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Symmetrical vs. Asymmetrical Tiller - Geometry Heavy

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Mo_coon-catcher:
I don’t worry about exact numbers too much anymore as long as the bow balances. Here’s a bow I did a couple years ago with a 10” difference in limb length and it shot about the same as any other bow. It felt wierd as it would tilt when drawn. I made sure limbs were balance by the angle of the string to limb tips and approximate curve they were making. It wasn’t a light bow either at 66# at 27”. It did end up popping a splinter about 3-4” from the bottom limb tip. But I got a solid year of shooting and a kill from it first. And for arrow pass I just center up my hand in the handle and shoot. If I make a dedicated spot I mark it 1/4” above my knuckle. No idea what the actual number comes to.

Kyle

Alex C:

--- Quote from: Jim Davis on January 30, 2024, 10:49:30 am ---There are so many factors that it is hard to keep track of them.

In my thinking, the part about the limb tips arriving back at brace height at the same time is the most important, no matter which factors are used to achieve that.

However, as long a bow doesn't behave inconsistently shot to shot, accuracy is totally up to the archer. Japanese Kyudo bows being one extreme example of bows of unequal limb length.

It is more unsettling to me that with three-under nocking, at release the force center jumps from the center of the three fingers to a point at the arrow nock, a couple of inches higher. But a huge percentage of archers successfully use three-under.

I think that the bottom line is that if the archer does the same thing every shot, the arrow will fly the same every shot.

--- End quote ---

I suppose limb mass is a third factor not explained by that diagram when it comes to tips arriving at brace height simultaneously.  A limb with significant set or knots, or something may need more mass to hold an equivalent energy (draw weight) as a more perfect limb.  I know nothing about Kyudo bows, but I'd be fascinated to get some measurements of limb deflection, energy storage, draw weight, etc. to see if they follow this concept to an extreme or maybe completely debunk it.

I agree with the three-under shooting - I shoot three-under and I've been thinking about how that changes stress dynamically.  It would seem that to make a bow perform well, the bottom limb must be under more stress at full draw, but then the change in angle 'A' on release must redistribute stress so that both limbs apply the same force.  I wonder if anyone's got input on bows shot three-under not lasting quite as long as bows shot split? Due to an overstressed bottom limb at FD.


--- Quote from: Selfbowman on January 31, 2024, 02:08:41 pm ---I’ve also pondered this with my limited math. I learned to put my arrow pass 1-1/4 inch above center of bow both limbs being the same from a glass bowyer years ago . Been doing it ever since. This is on a stiff handle bow. Now that being said that way has broken lots flight records. Yes can’t say it’s better cause I’ve never tried different but once. Did not see any difference making the limb longer. Also where do you hang your scale on the string when on tiller tree. I center the bow on the tree and have a line straight down from the center. I hang my scale on that line. I have noticed that scale will go to the side of the line when one limb is stronger. It goes to the stronger side . Ive been playing with lining the scale about 1/4-3/8 toward my arrow pass when tillering. The bottom line for me is on wood bows they settle in during brake in to the way the archer holds the bow. Glass bows no.

--- End quote ---

My thinking is that a longer top limb or a stronger bottom limb independently reach the same conclusion - no difference in the final force applied to/by the limbs.  So those bows with flight records, I'd love to know if the top limb is slightly weaker (even if unintentionally).  Like hanging a weight on both limbs - I'd expect the top limb to deflect farther with the same weight.

The draw line on my tillering tree is about 1" below the arrow pass, so if I tiller to a "symmetrical" tiller, I'm actually making the bottom limb slightly stiffer.  I'm trying to finish up a yew flatbow this weekend and I'll get some pictures/measurements to make sure that's actually what's going on.

Regarding a bow settling in, I'd imagine that is accomplishing the same result as the stiffer bottom limb, it's just happening through set, whether measureable or not.  If you've got a stronger top limb, it's going to be under more stress until it takes enough set so that the force applied to both limbs is equal.  That may be so little set that it's not really measurable, but I'd bet it's there.  That's actually something I'd really like to test!  I've got a PhD thesis to finish up, but maybe come summer I'll make a couple test bows and see if this is actually what happens during break-in.

Alex C:

--- Quote from: Mo_coon-catcher on January 31, 2024, 03:25:03 pm ---I don’t worry about exact numbers too much anymore as long as the bow balances. Here’s a bow I did a couple years ago with a 10” difference in limb length and it shot about the same as any other bow. It felt wierd as it would tilt when drawn. I made sure limbs were balance by the angle of the string to limb tips and approximate curve they were making. It wasn’t a light bow either at 66# at 27”. It did end up popping a splinter about 3-4” from the bottom limb tip. But I got a solid year of shooting and a kill from it first. And for arrow pass I just center up my hand in the handle and shoot. If I make a dedicated spot I mark it 1/4” above my knuckle. No idea what the actual number comes to.

Kyle

--- End quote ---

That'd be an awesome example to get measurements from! Do you still happen to have that bow? A quick sinew wrap at the splinter might be enought to measure deflection of each limb with maybe only 10-15lbs hanging off the tip.

Also, That's a real pretty bow! Those knots at the handle are just cool...

RyanY:
Great analysis. Thank you for sharing. Your paper on the yumi design will be due at the end of the semester.  ;D

Selfbowman:
Yes I think you will find that the top limb will settle in mostly during the build. If you measure the top limb strung about 4-6” from fade you find the measurement will be as much as a 1/4” bigger than that point compared to bottom  limb.

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