | check mag. | a(cal-chk) | r(cal-chk) |
+=================+==================+=============+=============+=============+=============+
| &#39;ydot&#39; | &#39;theta&#39; | 4.2930e+00 | 4.2930e+00 | 9.0195e-16 | 2.1010e-16 |
| &#39;check&#39; | &#39;theta&#39; | 3.8466e+02 | 3.8466e+02 | 1.1459e-13 | 2.9789e-16 |
+-----------------+------------------+-------------+-------------+-------------+-------------+
</pre></div>
</div>
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69 changes: 34 additions & 35 deletions examples/balanced_field/balanced_field.html
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Expand Up @@ -941,13 +941,13 @@ <h2>The ODE System<a class="headerlink" href="#the-ode-system" title="Permalink
<h3>The Aerodynamic Model<a class="headerlink" href="#the-aerodynamic-model" title="Permalink to this heading">#</a></h3>
<p>Both sets of equations of motion have common aerodynamic models.</p>
<p>First, the lift coefficient is computed using a model which assumes linearity in lift wrt the angle of attack.</p>
<div class="amsmath math notranslate nohighlight" id="equation-6a660f74-91e7-4393-91e4-4f11aa82633b">
<span class="eqno">(21)<a class="headerlink" href="#equation-6a660f74-91e7-4393-91e4-4f11aa82633b" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-37af8b08-297d-49da-a1d9-1502b38c46d9">
<span class="eqno">(21)<a class="headerlink" href="#equation-37af8b08-297d-49da-a1d9-1502b38c46d9" title="Permalink to this equation">#</a></span>\[\begin{align}
C_L &amp;= C_{L0} + \frac{\alpha}{\alpha_{max}} \left(C_{L-max} - C_{L0}\right)
\end{align}\]</div>
<p>Next, the drag-due-to-lift factor is computed (Equations 12.48 and 12.61 in Raymer[&#64;raymer2012aircraft]).</p>
<div class="amsmath math notranslate nohighlight" id="equation-31af6867-28f8-4d83-a2ee-317573f45d73">
<span class="eqno">(22)<a class="headerlink" href="#equation-31af6867-28f8-4d83-a2ee-317573f45d73" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-3dfcdfa9-d729-4ebf-82a4-c98570ec0246">
<span class="eqno">(22)<a class="headerlink" href="#equation-3dfcdfa9-d729-4ebf-82a4-c98570ec0246" title="Permalink to this equation">#</a></span>\[\begin{align}
K_{nom} &amp;= \frac{1}{ \pi AR e} \\
b &amp;= \frac{span}{2} \\
K &amp;= 33 K_{nom} \frac{ \left(\frac{h + h_w}{b} \right) ^{\frac{3}{2}}}{1.0 + 33 \left( \frac{h + h_w}{b}\right) ^{\frac{3}{2}}}
Expand All @@ -956,8 +956,8 @@ <h3>The Aerodynamic Model<a class="headerlink" href="#the-aerodynamic-model" tit
This causes this problem to be difficult to solve using a shooting method.
If the optimizer proposes a combination of initial states and a control history that results in altitude dropping significantly below zero, the propagation will fail.</p>
<p>Finally, the lift and drag are computed after computing the dynamic pressure.</p>
<div class="amsmath math notranslate nohighlight" id="equation-26834eb6-c009-4dea-a85a-fb15bc7809c3">
<span class="eqno">(23)<a class="headerlink" href="#equation-26834eb6-c009-4dea-a85a-fb15bc7809c3" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-ad7429b8-efb8-4b6d-b811-04cb618813c8">
<span class="eqno">(23)<a class="headerlink" href="#equation-ad7429b8-efb8-4b6d-b811-04cb618813c8" title="Permalink to this equation">#</a></span>\[\begin{align}
q &amp;= 0.5 \rho v^2 \\
L &amp;= q S C_L \\
D &amp;= q S \left( C_{D0} + K C_{L}^2 \right)
Expand All @@ -968,17 +968,17 @@ <h3>Stall Speed<a class="headerlink" href="#stall-speed" title="Permalink to thi
<p>This model relies on the ratio of the current true airspeed to stall speed (<span class="math notranslate nohighlight">\(\frac{v}{v_{stall}}\)</span>).
This constraint is used to trigger the beginning of rotation and is used as a boundary constraint at the end of the initial climb.
Stall speed is given by Equation 5.6 in Raymer[&#64;raymer2012aircraft].</p>
<div class="amsmath math notranslate nohighlight" id="equation-867d4820-e420-4735-a0aa-f6d6d2f4a8f3">
<span class="eqno">(24)<a class="headerlink" href="#equation-867d4820-e420-4735-a0aa-f6d6d2f4a8f3" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-f3180528-f82b-41c0-9260-3c87fc010a52">
<span class="eqno">(24)<a class="headerlink" href="#equation-f3180528-f82b-41c0-9260-3c87fc010a52" title="Permalink to this equation">#</a></span>\[\begin{align}
W &amp;= m g \\
v_{stall} &amp;= \sqrt{\frac{2 * W}{\rho S C_{L-max}}}
\end{align}\]</div>
</section>
<section id="runway-equations-of-motion">
<h3>Runway Equations of Motion<a class="headerlink" href="#runway-equations-of-motion" title="Permalink to this heading">#</a></h3>
<p>The runway equations of motion are used to integrate range and speed as the vehicle rolls along the runway.</p>
<div class="amsmath math notranslate nohighlight" id="equation-8ee7bb9a-27d2-4119-b148-366ead9dc0d1">
<span class="eqno">(25)<a class="headerlink" href="#equation-8ee7bb9a-27d2-4119-b148-366ead9dc0d1" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-a87e8317-e02b-4d90-8559-e8640cc9744b">
<span class="eqno">(25)<a class="headerlink" href="#equation-a87e8317-e02b-4d90-8559-e8640cc9744b" title="Permalink to this equation">#</a></span>\[\begin{align}
F_r &amp;= mg - L \cos \alpha - T \sin \alpha \\
\dot{v} &amp;= \frac{T \cos \alpha - D - F_r \mu_r}{m} \\
\dot{r} &amp;= v
Expand All @@ -1005,8 +1005,8 @@ <h3>Runway Equations of Motion<a class="headerlink" href="#runway-equations-of-m
<section id="flight-equations-of-motion">
<h3>Flight Equations of Motion<a class="headerlink" href="#flight-equations-of-motion" title="Permalink to this heading">#</a></h3>
<p>The flight equations of motion include two additional state variables: the flight-path angle (<span class="math notranslate nohighlight">\(\gamma\)</span>) and altitude (<span class="math notranslate nohighlight">\(h\)</span>).</p>
<div class="amsmath math notranslate nohighlight" id="equation-4a4a4fe6-5aa1-4205-8c46-ea23cca5a0e1">
<span class="eqno">(26)<a class="headerlink" href="#equation-4a4a4fe6-5aa1-4205-8c46-ea23cca5a0e1" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-8a32ebc4-0c60-4e04-ad04-9bf72cf3577a">
<span class="eqno">(26)<a class="headerlink" href="#equation-8a32ebc4-0c60-4e04-ad04-9bf72cf3577a" title="Permalink to this equation">#</a></span>\[\begin{align}
\dot{v} &amp;= \frac{T}{m} \cos \alpha - \frac{D}{m} - g \sin \gamma \\
\dot{\gamma} &amp;= \frac{T}{m v} \sin \alpha + \frac{L}{m v} - \frac{g \cos \gamma}{v} \\
\dot{h} &amp;= v \sin \gamma \\
Expand Down Expand Up @@ -1531,7 +1531,7 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;dymos.phase.phase.Phase at 0x7f154eb8f450&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;dymos.phase.phase.Phase at 0x7f3cba011890&gt;
</pre></div>
</div>
</div>
Expand Down Expand Up @@ -1733,20 +1733,19 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.0158 sec
Time to compute coloring: 0.0104 sec
Memory to compute coloring: 0.3750 MB
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Coloring for &#39;traj.phases.rto.rhs_all&#39; (class BalancedFieldODEComp)
Time to compute sparsity: 0.0163 sec
Time to compute coloring: 0.0103 sec
Memory to compute coloring: 0.1250 MB

Coloring for &#39;traj.phases.rto.rhs_all&#39; (class BalancedFieldODEComp)

Jacobian shape: (132, 60) (10.13% nonzero)
FWD solves: 16 REV solves: 0
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.0165 sec
Time to compute coloring: 0.0102 sec
Time to compute sparsity: 0.0159 sec
Time to compute coloring: 0.0099 sec
Memory to compute coloring: 0.0000 MB

Coloring for &#39;traj.phases.v1_to_vr.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1756,8 +1755,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.0155 sec
Time to compute coloring: 0.0098 sec
Time to compute sparsity: 0.0159 sec
Time to compute coloring: 0.0099 sec
Memory to compute coloring: 0.0000 MB

Coloring for &#39;traj.phases.rotate.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1767,8 +1766,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.0159 sec
Time to compute coloring: 0.0100 sec
Time to compute sparsity: 0.0163 sec
Time to compute coloring: 0.0099 sec
Memory to compute coloring: 0.0000 MB

Coloring for &#39;traj.phases.climb.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1778,12 +1777,12 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 111 (85.59% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.0323 sec
Time to compute coloring: 0.0186 sec
Memory to compute coloring: 0.1250 MB
Time to compute sparsity: 0.0334 sec
Time to compute coloring: 0.0188 sec
Memory to compute coloring: 0.2500 MB
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Full total jacobian for problem &#39;problem&#39; was computed 3 times, taking 0.9892934480000122 seconds.
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Full total jacobian for problem &#39;problem&#39; was computed 3 times, taking 0.9905034299999897 seconds.
Total jacobian shape: (178, 166)


Expand All @@ -1792,10 +1791,10 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 14 vs 166 (91.57% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.9893 sec
Time to compute coloring: 0.1047 sec
Time to compute sparsity: 0.9905 sec
Time to compute coloring: 0.0685 sec
Memory to compute coloring: 0.0000 MB
Coloring created on: 2024-08-23 12:47:33
Coloring created on: 2024-08-29 21:45:04
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/core/total_jac.py:1646: DerivativesWarning:Constraints or objectives [(&#39;traj.phases.climb-&gt;path_constraint-&gt;gam&#39;, inds=[(0, 0)])] cannot be impacted by the design variables of the problem.
Expand All @@ -1816,11 +1815,11 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Driver: pyOptSparseDriver
success : True
iterations : 25
runtime : 3.0922E+00 s
runtime : 3.0520E+00 s
model_evals : 25
model_time : 7.2278E-02 s
model_time : 7.2237E-02 s
deriv_evals : 24
deriv_time : 1.1742E+00 s
deriv_time : 1.1898E+00 s
exit_status : SUCCESS
</pre></div>
</div>
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28 changes: 14 additions & 14 deletions examples/balanced_field/balanced_field_funccomp.html
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Expand Up @@ -1258,8 +1258,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.2268 sec
Time to compute coloring: 0.0106 sec
Time to compute sparsity: 0.2325 sec
Time to compute coloring: 0.0105 sec
Memory to compute coloring: 0.1250 MB
</pre></div>
</div>
Expand All @@ -1273,8 +1273,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.1899 sec
Time to compute coloring: 0.0115 sec
Time to compute sparsity: 0.1922 sec
Time to compute coloring: 0.0119 sec
Memory to compute coloring: 0.0000 MB
</pre></div>
</div>
Expand All @@ -1288,8 +1288,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.1906 sec
Time to compute coloring: 0.0120 sec
Time to compute sparsity: 0.1944 sec
Time to compute coloring: 0.0123 sec
Memory to compute coloring: 0.0000 MB
</pre></div>
</div>
Expand All @@ -1303,8 +1303,8 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 60 (73.33% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.2942 sec
Time to compute coloring: 0.0108 sec
Time to compute sparsity: 0.2999 sec
Time to compute coloring: 0.0105 sec
Memory to compute coloring: 0.0000 MB
</pre></div>
</div>
Expand All @@ -1318,12 +1318,12 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 16 vs 111 (85.59% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.2773 sec
Time to compute coloring: 0.0194 sec
Time to compute sparsity: 0.2794 sec
Time to compute coloring: 0.0193 sec
Memory to compute coloring: 0.1250 MB
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Full total jacobian for problem &#39;problem&#39; was computed 3 times, taking 3.245863141999962 seconds.
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Full total jacobian for problem &#39;problem&#39; was computed 3 times, taking 3.2553110800000127 seconds.
Total jacobian shape: (178, 166)


Expand All @@ -1332,10 +1332,10 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Total colors vs. total size: 14 vs 166 (91.57% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 3.2459 sec
Time to compute coloring: 0.0698 sec
Time to compute sparsity: 3.2553 sec
Time to compute coloring: 0.0726 sec
Memory to compute coloring: 0.2500 MB
Coloring created on: 2024-08-23 12:47:44
Coloring created on: 2024-08-29 21:45:15
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/core/total_jac.py:1646: DerivativesWarning:Constraints or objectives [(&#39;traj.phases.climb-&gt;path_constraint-&gt;gam&#39;, inds=[(0, 0)])] cannot be impacted by the design variables of the problem.
Expand Down
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