Some thoughts on Archer's Paradox

[blindarcher]

While sitting around and contemplating the fuzz in my navel, my mind wandered to thoughts about archer's paradox.  Many, many moons ago my aunt who competed as an archer in college taught me to roll the string using just the tips of my fingers of my draw hand to keep the arrow in contact with arrow rest.  This is the Mediterranean grip as taught to me.  Rolling one's fingers applies a torque to the string and results in a reaction force at the arrow rest approximated as torque divided by the draw length.  My theory is that once the string is released, the reaction force is instantly opposed by a lateral force at the nock (string end).  The lateral force multiplied by the lateral stiffness of the drawn string results in an initial lateral displacement of string and arrow nock.  A rough estimate for a 55-lb bow, 28-inch draw, an estimated lateral stiffness of 3.58 lb/in and an assumed torque of 2 lb*in resulted in a lateral displacement of 0.275 inches; not unrealistic.  Now I imagine that with a 125 grain arrowhead, an axial load of just over 16-lbs along the arrow shaft is associated with instantly accelerating the arrow.  The combination of axial load with lateral offset at the nock end will setup a lateral vibration often described as the arrow snaking around the bow.  The amount of lateral oscillatory deformation of the  arrow is a function of arrow spine (stiffness), which can be estimated as well as the frequency of vibration.  Some have used a free-free assumption for boundary conditions for frequency estimation.  I  am not convinced that this is appropriate and wonder if a fix-hinged assumption is better.  Anyway, this is as far as my mind has wandered on this subject and I will get back to  contemplating the fuzz in my navel.  I need to get a life.

[Pat B]

Whoo, my navel fuzz is hurting after reading that.       I know a lot of beginners have a tendency to grip the string forcing the arrow off the shelf. A rigid finger hook it the way to pull the string, either at the first crease in your finger or the back crease.. 

[bradsmith2010]

well it is , ,,, what it is,, if you have need to understand it great,, if not,, just practice till it hits where you want

[Hawkdancer]

Methinks this is overthinking the problem if any!  Like Brad said practice until you hit where you are aiming, and everything is good.  Actually works with atlatl, tomahawk, knife, spear, and firearms, too!  Science is good, but it can be overthinking and creating a problem, instead of solving one!  BS! MS, and PH.D. is the jest!  After we hit where we aim every time, we can think about the why is that happening.
Hawkdancer

[JackCrafty]

Watch this video. There isn't much of an effect of string torque.  Lateral displacement at the arrow nock is more a result of the fingers being an obstacle to the release.

https://www.youtube.com/watch?v=jUOuHH9GojQ

(the video has a lot of dead time at the beginning... kind of annoying but be patient)

[sleek]

Ever see a car spin its tires at a dead stop? The string does the same thing inside the nock. Its just burning rubber as it unwinds with no affect on arrow flight.

[willie]

free- hinged possibly, at least free in all but one direction.
another interesting video is here
https://www.youtube.com/watch?v=96KGWC0PB6s

interesting secondary vibes can be seen at 42 seconds

[Pat B]

It always amazes me that more arrows don't break with the gyrations they go through after the release.