Good comment on the Art and the Mastery.
We must all learn to crawl before we can walk.
Here are a few of my observations.
As for the flat path of the rod tip or the straight-line path of the rod tip.
What dose the straight flat line path of the rod tip(SLPT) do.
First we must look at how you are forming the loop and how the path of the rod tip comes into play.
On a Speycast the Dynamic ((anchor leg) which will become the top leg of the loop) leg must be kept under constant tension and should form a ascending d-loop (more so with long belly lines than with short).
This Dynamic leg will become the upper leg of the loop and must be reaming fairly flat until we arrive at the firing position
At this point many people will drift the rod tip up and back to obtain even more length to their rod stroke. From the firing point to the stop stroke should be have slight upward trajectory this will maintain a tight loop provide the caster dose his part at the stop.
Mainly stopping the rod I high position.
By keeping the SLPT we can be assured that out cast will go in a straight line from our firing position and our loop will roll out and finish in a straight line from where it was
The Under hand and SLPT
The use of the lower hand in the underhand cast give a large amount of speed to the rod tip which will react in a forward motion and not now even though you are pulling it down like a double haul
The upper hand set the tip position at the stop some caster use the underhand stopping at their belly provides the stop Others will us the upper hand stop and In doing the this the moment when you rod feel the movement of the lower hand your top hand acts like a pivot to stop the rod.
If you have a chance to film a good under hand caster Such as I did with Dana At the Sandy River Conclave and do it with fast enough speed.
I shot Dana at 15,000/1 of a second you can see many thing that become apparent with you slow it down to 20 frames a Second.
By studying these tapes and excretes from other under hand casters you can soon see just when and how to apply the under hand.
Just a few thoughts on the SLPT