Vern,
I never really read up on it that much. Do a google search for "physics of fly casting" and you'll likely come up with some simple reading material, and names of authors if you want to get more serious. Unless you really want to get into the math of it, I think it's pretty straight forward. Of course, doing it is a different thing altogether, I can talk a good game but I'm really not a very good caster.
The rod indeed acts as a spring. This is a whole separate physics description from the hand on the rod. That was describing the best way to transfer energy from the hand to the rod, what you are talking about is how to transfer energy from the rod to the line. Doing both as efficiently as possible, obviously, leads to the most efficient cast, but it is two seperate energy transfers that have almost nothing to do with each other. The transfer from rod tip to line has almost nothing to do with the weight of the reel either, provided the weight of the reel is below the fulcrum, and I've never seen a rod so misbalanced that this isn't the case.
The spring action of the rod: Think of it as potential and kinetic energy, the rod stores the energy as potential energy. Line straight out on the water, you moving the rod tip back is "loading" the rod, like loading a spring. A haul here adds a little more energy. You should always be accelerating back, so that you're continuously loading it more and more and not allowing it to unload any of that energy before you want it to, and the line stays straight so that its weight and friction is always at a maximum. You unload the rod by abruptly stopping the rod tip, which changes all that potential energy stored in the rod into kinetic energy in the line, throwing it behind you. This stopping of the rod should be done at a height so that the line follows a straight line back. Now you want to wait until the line straightens out, so that when you start the forward stroke, you are pulling against the maximum weight AND momentum of the line, another haul here adds even more energy to the rod. You accelerate the stroke as before. That keeps the line straight behind the rod tip, i.e. maximum loading. Again you stop the rod and transfer the potential energy in the rod into kinetic energy in the line.
In a vacuum, you can keep right on going, adding more and more energy with each back/forward stroke, and cast really, really far. In reality, air resistance takes its toll, and when you reach a certain energy in the line air resistance takes it at the same rate you add it. This is why shooting a line is successful, you have enough energy in the system to cast that line, but you don't want it flinging around because then its adding more air resistance and taking away energy during the false casting.
When describing energy transfer from rod to line, its actually much more like a whip than a bow or lever. And just like a whip, the less stiff the line the better it'll be. Those old silk lines were actually far superior in casting mechanics as a modern line, of course most of us are willing to sacrifice that performance so we don't have that horrible maintenance. And unfortunately, the most efficient cast ends in the Orvis model "arm forward" pose and a straight line and leader. From a fishing perspective, you want to shock the line before it hits the water so that you DON'T straighten the leader or the line, that Orvis model might score distance points but he's a crappy fisherman.
As far as the action of the rod: Do a casting motion without any line. When you stop the rod, say, on a backcast, the momentum of the rod itself will actually slightly load the rod in preparation for a forward cast, thats without any line whatsoever. You want that maximum natural loading to occur precisely as you would start the forward cast, you're getting more energy in the rod than the line itself will impart. It's a timing thing. When Humphries talks about loading a rod without a backcast by "getting it in motion", this is what he's talking about, and its incredibly useful in tight brush situations, if only I could actually get the timing right.....
Of course, that timing is different depending on a lot of factors, but mainly, on how fast the line straightens out behind you, which is a function of how fast you threw it back to begin with. So, the most efficient action depends on the caster, and how fast they are moving the line, the action itself doesn't move the line any quicker. However, the successful distance casters do generate more momentum in a cast due to higher line speed, and thus a faster action is going to fit them better. If your casting stroke is slower, then you're most efficient action is slower.
