# Introduction
Waverider Generator is a python package which can be used to generate hypersonic waveriders based on an efficient parametrisation described in [1].
The method makes use of the oscultating cone inverse design method and four design parameters `X1`, `X2`, `X3` and `X4`.
Please consult the paper referenced for any further clarification on the geometrical meaning of these inputs.
<p align="center">
<img src="https://github.com/jade5638/waverider_generator/blob/main/waverider_example.png?raw=true" alt="Waverider example" width="500"/>
</p>
<p align="center">Example of generated waverider</p>
## Coordinate System
The coordinate system is defined such that:
- $x$ is the streamwise direction
- $y$ is the transverse direction
- $z$ is the spanwise direction
with the origin at the tip of the waverider.
<p align="center">
<img src="https://github.com/jade5638/waverider_generator/blob/main/waverider_axes.png?raw=true" alt="Coordinate System" width="500"/>
</p>
<p align="center">Coordinate System</p>
## Flow Field
### Oblique Shock
In the flat region of the shockwave, the lower surface is determined via the $\theta$- $\beta$ - $M_{\infty}$ equation, which relates the deflection angle $\theta$ to the shock angle $\beta$ in an oblique shock.
$$
\tan(\theta) = \frac{2 \cot\left(\beta\right) \left(M_{\infty}^2 \sin^2\left(\beta \right) - 1\right)}{M_{\infty}^2 (\gamma + \cos\left(2 \beta\right)) + 2}
$$
Where $\gamma=1.4$ is the ratio of specific heats for air and $M_{\infty}$ is the freestream Mach number.
### Osculating Cone Theory
In the curved region of the shockwave, the osculating cone theory is used whereby conical flow is locally applied at each osculating plane.
The Taylor-Maccoll ODE, which describes conical flow, is solved and the resulting streamlines are propagated until the back of the waverider is reached to produce the lower surface.
See [2] for more information on the Osculating Cone Theory.
## Required Inputs
- Design parameters `X1`, `X2`, `X3` and `X4`. Note this is entered as a list `dp` of four elements where the parameters are organised in the order listed here. Refer to the examples.
- Freestream Mach number `M_inf`.
- Shock angle in degrees `beta`.
- Height of the waverider at the base plane `height`. Note that the length of the waverider is determined as $height/\tan(\theta)$ so a user may choose to determine the height required for a desired length.
- Width of the waverider `width`. Note that this refers to half of the total width of the waverider due to the symmetry.
- Number of points to be used for interpolating the shockwave and the upper surface curve (`n_shockwave` and `n_upper_surface` respectively). Both are integers greater than 10 to preserve quality.
## Optional Inputs
- Number of osculating planes used in the generation of the geometry `n_planes`. Note that this doesn't include the symmetry plane and the tip. A minimum number of planes is set at 10 to preserve quality and this is the default value.
- Number of points in the streamwise direction for the generation of the upper surface as well as the flat part of the shockwave on the lower surface `n_streamwise`. A minimum is set at 10 to preserve quality and this is the default value.
- Maximum step to be used in the tracing of the streamlines for the lower surface `delta_streamwise`. Note this is entered as a percentage of the length of the waverider and a maximum is set at 20% to preserve quality. The default value is 5%.
## Summary of inputs
|Input|Type|Conditions|
|:-------------:|:--------------:|:--------------:|
| `X1`, `X2`, `X3` and `X4` | `list` | $0\leq X2,X3,X4 \leq 1$ <br> $0 \leq X1 < 1$ <br> $\frac{X2}{\left(1-X1\right)^4}\leq\ \frac{7}{64}\left(\frac{width}{height}\right)^4$<br>(see [1] for more information on this design condition) |
| `M_inf` | `float`, `int` | `M_inf>0` |
|`beta`| `float`, `int`| `0<beta<90`|
|`height`| `float`, `int`| `height>0`|
|`width`| `float`, `int`| `width>0`|
|`n_shockwave` and `n_upper_surface`| `int`| `n_shockwave,n_upper_surface>=10`
|`n_planes`|`int`|`n_planes>=10`|
|`n_streamise`|`int`|`n_streamwise>=10`|
|`delta_streamise`|`float`|`0<delta_streamwise<=0.2`|
# Usage and functionality
A user can create a `waverider` instance by importing the `waverider` class from `waverider_generator.generator`. Everything takes place inside the class constructor so the user only needs to initialise the instance to create the geometry. An example is shown below: <br>
```python
from waverider_generator.generator import waverider as wr
M_inf=5
beta=15
height=1.34
width=3
dp=[0.11,0.63,0,0.46]
n_planes=20
n_streamwise=10
delta_streamwise=0.1
waverider=wr(M_inf=M_inf,beta=beta,height=height,width=width,dp=dp,n_upper_surface=10000,n_shockwave=10000,n_planes=n_planes,n_streamwise=n_streamwise,delta_streamise=delta_streamwise)
```
## CAD Export
To export the geometry into a file CAD, the user can import the `to_CAD` function from `waverider_generator.cad_export`. An example is shown below: <br>
```python
#%%
# assuming a waverider instance has been created with the code above
from waverider_generator.cad_export import to_CAD
waverider_cad=to_CAD(waverider=waverider,sides='both',export=True,filename='waverider.step',scale=1000)
waverider_cad
```
The `to_CAD` function is detailed below:
|Input|Type|Conditions|Description|
|:-------------:|:--------------:|:--------------:|:--------------:|
| `waverider` | `waverider` | NA|`waverider` instance|
| `sides`| `str` | `"left"`, `"right"` or `"both"` <br> | Side(s) of the waverider to generate in the CAD|
|`export`| `bool` |`True` or `False`| Setting this to `True` exports the CAD to the current directory, `False` does not|
|`filename`| `str`| The extension must be one which `cadquery` can generate a CAD file in| Name of the CAD file to be created|
|`scale` (optional)|`float`,`int`| `scale>0`| Scale factor by which the final geometry is scaled. By default, cadquery exports geometries in mm so the default value for `scale` is 1000 to obtain dimensions in meters. Setting this to 1 keeps the dimensions in mm. It is recommended to keep the default value of 1000 and work in meters from the start.
|Output|Type|Conditions|Description|
|:-------------:|:--------------:|:--------------:|:--------------:|
`waverider_cad`| `cq.Solid` (cadquery solid) | NA | A cadquery solid corresponding to the waverider generated. This can be previewed in a Jupyter Notebook, therefore avoiding the step of exporting and importing into a seperate CAD software each time.|
<p align="center">
<img src="https://github.com/jade5638/waverider_generator/blob/main/cad_preview_example.png?raw=true" alt="Jupyter Notebook CAD preview example" width="500"/>
</p>
<p align="center">Jupyter Notebook CAD preview example</p>
## Plotting tools
The package also allows the user to plot basic figures to analyse the geometry generated before a CAD export. This is done by importing `Plot_Base_Plane` and `Plot_Leading_Edge` from `waverider_generator.plotting_tools`. An example, also included as an example file, is shown below
**Note** that the `latex` input into the plotting functions is a boolean and determines whether or not to plot the figure with the default LaTex font. The user is required to install a LaTex distribution on their system for this feature to work.
```python
#%%
from waverider_generator.generator import waverider as wr
from waverider_generator.plotting_tools import Plot_Base_Plane,Plot_Leading_Edge
import matplotlib.pyplot as plt
M_inf=5
beta=15
height=1.34
width=3
dp=[0.11,0.63,0,0.46]
n_planes=20
n_streamwise=10
delta_streamwise=0.1
waverider=wr(M_inf=M_inf,beta=beta,height=height,width=width,dp=dp,n_upper_surface=10000,n_shockwave=10000,n_planes=n_planes,n_streamwise=n_streamwise,delta_streamise=delta_streamwise)
#%%
'''
PLOT BASE PLANE
'''
base_plane=Plot_Base_Plane(waverider=waverider,latex=True)
#%%
'''
PLOT LEADING EDGE
'''
leading_edge=Plot_Leading_Edge(waverider=waverider=True,latex=True)
plt.show()
```
<p align="center">
<img src="https://raw.githubusercontent.com/jade5638/waverider_generator/2c5aba1915e3e87223f8f3444c2ae3c8b66c77a5/base_plane.svg" alt="Base Plane" width="500"/>
</p>
<p align="center">Base Plane</p>
<p align="center">
<img src="https://raw.githubusercontent.com/jade5638/waverider_generator/2c5aba1915e3e87223f8f3444c2ae3c8b66c77a5/leading_edge.svg" alt="LE" width="300"/>
</p>
<p align="center">Leading Edge Plot</p>
# Dependencies
The package requires the following libraries to be installed:
- numpy
- cadquery
- scipy
- matplotlib
Optional:
- a LaTex distribution such as MiKTex (refer to previous section)
# License
MIT License
Copyright (c) 2024 jade5638
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
# Citing
Please use the reference.bib file included to reference this work.
-----------
# References
[1] Jiwon Son, Chankyu Son, and Kwanjung Yee.
'A Novel Direct Optimization Framework for Hypersonic Waverider Inverse Design Methods'.
In: Aerospace 9.7 (June 2022), p. 348. issn: 2226-4310. doi: 10.3390/aerospace9070348.
[2] Helmut Sobieczky, F Dougherty, and Kevin Jones.
“Hypersonic Waverider Design from Given Shock Waves”. In: May 1990
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"description": "# Introduction\n\nWaverider Generator is a python package which can be used to generate hypersonic waveriders based on an efficient parametrisation described in [1].\nThe method makes use of the oscultating cone inverse design method and four design parameters `X1`, `X2`, `X3` and `X4`. \nPlease consult the paper referenced for any further clarification on the geometrical meaning of these inputs. \n\n<p align=\"center\">\n <img src=\"https://github.com/jade5638/waverider_generator/blob/main/waverider_example.png?raw=true\" alt=\"Waverider example\" width=\"500\"/>\n</p>\n<p align=\"center\">Example of generated waverider</p>\n\n## Coordinate System\nThe coordinate system is defined such that:\n- $x$ is the streamwise direction\n- $y$ is the transverse direction\n- $z$ is the spanwise direction\n\nwith the origin at the tip of the waverider.\n\n<p align=\"center\">\n <img src=\"https://github.com/jade5638/waverider_generator/blob/main/waverider_axes.png?raw=true\" alt=\"Coordinate System\" width=\"500\"/>\n</p>\n<p align=\"center\">Coordinate System</p>\n\n## Flow Field\n\n### Oblique Shock\nIn the flat region of the shockwave, the lower surface is determined via the $\\theta$- $\\beta$ - $M_{\\infty}$ equation, which relates the deflection angle $\\theta$ to the shock angle $\\beta$ in an oblique shock. \n\n$$\n\\tan(\\theta) = \\frac{2 \\cot\\left(\\beta\\right) \\left(M_{\\infty}^2 \\sin^2\\left(\\beta \\right) - 1\\right)}{M_{\\infty}^2 (\\gamma + \\cos\\left(2 \\beta\\right)) + 2}\n$$\n\nWhere $\\gamma=1.4$ is the ratio of specific heats for air and $M_{\\infty}$ is the freestream Mach number.\n\n### Osculating Cone Theory\n\nIn the curved region of the shockwave, the osculating cone theory is used whereby conical flow is locally applied at each osculating plane. \nThe Taylor-Maccoll ODE, which describes conical flow, is solved and the resulting streamlines are propagated until the back of the waverider is reached to produce the lower surface.\nSee [2] for more information on the Osculating Cone Theory.\n\n## Required Inputs\n- Design parameters `X1`, `X2`, `X3` and `X4`. Note this is entered as a list `dp` of four elements where the parameters are organised in the order listed here. Refer to the examples.\n- Freestream Mach number `M_inf`.\n- Shock angle in degrees `beta`.\n- Height of the waverider at the base plane `height`. Note that the length of the waverider is determined as $height/\\tan(\\theta)$ so a user may choose to determine the height required for a desired length.\n- Width of the waverider `width`. Note that this refers to half of the total width of the waverider due to the symmetry.\n- Number of points to be used for interpolating the shockwave and the upper surface curve (`n_shockwave` and `n_upper_surface` respectively). Both are integers greater than 10 to preserve quality.\n## Optional Inputs\n- Number of osculating planes used in the generation of the geometry `n_planes`. Note that this doesn't include the symmetry plane and the tip. A minimum number of planes is set at 10 to preserve quality and this is the default value.\n- Number of points in the streamwise direction for the generation of the upper surface as well as the flat part of the shockwave on the lower surface `n_streamwise`. A minimum is set at 10 to preserve quality and this is the default value.\n- Maximum step to be used in the tracing of the streamlines for the lower surface `delta_streamwise`. Note this is entered as a percentage of the length of the waverider and a maximum is set at 20% to preserve quality. The default value is 5%.\n\n## Summary of inputs\n|Input|Type|Conditions|\n|:-------------:|:--------------:|:--------------:|\n| `X1`, `X2`, `X3` and `X4` | `list` | $0\\leq X2,X3,X4 \\leq 1$ <br> $0 \\leq X1 < 1$ <br> $\\frac{X2}{\\left(1-X1\\right)^4}\\leq\\ \\frac{7}{64}\\left(\\frac{width}{height}\\right)^4$<br>(see [1] for more information on this design condition) |\n| `M_inf` | `float`, `int` | `M_inf>0` |\n|`beta`| `float`, `int`| `0<beta<90`|\n|`height`| `float`, `int`| `height>0`|\n|`width`| `float`, `int`| `width>0`|\n|`n_shockwave` and `n_upper_surface`| `int`| `n_shockwave,n_upper_surface>=10`\n|`n_planes`|`int`|`n_planes>=10`|\n|`n_streamise`|`int`|`n_streamwise>=10`|\n|`delta_streamise`|`float`|`0<delta_streamwise<=0.2`|\n\n# Usage and functionality\n\nA user can create a `waverider` instance by importing the `waverider` class from `waverider_generator.generator`. Everything takes place inside the class constructor so the user only needs to initialise the instance to create the geometry. An example is shown below: <br>\n```python\nfrom waverider_generator.generator import waverider as wr\nM_inf=5\nbeta=15\nheight=1.34\nwidth=3\ndp=[0.11,0.63,0,0.46]\nn_planes=20\nn_streamwise=10\ndelta_streamwise=0.1\nwaverider=wr(M_inf=M_inf,beta=beta,height=height,width=width,dp=dp,n_upper_surface=10000,n_shockwave=10000,n_planes=n_planes,n_streamwise=n_streamwise,delta_streamise=delta_streamwise)\n```\n## CAD Export\nTo export the geometry into a file CAD, the user can import the `to_CAD` function from `waverider_generator.cad_export`. An example is shown below: <br>\n\n```python\n#%%\n# assuming a waverider instance has been created with the code above\nfrom waverider_generator.cad_export import to_CAD\n\nwaverider_cad=to_CAD(waverider=waverider,sides='both',export=True,filename='waverider.step',scale=1000)\nwaverider_cad\n```\n\nThe `to_CAD` function is detailed below:\n\n|Input|Type|Conditions|Description|\n|:-------------:|:--------------:|:--------------:|:--------------:|\n| `waverider` | `waverider` | NA|`waverider` instance|\n| `sides`| `str` | `\"left\"`, `\"right\"` or `\"both\"` <br> | Side(s) of the waverider to generate in the CAD|\n|`export`| `bool` |`True` or `False`| Setting this to `True` exports the CAD to the current directory, `False` does not|\n|`filename`| `str`| The extension must be one which `cadquery` can generate a CAD file in| Name of the CAD file to be created|\n|`scale` (optional)|`float`,`int`| `scale>0`| Scale factor by which the final geometry is scaled. By default, cadquery exports geometries in mm so the default value for `scale` is 1000 to obtain dimensions in meters. Setting this to 1 keeps the dimensions in mm. It is recommended to keep the default value of 1000 and work in meters from the start.\n\n|Output|Type|Conditions|Description|\n|:-------------:|:--------------:|:--------------:|:--------------:|\n`waverider_cad`| `cq.Solid` (cadquery solid) | NA | A cadquery solid corresponding to the waverider generated. This can be previewed in a Jupyter Notebook, therefore avoiding the step of exporting and importing into a seperate CAD software each time.|\n\n<p align=\"center\">\n <img src=\"https://github.com/jade5638/waverider_generator/blob/main/cad_preview_example.png?raw=true\" alt=\"Jupyter Notebook CAD preview example\" width=\"500\"/>\n</p>\n<p align=\"center\">Jupyter Notebook CAD preview example</p>\n\n## Plotting tools\n\nThe package also allows the user to plot basic figures to analyse the geometry generated before a CAD export. This is done by importing `Plot_Base_Plane` and `Plot_Leading_Edge` from `waverider_generator.plotting_tools`. An example, also included as an example file, is shown below\n\n**Note** that the `latex` input into the plotting functions is a boolean and determines whether or not to plot the figure with the default LaTex font. The user is required to install a LaTex distribution on their system for this feature to work.\n\n```python\n#%%\nfrom waverider_generator.generator import waverider as wr\nfrom waverider_generator.plotting_tools import Plot_Base_Plane,Plot_Leading_Edge\nimport matplotlib.pyplot as plt\n\nM_inf=5\nbeta=15\nheight=1.34\nwidth=3\ndp=[0.11,0.63,0,0.46]\nn_planes=20\nn_streamwise=10\ndelta_streamwise=0.1\nwaverider=wr(M_inf=M_inf,beta=beta,height=height,width=width,dp=dp,n_upper_surface=10000,n_shockwave=10000,n_planes=n_planes,n_streamwise=n_streamwise,delta_streamise=delta_streamwise)\n#%%\n'''\nPLOT BASE PLANE\n'''\nbase_plane=Plot_Base_Plane(waverider=waverider,latex=True)\n#%%\n'''\nPLOT LEADING EDGE\n'''\nleading_edge=Plot_Leading_Edge(waverider=waverider=True,latex=True)\nplt.show()\n```\n<p align=\"center\">\n <img src=\"https://raw.githubusercontent.com/jade5638/waverider_generator/2c5aba1915e3e87223f8f3444c2ae3c8b66c77a5/base_plane.svg\" alt=\"Base Plane\" width=\"500\"/>\n</p>\n<p align=\"center\">Base Plane</p>\n<p align=\"center\">\n <img src=\"https://raw.githubusercontent.com/jade5638/waverider_generator/2c5aba1915e3e87223f8f3444c2ae3c8b66c77a5/leading_edge.svg\" alt=\"LE\" width=\"300\"/>\n</p>\n<p align=\"center\">Leading Edge Plot</p>\n\n# Dependencies\nThe package requires the following libraries to be installed:\n- numpy\n- cadquery\n- scipy\n- matplotlib\n\nOptional:\n- a LaTex distribution such as MiKTex (refer to previous section) \n\n# License\nMIT License\n\nCopyright (c) 2024 jade5638\n\nPermission is hereby granted, free of charge, to any person obtaining a copy\nof this software and associated documentation files (the \"Software\"), to deal\nin the Software without restriction, including without limitation the rights\nto use, copy, modify, merge, publish, distribute, sublicense, and/or sell\ncopies of the Software, and to permit persons to whom the Software is\nfurnished to do so, subject to the following conditions:\n\nThe above copyright notice and this permission notice shall be included in all\ncopies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\nFITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\nAUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\nLIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\nOUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE\nSOFTWARE.\n\n# Citing\n\nPlease use the reference.bib file included to reference this work. \n\n-----------\n# References\n\n[1] Jiwon Son, Chankyu Son, and Kwanjung Yee. \n'A Novel Direct Optimization Framework for Hypersonic Waverider Inverse Design Methods'.\nIn: Aerospace 9.7 (June 2022), p. 348. issn: 2226-4310. doi: 10.3390/aerospace9070348.\n\n[2] Helmut Sobieczky, F Dougherty, and Kevin Jones.\n\u201cHypersonic Waverider Design from Given Shock Waves\u201d. In: May 1990\n",
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