How do you calculate ellipse coefficients a0-a4 for engineering libraries?
(Problem # 29197)
In order to calculate flow area and wetted perimeter for an ellipse, the program uses a fourth-order polynomial relationship to relate the ratio of depth/rise (x) to wetted perimeter (y).
y = a0 + a1x + a2x2 + a3x3 + a4x4
In order to determine the coefficients a0 - a4 you must first calculate a set of points relating depth/rise to wetted perimeter and then perform an analysis to determine the best fit fourth-order polynomial for the set of points using the least-squares method or some other regression analysis.
You can also generate the coefficients using attached applet.
Extract the contents of the .zip file to a folder. Open the file calculator.html in Internet Explorer.
Enter in the rise and span of the ellipse in inches and then click the Calculate button. You can copy and paste the coefficients into the Engineering Libraries by pressing Ctrl + C to copy and Ctrl + V to paste.
Note: this applet is quite old and may have compatibility problems with some operating systems or browsers. Security settings may need to be adjusted and/or an older computer may need to be used to open it.