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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; | 1.6330e+01 | 1.6330e+01 | 2.1869e-15 | 1.3392e-16 | |
| &#39;check&#39; | &#39;theta&#39; | 1.0081e+04 | 1.0081e+04 | 1.8190e-12 | 1.8043e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;check&#39; | &#39;v&#39; | 3.9897e+00 | 3.9897e+00 | 0.0000e+00 | 0.0000e+00 | |
| &#39;check&#39; | &#39;v&#39; | 3.3183e+01 | 3.3183e+01 | 3.1402e-16 | 9.4632e-18 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;theta&#39; | 1.7045e+01 | 1.7045e+01 | 8.8818e-16 | 5.2106e-17 | |
| &#39;vdot&#39; | &#39;theta&#39; | 1.5793e+01 | 1.5793e+01 | 2.6645e-15 | 1.6872e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;vdot&#39; | &#39;v&#39; | 0.0000e+00 | 0.0000e+00 | 0.0000e+00 | nan | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;theta&#39; | 8.3835e+00 | 8.3835e+00 | 8.9509e-16 | 1.0677e-16 | |
| &#39;xdot&#39; | &#39;theta&#39; | 9.9440e+00 | 9.9440e+00 | 4.5860e-16 | 4.6118e-17 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;xdot&#39; | &#39;v&#39; | 1.7382e+00 | 1.7382e+00 | 1.5701e-16 | 9.0331e-17 | |
| &#39;xdot&#39; | &#39;v&#39; | 1.6104e+00 | 1.6104e+00 | 1.5705e-16 | 9.7520e-17 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;theta&#39; | 1.3959e+01 | 1.3959e+01 | 1.2561e-15 | 8.9985e-17 | |
| &#39;ydot&#39; | &#39;theta&#39; | 9.0078e+00 | 9.0078e+00 | 1.8843e-15 | 2.0919e-16 | |
+-----------------+------------------+-------------+-------------+-------------+-------------+------------+
| &#39;ydot&#39; | &#39;v&#39; | 1.4067e+00 | 1.4067e+00 | 1.1102e-16 | 7.8924e-17 | |
| &#39;ydot&#39; | &#39;v&#39; | 1.5513e+00 | 1.5513e+00 | 1.5701e-16 | 1.0121e-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;check&#39; | &#39;theta&#39; | 1.6330e+01 | 1.6330e+01 | 2.1869e-15 | 1.3392e-16 |
| &#39;ydot&#39; | &#39;theta&#39; | 9.0078e+00 | 9.0078e+00 | 1.8843e-15 | 2.0919e-16 |
+-----------------+------------------+-------------+-------------+-------------+-------------+
</pre></div>
</div>
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65 changes: 32 additions & 33 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-918fbb7e-a09d-4cdb-81b4-e73fac659af5">
<span class="eqno">(21)<a class="headerlink" href="#equation-918fbb7e-a09d-4cdb-81b4-e73fac659af5" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-606cf23e-e668-498a-bcc4-e0b41d46e0fe">
<span class="eqno">(21)<a class="headerlink" href="#equation-606cf23e-e668-498a-bcc4-e0b41d46e0fe" 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-8087d988-6e45-4cd8-81bd-a35d924149dd">
<span class="eqno">(22)<a class="headerlink" href="#equation-8087d988-6e45-4cd8-81bd-a35d924149dd" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-2ff8dcda-3ddf-4eb2-84ff-ebfec5741f17">
<span class="eqno">(22)<a class="headerlink" href="#equation-2ff8dcda-3ddf-4eb2-84ff-ebfec5741f17" 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-7e131739-7a44-4dba-a919-ea4f451bba34">
<span class="eqno">(23)<a class="headerlink" href="#equation-7e131739-7a44-4dba-a919-ea4f451bba34" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-0c8d2831-8300-40d8-94c4-f31b949c994b">
<span class="eqno">(23)<a class="headerlink" href="#equation-0c8d2831-8300-40d8-94c4-f31b949c994b" 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-c63774cb-03c4-4e7a-bf7c-d212199e6f02">
<span class="eqno">(24)<a class="headerlink" href="#equation-c63774cb-03c4-4e7a-bf7c-d212199e6f02" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-20e71ff6-8e2b-4409-9365-a0944d14fb91">
<span class="eqno">(24)<a class="headerlink" href="#equation-20e71ff6-8e2b-4409-9365-a0944d14fb91" 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-7f2d25a3-d9ac-4328-8b04-f0c70274a0aa">
<span class="eqno">(25)<a class="headerlink" href="#equation-7f2d25a3-d9ac-4328-8b04-f0c70274a0aa" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-8f0ef7d4-e539-4588-8843-25949b72504c">
<span class="eqno">(25)<a class="headerlink" href="#equation-8f0ef7d4-e539-4588-8843-25949b72504c" 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-416c0676-7323-44e1-8a53-7c4322b072df">
<span class="eqno">(26)<a class="headerlink" href="#equation-416c0676-7323-44e1-8a53-7c4322b072df" title="Permalink to this equation">#</a></span>\[\begin{align}
<div class="amsmath math notranslate nohighlight" id="equation-05f8835b-3899-4a38-a7d1-d955545192a6">
<span class="eqno">(26)<a class="headerlink" href="#equation-05f8835b-3899-4a38-a7d1-d955545192a6" 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 0x7f27407db490&gt;
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;dymos.phase.phase.Phase at 0x7f3f7022f2d0&gt;
</pre></div>
</div>
</div>
Expand Down Expand Up @@ -1733,19 +1733,18 @@ <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: 0.0165 sec
Time to compute coloring: 0.0104 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>Coloring for &#39;traj.phases.rto.rhs_all&#39; (class BalancedFieldODEComp)
Time to compute sparsity: 0.0163 sec
Time to compute coloring: 0.0105 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: 0.0156 sec
Time to compute sparsity: 0.0159 sec
Time to compute coloring: 0.0099 sec
Memory to compute coloring: 0.0000 MB

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: 0.0097 sec
Time to compute sparsity: 0.0158 sec
Time to compute coloring: 0.0098 sec
Memory to compute coloring: 0.0000 MB

Coloring for &#39;traj.phases.rotate.rhs_all&#39; (class BalancedFieldODEComp)
Expand All @@ -1767,7 +1766,7 @@ <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 sparsity: 0.0157 sec
Time to compute coloring: 0.0099 sec
Memory to compute coloring: 0.0000 MB

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: 0.0324 sec
Time to compute sparsity: 0.0330 sec
Time to compute coloring: 0.0188 sec
Memory to compute coloring: 0.2500 MB
Memory to compute coloring: 0.0000 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 1.0517292810000072 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 1.024991416999967 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: 1.0517 sec
Time to compute coloring: 0.0672 sec
Memory to compute coloring: 0.0000 MB
Coloring created on: 2024-08-15 15:58:22
Time to compute sparsity: 1.0250 sec
Time to compute coloring: 0.0714 sec
Memory to compute coloring: 0.1250 MB
Coloring created on: 2024-08-19 22:08:04
</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 Down Expand Up @@ -1868,11 +1867,11 @@ <h2>Building and running the problem<a class="headerlink" href="#building-and-ru
Driver: pyOptSparseDriver
success : True
iterations : 25
runtime : 3.1427E+00 s
runtime : 3.0601E+00 s
model_evals : 25
model_time : 7.3668E-02 s
model_time : 7.1345E-02 s
deriv_evals : 24
deriv_time : 1.1960E+00 s
deriv_time : 1.1647E+00 s
exit_status : SUCCESS
</pre></div>
</div>
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24 changes: 12 additions & 12 deletions examples/balanced_field/balanced_field_funccomp.html
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Expand Up @@ -1259,7 +1259,7 @@ <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: 0.2352 sec
Time to compute sparsity: 0.2338 sec
Time to compute coloring: 0.0105 sec
Memory to compute coloring: 0.1250 MB
</pre></div>
Expand All @@ -1274,8 +1274,8 @@ <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: 0.1925 sec
Time to compute coloring: 0.0112 sec
Time to compute sparsity: 0.1902 sec
Time to compute coloring: 0.0109 sec
Memory to compute coloring: 0.0000 MB
</pre></div>
</div>
Expand All @@ -1289,8 +1289,8 @@ <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: 0.1937 sec
Time to compute coloring: 0.0112 sec
Time to compute sparsity: 0.1923 sec
Time to compute coloring: 0.0120 sec
Memory to compute coloring: 0.0000 MB
</pre></div>
</div>
Expand All @@ -1304,7 +1304,7 @@ <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: 0.3056 sec
Time to compute sparsity: 0.2903 sec
Time to compute coloring: 0.0106 sec
Memory to compute coloring: 0.0000 MB
</pre></div>
Expand All @@ -1319,12 +1319,12 @@ <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: 0.2801 sec
Time to compute sparsity: 0.2781 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 3.264605084999971 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 3.2309012659999894 seconds.
Total jacobian shape: (178, 166)


Expand All @@ -1333,10 +1333,10 @@ <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: 3.2646 sec
Time to compute coloring: 0.0685 sec
Memory to compute coloring: 0.2500 MB
Coloring created on: 2024-08-15 15:58:34
Time to compute sparsity: 3.2309 sec
Time to compute coloring: 0.0688 sec
Memory to compute coloring: 0.1250 MB
Coloring created on: 2024-08-19 22:08:16
</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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