Cosine Curve - Tank settlement evaluation 5

[Restivehorse]

I am in the process of creating a cosine curve for the settlement survey in accordance with API 653 annex B.2.2.4 and B2.2.5. I have read through the entire annex and am pretty understanding of it, though cannot seem to understand how to acquire appropriate predicted elevations.

In API 653 it says: Where Elevpred is the elevation predicted by the cosine curve at angle theta. A typical starting point for a computer
best-fit cosine curve is a least-square fit where a, b, and c are chosen to minimize the sum of the square of the
differences between measured and predicted elevations.

However, no where in the code does it specify what R2, a , b, and C values area derived from?

R2 ≥ 0.9
Elevpred = a + b × cos (theta + c)

Can anyone help me to get R2, a , b, and c values in excel sheet attached below:

Tank parameters and elevation (height) value of tank observation is shown in excel file attached

Thanks

 

[Geoff13]

See my 21-Jun-2023 post above for explanation of a, b and c.

I use Solver to find the values of a, b and c that provide the best fit, as I discussed in my 28-Jun-2023 posting above. While trial-and-error may or may not get you these values after a lot of work, Solver will get the answer in a fraction of a second.