### Setup OpenMDAO Problem

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/_sources/tutorials/minimal_example.rst.txt

Initializes the OpenMDAO problem with the MissionAnalysis model and configures the Newton solver for steady flight force balance.

```python
prob = om.Problem()
prob.model = MissionAnalysis(num_nodes=11)
prob.model.nonlinear_solver = om.NewtonSolver(solve_subsystems=True)
prob.model.nonlinear_solver.options['maxiter'] = 10
prob.model.nonlinear_solver.options['iprint'] = 2
prob.model.linear_solver = om.DirectSolver()
prob.setup()
```

--------------------------------

### Setup and Run TBM Analysis

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/tutorials/turboprop.html

Configures the OpenMDAO problem, sets mission parameters, and provides initial guesses for convergence.

```python
def run_tbm_analysis():
    # Set up OpenMDAO to analyze the airplane
    nn = 11
    prob = om.Problem()
    prob.model = TBMAnalysisGroup(num_nodes=nn)
    prob.model.nonlinear_solver = om.NewtonSolver(iprint=2, solve_subsystems=True)
    prob.model.linear_solver = om.DirectSolver()
    prob.setup()

    # Set required mission parameters. Each phase needs a vertical speed and airspeed.
    # The entire mission needs a cruise altitude and range.
    prob.set_val("climb.fltcond|vs", np.full(nn, 1500.0), units="ft/min")
    prob.set_val("climb.fltcond|Ueas", np.full(nn, 124.0), units="kn")
    prob.set_val("cruise.fltcond|vs", np.full(nn, 0.01), units="ft/min")
    prob.set_val("cruise.fltcond|Ueas", np.full(nn, 201.0), units="kn")
    prob.set_val("descent.fltcond|vs", np.full(nn, -600.0), units="ft/min")
    prob.set_val("descent.fltcond|Ueas", np.full(nn, 140.0), units="kn")

    prob.set_val("cruise|h0", 28e3, units="ft")
    prob.set_val("mission_range", 500, units="nmi")

    # Guesses for takeoff speeds to help with convergence
    prob.set_val("v0v1.fltcond|Utrue", np.full(nn, 50), units="kn")
    prob.set_val("v1vr.fltcond|Utrue", np.full(nn, 85), units="kn")
    prob.set_val("v1v0.fltcond|Utrue", np.full(nn, 85), units="kn")
```

--------------------------------

### Configure Model Setup and Inputs/Outputs

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/tutorials/minimal_example.html

Sets up required OpenConcept inputs, custom aircraft parameters, and model outputs, while declaring partial derivatives using the complex step method.

```python
def setup(self):
    nn = self.options["num_nodes"]

    # ======== Inputs passed from the mission analysis ========
    # These are required by OpenConcept
    self.add_input("fltcond|CL", shape=nn)  # lift coefficient
    self.add_input("throttle", shape=nn)  # throttle from 0 to 1

    # These are additional inputs used by the model
    self.add_input("fltcond|q", shape=nn, units="Pa")  # dynamic pressure
    self.add_input("ac|geom|wing|S_ref", shape=1, units="m**2")  # wing planform area
    self.add_input("ac|weights|TOW", shape=1, units="kg")  # constant weight value
    self.add_input("ac|propulsion|max_thrust", shape=1, units="N")
    self.add_input("ac|aero|L_over_D", shape=1)

    # ======== Outputs sent back to the mission analysis ========
    self.add_output("weight", shape=nn, units="kg")
    self.add_output("drag", shape=nn, units="N")
    self.add_output("thrust", shape=nn, units="N")

    # ======== Use complex step for this simple example ========
    self.declare_partials(["*"], ["*"], method="cs")
```

--------------------------------

### Define Mission Setup

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/tutorials/integrator.html

Configures independent variables and adds a mission subsystem to the OpenMDAO model.

```python
def setup(self):
    iv = self.add_subsystem("ac_vars", om.IndepVarComp(), promotes_outputs=["*"])
    iv.add_output("ac|geom|wing|S_ref", val=25.0, units="m**2")
    iv.add_output("ac|weights|TOW", val=5e3, units="kg")
    iv.add_output("ac|propulsion|max_thrust", val=1e4, units="N")
    iv.add_output("ac|propulsion|TSFC", val=20.0, units="g/kN/s")
    iv.add_output("ac|aero|L_over_D", val=10.0)

    # Define the mission
    self.add_subsystem(
        "mission",
        BasicMission(aircraft_model=AircraftWithFuelBurn, num_nodes=self.options["num_nodes"]),
        promotes_inputs=["ac|*"],
    )
```

--------------------------------

### Setup OpenMDAO Problem

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/tutorials/minimal_example.html

Initializes the OpenMDAO problem with the MissionAnalysis model, configures Newton and Direct solvers, and sets mission profile parameters.

```python
def setup_problem(model=MissionAnalysis):
    """
    Define the OpenMDAO problem
    """
    nn = 11
    prob = om.Problem()
    prob.model = model(num_nodes=nn)

    # Set up the solver
    prob.model.nonlinear_solver = om.NewtonSolver(iprint=2, solve_subsystems=True)
    prob.model.linear_solver = om.DirectSolver()

    # Set up the problem
    prob.setup()

    # Define the mission profile by setting vertical speed and airspeed for each segment
    prob.set_val("mission.climb.fltcond|vs", np.full(nn, 500.0), units="ft/min")
    prob.set_val("mission.cruise.fltcond|vs", np.full(nn, 0.0), units="ft/min")
    prob.set_val("mission.descent.fltcond|vs", np.full(nn, -500.0), units="ft/min")
    prob.set_val("mission.climb.fltcond|Ueas", np.full(nn, 150.0), units="kn")
    prob.set_val("mission.cruise.fltcond|Ueas", np.full(nn, 200.0), units="kn")
    prob.set_val("mission.descent.fltcond|Ueas", np.full(nn, 150.0), units="kn")

    # The mission also needs the cruise altitude and the range
    prob.set_val("mission.cruise|h0", 15e3, units="ft")
    prob.set_val("mission.mission_range", 400.0, units="nmi")

    return prob
```

--------------------------------

### Run Integrator Script

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/_sources/tutorials/integrator.rst.txt

Executes the problem setup and adds variables of interest for plotting.

```python
    # rst Run (beg)
    prob.setup()
    prob.run_model()
    print('Fuel burned:', prob.get_val('mission.fuel_integrator.fuel_burned_final', units='kg'))
    # rst Run (end)
```

--------------------------------

### Initialize Integrator

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/_sources/tutorials/integrator.rst.txt

Configures the Integrator component with integration points, time setup, and integration scheme.

```python
        self.add_subsystem('fuel_integrator', Integrator(num_nodes=nn, diff_units='s', time_setup='duration', method='simpson'))
        self.add_subsystem('fuel_burn_comp', AddIntegratedQuantity(name='fuel_burned', rate_name='fuel_flow', units='kg'))
        self.connect('fuel_burn_comp.fuel_burned', 'fuel_integrator.fuel_burned')
        self.connect('fuel_flow', 'fuel_integrator.fuel_flow')
```

--------------------------------

### Setup Problem and Mission Profile

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/_sources/tutorials/turboprop.rst.txt

Configures the OpenMDAO problem, sets initial guesses for takeoff speeds, and adjusts throttle settings for takeoff segments.

```python
    # rst Setup problem (beg)
    prob = om.Problem()
    prob.model = om.Group()
    
    # ... (setup code omitted for brevity) ...
    
    # Set initial guesses for the takeoff speeds
    # This helps the solver converge more quickly
    prob.set_val('mission.takeoff.v0', 0.0, units='kn')
    prob.set_val('mission.takeoff.v1', 80.0, units='kn')
    prob.set_val('mission.takeoff.vr', 90.0, units='kn')
    prob.set_val('mission.takeoff.v2', 100.0, units='kn')
    
    # Set the structural fudge factor
    # This is a multiplier on the structural weights to account for
    # additional weights not modeled by the empty weight component
    prob.set_val('structural_fudge', 1.1)
    
    # Decrease the throttle values for the takeoff segments
    # The default is 1.0, but we set it to 0.826 for the takeoff
    prob.set_val('mission.takeoff.throttle', 0.826)
    # rst Setup problem (end)
```

--------------------------------

### openconcept.utilities.linearinterp.LinearInterpolator

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/_srcdocs/packages/utilities/linearinterp.html

A component that creates a linearly interpolated set of points including the start and end values.

```APIDOC
## class LinearInterpolator

### Description
Creates a linearly interpolated set of points including two end points.

### Inputs
- **start_val** (float) - Starting value (units set from "units" option)
- **end_val** (float) - Ending value (units set from "units" option)

### Outputs
- **vec** (float) - Vector of linearly interpolated points

### Options
- **units** (str, None) - Units for inputs and outputs
- **num_nodes** (int) - Number of linearly interpolated points to produce (minimum/default 2)
```

--------------------------------

### Initialize OpenConcept Model Options

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/tutorials/minimal_example.html

Defines the required num_nodes and flight_phase options for an OpenConcept aircraft model.

```python
def initialize(self):
    self.options.declare("num_nodes", default=1, desc="Number of analysis points per phase")
    self.options.declare("flight_phase", default=None)  # required by OpenConcept but unused in this example
```

--------------------------------

### Initialize Model Options

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/tutorials/turboprop.html

Initializes the model options for number of nodes and flight phase.

```python
def initialize(self):
    self.options.declare("num_nodes", default=1)
    self.options.declare("flight_phase", default=None)
```

--------------------------------

### Configure TBM analysis problem

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/tutorials/turboprop.html

Initializes the OpenMDAO problem with solvers, mission parameters, and takeoff segment guesses for the TBM aircraft model.

```python
def run_tbm_analysis():
    # Set up OpenMDAO to analyze the airplane
    nn = 11
    prob = om.Problem()
    prob.model = TBMAnalysisGroup(num_nodes=nn)
    prob.model.nonlinear_solver = om.NewtonSolver(iprint=2, solve_subsystems=True)
    prob.model.linear_solver = om.DirectSolver()
    prob.setup()

    # Set required mission parameters. Each phase needs a vertical speed and airspeed.
    # The entire mission needs a cruise altitude and range.
    prob.set_val("climb.fltcond|vs", np.full(nn, 1500.0), units="ft/min")
    prob.set_val("climb.fltcond|Ueas", np.full(nn, 124.0), units="kn")
    prob.set_val("cruise.fltcond|vs", np.full(nn, 0.01), units="ft/min")
    prob.set_val("cruise.fltcond|Ueas", np.full(nn, 201.0), units="kn")
    prob.set_val("descent.fltcond|vs", np.full(nn, -600.0), units="ft/min")
    prob.set_val("descent.fltcond|Ueas", np.full(nn, 140.0), units="kn")

    prob.set_val("cruise|h0", 28e3, units="ft")
    prob.set_val("mission_range", 500, units="nmi")

    # Guesses for takeoff speeds to help with convergence
    prob.set_val("v0v1.fltcond|Utrue", np.full(nn, 50), units="kn")
    prob.set_val("v1vr.fltcond|Utrue", np.full(nn, 85), units="kn")
    prob.set_val("v1v0.fltcond|Utrue", np.full(nn, 85), units="kn")

    # Set some airplane-specific values. The throttle edits are to derate the takeoff power of the PT6A
    prob["climb.OEW.structural_fudge"] = 1.67
    prob["v0v1.throttle"] = np.full(nn, 0.826)
    prob["v1vr.throttle"] = np.full(nn, 0.826)
    prob["rotate.throttle"] = np.full(nn, 0.826)

    return prob
```

--------------------------------

### Execute Problem and Print Results

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/_sources/tutorials/turboprop.rst.txt

Runs the optimization/analysis and outputs key performance metrics, followed by plotting the takeoff mission phase.

```python
    # rst Run (beg)
    # Run the problem
    prob.run_model()
    
    # Print some values from the solved problem
    print('Takeoff distance:', prob.get_val('mission.takeoff.distance', units='ft'))
    print('Fuel used:', prob.get_val('mission.fuel_used', units='lb'))
    
    # Plot the takeoff portion of the mission
    # The plotting section from previous tutorials is used here
    # to add a plot showing the takeoff portion of the mission
    plot_takeoff(prob)
    # rst Run (end)
```

--------------------------------

### VectorSplitComp.__init__

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/_srcdocs/packages/utilities.math/combine_split_comp.html

Initializes the VectorSplitComp component to split input vectors into multiple output variables.

```APIDOC
## VectorSplitComp.__init__(output_names=None, input_name=None, vec_sizes=None, length=1, val=1.0, **kwargs)

### Description
Initializes a system to split a single input vector into multiple output vectors.

### Parameters
- **output_names** (iterable of str) - Required - Names of the output (split) variables in this component’s namespace.
- **input_name** (str) - Required - Name of the input variable for this system.
- **vec_sizes** (iterable of int) - Required - Lengths of the first dimension of each input vector.
- **length** (int) - Optional - Length of the second dimension of the input and output vectors. Default is 1.
- **val** (float or list or tuple or ndarray) - Optional - Initial value of the variable. Default is 1.0.
- **kwargs** (str) - Optional - Additional arguments such as units or description.
```

--------------------------------

### Add and Configure an Integrator

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/tutorials/integrator.html

Instantiate an Integrator component and define the integrand to perform numerical integration.

```python
integ = self.add_subsystem(
    "fuel_integrator", Integrator(num_nodes=nn, diff_units="s", time_setup="duration", method="simpson")
)
integ.add_integrand("fuel_burned", rate_name="fuel_flow", units="kg")

self.connect("fuel_flow_calc.fuel_flow", "fuel_integrator.fuel_flow")
```

--------------------------------

### Import Necessary Modules

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/tutorials/minimal_example.html

Initial imports required for OpenMDAO, OpenConcept mission analysis, and NumPy.

```python
import openmdao.api as om
from openconcept.mission import BasicMission
import numpy as np


```

--------------------------------

### Execute Analysis and Visualize Results

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/tutorials/minimal_example.html

Runs the model, generates an N2 diagram, and creates matplotlib plots for altitude, vertical speed, airspeed, and throttle.

```python
if __name__ == "__main__":
    # Process command line argument to optionally not show figures and N2 diagram
    import argparse

    parser = argparse.ArgumentParser()
    parser.add_argument(
        "--hide_visuals",
        default=False,
        action="store_true",
        help="Do not show matplotlib figure or open N2 diagram in browser",
    )
    hide_viz = parser.parse_args().hide_visuals

    # Setup the problem and run the analysis
    prob = setup_problem()
    prob.run_model()

    # Generate N2 diagram
    om.n2(prob, outfile="minimal_example_n2.html", show_browser=not hide_viz)

    # Create plot with results
    import matplotlib.pyplot as plt

    fig, axs = plt.subplots(2, 2, constrained_layout=True)
    axs = axs.flatten()  # change 2x2 mtx of axes into 4-element vector

    # Define variables to plot
    plot_vars = [
        {"var": "fltcond|h", "name": "Altitude", "units": "ft"},
        {"var": "fltcond|vs", "name": "Vertical speed", "units": "ft/min"},
        {"var": "fltcond|Utrue", "name": "True airspeed", "units": "kn"},
        {"var": "throttle", "name": "Throttle", "units": None},
    ]

    for idx_fig, var in enumerate(plot_vars):
        axs[idx_fig].set_xlabel("Range (nmi)")
        axs[idx_fig].set_ylabel(f"{var['name']}" if var["units"] is None else f"{var['name']} ({var['units']})")

        # Loop through each flight phase and plot the current variable from each
        for phase in ["climb", "cruise", "descent"]:
            axs[idx_fig].plot(
                prob.get_val(f"mission.{phase}.range", units="nmi"),
                prob.get_val(f"mission.{phase}.{var['var']}", units=var["units"]),
                "-o",
                c="tab:blue",
                markersize=2.0,
            )

    fig.savefig("minimal_example_results.svg", transparent=True)
    if not hide_viz:
        plt.show()
```

--------------------------------

### Importing OpenConcept components for turboprop modeling

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/tutorials/turboprop.html

Required imports for the TBM 850 aircraft model, including propulsion, aerodynamics, weight, and mission analysis modules.

```python
import numpy as np
import openmdao.api as om

# OpenConcept imports for the airplane model
from openconcept.propulsion import TurbopropPropulsionSystem
from openconcept.aerodynamics import PolarDrag
from openconcept.weights import SingleTurboPropEmptyWeight
from openconcept.mission import FullMissionAnalysis
from openconcept.examples.aircraft_data.TBM850 import data as acdata
from openconcept.utilities import AddSubtractComp, Integrator, DictIndepVarComp
```

--------------------------------

### Configure Mission Profile Parameters

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/tutorials/minimal_example.html

Sets vertical speed, airspeed, cruise altitude, and range for mission segments.

```python
# Define the mission profile by setting vertical speed and airspeed for each segment
    prob.set_val("mission.climb.fltcond|vs", np.full(nn, 500.0), units="ft/min")
    prob.set_val("mission.cruise.fltcond|vs", np.full(nn, 0.0), units="ft/min")
    prob.set_val("mission.descent.fltcond|vs", np.full(nn, -500.0), units="ft/min")
    prob.set_val("mission.climb.fltcond|Ueas", np.full(nn, 150.0), units="kn")
    prob.set_val("mission.cruise.fltcond|Ueas", np.full(nn, 200.0), units="kn")
    prob.set_val("mission.descent.fltcond|Ueas", np.full(nn, 150.0), units="kn")

    # The mission also needs the cruise altitude and the range
    prob.set_val("mission.cruise|h0", 15e3, units="ft")
    prob.set_val("mission.mission_range", 400.0, units="nmi")

    return prob
```

--------------------------------

### Run Mission Analysis

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/_sources/tutorials/minimal_example.rst.txt

Executes the mission analysis model after the problem has been configured.

```python
prob.run_model()
```

--------------------------------

### Add Weight and Fuel Integration Subsystems

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/tutorials/turboprop.html

Configures the OEW estimation, fuel flow integration, and weight calculation components within the OpenConcept model.

```python
# Empty weight calculation; requires many aircraft inputs, see SingleTurboPropEmptyWeight source for more details.
# This OEW calculation is not used in the weight calculation, but it is a useful output for aircraft design/optimization.
self.add_subsystem(
    "OEW",
    SingleTurboPropEmptyWeight(),
    promotes_inputs=["*", ("P_TO", "ac|propulsion|engine|rating")],
    promotes_outputs=["OEW"],
)
self.connect("propmodel.prop1.component_weight", "W_propeller")
self.connect("propmodel.eng1.component_weight", "W_engine")

# Airplanes that consume fuel need to integrate fuel usage across the mission and subtract it from TOW
intfuel = self.add_subsystem(
    "intfuel",
    Integrator(num_nodes=nn, method="simpson", diff_units="s", time_setup="duration"),
    promotes_outputs=["fuel_used_final"],
)
intfuel.add_integrand("fuel_used", rate_name="fuel_flow", val=1.0, units="kg")
self.connect("propmodel.fuel_flow", "intfuel.fuel_flow")

# Compute weight as MTOW minus fuel burned (assumes takeoff at MTOW)
self.add_subsystem(
    "weight",
    AddSubtractComp(
        output_name="weight",
        input_names=["ac|weights|MTOW", "fuel_used"],
        units="kg",
        vec_size=[1, nn],
        scaling_factors=[1, -1],
    ),
    promotes_inputs=["ac|weights|MTOW"],
    promotes_outputs=["weight"],
)
self.connect("intfuel.fuel_used", "weight.fuel_used")
```

--------------------------------

### openconcept.atmospherics.density_comp.DensityComp

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/_srcdocs/packages/atmospherics/density_comp.html

An OpenMDAO ExplicitComponent that computes density from pressure and temperature.

```APIDOC
## class openconcept.atmospherics.density_comp.DensityComp(**kwargs)

### Description
This component computes density from pressure and temperature. It is adapted from the methodology described by Jasa, Hwang, and Martins (2018).

### Inputs
- **fltcond|p** (float) - Pressure at flight condition (vector, Pa)
- **fltcond|T** (float) - Temperature at flight condition (vector, K)

### Outputs
- **fltcond|rho** (float) - Density at flight condition (vector, kg/m^3)

### Options
- **num_nodes** (int) - Number of analysis points to run, i.e. length of vector inputs (scalar, dimensionless)
```

--------------------------------

### CFM56()

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/_srcdocs/packages/propulsion/cfm56.html

Initializes the CFM56 turbofan engine component.

```APIDOC
## CFM56(num_nodes=1, plot=False)

### Description
Returns an OpenMDAO component for an engine deck to model the CFM56 turbofan.

### Parameters
- **num_nodes** (int) - Optional - Number of analysis points to run (sets vector length; default 1).
- **plot** (bool) - Optional - Whether to plot results (default False).

### Inputs
- **throttle** (float) - Engine throttle (0 to 1+). Controls power and fuel flow.
- **fltcond|h** (float) - Altitude.
- **fltcond|M** (float) - Mach number.

### Outputs
- **thrust** (float) - Thrust developed by the engine (lbf).
- **fuel_flow** (float) - Fuel flow consumed (lbm/s).
- **T4** (float) - Turbine inlet temperature (Rankine).
```

--------------------------------

### Importing Integrator and Dependencies

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/tutorials/integrator.html

Required imports for integrating OpenConcept components and the Integrator class.

```python
import openmdao.api as om
from openconcept.examples.minimal import Aircraft, setup_problem  # build off this aircraft model
from openconcept.mission import BasicMission
from openconcept.utilities import Integrator
```

--------------------------------

### Run Mission Analysis and Plot Results

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/tutorials/integrator.html

Executes the mission analysis problem and generates plots for flight conditions and fuel consumption metrics.

```python
if __name__ == "__main__":
    # Process command line argument to optionally not show figures and N2 diagram
    import argparse

    parser = argparse.ArgumentParser()
    parser.add_argument(
        "--hide_visuals",
        default=False,
        action="store_true",
        help="Do not show matplotlib figure or open N2 diagram in browser",
    )
    hide_viz = parser.parse_args().hide_visuals

    # Setup the problem and run the analysis
    prob = setup_problem(model=MissionAnalysisWithFuelBurn)
    prob.run_model()

    # Generate N2 diagram
    om.n2(prob, outfile="minimal_integrator_n2.html", show_browser=not hide_viz)

    # Create plot with results
    import matplotlib.pyplot as plt

    fig, axs = plt.subplots(2, 3, figsize=[9, 4.8], constrained_layout=True)
    axs = axs.flatten()  # change 2x3 mtx of axes into 4-element vector

    # Define variables to plot
    plot_vars = [
        {"var": "fltcond|h", "name": "Altitude", "units": "ft"},
        {"var": "fltcond|vs", "name": "Vertical speed", "units": "ft/min"},
        {"var": "fltcond|Utrue", "name": "True airspeed", "units": "kn"},
        {"var": "throttle", "name": "Throttle", "units": None},
        {"var": "fuel_flow_calc.fuel_flow", "name": "Fuel flow", "units": "g/s"},
        {"var": "weight", "name": "Weight", "units": "kg"},
    ]

    for idx_fig, var in enumerate(plot_vars):
        axs[idx_fig].set_xlabel("Range (nmi)")
        axs[idx_fig].set_ylabel(f"{var['name']}" if var["units"] is None else f"{var['name']} ({var['units']})")

        # Loop through each flight phase and plot the current variable from each
        for phase in ["climb", "cruise", "descent"]:
            axs[idx_fig].plot(
                prob.get_val(f"mission.{phase}.range", units="nmi"),
                prob.get_val(f"mission.{phase}.{var['var']}", units=var["units"]),
                "-o",
                c="tab:blue",
                markersize=2.0,
            )

    fig.savefig("minimal_integrator_results.svg", transparent=True)
    if not hide_viz:
        plt.show()
```

--------------------------------

### ElementMultiplyDivideComp

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/_srcdocs/packages/utilities.math/multiply_divide_comp.html

Initializes a new instance of the ElementMultiplyDivideComp class to perform vectorized element-wise multiplication and division.

```APIDOC
## class openconcept.utilities.math.multiply_divide_comp.ElementMultiplyDivideComp

### Description
Compute a vectorized element-wise multiplication and/or division. The result is calculated as (a * b / c ...) * scaling_factor.

### Constructor
`ElementMultiplyDivideComp(output_name=None, input_names=None, vec_size=1, length=1, val=1.0, scaling_factor=1, divide=None, input_units=None, **kwargs)`

### Parameters
- **output_name** (str) - Required - Name of the result variable.
- **input_names** (iterable of str) - Required - Names of the input variables.
- **vec_size** (int) - Optional - Length of the first dimension of the input/output vectors. Default is 1.
- **length** (int) - Optional - Length of the second dimension of the input/output vectors. Default is 1.
- **scaling_factor** (numeric) - Optional - Scaling factor to apply to the whole system. Default is 1.
- **divide** (iterable of bool or None) - Optional - True to use division, False to use multiplication. Default is None.
- **val** (float/list/tuple/ndarray) - Optional - Initial value of the variable. Default is 1.0.
- **input_units** (iterable of str) - Optional - Units for each input vector.

### Methods
#### add_equation(output_name, input_names, vec_size=1, length=1, val=1.0, res_units=None, desc='', lower=None, upper=None, ref=1.0, ref0=0.0, res_ref=None, scaling_factor=1, divide=None, input_units=None, tags=None)
Adds a multiplication/division relation to the component.
```

--------------------------------

### Define Mission with Integrator

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/_sources/tutorials/integrator.rst.txt

Sets up the mission analysis component using the AircraftWithFuelBurn model.

```python
    # rst Mission (beg)
    prob.model.add_subsystem('mission', MissionWithFuelBurn(num_nodes=nn, aircraft_model=AircraftWithFuelBurn))
    prob.model.set_val('mission.ac|propulsion|TSFC', 0.5, units='1/hr')
    # rst Mission (end)
```

--------------------------------

### Implement Compute Method

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/tutorials/minimal_example.html

Defines the compute method to calculate weight, thrust, and drag based on input parameters.

```python
def compute(self, inputs, outputs):
    outputs["weight"] = inputs["ac|weights|TOW"]
    outputs["thrust"] = inputs["throttle"] * inputs["ac|propulsion|max_thrust"]
    outputs["drag"] = (
        inputs["fltcond|q"] * inputs["fltcond|CL"] * inputs["ac|geom|wing|S_ref"] / inputs["ac|aero|L_over_D"]
    )
```

--------------------------------

### Define a minimal aircraft model and mission analysis

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/tutorials/minimal_example.html

This script defines an explicit OpenMDAO component for aircraft physics and a group for mission analysis, followed by a function to configure the OpenMDAO problem.

```python
"""
This is a minimal example meant to show the absolute
simplest aircraft model and mission analysis you can
set up. This does not use OpenConcept's models for
the aircraft propulsion and aerodynamics, but it
does use the mission analysis methods.
"""

# rst Imports (beg)
import openmdao.api as om
from openconcept.mission import BasicMission
import numpy as np

# rst Imports (end)


# rst Aircraft (beg)
class Aircraft(om.ExplicitComponent):
    """
    An overly simplified aircraft model. This one is defined as an explicit component to use simple equations
    to compute weight, drag, and thrust. In practice, it would be an OpenMDAO group that integrates models for
    propulsion, aerodynamics, weights, etc.
    """

    # rst Options
    def initialize(self):
        self.options.declare("num_nodes", default=1, desc="Number of analysis points per phase")
        self.options.declare("flight_phase", default=None)  # required by OpenConcept but unused in this example

    # rst Setup
    def setup(self):
        nn = self.options["num_nodes"]

        # ======== Inputs passed from the mission analysis ========
        # These are required by OpenConcept
        self.add_input("fltcond|CL", shape=nn)  # lift coefficient
        self.add_input("throttle", shape=nn)  # throttle from 0 to 1

        # These are additional inputs used by the model
        self.add_input("fltcond|q", shape=nn, units="Pa")  # dynamic pressure
        self.add_input("ac|geom|wing|S_ref", shape=1, units="m**2")  # wing planform area
        self.add_input("ac|weights|TOW", shape=1, units="kg")  # constant weight value
        self.add_input("ac|propulsion|max_thrust", shape=1, units="N")
        self.add_input("ac|aero|L_over_D", shape=1)

        # ======== Outputs sent back to the mission analysis ========
        self.add_output("weight", shape=nn, units="kg")
        self.add_output("drag", shape=nn, units="N")
        self.add_output("thrust", shape=nn, units="N")

        # ======== Use complex step for this simple example ========
        self.declare_partials(["*"], ["*"], method="cs")

    # rst Compute
    def compute(self, inputs, outputs):
        outputs["weight"] = inputs["ac|weights|TOW"]
        outputs["thrust"] = inputs["throttle"] * inputs["ac|propulsion|max_thrust"]
        outputs["drag"] = (
            inputs["fltcond|q"] * inputs["fltcond|CL"] * inputs["ac|geom|wing|S_ref"] / inputs["ac|aero|L_over_D"]
        )
        # rst Aircraft (end)


# rst Mission (beg)
class MissionAnalysis(om.Group):
    """
    OpenMDAO group for basic three-phase climb, cruise, descent mission.
    The only top-level aircraft variable that the aircraft model uses is
    the wing area, so that must be defined.
    """

    def initialize(self):
        self.options.declare("num_nodes", default=1, desc="Number of analysis points per phase")

    def setup(self):
        iv = self.add_subsystem("ac_vars", om.IndepVarComp(), promotes_outputs=["*"])
        iv.add_output("ac|geom|wing|S_ref", val=25.0, units="m**2")
        iv.add_output("ac|weights|TOW", val=5e3, units="kg")
        iv.add_output("ac|propulsion|max_thrust", val=1e4, units="N")
        iv.add_output("ac|aero|L_over_D", val=10.0)

        # Define the mission
        self.add_subsystem(
            "mission",
            BasicMission(aircraft_model=Aircraft, num_nodes=self.options["num_nodes"]),
            promotes_inputs=["ac|*"],
        )
        # rst Mission (end)


# rst Setup problem (beg)
def setup_problem(model=MissionAnalysis):
    """
    Define the OpenMDAO problem
    """
    nn = 11
    prob = om.Problem()
    prob.model = model(num_nodes=nn)

    # Set up the solver
    prob.model.nonlinear_solver = om.NewtonSolver(iprint=2, solve_subsystems=True)
    prob.model.linear_solver = om.DirectSolver()

    # Set up the problem
    prob.setup()
```

--------------------------------

### Configure Aircraft Parameters

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/tutorials/turboprop.html

Sets structural fudge factors and throttle settings for the PT6A engine to derate takeoff power.

```python
    # Set some airplane-specific values. The throttle edits are to derate the takeoff power of the PT6A
    prob["climb.OEW.structural_fudge"] = 1.67
    prob["v0v1.throttle"] = np.full(nn, 0.826)
    prob["v1vr.throttle"] = np.full(nn, 0.826)
    prob["rotate.throttle"] = np.full(nn, 0.826)

    return prob
```

--------------------------------

### SimpleBattery

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/_srcdocs/packages/energy_storage/battery.html

A basic battery component that tracks power limits and generates heat, inheriting from OpenMDAO ExplicitComponent.

```APIDOC
## SimpleBattery

### Description
SimpleBattery is a component that models basic battery power limits and heat generation without tracking state of charge.

### Inputs
- **battery_weight** (float) - Weight of the battery pack (kg)
- **elec_load** (float) - Electric power draw upstream (W)

### Outputs
- **max_energy** (float) - Total energy at 100% SOC (Wh)
- **heat_out** (float) - Waste heat produced (W)
- **component_cost** (float) - Nonrecurring cost (USD)
- **component_sizing_margin** (float) - Sizing margin (dimensionless)

### Options
- **num_nodes** (int) - Number of analysis points
- **efficiency** (float) - Shaft power efficiency (0.0 to 1.0)
- **specific_power** (float) - Rated power per unit weight (W/kg)
- **specific_energy** (float) - Energy per unit weight (Wh/kg)
- **cost_inc** (float) - Cost per unit weight (USD/kg)
- **cost_base** (float) - Base cost (USD)
```

--------------------------------

### Define Mission Parameters with DictIndepVarComp

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/_sources/tutorials/turboprop.rst.txt

Uses a nested dictionary to define aircraft parameters, allowing for centralized configuration outside the main run script.

```python
    # rst Mission (beg)
    # Add aircraft parameters from the data file
    # The DictIndepVarComp allows us to define parameters in a separate file
    # and then pull them into the OpenMDAO problem
    ivc = prob.model.add_subsystem('params', om.IndepVarComp(), promotes=['*'])
    
    # We use a DictIndepVarComp to load the parameters from the TBM850 data file
    # This is a convenient way to manage a large number of parameters
    # The keys are separated by a pipe '|' to access nested dictionary values
    ivc = prob.model.add_subsystem('params', DictIndepVarComp(TBM850_data), promotes=['*'])
    ivc.add_output_from_dict('ac|weights|MTOW', 'MTOW')
    ivc.add_output_from_dict('ac|weights|W_fuel_max', 'W_fuel_max')
    ivc.add_output_from_dict('ac|aero|CLmax_land', 'CLmax_land')
    ivc.add_output_from_dict('ac|aero|CLmax_takeoff', 'CLmax_takeoff')
    ivc.add_output_from_dict('ac|aero|CD0_TO', 'CD0_TO')
    ivc.add_output_from_dict('ac|aero|CD0_cruise', 'CD0_cruise')
    ivc.add_output_from_dict('ac|aero|e', 'e')
    ivc.add_output_from_dict('ac|aero|AR', 'AR')
    ivc.add_output_from_dict('ac|aero|span', 'span')
    ivc.add_output_from_dict('ac|geom|S_ref', 'S_ref')
    
    # Add the mission group
    # The FullMissionAnalysis includes a balanced field length calculation
    # which is a more advanced mission analysis than the BasicMission
    prob.model.add_subsystem('mission', FullMissionAnalysis(num_nodes=11, 
                                                            aircraft_model=TBM850Turboprop,
                                                            takeoff_strategy='balanced_field'),
                             promotes_inputs=['*'],
                             promotes_outputs=['*'])
    # rst Mission (end)
```

--------------------------------

### Integrate Fuel Usage and Calculate Weight

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/tutorials/turboprop.html

Integrates fuel flow over time and subtracts the consumed fuel from the maximum takeoff weight.

```python
# Airplanes that consume fuel need to integrate fuel usage across the mission and subtract it from TOW
intfuel = self.add_subsystem(
    "intfuel",
    Integrator(num_nodes=nn, method="simpson", diff_units="s", time_setup="duration"),
    promotes_outputs=["fuel_used_final"],
)
intfuel.add_integrand("fuel_used", rate_name="fuel_flow", val=1.0, units="kg")
self.connect("propmodel.fuel_flow", "intfuel.fuel_flow")

# Compute weight as MTOW minus fuel burned (assumes takeoff at MTOW)
self.add_subsystem(
    "weight",
    AddSubtractComp(
        output_name="weight",
        input_names=["ac|weights|MTOW", "fuel_used"],
        units="kg",
        vec_size=[1, nn],
        scaling_factors=[1, -1],
    ),
    promotes_inputs=["ac|weights|MTOW"],
    promotes_outputs=["weight"],
),
self.connect("intfuel.fuel_used", "weight.fuel_used")
```

--------------------------------

### Cite OpenAeroStruct Integration Paper

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/_sources/index.rst.txt

BibTeX entry for referencing the journal paper regarding aerostructural wing optimization.

```bibtex
@article{Adler2022d,
	author = {Adler, Eytan J. and Martins, Joaquim R. R. A.},
	doi = {10.2514/1.c037096},
	issn = {1533-3868},
	journal = {Journal of Aircraft},
	month = {December},
	publisher = {American Institute of Aeronautics and Astronautics},
	title = {Efficient Aerostructural Wing Optimization Considering Mission Analysis},
	year = {2022}
	}
```

--------------------------------

### Cite the OpenAeroStruct journal paper

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/index.html

BibTeX entry for referencing the aerostructural wing optimization methodology.

```bibtex
@article{Adler2022d,
    author = {Adler, Eytan J. and Martins, Joaquim R. R. A.},
    doi = {10.2514/1.c037096},
    issn = {1533-3868},
    journal = {Journal of Aircraft},
    month = {December},
    publisher = {American Institute of Aeronautics and Astronautics},
    title = {Efficient Aerostructural Wing Optimization Considering Mission Analysis},
    year = {2022}
    }
```

--------------------------------

### BibTeX Citation for Thermal Management System Paper

Source: https://mdolab-openconcept.readthedocs-hosted.com/en/latest/_sources/publications.rst.txt

Use this BibTeX entry to cite the 2022 Aerospace journal paper on thermal management system optimization.

```bibtex
@article{Adler2022b,
	article-number = {243},
	author = {Adler, Eytan J. and Brelje, Benjamin J. and Martins, Joaquim R. R. A.},
	doi = {10.3390/aerospace9050243},
	issn = {2226-4310},
	journal = {Aerospace},
	keywords = {OpenMDAO, OpenConcept},
	month = apr,
	number = {5},
	title = {Thermal Management System Optimization for a Parallel Hybrid Aircraft Considering Mission Fuel Burn},
	volume = {9},
	year = {2022}
}
```