So called "asym" bows require some positive tiller just not as much positive.
How come nobody talked about nock travel?
IMHO, this topic cannot be completely or accurately discussed without understanding the phenomenon, and it's impliications for tuning, and "tiller."
Tillering, in the classical use of the word, is after all simply an effort to control the vertical travel of the arrow, with the objective to have the arrow leave the bow as close to perpendicular to the string as practical but with enough room for adjustment with nock point to avoid interference with the arrow rest. The definition of the word is instructive in this regard:
http://www.merriam-webster.com/dictionary/tiller[4]
Practice from antiquity, as it relates to all natural bows, would be informative here as well I think. Arrow pass at or near center enjoys an advantage as I understand it, particularly in bendy handle designs for obvious reasons. It was not until bows with very stiff risers, deep palm swell and glass limbs were introduced that we became fascinated with having the fulcrum of the bow hand be at dimensional center, as I understand it. For good reason, introducing this asymetry does nothing but tax the material in the upper limb unnecessariy, in my view. If you are using material with gobs of extra work capacity and can afford to, I can see how it is much simpler to setup a form and devise a lam taper formula to glue up this type of bow.
Why do people, not in this discussion but in general, historically, at least in the period after and mostly influenced by TBB as far as I can tell, refer to bows where arrow pass is 1" to 2" above center as being "symetrical?" In fact they are bows with shorter upper limb. Then, when confronted with this conundrum they refer to bows with arrow pass at center as, oddly, "shorter lower limb" when in fact they are equal lower limb? It makes this discussion so much more difficult. I'd argue symetrical better describes a bow where arrow pass is at dimensional center. Regardless of where we position our hands while drawing a bow, what the arrow sees on the loose is the only thing that matters. And when you look at the position of the nock point on a bow where arrow pass is above center, it sure as heck ain't symetrical, rather the upper segment is significantly shorter.
Sorry, can't agree symetrical bows are generally or universally "harder" to build, just different. It's all about what you get used to. If anything asym bows, arrow pass above center, are harder to build because one must compensate doubly, once for the inherent asym of the archers' hand position, and in addition for the asym introducted by raising the arrow pass above center.
Great discussion so far. Would love to hear nock travel, spring theory discussed.