# [AeroSandbox](https://peterdsharpe.github.io/AeroSandbox/) :airplane:
by [Peter Sharpe](https://peterdsharpe.github.io) (<pds [at] mit [dot] edu>)
[](https://pepy.tech/project/aerosandbox)
[](https://pepy.tech/project/aerosandbox)
[](https://github.com/peterdsharpe/AeroSandbox/actions/workflows/run-pytest.yml)
[](https://pypi.python.org/pypi/aerosandbox)
[](https://aerosandbox.readthedocs.io/en/master/?badge=master)
[](https://opensource.org/licenses/MIT)
**AeroSandbox is a Python package that helps you design and optimize aircraft and other engineered systems.**
At its heart, AeroSandbox is an optimization suite that combines the ease-of-use of [familiar NumPy syntax](aerosandbox/numpy) with the power of [modern automatic differentiation](./tutorial/10%20-%20Miscellaneous/03%20-%20Resources%20on%20Automatic%20Differentiation.md).
This automatic differentiation dramatically improves optimization performance on large problems: **design problems with tens of thousands of decision variables solve in seconds on a laptop**. AeroSandbox also comes with dozens of end-to-end-differentiable aerospace physics models, allowing you to **simultaneously optimize an aircraft's aerodynamics, structures, propulsion, mission trajectory, stability, and more.**
Keeping AeroSandbox easy to learn and use is a top priority. *Complexity is optional* - you can use AeroSandbox's built-in physics models where helpful, or you can drop in arbitrary custom physics models of your own.
```
pip install aerosandbox[full]
```
-----
### What can I do with AeroSandbox?
Use AeroSandbox to design and optimize entire aircraft:
<table>
<tr>
<td width="50%" valign="top">
<p align="center">
<a href="https://github.com/peterdsharpe/Feather-RC-Glider"><i>Feather</i> (an ultra-lightweight 1-meter-class RC motor glider)</a>
</p>
<img src="https://raw.githubusercontent.com/peterdsharpe/Feather-RC-Glider/master/CAD/feather.png" alt="Feather first page">
</td>
<td width="50%" valign="top">
<p align="center">
<a href="https://github.com/peterdsharpe/solar-seaplane-preliminary-sizing"><i>SEAWAY-Mini</i> (a solar-electric, 13' wingspan seaplane)</a>
</p>
<img src="https://raw.githubusercontent.com/peterdsharpe/solar-seaplane-preliminary-sizing/main/CAD/renders/seaway_mini_packet_Page_1.png" alt="Seaway-Mini first page">
</td>
</tr>
</table>
Use AeroSandbox to support real-world aircraft development programs, all the way from your very first sketch to your first-flight and beyond:
<table>
<tr>
<td width="50%" valign="top">
<p align="center">
<a href="https://github.com/peterdsharpe/DawnDesignTool">Initial concept sketches + sizing of <i>Dawn</i> (a solar-electric airplane for climate science research) in AeroSandbox, Spring 2020</a>
</p>
<img src="./media/images/dawn1-first-sketch.png" alt="Dawn initial design">
</td>
<td width="50%" valign="top">
<p align="center">
<a href="https://youtu.be/CyTzx9UCvyo"><i>Dawn</i> (later renamed <i>SACOS</i>) in first flight, Fall 2022</a>
</p>
<p align="center"><a href="https://www.electra.aero/news/sacos-first-flight">(A massive build effort with excellent engineering and coordination by Electra.aero!)</a></p>
<img src="./media/images/SACOS%20First%20Flight%20Zoomed.jpg" alt="SACOS first flight">
</td>
</tr>
</table>
Use AeroSandbox to explore counterintuitive, complicated design tradeoffs, all at the earliest stages of conceptual design *where these insights make the most difference*:
<table>
<tr>
<td width="33%" valign="top">
<p align="center">
<a href="https://github.com/peterdsharpe/DawnDesignTool">Exploring how big a solar airplane needs to be to fly, as a function of seasonality and latitude</a>
</p>
<img src="https://github.com/peterdsharpe/DawnDesignTool/raw/master/docs/30kg_payload.svg" alt="Dawn seasonality latitude tradespace">
</td>
<td width="33%" valign="top">
<p align="center">
<a href="https://www.popularmechanics.com/military/aviation/a13938789/mit-developing-mach-08-rocket-drone-for-the-air-force/">Exploring how the mission range of <i>Firefly</i>, a Mach 0.8 rocket drone, changes if we add an altitude limit, simultaneously optimizing aircraft design and trajectories</a>
</p>
<img src="./media/images/firefly-range-ceiling-trade.png" alt="Firefly range ceiling trade">
</td>
<td width="33%" valign="top">
<p align="center">
<a href="https://github.com/peterdsharpe/transport-aircraft">Exploring how many LH2 aircraft classes an airline fleet needs to cover the market, considering off-design performance</a>
</p>
<img src="https://github.com/peterdsharpe/transport-aircraft/raw/master/figures/lh2_market_segmentation_2.svg" alt="LH2 Market Coverage">
</td>
</tr>
</table>
Use AeroSandbox as a pure aerodynamics toolkit:
<table>
<tr>
<td width="33%" valign="top">
<p align="center">
<a href="https://github.com/peterdsharpe/AeroSandbox/blob/master/tutorial/06%20-%20Aerodynamics/01%20-%20AeroSandbox%203D%20Aerodynamics%20Tools/01%20-%20Vortex%20Lattice%20Method/01%20-%20Vortex%20Lattice%20Method.ipynb">VLM simulation of a glider, aileron deflections of +-30°</a>
</p>
<img src="./media/images/vlm3_with_control_surfaces.png" alt="VLM simulation">
</td>
<td width="33%" valign="top">
<p align="center">
<a href="https://github.com/peterdsharpe/AeroSandbox/blob/master/tutorial/06%20-%20Aerodynamics/01%20-%20AeroSandbox%203D%20Aerodynamics%20Tools/01%20-%20Vortex%20Lattice%20Method/01%20-%20Vortex%20Lattice%20Method.ipynb">Aerodynamic shape optimization of a wing planform, using an arbitrary objective and constraints</a>
</p>
<img src="./media/images/wing_optimization.png" alt="Wing optimization">
</td>
<td width="33%" valign="top">
<p align="center">
<a href="https://github.com/peterdsharpe/AeroSandbox/blob/master/tutorial/06%20-%20Aerodynamics/02%20-%20AeroSandbox%202D%20Aerodynamics%20Tools/02%20-%20NeuralFoil%20Optimization.ipynb">Optimize airfoil shapes with aerodynamic, structural, and manufacturing considerations</a>
</p>
<img src="./media/images/airfoil_optimization.png" alt="Airfoil optimization">
</td>
</tr>
</table>
Among many other discplines:
<table>
<tr>
<td width="50%" valign="top">
<p align="center">
Structural optimization of a composite tube spar
</p>
<img src="./media/images/beam-optimization.png" alt="Beam optimization">
</td>
<td width="50%" valign="top">
<p align="center">
<a href="https://github.com/peterdsharpe/AeroSandbox/blob/master/aerosandbox/library/propulsion_electric.py">Electric motor analysis for propeller matching</a>
</p>
<img src="./media/images/motor_perf.png" alt="Motor performance">
</td>
</tr>
<tr>
<td>
<p align="center" valign="top">
<a href="https://github.com/peterdsharpe/transport-aircraft">Tools to analyze unconventional propulsion (e.g., LH2)</a>
</p>
<img src="https://github.com/peterdsharpe/transport-aircraft/raw/master/figures/three_view_annotated.svg" alt="LH2 airplane three-view">
</td>
<td>
<p align="center" valign="top">
<a href="https://github.com/peterdsharpe/AeroSandbox/tree/master/aerosandbox/library/weights">Detailed weights estimation for aircraft ranging from micro-UAVs to airliners</a>
</p>
<img src="https://github.com/peterdsharpe/transport-aircraft/raw/master/figures/mass_budget.png" alt="Mass Budget">
</td>
</tr>
</table>
Easily interface AeroSandbox with all your favorite tools:
<table>
<tr>
<td width="33%" valign="top">
<p align="center">
Other conceptual design tools (AVL, XFLR5, XFoil, ASWING, MSES, etc.)
</p>
<img src="./media/images/airfoil_contours.png" alt="XFoil">
</td>
<td width="33%" valign="top">
<p align="center">
CAD tools via STEP export (SolidWorks, Fusion 360, etc.)
</p>
<p align="center">
(STL, OBJ, etc. supported too)
</p>
<img src="https://github.com/peterdsharpe/solar-seaplane-preliminary-sizing/raw/main/CAD/renders/raytrace-lowres.jpg" alt="CAD">
</td>
<td width="33%" valign="top">
<p align="center">
User-provided models + code (for custom aerodynamics, structures, propulsion, or anything else - e.g., for optimizing flight through a probabilistic wind field, shown below)
</p>
<img src="./media/images/wind_speeds_model.png" alt="Wind speed">
</td>
</tr>
</table>
Or, throw all the airplane-design-specific code out entirely, and use AeroSandbox purely as an optimization solver or as a solver for nonlinear systems of equations (or ODEs, or PDEs):
<table>
<tr>
<td width="50%" valign="top">
<p align="center">
<a href="https://github.com/peterdsharpe/AeroSandbox/blob/develop/tutorial/01%20-%20Optimization%20and%20Math/01%20-%202D%20Rosenbrock.ipynb">Optimize the 2D Rosenbrock function</a>
</p>
<img src="./media/images/optimization.png" alt="Optimization">
</td>
<td width="50%" valign="top">
<p align="center">
<a href="https://github.com/peterdsharpe/AeroSandbox/tree/develop/tutorial/03%20-%20Trajectory%20Optimization%20and%20Optimal%20Control/01%20-%20Solving%20ODEs%20with%20AeroSandbox">Specify the Falkner Skan ODE (nonlinear, 3rd-order BVP) and let AeroSandbox automatically take care of the discretization, solution, and even inverse solving.</a>
</p>
<img src="./media/images/falkner-skan.png" alt="FS ODE">
</td>
</tr>
</table>
And much, much more. Best of all, combine these tools arbitrarily without any loss in optimization speed and without any tedious derivative math, all thanks to AeroSandbox's end-to-end automatic-differentiability.
## Getting Started
### Installation
In short:
* `pip install aerosandbox[full]` for a complete install.
* `pip install aerosandbox` for a lightweight (headless) installation with minimal dependencies. All optimization, numerics, and physics models are included, but optional visualization dependencies are skipped.
For more installation details (e.g., if you're new to Python), [see here](./INSTALLATION.md).
### Tutorials, Examples, and Documentation
To get started, [check out the tutorials folder here](./tutorial/)! All tutorials are viewable in-browser, or you can open them as Jupyter notebooks by cloning this repository.
For a more detailed and theory-heavy introduction to AeroSandbox, please see the [author's PhD thesis](./tutorial/sharpe-pds-phd-AeroAstro-2024-thesis.pdf) and [master's thesis](./tutorial/sharpe-pds-sm-AeroAstro-2021-thesis.pdf).
For a developer-oriented description of AeroSandbox internal modules, [please see the developer README](aerosandbox/README.md).
For fully-detailed API documentation, see [the documentation website](https://aerosandbox.readthedocs.io/en/master/).
You can print documentation and examples for any AeroSandbox object by using the built-in `help()` function (e.g., `help(asb.Airplane)`). AeroSandbox code is also documented *extensively* in the source and contains hundreds of unit test examples, so examining the source code can also be useful.
### Usage Details
#### Units
One final point to note: **all inputs and outputs to AeroSandbox are expressed in base SI units, or derived units thereof** (e.g., m, kg, sec, N, m/s, J, Pa). Since this unit system is [coherent](https://en.wikipedia.org/wiki/Coherence_(units_of_measurement)), an [enormous number of quantities](https://en.wikipedia.org/wiki/SI_derived_unit) can be converted without any scaling factors. This improves readability and reduces the likelihood of errors.
There are only two exceptions to this SI-everywhere rule:
1. If alternate units are noted in a variable name's suffix. For example:
* `battery_capacity` → Joules
* `battery_capacity_watt_hours` → Watt-hours
* `aircraft_endurance` → Seconds
* `aircraft_endurance_hours` → Hours
2. Angle of attack (`alpha`, α) and sideslip angle (`beta`, β) are given in degrees due to long-standing aerospace convention. All other angles and angular rates use radians.
Also, in case of any confusion on the units of a function's inputs and outputs, units are listed on all function docstrings.
If you wish to use other units, consider using [`aerosandbox.tools.units`](./aerosandbox/tools/units.py) to convert easily.
## Project Details
### Contributing
Please feel free to join the development of AeroSandbox - contributions are always so welcome! If you have a change you'd like to make, the easiest way to do that is by submitting a pull request.
The text file [`CONTRIBUTING.md`](./CONTRIBUTING.md) has more details for developers and power users.
If you've already made several additions and would like to be involved in a more long-term capacity, please message me!
Contact information can be found next to my name near the top of this README.
### Donating
If you like this software, please consider donating to support development [via PayPal](https://paypal.me/peterdsharpe)
or [GitHub Sponsors](https://github.com/sponsors/peterdsharpe/)! Proceeds will go towards more coffee for the grad students.
### Bugs
Please, please report all bugs by [creating a new issue](https://github.com/peterdsharpe/AeroSandbox/issues)!
### Versioning
AeroSandbox loosely uses [semantic versioning](https://semver.org/), which should give you an idea of whether or not you can probably expect backward-compatibility and/or new features from any given update.
For more details, see the [changelog](./CHANGELOG.md).
### Citation & Commercial Use
If you find AeroSandbox useful in your research, please cite the following publications:
[The author's PhD thesis](./tutorial/sharpe-pds-phd-AeroAstro-2024-thesis.pdf):
```bibtex
@phdthesis{aerosandbox_phd_thesis,
title = {Accelerating Practical Engineering Design Optimization with Computational Graph Transformations},
author = {Sharpe, Peter D.},
school = {Massachusetts Institute of Technology},
year = {2024},
note = {Available at \url{https://dspace.mit.edu/handle/1721.1/157809}}
}
```
[The author's Master's thesis](./tutorial/sharpe-pds-sm-AeroAstro-2021-thesis.pdf):
```bibtex
@mastersthesis{aerosandbox_masters_thesis,
title = {AeroSandbox: A Differentiable Framework for Aircraft Design Optimization},
author = {Sharpe, Peter D.},
school = {Massachusetts Institute of Technology},
year = {2021},
note = {Available at \url{https://dspace.mit.edu/handle/1721.1/140023}}
}
```
Commercial users: I'm more than happy to discuss consulting work for active AeroSandbox support if this package proves helpful - use the email address in the header of this README to get in touch.
#### License
[MIT License applies, full terms here](LICENSE.txt). In short: use AeroSandbox for anything you want (commercial or non-commercial). AeroSandbox is released in hope that it will be useful but without any warranty of merchantability (either express or implied).
If you use AeroSandbox, public attribution is appreciated. In particular, it's especially helpful when industry users share when and how they're using AeroSandbox, since it helps the team prioritize feature development.
## Stargazers over time
[](https://starchart.cc/peterdsharpe/AeroSandbox)
## Supported by
<a href="https://jb.gg/OpenSourceSupport"><img src="https://resources.jetbrains.com/storage/products/company/brand/logos/jetbrains.svg" alt="JetBrains logo."></a>
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"description": "# [AeroSandbox](https://peterdsharpe.github.io/AeroSandbox/) :airplane:\n\nby [Peter Sharpe](https://peterdsharpe.github.io) (<pds [at] mit [dot] edu>)\n\n[](https://pepy.tech/project/aerosandbox)\n[](https://pepy.tech/project/aerosandbox)\n[](https://github.com/peterdsharpe/AeroSandbox/actions/workflows/run-pytest.yml)\n[](https://pypi.python.org/pypi/aerosandbox)\n[](https://aerosandbox.readthedocs.io/en/master/?badge=master)\n[](https://opensource.org/licenses/MIT)\n\n**AeroSandbox is a Python package that helps you design and optimize aircraft and other engineered systems.**\n\nAt its heart, AeroSandbox is an optimization suite that combines the ease-of-use of [familiar NumPy syntax](aerosandbox/numpy) with the power of [modern automatic differentiation](./tutorial/10%20-%20Miscellaneous/03%20-%20Resources%20on%20Automatic%20Differentiation.md).\n\nThis automatic differentiation dramatically improves optimization performance on large problems: **design problems with tens of thousands of decision variables solve in seconds on a laptop**. AeroSandbox also comes with dozens of end-to-end-differentiable aerospace physics models, allowing you to **simultaneously optimize an aircraft's aerodynamics, structures, propulsion, mission trajectory, stability, and more.** \n\nKeeping AeroSandbox easy to learn and use is a top priority. *Complexity is optional* - you can use AeroSandbox's built-in physics models where helpful, or you can drop in arbitrary custom physics models of your own.\n\n```\npip install aerosandbox[full]\n```\n\n-----\n\n### What can I do with AeroSandbox?\n\nUse AeroSandbox to design and optimize entire aircraft:\n\n<table>\n <tr>\n <td width=\"50%\" valign=\"top\">\n <p align=\"center\">\n <a href=\"https://github.com/peterdsharpe/Feather-RC-Glider\"><i>Feather</i> (an ultra-lightweight 1-meter-class RC motor glider)</a>\n </p>\n <img src=\"https://raw.githubusercontent.com/peterdsharpe/Feather-RC-Glider/master/CAD/feather.png\" alt=\"Feather first page\">\n </td>\n <td width=\"50%\" valign=\"top\">\n <p align=\"center\">\n <a href=\"https://github.com/peterdsharpe/solar-seaplane-preliminary-sizing\"><i>SEAWAY-Mini</i> (a solar-electric, 13' wingspan seaplane)</a>\n </p>\n <img src=\"https://raw.githubusercontent.com/peterdsharpe/solar-seaplane-preliminary-sizing/main/CAD/renders/seaway_mini_packet_Page_1.png\" alt=\"Seaway-Mini first page\">\n </td>\n </tr>\n</table>\n\nUse AeroSandbox to support real-world aircraft development programs, all the way from your very first sketch to your first-flight and beyond:\n\n<table>\n <tr>\n <td width=\"50%\" valign=\"top\">\n <p align=\"center\">\n <a href=\"https://github.com/peterdsharpe/DawnDesignTool\">Initial concept sketches + sizing of <i>Dawn</i> (a solar-electric airplane for climate science research) in AeroSandbox, Spring 2020</a>\n </p>\n <img src=\"./media/images/dawn1-first-sketch.png\" alt=\"Dawn initial design\">\n </td>\n <td width=\"50%\" valign=\"top\">\n <p align=\"center\">\n <a href=\"https://youtu.be/CyTzx9UCvyo\"><i>Dawn</i> (later renamed <i>SACOS</i>) in first flight, Fall 2022</a>\n </p>\n <p align=\"center\"><a href=\"https://www.electra.aero/news/sacos-first-flight\">(A massive build effort with excellent engineering and coordination by Electra.aero!)</a></p>\n <img src=\"./media/images/SACOS%20First%20Flight%20Zoomed.jpg\" alt=\"SACOS first flight\">\n </td>\n </tr>\n</table>\n\nUse AeroSandbox to explore counterintuitive, complicated design tradeoffs, all at the earliest stages of conceptual design *where these insights make the most difference*:\n\n<table>\n\t<tr>\n\t\t<td width=\"33%\" valign=\"top\">\n\t\t\t<p align=\"center\">\n\t\t\t\t<a href=\"https://github.com/peterdsharpe/DawnDesignTool\">Exploring how big a solar airplane needs to be to fly, as a function of seasonality and latitude</a>\n\t\t\t</p>\n\t\t\t<img src=\"https://github.com/peterdsharpe/DawnDesignTool/raw/master/docs/30kg_payload.svg\" alt=\"Dawn seasonality latitude tradespace\">\n\t\t</td>\n\t\t<td width=\"33%\" valign=\"top\">\n\t\t\t<p align=\"center\">\n\t\t\t\t<a href=\"https://www.popularmechanics.com/military/aviation/a13938789/mit-developing-mach-08-rocket-drone-for-the-air-force/\">Exploring how the mission range of <i>Firefly</i>, a Mach 0.8 rocket drone, changes if we add an altitude limit, simultaneously optimizing aircraft design and trajectories</a>\n\t\t\t</p>\n\t\t\t<img src=\"./media/images/firefly-range-ceiling-trade.png\" alt=\"Firefly range ceiling trade\">\n\t\t</td>\n\t\t<td width=\"33%\" valign=\"top\">\n\t\t\t<p align=\"center\">\n\t\t\t\t<a href=\"https://github.com/peterdsharpe/transport-aircraft\">Exploring how many LH2 aircraft classes an airline fleet needs to cover the market, considering off-design performance</a>\n\t\t\t</p>\n\t\t\t<img src=\"https://github.com/peterdsharpe/transport-aircraft/raw/master/figures/lh2_market_segmentation_2.svg\" alt=\"LH2 Market Coverage\">\n\t\t</td>\n\t</tr>\n</table>\n\nUse AeroSandbox as a pure aerodynamics toolkit:\n\n<table>\n\t<tr>\n\t\t<td width=\"33%\" valign=\"top\">\n\t\t\t<p align=\"center\">\n\t\t\t\t<a href=\"https://github.com/peterdsharpe/AeroSandbox/blob/master/tutorial/06%20-%20Aerodynamics/01%20-%20AeroSandbox%203D%20Aerodynamics%20Tools/01%20-%20Vortex%20Lattice%20Method/01%20-%20Vortex%20Lattice%20Method.ipynb\">VLM simulation of a glider, aileron deflections of +-30\u00b0</a>\n\t\t\t</p>\n\t\t\t<img src=\"./media/images/vlm3_with_control_surfaces.png\" alt=\"VLM simulation\">\n\t\t</td>\n\t\t<td width=\"33%\" valign=\"top\">\n\t\t\t<p align=\"center\">\n\t\t\t\t<a href=\"https://github.com/peterdsharpe/AeroSandbox/blob/master/tutorial/06%20-%20Aerodynamics/01%20-%20AeroSandbox%203D%20Aerodynamics%20Tools/01%20-%20Vortex%20Lattice%20Method/01%20-%20Vortex%20Lattice%20Method.ipynb\">Aerodynamic shape optimization of a wing planform, using an arbitrary objective and constraints</a>\n\t\t\t</p>\n\t\t\t<img src=\"./media/images/wing_optimization.png\" alt=\"Wing optimization\">\n\t\t</td>\n\t\t<td width=\"33%\" valign=\"top\">\n\t\t\t<p align=\"center\">\n\t\t\t\t<a href=\"https://github.com/peterdsharpe/AeroSandbox/blob/master/tutorial/06%20-%20Aerodynamics/02%20-%20AeroSandbox%202D%20Aerodynamics%20Tools/02%20-%20NeuralFoil%20Optimization.ipynb\">Optimize airfoil shapes with aerodynamic, structural, and manufacturing considerations</a>\n\t\t\t</p>\n\t\t\t<img src=\"./media/images/airfoil_optimization.png\" alt=\"Airfoil optimization\">\n\t\t</td>\n\t</tr>\n</table>\n\nAmong many other discplines:\n\n<table>\n\t<tr>\n\t\t<td width=\"50%\" valign=\"top\">\n\t\t\t<p align=\"center\">\n\t\t\t\tStructural optimization of a composite tube spar\n\t\t\t</p>\n\t\t\t<img src=\"./media/images/beam-optimization.png\" alt=\"Beam optimization\">\n\t\t</td>\n\t\t<td width=\"50%\" valign=\"top\">\n\t\t\t<p align=\"center\">\n\t\t\t\t<a href=\"https://github.com/peterdsharpe/AeroSandbox/blob/master/aerosandbox/library/propulsion_electric.py\">Electric motor analysis for propeller matching</a>\n\t\t\t</p>\n\t\t\t<img src=\"./media/images/motor_perf.png\" alt=\"Motor performance\">\n\t\t</td>\n\t</tr>\n\t<tr>\n\t\t<td>\n\t\t\t<p align=\"center\" valign=\"top\">\n\t\t\t\t<a href=\"https://github.com/peterdsharpe/transport-aircraft\">Tools to analyze unconventional propulsion (e.g., LH2)</a>\n\t\t\t</p>\n\t\t\t<img src=\"https://github.com/peterdsharpe/transport-aircraft/raw/master/figures/three_view_annotated.svg\" alt=\"LH2 airplane three-view\">\n\t\t</td>\n\t\t<td>\n\t\t\t<p align=\"center\" valign=\"top\">\n\t\t\t\t<a href=\"https://github.com/peterdsharpe/AeroSandbox/tree/master/aerosandbox/library/weights\">Detailed weights estimation for aircraft ranging from micro-UAVs to airliners</a>\n\t\t\t</p>\n\t\t\t<img src=\"https://github.com/peterdsharpe/transport-aircraft/raw/master/figures/mass_budget.png\" alt=\"Mass Budget\">\n\t\t</td>\n</tr>\n</table>\n\nEasily interface AeroSandbox with all your favorite tools:\n\n<table>\n <tr>\n <td width=\"33%\" valign=\"top\">\n <p align=\"center\">\n Other conceptual design tools (AVL, XFLR5, XFoil, ASWING, MSES, etc.)\n </p>\n <img src=\"./media/images/airfoil_contours.png\" alt=\"XFoil\">\n </td> \n <td width=\"33%\" valign=\"top\">\n <p align=\"center\">\n CAD tools via STEP export (SolidWorks, Fusion 360, etc.)\n </p>\n\t\t\t\t<p align=\"center\">\n\t\t\t\t(STL, OBJ, etc. supported too)\n\t\t\t\t</p>\n <img src=\"https://github.com/peterdsharpe/solar-seaplane-preliminary-sizing/raw/main/CAD/renders/raytrace-lowres.jpg\" alt=\"CAD\">\n </td>\n <td width=\"33%\" valign=\"top\">\n\t\t\t<p align=\"center\">\n\t\t\t\tUser-provided models + code (for custom aerodynamics, structures, propulsion, or anything else - e.g., for optimizing flight through a probabilistic wind field, shown below) \n\t\t\t</p>\n\t\t\t<img src=\"./media/images/wind_speeds_model.png\" alt=\"Wind speed\">\n\t\t</td>\n\t</tr>\n</table>\n\nOr, throw all the airplane-design-specific code out entirely, and use AeroSandbox purely as an optimization solver or as a solver for nonlinear systems of equations (or ODEs, or PDEs):\n\n<table>\n\t<tr>\n\t\t<td width=\"50%\" valign=\"top\">\n\t\t\t<p align=\"center\">\n\t\t\t\t<a href=\"https://github.com/peterdsharpe/AeroSandbox/blob/develop/tutorial/01%20-%20Optimization%20and%20Math/01%20-%202D%20Rosenbrock.ipynb\">Optimize the 2D Rosenbrock function</a>\n\t\t\t</p>\n\t\t\t<img src=\"./media/images/optimization.png\" alt=\"Optimization\">\n\t\t</td>\n\t\t<td width=\"50%\" valign=\"top\">\n\t\t\t<p align=\"center\">\n\t\t\t\t<a href=\"https://github.com/peterdsharpe/AeroSandbox/tree/develop/tutorial/03%20-%20Trajectory%20Optimization%20and%20Optimal%20Control/01%20-%20Solving%20ODEs%20with%20AeroSandbox\">Specify the Falkner Skan ODE (nonlinear, 3rd-order BVP) and let AeroSandbox automatically take care of the discretization, solution, and even inverse solving.</a>\n\t\t\t</p>\n\t\t\t<img src=\"./media/images/falkner-skan.png\" alt=\"FS ODE\">\n\t\t</td>\n</tr>\n</table>\n\nAnd much, much more. Best of all, combine these tools arbitrarily without any loss in optimization speed and without any tedious derivative math, all thanks to AeroSandbox's end-to-end automatic-differentiability.\n\n## Getting Started\n\n### Installation\n\nIn short:\n\n* `pip install aerosandbox[full]` for a complete install.\n\n* `pip install aerosandbox` for a lightweight (headless) installation with minimal dependencies. All optimization, numerics, and physics models are included, but optional visualization dependencies are skipped.\n\nFor more installation details (e.g., if you're new to Python), [see here](./INSTALLATION.md).\n\n### Tutorials, Examples, and Documentation\n\nTo get started, [check out the tutorials folder here](./tutorial/)! All tutorials are viewable in-browser, or you can open them as Jupyter notebooks by cloning this repository.\n\nFor a more detailed and theory-heavy introduction to AeroSandbox, please see the [author's PhD thesis](./tutorial/sharpe-pds-phd-AeroAstro-2024-thesis.pdf) and [master's thesis](./tutorial/sharpe-pds-sm-AeroAstro-2021-thesis.pdf).\n\nFor a developer-oriented description of AeroSandbox internal modules, [please see the developer README](aerosandbox/README.md).\n\nFor fully-detailed API documentation, see [the documentation website](https://aerosandbox.readthedocs.io/en/master/).\n\nYou can print documentation and examples for any AeroSandbox object by using the built-in `help()` function (e.g., `help(asb.Airplane)`). AeroSandbox code is also documented *extensively* in the source and contains hundreds of unit test examples, so examining the source code can also be useful.\n\n### Usage Details\n\n#### Units\n\nOne final point to note: **all inputs and outputs to AeroSandbox are expressed in base SI units, or derived units thereof** (e.g., m, kg, sec, N, m/s, J, Pa). Since this unit system is [coherent](https://en.wikipedia.org/wiki/Coherence_(units_of_measurement)), an [enormous number of quantities](https://en.wikipedia.org/wiki/SI_derived_unit) can be converted without any scaling factors. This improves readability and reduces the likelihood of errors.\n\nThere are only two exceptions to this SI-everywhere rule:\n1. If alternate units are noted in a variable name's suffix. For example:\n\n * `battery_capacity` \u2192 Joules\n * `battery_capacity_watt_hours` \u2192 Watt-hours\n * `aircraft_endurance` \u2192 Seconds\n * `aircraft_endurance_hours` \u2192 Hours\n\n2. Angle of attack (`alpha`, \u03b1) and sideslip angle (`beta`, \u03b2) are given in degrees due to long-standing aerospace convention. All other angles and angular rates use radians. \n \nAlso, in case of any confusion on the units of a function's inputs and outputs, units are listed on all function docstrings.\n\nIf you wish to use other units, consider using [`aerosandbox.tools.units`](./aerosandbox/tools/units.py) to convert easily.\n\n## Project Details\n\n### Contributing\n\nPlease feel free to join the development of AeroSandbox - contributions are always so welcome! If you have a change you'd like to make, the easiest way to do that is by submitting a pull request.\n\nThe text file [`CONTRIBUTING.md`](./CONTRIBUTING.md) has more details for developers and power users.\n\nIf you've already made several additions and would like to be involved in a more long-term capacity, please message me!\nContact information can be found next to my name near the top of this README.\n\n### Donating\n\nIf you like this software, please consider donating to support development [via PayPal](https://paypal.me/peterdsharpe)\nor [GitHub Sponsors](https://github.com/sponsors/peterdsharpe/)! Proceeds will go towards more coffee for the grad students.\n\n### Bugs\n\nPlease, please report all bugs by [creating a new issue](https://github.com/peterdsharpe/AeroSandbox/issues)!\n\n### Versioning\n\nAeroSandbox loosely uses [semantic versioning](https://semver.org/), which should give you an idea of whether or not you can probably expect backward-compatibility and/or new features from any given update.\n\nFor more details, see the [changelog](./CHANGELOG.md).\n\n### Citation & Commercial Use\n\nIf you find AeroSandbox useful in your research, please cite the following publications:\n\n[The author's PhD thesis](./tutorial/sharpe-pds-phd-AeroAstro-2024-thesis.pdf):\n\n```bibtex\n@phdthesis{aerosandbox_phd_thesis,\n title = {Accelerating Practical Engineering Design Optimization with Computational Graph Transformations},\n author = {Sharpe, Peter D.},\n school = {Massachusetts Institute of Technology}, \n year = {2024},\n note = {Available at \\url{https://dspace.mit.edu/handle/1721.1/157809}}\n}\n```\n\n[The author's Master's thesis](./tutorial/sharpe-pds-sm-AeroAstro-2021-thesis.pdf):\n\n```bibtex\n@mastersthesis{aerosandbox_masters_thesis,\n title = {AeroSandbox: A Differentiable Framework for Aircraft Design Optimization},\n author = {Sharpe, Peter D.},\n school = {Massachusetts Institute of Technology},\n year = {2021},\n note = {Available at \\url{https://dspace.mit.edu/handle/1721.1/140023}}\n}\n```\n\nCommercial users: I'm more than happy to discuss consulting work for active AeroSandbox support if this package proves helpful - use the email address in the header of this README to get in touch.\n\n#### License\n\n[MIT License applies, full terms here](LICENSE.txt). In short: use AeroSandbox for anything you want (commercial or non-commercial). AeroSandbox is released in hope that it will be useful but without any warranty of merchantability (either express or implied). \n\nIf you use AeroSandbox, public attribution is appreciated. In particular, it's especially helpful when industry users share when and how they're using AeroSandbox, since it helps the team prioritize feature development.\n\n## Stargazers over time\n\n[](https://starchart.cc/peterdsharpe/AeroSandbox) \n\n## Supported by\n\n<a href=\"https://jb.gg/OpenSourceSupport\"><img src=\"https://resources.jetbrains.com/storage/products/company/brand/logos/jetbrains.svg\" alt=\"JetBrains logo.\"></a>\n",
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