I'm looking for an equation based on an excel-graph and an model-equation (=a + b cos(alpha - phi).

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I have a table with factors who can transform a regional windspeed to a local windspeed. The factors are calculated for different wind direction and speed sectors as shown in the table (fig. 2). Now I would like to obtain from the plotted graph (fig. 1) a function that theoretically fits the egg-shaped graph in the form of "a + b cos(alpha - phi)".

What I already know: a = average of the factors (for sure) b = something to do with the amplitude (?) alpha = a wind angle I suppose (?) phi = something to do with max and min (like here at 0° and 180° I would say)

It may be that this only goes for a well-defined speed sector, like 6-8 m/s

Thank you in advance! Sebastian

plotted graph of the table with factors (fig. 2)

table with factors per winddirection en windspeed sector