I initially was not going to post but since the discussion from the other forum was referenced here including a plot of the data from nominal values vs sandor's results, I've decided to post regarding the data itself. A week or so ago I plotted the difference between the results obtained and flat earth nominal calculations for the expected laser heights for each point of his data. I noticed a lack of random noise that I would typically expect in uncontrolled datasets (due to uncontrolled variables like boat movement, drift, currents, measurement inaccuracy, beam divergence and lack of centering, etc.). What I noticed were what looked like patterns in the differences instead that I would not expect in such a data set.
Plot of differences in Sandor's results and expected flat earth laser heights at each point along the path:
Last night, I took another look at the data. I decided to plot the change between points along the path for both Sandor's data and the flat earth nominal heights. To say that differently, the difference between point C1 & C2; C2 & C3, so on so forth. This is shown in the dRes and dNom columns below. Then I computed the difference of those two values as shown in the dNom - dRes column below. What I noticed is that in for the second half of the data that the change in height always deviated by 0.00 or 0.01 from the expected change between corresponding points in the path. This would show a slight divergence getting larger and larger if the curves were plotted.
What was more interesting though were the results for the first half of the data points. I noticed that for the first half, expected changes between points did occur (as in matched or only deviated by 0.01) but that it was fanned out over multiple points. I attempted to highlight this in red and green below. For example the changes of 0.02 + 0.04 shown in red for dRes match the change of 0.06 shown in green for dNom. It almost looks to me that there was an attempt to compensate for the difference between the obtained results and nominal values and that this resulted in patterns occurring in the results; as opposed to what one would expect: random noise. In the coalesced column, I show that if you treat these deviations as single additive points (E.g. Adding C1 and C2 differences together) what you end up with is a net difference of only 0.01 maximum along any point of the path from expected values. This does not all appear to be realistic to me for a data set obtained with such uncontrolled variables. What I would have expected to see was simple random deviation from nominal values and under and overshooting randomly at various points along the path. Instead what we see is either the perfectly expected change, or under shooting of the change that ultimately results in the curves beginning to linearly diverge.
Deltas between point N and N+1 for all points along the path for the obtained results (dRes) and nominal expected flat earth results (dNom):
Graph of curves diverging (from Boxer):
