Originally Posted by mike1127
I looked at the graphs (spreadsheet) but what I can't figure out is what the "approx" column is. Do you know? It's the column plotted as a purple line in all the plots.
You'll have to get Tangent to describe it in more detail, but essentially, the purple, "approx" graph is a plot/values of a curve-fitted equation for the measured data. If the relationship between the knob travel and pot response was linear, then a simple linear-regression line-fit would suffice to "linearize" the scatter of the data. The response of a volume pot is much more complex, though, and follows a logarithmic relationship. So, a curve-fit program is used. He mentions several programs in the text.
One way to look at the purple curves/lines or "approx" column is that these are the values of the pot's performance if it perfectly followed the theoretical response for its design. You're always going to get data "scatter" when you measure a system in the real world. (It's one reason pure-objectivists fall short of predicting real-world performance.) However, if you can "curve-fit" the data to a reasonably approximate curve, you should be able to predict performance over a wide range of conditions - without specifically measuring the data at every instance. For instance for the RK27, the approximate curve-fit matches very well with the plotted data. The actual equation that resulted from the curve-fit can give you an excellent approximation of the pot response at any point that was not measured - 5 degrees, 48 degrees, 92.5 degrees, etc., etc.
If you've ever computer-programmed, think of the difference between a look-up table to determine values and then cumbersome interpolation routines to estimate in-between values, vs. a single, self-contained equation.
Similarly, you can use a curve-fit to demonstrate deviation of the measured data from "ideal," which is what I think Tangent is trying to show here.