Walter & Group........
From Eric Cook:-
Gordy,
Forgive me for not letting this one go. I now see what you and Walter are talking about ("must always be acceleration") and I want to thank you both for the refresher in kinematics. I was thinking too "linearly" and feel somewhat foolish for not seeing it from the beginning. To see if I am truly correct in my reasoning, this is what I have concluded from the discussion (looking for a more non-technical explanation):
We are looking for the resultant, total acceleration which is the square root of sum of the squares of the centripetal (radial from rod tip to the pivot point of rotation) acceleration and the tangential acceleration. Here we have a tangential acceleration of zero (constant angular velocity), so that term drops out. Centripetal acceleration is equal to the angular velocity squared times the radius (distance from the rod tip to the pivot point). Neither of these are zero so yes, there will always be acceleration due to angular motion.
Looking at this deeper shows how amazing it is that we are able to achieve anything close to SLP of the rod tip with all of the changes in rod bend, pivot points (especially for a more open styled caster), etc. during even a single casting stroke. As Peter Lami pointed out to me, the human brain is so complex that we are able make all of these calculations quickly and accurately even if we aren’t aware of the explained physics involved or even know that we are doing it (paraphrased).
Eric
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Eric....
All in how we look at it ..... for in the end, we have to translate this information into our casting and, more importantly, into our teaching. Peter Lami is correct with his statement about the human brain.
Hard for me to digest is the teaching that with rotation, we have both centrifugal as well as centripetal forces working at the same time despite the fact that they can be equal and opposite forces and, therefore, would seem to be mutually exclusive.
One thing that excites me is your concept of how the flexible fly rod can be subjected to a combination of translational (linear) and rotatory (angular) forces and movements at the handle and end up with an almost linear movement with practically no rotation at the tip when an efficient caster yields an almost true straight line path of the rod tip !!
This would be impossible with an inflexible rod such as a broomstick.
Food for thought : Just as we may reach the point of being able to conciously transfer thoughts from one person to another without the use of the spoken word or electronics as we now know them, we may be able to come up with the perfect fly rod.
This one will be capable of responding to the caster's thoughts as it changes length, weight and flexural profile to suit the task at hand.
Gordy
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