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Spining tapered shafts

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jeffp51:
extra length affects the dynamic spine.  You have a mass at the end of a rod, and a force applied to the other end.  When you release the string, the mass at the tip resists acceleration (inertia) causing the shaft to flex.  A longer shaft means more leverage, which means more flex, so a longer arrow has to be stiffer than a shorter one to have the same amount of flex.  Likewise, a heavier weight on the tip means more inertia to overcome causing more dynamic flex.  Hence an arrow with a heavier tip will need to be stiffer to have the same amount of flex as a lighter tipped arrow.  the opposite in both cases is also true, of course.

So we have to measure static spine on the tester, which means we need repeatable results (measuring from the same point with the same weight every time), and under stand that dynamic spine is going to be different based on length, tip mass, and amount of flex (archer's paradox) needed to get around the grip of the bow.

The right length for an arrow is the length that lets you shoot most consistently--and at least as long as your draw.
I try to get my arrows as consistently the same as I can so that I can eliminate differences in arrow build as much as possible when trying to figure out what is wrong with my shot.  I suspect that gripping the bow to hard, inconsistent anchor, bad release, inconsistent form contribute to a bad shot far more than slightly off arrows, but if your arrows don't match, you can't see what else is wrong.

Knoll:
Well written, Jeff. Thank you.

TSA:
a clear and concise explanation Jeff, well done!

Hawkdancer:
Makes sense, Jeff.  I assume there will always be some deviation in any set of arrows, at least for weight, spine, I think would pretty close.  One other question, how close a reading does one get trying to spine test finished arrows?  I know bare shaft is better, but I don't really want to rework good fletching.  I am working my shoots as close to weight and spine as I can to match my bows, and I think, to dedicate  a set to each bow.  Hope I haven't high jacked the thread, and my questions make sense.  Thanks,
Hawkdancer

jeffp51:
I have a modified spine tester, since I am too cheap to spring for one of those fancy ones with the big long levered pointer on it.  I suspend a digital caliper over an arrow shaft--the caliper is clamped to a shelf over the workbench.  the arrow shaft sits on two hooks 26" apart.  I move the pin end of the caliper down until it sits on the top of the shaft and zero out the caliper, and then I hang a two pound weight from the middle of the shaft and move the caliper pin down until it just touches the shaft.  It helps to shine a light through the gap until it just meets the arrow.  My caliper is accurate to .001" and the AMO chart is also measured in thousandths of an inch.  But I find that repeated measurements will yield results that vary by .005" or so, so I am probably only accurate to the hundredths of an inch.  I take several measurements and average them out.

Most professionally sold arrows match to within 5# of spine, (although I think TSA is closer than that) so my match at .01 is inside of what is likely tolerable, especially given my inconsistencies in other areas of my shooting.

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