When attempting to analyze a difficult problem, it is usually a good idea to make simplifying assumptions which do not remove the essence of the problem. We will assume that the line is level except for the taper at the tip, that it is limp, and does not stretch. The leader is an extension of the fly line. Gravity and air friction will also be neglected.
The principal physical laws involved are conservation of energy and conservation of momentum.
The transfer of momentum is mediated by the tension of the line (momentum change = force times time).
I dig into my file to find Ed Mosser’s article in the Flyfisher Fall 1980. Ed sent it to me in the 80s (he just tear off the pages of a magazine). All these elements are important and show two things:
1) Air friction is neglected, although this is the main issue in casting: if we use a thick and rather heavy line, it is just to transport an air resistant fly in the distance. That said COE is correct regarding the assumptions of the article, but to me “the essence of the problem”, which is air drag, is removed by this assumption.
2) There is a contradiction when saying COM is applied and that a change occurs because of line tension, which in itself means there is no COM in this situation. It is a purist view and I understand that making an article accessible to everyone might need discarding some rules to capture attention.
It is generally difficult to say that conservation (of energy, of momentum) is not respected; the reason is to help understanding an ideal situation which shows how the fly leg moves as its length diminishes. Then you describe exceptions to the rule to come back to reality. This has not been fully done in the article because air resistance is not taken into account, while line tension is, but again, this is correct regarding the declared assumptions.
Slight comment on the “centrifugal” force: to keep the loop rolling over there is centripetal force acting on the loop. If you integrate it on the half circle of that loop you find the common value of line tension pulling on both ends of the loop, the loop itself pulling on both legs. So there is tension as long as the loop is rolling over. This simple calculation is possible thanks to the first assumption. If you take air friction in account, the tension on the fly leg is lower than the tension on the rod leg because of air drag on the loop (Hendry’s Thesis). That tension pulls on the fly leg and fights again the air resistance on the fly leg too.
The “motor” of the system is not the loop only; it is all the moving parts of the line. They carry the energy necessary to send the fly in the distance.
I have used the stroboscopic data of this article to create my first casting model, so I agree with numbers although their interpretation is arguable. Globally, the authors consider that if the energy does not come from rod elasticity, then it comes from the swing, in other words from arm lever. Interestingly, it is mentioned that the spring energy may not go into the line but rather in the counter flex, on which I do agree. In some cases, all the rod elastic energy may go into the counter flex. The logic conclusion would be that nearly all the line energy comes from the “swing”. What is qualified is the fact that the elastic energy represents 17% of line energy, the result of a comparison, but not that this elastic energy goes into the line (no proof up to now). On the other hand it can be shown that pure swing energy (arm lever) is about 55% to 60% of line energy and that the remaining part is due to rod elasticity indirectly. As mentioned a couple of times, there is no way to split neatly leverage and elasticity in terms of energy. The elasticity of the rod implies that the caster add the “17%” needed energy to comply with the rotation speed of the tackle, and in return, he gets an interesting increase in kinetic energy of the line, the 40% to 45% energy which are not coming from pure leverage. There is no suitable name to describe this part of line energy; it comes from both the elasticity and the leverage, but when there is no rod elasticity, there is not such contribution.