Any rule of thumb for amplitude distribution in series fed patch arrays?

Recently i made some calculations on series fed patch arrays using array factor, etc.. www.antenna-theory.com/arrays/arrayfactor.php But also it is interesting that using different tapered feeding lines it is possible to reduce side lobes. It is all about how much power will go to the patch. Most sources refer to some coefficient = 1/2, 2/3, 3/4, 4/5, 5/6... For example, if we choose 5/6, then 1/6 of power goes to the first patch and 5/6 will go to the next tee connection. Second patch will get 1/6 of (5/6). And so on. I think there must be some rule of thumb to select this coefficient based on patches count. At least if taper is the same for all patches. The more patches we use, the smaller coefficient must be. If coefficient would be too big, then for small arrays last patches will get no power. Of course simulations and optimizations can be done in some software (that is not free), but i am more interested in some simple recommendations, that can be used to choose some tapered coefficients and then tune things by hand using formulas i got...