Previously, we have tried to straighten the sides of the best-evolved curved antenna in elog 229. However, there were potential issues with how closely this line resembled the curve of the antenna.

So, I attempted to create another straightened sides antenna using a linear regression model to find the best fitting line for the curve to create an antenna.

I made a Python notebook to separate the equations for each curve into 1000 discrete points. Then I ran a linear regression model to fit a curve of the points 1 - n, and a second curve of the n - 1000 points, looping from n = 2 to n = 999.

These results are from the combined output with the least squared error compared to the original.

Pictured is a plot showing the two sides of the curved bicone in red and blue, with the best fitting lines for each in black as well as a model in XF.

Results:

The antenna has a fitness score of 3.80627 with an error of 0.0759725.

This is much lower than the 5.71 of the curved antenna and 5.11 of the other attempt at straightening.

For the next attempt, we could consider constraining the endpoints to be the same as the original antenna to conserve the radius, and/or adding an extra line to fit the curve.

I've also attached a picture of what my notebook found for fitting 3 lines to the curve (not modeled or tested).

Professor Chen recommended using 3 sides and constraining the outer radii of the cones to match the original curved design.

Path to linear regression notebook: /users/PAS1960/dylanwells1629/developing/notebook.ipynb

Path to XF project: /users/PAS1960/dylanwells1629/straightened.xf