Hi All. I struggle with the concept of dynamic arrow spine. The following are thoughts I have that may be correct or incorrect, so feedback is more than welcome. I just have trouble putting all the pieces together:
1. The arrow itself has a natural frequency, depending on distance between end conditions (e.g. draw length defined by arrow nock point and handle).
2. I struggle with what those end conditions really are, such as pinned-free, free-free, pinned with lateral spring constant-free, etc.?
3. I imagine that as the string rolls off the fingers, there is a lateral displacement of the string adding elastic energy to the system in addition to the arrow stiffness as well as a displacement constraint. How important is this? Should I be thinking of a bow/arrow system lateral frequency and not just arrow?
4. I imagine the arrowhead may affect the natural frequency of the arrow and maybe reduce it? How much does this contribute to the vibrational response relative to arrow stiffness?
5. If for instance the correct end conditions for the arrow is free-free, then I imagine that the frequency of vibration is independent of draw weight for given draw length. However, the amplitude of lateral displacement may be a function of draw weight, maybe?
6. So, whatever the correct means to characterize the arrow's frequency of vibration might be, it is my understanding that the period of vibration (1/frequency) should be in proper ratio with the time for the arrow to leave the bow after release to avoid the arrow backend from slapping the handle. The time for the arrow to leave the bow is a function of bow stored energy (area under static force/draw curve), bow efficiency, arrow mass and draw length.
It is the method to characterize the arrow natural frequency that alludes me. Specifically, end conditions and how important are the mass of the arrowhead and lateral stiffness of the string?
Cheers!
Jon
