diff --git a/contributing/contributing.html b/contributing/contributing.html index ac50be169..82aee075b 100644 --- a/contributing/contributing.html +++ b/contributing/contributing.html @@ -561,6 +561,7 @@

Notebook Creation#

Both sets of equations of motion have common aerodynamic models.

First, the lift coefficient is computed using a model which assumes linearity in lift wrt the angle of attack.

-
-(21)#\[\begin{align} +
+(21)#\[\begin{align} C_L &= C_{L0} + \frac{\alpha}{\alpha_{max}} \left(C_{L-max} - C_{L0}\right) \end{align}\]

Next, the drag-due-to-lift factor is computed (Equations 12.48 and 12.61 in Raymer[@raymer2012aircraft]).

-
-(22)#\[\begin{align} +
+(22)#\[\begin{align} K_{nom} &= \frac{1}{ \pi AR e} \\ b &= \frac{span}{2} \\ K &= 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}}} @@ -591,8 +591,8 @@

The Aerodynamic Model

Finally, the lift and drag are computed after computing the dynamic pressure.

-
-(23)#\[\begin{align} +
+(23)#\[\begin{align} q &= 0.5 \rho v^2 \\ L &= q S C_L \\ D &= q S \left( C_{D0} + K C_{L}^2 \right) @@ -603,8 +603,8 @@

Stall Speed\(\frac{v}{v_{stall}}\)). 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[@raymer2012aircraft].

-
-(24)#\[\begin{align} +
+(24)#\[\begin{align} W &= m g \\ v_{stall} &= \sqrt{\frac{2 * W}{\rho S C_{L-max}}} \end{align}\]
@@ -612,8 +612,8 @@

Stall Speed

Runway Equations of Motion#

The runway equations of motion are used to integrate range and speed as the vehicle rolls along the runway.

-
-(25)#\[\begin{align} +
+(25)#\[\begin{align} F_r &= mg - L \cos \alpha - T \sin \alpha \\ \dot{v} &= \frac{T \cos \alpha - D - F_r \mu_r}{m} \\ \dot{r} &= v @@ -640,8 +640,8 @@

Runway Equations of Motion

Flight Equations of Motion#

The flight equations of motion include two additional state variables: the flight-path angle (\(\gamma\)) and altitude (\(h\)).

-
-(26)#\[\begin{align} +
+(26)#\[\begin{align} \dot{v} &= \frac{T}{m} \cos \alpha - \frac{D}{m} - g \sin \gamma \\ \dot{\gamma} &= \frac{T}{m v} \sin \alpha + \frac{L}{m v} - \frac{g \cos \gamma}{v} \\ \dot{h} &= v \sin \gamma \\ @@ -1165,7 +1165,7 @@

Building and running the problem -
<dymos.phase.phase.Phase at 0x7f01bcf53af0>
+
<dymos.phase.phase.Phase at 0x7f75608036d0>
@@ -1309,8 +1309,9 @@

Building and running the problem
INFO: checking out_of_order
 

INFO:check_config:checking out_of_order
@@ -1426,20 +1427,19 @@ 
Building and running the problem
Coloring for 'traj.phases.rto.rhs_all' (class BalancedFieldODEComp)
+
+Coloring for 'traj.phases.rto.rhs_all' (class BalancedFieldODEComp)
 
 Jacobian shape: (132, 60)  ( 9.79% nonzero)
 FWD solves: 16   REV solves: 0
 Total colors vs. total size: 16 vs 60  (73.3% improvement)
 
 Sparsity computed using tolerance: 1e-25
-Time to compute sparsity: 0.020197 sec.
-Time to compute coloring: 0.014614 sec.
+Time to compute sparsity: 0.024386 sec.
+Time to compute coloring: 0.017943 sec.
 Memory to compute coloring: 0.000000 MB.
 
 Coloring for 'traj.phases.v1_to_vr.rhs_all' (class BalancedFieldODEComp)
@@ -1449,8 +1449,8 @@ 
Building and running the problem
Full total jacobian was computed 3 times, taking 1.429048 seconds.
+
Full total jacobian was computed 3 times, taking 1.872126 seconds.
 Total jacobian shape: (178, 166) 
 
 
@@ -1486,8 +1486,8 @@ 
Building and running the problem
/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/recorders/sqlite_recorder.py:227: UserWarning:The existing case recorder file, dymos_solution.db, is being overwritten.
+

+

 
INFO: checking out_of_order
 

 

-
/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/recorders/sqlite_recorder.py:227: UserWarning:The existing case recorder file, dymos_solution.db, is being overwritten.
-INFO:check_config:checking out_of_order
+
INFO:check_config:checking out_of_order
 

 

 
INFO: checking system
@@ -988,14 +990,14 @@ 
Building and running the problem
Coloring for 'traj.phases.br_to_v1.rhs_all' (class ExplicitFuncComp)
 
-Jacobian shape: (132, 60)  ( 9.79% nonzero)
+Jacobian shape: (132, 60)  ( 9.81% nonzero)
 FWD solves: 16   REV solves: 0
 Total colors vs. total size: 16 vs 60  (73.3% improvement)
 
 Sparsity computed using tolerance: 1e-25
-Time to compute sparsity: 0.345507 sec.
-Time to compute coloring: 0.068077 sec.
-Memory to compute coloring: 1.644531 MB.
+Time to compute sparsity: 0.464049 sec.
+Time to compute coloring: 0.095167 sec.
+Memory to compute coloring: 0.000000 MB.
 

 

 
/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/core/system.py:1659: DerivativesWarning:'traj.phases.rto.rhs_all' <class ExplicitFuncComp>: No partials found but coloring was requested.  Declaring ALL partials as dense (method='jax')
@@ -1003,13 +1005,13 @@ 
Building and running the problem
Coloring for 'traj.phases.rto.rhs_all' (class ExplicitFuncComp)
 
-Jacobian shape: (132, 60)  ( 9.79% nonzero)
+Jacobian shape: (132, 60)  ( 9.77% nonzero)
 FWD solves: 16   REV solves: 0
 Total colors vs. total size: 16 vs 60  (73.3% improvement)
 
 Sparsity computed using tolerance: 1e-25
-Time to compute sparsity: 0.326953 sec.
-Time to compute coloring: 0.068471 sec.
+Time to compute sparsity: 0.435331 sec.
+Time to compute coloring: 0.091807 sec.
 Memory to compute coloring: 0.000000 MB.
 

 

@@ -1023,8 +1025,8 @@ 
Building and running the problem
Full total jacobian was computed 3 times, taking 4.719833 seconds.
+
Full total jacobian was computed 3 times, taking 6.299375 seconds.
 Total jacobian shape: (178, 166) 
 
 
@@ -1067,8 +1069,8 @@ 
Building and running the problem
 
System dynamics#

 
From the free-body diagram above, the evolution of the state variables is given by the following ordinary differential equations (ODE).

-

-(13)#\[\begin{align}
+

+(13)#\[\begin{align}
     \frac{d x}{d t} &= v \sin(\theta) \\
     \frac{d y}{d t} &= -v \cos(\theta) \\
     \frac{d v}{d t} &= g \cos(\theta)
@@ -556,8 +556,8 @@ 
The initial and final conditions
-(14)#\[\begin{align}
+

+(14)#\[\begin{align}
     x_0 &= 0 \\
     y_0 &= 10 \\
     v_0 &= 0
@@ -565,8 +565,8 @@ 
The initial and final conditions
-(15)#\[\begin{align}
+

+(15)#\[\begin{align}
     x_f &= 10 \\
     y_f &= 5 \\
     v_f &= \mathrm{free}
@@ -732,27 +732,27 @@ 
Testing the ODE
Model viewer data has already been recorded for Driver.
 

 

-
Full total jacobian was computed 3 times, taking 0.030923 seconds.
+
Full total jacobian was computed 3 times, taking 0.036669 seconds.
 Total jacobian shape: (40, 50) 
 
 
@@ -862,8 +862,8 @@ 
Solving the problem with Legendre-Gauss-Lobatto collocation in Dymos

 

@@ -1016,7 +1016,7 @@ 
Solving the problem with Legendre-Gauss-Lobatto collocation in Dymos
/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/recorders/sqlite_recorder.py:227: UserWarning:The existing case recorder file, dymos_solution.db, is being overwritten.
 

 

-
Full total jacobian was computed 3 times, taking 0.017201 seconds.
+
Full total jacobian was computed 3 times, taking 0.022284 seconds.
 Total jacobian shape: (12, 51) 
 
 
@@ -1025,10 +1025,10 @@ 
Solving the problem with Legendre-Gauss-Lobatto collocation in DymosSolving the problem with Legendre-Gauss-Lobatto collocation in Dymos

 

diff --git a/examples/brachistochrone/brachistochrone_tandem_phases.html b/examples/brachistochrone/brachistochrone_tandem_phases.html
index d9edc83b9..75990ff8f 100644
--- a/examples/brachistochrone/brachistochrone_tandem_phases.html
+++ b/examples/brachistochrone/brachistochrone_tandem_phases.html
@@ -682,7 +682,7 @@ 
Setup and run
Model viewer data has already been recorded for Driver.
 

 

-
Full total jacobian was computed 3 times, taking 0.284912 seconds.
+
Full total jacobian was computed 3 times, taking 0.340832 seconds.
 Total jacobian shape: (223, 287) 
 

 

@@ -691,9 +691,9 @@ 
Setup and run
/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/visualization/opt_report/opt_report.py:634: UserWarning: Attempting to set identical low and high ylims makes transformation singular; automatically expanding.
@@ -1482,10 +1482,10 @@ 
Plots#
     
   
   
-    

+