The reason a bullwhip cracks (tip exceeds speed of sound) and a fly cast does what it does is due to pretty much the same physics. When the cast is launched, when the whip is stroked, the whole line/whip is in motion and has an initial kinetic energy. As the cast/whip straightens out, the energy what was in the part that goes straight gets transferred into the ever decreasing mass of the moving part, accelerating it. In the case of the whip, the effect of air resistance is not enough to prevent the tip reaching the speed of sound and cracking. In the case of a well executed fly cast, the effect of air resistance and the front taper is just enough to bring the fly to a stop just as the line is straightened out. You all knew there had to be an S&M connection to flycasting, You just didn't know what it was.  Now you do.

When we discuss the mechanics of a fly cast, we can't use the simplest statement of Newton's 2nd law, F = ma, but the more general statement that force is equal to the rate of change of momentum with time. Momentum being the product of mass and velocity, we take account of the changing mass of the moving part of the line with the v dm/dt factor.  (Mike McGuire)

Let's leave the kinky stuff aside :>)  The bullwhip is out of the picture at the beginning of the forward of a well executed, the rod is becoming fully loaded/overloaded as the arm moves forward,  the line is being accelerated forward now we start to consider why the cast falls apart.  (Al Baldauski)

I think we need to define what we mean by the beginning.  Is at the point where the back cast is completed and the rod starts to move forward,  or at the point where the rod is stopped and the cast launched? In the latter case it's clear that given same size loop and launch velocity that the advantage goes to the heavier line. In the former case it's a question to what extent a rod limits ability to achieve that same size loop and launch velocity.  (Mike McGuire)

I take your point.  Each rod has a limit on how much line can be aerialized either the backcast or forcast (not necessarily equally).  The more line "under control" in the backcast, the more likely you'll have control and hence velocity on the forcast.  So I guess one can't really define a beginning point, it's all important.  As to the question of heavy line vs light line casting farther:  I'm guessing the heavy line wins.  I don't know how to prove it, though.  Other than a competition between two rods of the same taper and length designed for two different line wts cast by multiple "good" casters and averaged.  (Al Baldauski)

I really fail to see in what respect 'ma' differs from 'change of momentum with time', since acceleration is the rate of change of velocity with time. Surely a little basic mathematics has the two rhs expressions being equal. The concept is complicated enough as it is, without making it more so.  To determine a point of failure it is not necessary to have the mass changing for any given calculation; you just have to do a series of calculations, each with a little more line mass.  (Peter McKean)

Aren't both mass and acceleration changing throughout the cast as more line exits the rod?  (Dave Burley)

My point is  that it does not need to be a changing mass.  We do not, for the purpose of experiment at least, have to perform a traditional casting routine where we seamlessly (?) let out more and more line until we collapse the whole gizmo.  We could, surely, do the calculations on a series of set line masses, increasing by aliquots until we reach collapse.

But you know, you have to remember that I am a biologist and not an engineer, and that my primary entry was couched more in the form of a question than a statement.   Somebody tells me I am quite wrong, I am perfectly happy with that, as the object is to learn something here.  I am not a rod designer, either, but find the subject as presented to be fascinating!  (Peter McKean)

I was just making the comment in a roundabout way that if this was an easy subject it would be no fun.

My point was that as the cast progresses and the line feeds out, the total mass (not the mass per length) of the line hanging beyond the tip of the rod is changing with time = dm/dt. Ditto the acceleration (positive or negative) is changing = da/dt.

I think it is pretty obvious that in an unassisted cast the mass of line in the air increases and the acceleration decreases, since the energy imparted by the caster is a fixed number once the forward motion of the rod is stopped.  There may still be potential energy in the bent rod being converted to kinetic energy.

In my first college Physics lecture and before I knew Calculus, I whispered to the fellow next to me.  "Pssst, what is that fraction dx/dt ?"  {8^)  (Dave Burley)

In the case of a  flycast, both the velocity and the mass of the moving part are changing with time and have to be accounted for to correctly describe the  motion. Thus the total force acting on the line is m dv/dt + v dm/dt. In more simple dynamical situations where mass is not changing, dm/dt is zero.  As Einstein said, scientific explanations should be as simple as possible but not more so.  (Mike McGuire)