WARNING -- Some may not want to read the rest of the post unless you're masochistic or have already taken painkillers...
Originally posted by DCM:
I like the engineer in you. I've chased that bunny trail a bunch, mostly in the context of nock travel, up and down, and the interlationship with limb/string lenght and static tiller. Seems like the more asymetry, the more tiller, the more nock travel. At one time "negative" tiller was suggested as appropriate for the typical arrow pass above center construct, and I thought effect of nock travel would negate it's use, even though it seemed plausible in terms of balancing the strain on the upper limb, relative the lower which gets a free ride on two accounts, being stiffer and longer.
On the three under question, maybe because it gets more "free travel" before the lower limb "sees" the arrow?
This stuff breaks my brain everytime I entertain it. To be so "simple" traditioal bows are maddening complex to model, imho.
Yeah, see, this is the kind of stuff I contemplate while going to sleep at night. Which is probably why I never get a decent night's sleep.
Once the string is tight to the arrow, it is the arrow nock location that would determine the tiller of the bow during the rest of the shot. But there is that transition period between where the string is released, and where it draws a tight V to the arrow. And how that transition occurs can affect where that nock actually ends up on the string assuming you don't have top and bottom nock points.
See if this makes sense to anyone:
At the instant of release, imagine the back of your string (or bottom of the "V" shape) is actually about where your middle finger was, and the arrow nock is slightly above that. The action of the lower limb is pulling against that slack in the string ("free travel") and so accelerates very quickly with really only its own mass to work against. The upper limb sees the arrow nock, but since it's not in the bottom of the V, it's relatively free to travel down the string until it reaches that bottom (assuming your nock isn't that tight.) In this sense the top limb is also accelerating only against the slack in the string and the arrow starts to slide down the string slightly.
At the moment the string slack is gone, a bow with positive tiller will have a bottom limb moving forward faster and with more kinetic energy than the top limb. This leads to unequal force at the arrow nock point, and the nock would want to slide back up the string slightly until it hits the nock point on your string.
A three under release moves the bottom of your string V farther from the arrow, which would cause the arrow to slide down the string farther before the slack is gone. Adding a bit more positive tiller would therefore be useful in sending the arrow nock back up the additional distance to the nock point when the slack is gone.
Ok, that is all well in good if your arrow is really seeing low enough friction to slide on the string. With a tight nock this might all be moot. But the forces are high, so maybe... When I got up this morning, I decided to go look. My new little self bow is sporting an ad hoc spectra braided string with some serving that doesn't really bring it anywhere near tight in the nock. It's also showing a little wearing in after several hundred shots. And you know what? The wear area is about twice the thickness of my nocks. It definitely looks like the nock is traveling on the string slightly at release. A bit more positive tiller might help keep it tighter to the nock point....
All said and done though, I think we're talking about something that happens in the first few fractions of a second during the shot with effects that are small and probably overcome by other factors by the time the arrow is clear of the bow. But what fun is that?
Ok, sorry about that. I just couldn't help myself.