On Nov 10, 3:20*pm, "
wrote:
It would seem obvious that the force required to tension the line is not
used to accelerate it.

It is the same force. Ignore gravity and imagine a fly line suspended
horizontally. Add a force to one end. the line will accelerate in
that direction (F=ma) for as long as the force is applied. The longer
the duration of the force, the faster the line moves. The velocity at
any time is the acceleration times the time (v = at).

If you further acclerate the line with a haul, that adds to the
velocity imparted by the rod tip, and V = v(rod tip) + v(hauling
speed). Walla, greater line speed, longer casting distance. That's
a gross simplification without considering the flexure of the rod tip,
but it's the basic model.

As near as I can speculate based on my knowledge of the physics and my
ineptitude at actually doing it, my guess is there's a "magic" timing
and speed for which the haul effect is maximized without being mostly
attenuated by sudden tip flexure from the added load; but I'm
convinced in this endeavor, the art is of far more beauty than the
mathematics.