Good answers guy's and maybe I misunderstood the question but,,,
Don't cut through the rings on the back of the bow where you chased a ring. Tappering occurs on the belly and side profile.
The vertical grain & growth rings may be the confusion in terminology for you; they are not the same.
Vertical grain refers to the fine vertical grain contained within each ring and running the length, end to end of the stave or bow. Most self bow profiles follow this vertical grain to some degree; until the limb tappers to suite your preference.
Compromising this vertical grain is not as bad as compromising your well chased growth ring backing that is the integrity of you future bow.
Chances are if you saw a stave and not let your drawknife follow this vertical grain along the profile and around knots, it may just weaken the integrity along the backing and sides causing a limb to split along the edges of the profile. Hence the wording: Follow the grain or don't cut through the grain.
When marking the center line try and follow this vertical grain in the wood. Then most likely your measurements described in the responses above this one will also follow the vertical grain to some degree.