The Formula for the Curve of a Trumpet Bell
Submitted by Abraxas on April 10, 2018 - 8:45pm
I'm guessing this problem belongs to integral calculus:
I've been tasked with making some anvils, on a metal lathe, for the repair of brass instrument bells. I need to calculate corresponding X-Y values along the curve of that bell.One side only as it's symmetrical. I can certainly take sample measurements at frequent intervals of the bell, but I don't know how to come up with the formula for the curve that will allow me to create a chart of the thousands of points I need to accurately machine it. Any ideas ? Salamat/Thanks.
- Add new comment
- 775 reads
I am not sure if this will
I am not sure if this will work, but the equation of Normal Distribution in Statistics is called a bell shaped curve due to the fact that it is in the form of a bell. The equation is
$$ f(x) = \dfrac{1}{\sigma \sqrt{2\pi}}e^{-\dfrac{1}{2} \left( \dfrac{x - \mu}{\sigma} \right)^2} $$
You may randomly assign the value of $\sigma$ and see if the size of bell fits to what you desire.
2021 Update
I just stumbled upon this page: https://www.desmos.com/calculator/3iioyvma2l
Add new comment