Very nicely described; Lefty has a way of putting things in simple understandable terms.
However TjP describes more than just curvature in the line in fact some of the description implies recoil and agressive stroke power, and he began without a leader which further promotes recoil especially when the power is high.
The "line follows the tip" analogy has a lot of merit but I have to wonder if it's the root cause here.
Line follows rod tip of course, but only if the line has momentum in that direction. Otherwise it just opens the loop.
Let's say I cast a 70 foot false cast with a longbelly line. I am tracking the line in a fairly small imaginary cylinder in the air, parallel to the ground and about 10 feet off the ground.
Suddenly, I drop the rod tip to the ground on the forward cast. If we over-simplify the description "line follows the rod tip" then we should expect that the line goes to the ground.
However you will note that the momentum of the line at the 10ft altitude and forward vector wants to continue in that track despite what the rod tip does.
To your point if the rod tip had been pulling the line in a different track through the stroke from start to finish, then the line will go in that direction accordingly.
I like very much to use simple tips as well but instead of focusing only on the rod tip (which is important) I also put some emphasis on the line itself and have gotten much better reactions from students in terms of application of power and tracking.
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