E=mc^2 says that the energy is equal to the mass, AFTMA standards say that the first 30' of any line of a given size will weigh the same +/- , it follows then that any taper or profile of line within a size will have the same stored energy and thus, if accelerated equally (F+ma) will transmit exactly the same energy into turn over of the leader/fly. (it may be that the front taper decelerates because of reduced mass/foot, dissipating some speed/energy/force and giving a softer gentler presentation?)
AFTMA standards- https://www.affta.or...eight_specs.pdf
You have the wrong formula. E=mc^2 is Einstein's formula for the equivalence of energy to mass. There is no conversion of the mass of a fly line into energy during a fly cast. Einstein's formula explains the release of atomic energy in a nuclear reactor or in the sun where hydrogen atoms are converted to helium with the loss of mass and the release of energy
The formula you want is for kinetic energy, KE= (mv^2)/2 = one half mass times velocity squared. Momentum is P=mv
For a tapered line, the mass gradually decreases and therefore the velocity increases. Also the decreasing taper accelerates the velocity of the fly line. It is the bullwhip effect in which the degree of taper and the initial mass speeds the velocity of the whip so that it can travel at twice the speed of sound. The loop of the whip creates the crack and the same thing happens when a caster "pops" his cast.
A taper allows the fly line designer to modify the taper for casting heavy flies with a steep bass bug taper or gently land a fly for spring creeks with a long gentle taper.
"In order to propel a fishing fly through the air toward the distant quarry, a rather massive line, to which the fly is attached, is cast. As the cast line rolls out, the fly actually accelerates horizontally and seems to defy physical law. The phenomenon is modeled simplistically to determine the magnitude of this effect. In the absence of air drag, the fly can accelerate to increase its velocity by an order of magnitude. Air friction dramatically decreases the effect, but some fly acceleration is still predicted. By tapering the flyline in various ways, the fly velocity history can be significantly modified, and some tapers are predicted to perform better than others.”
The taper ALWAYS increases the velocity of the line. This is the result of the conservation energy. This is a law of physics so "(it may be that the front taper decelerates because of reduced mass/foot, dissipating some speed/energy/force and giving a softer gentler presentation?) is not true. The taper does NOT decrease energy or speed.
What happens is the air resistance decreases the forward velocity which decrease the KE as the cast progresses and the mass of the line in the fly leg is decreases. The fly leg is the part of the line that has forward velocity and the rod leg is fixed and stationary and has no KE.
It is the fly caster that modulates the energy input to match the fly line taper so a fly lands gently or the cast bounces back if too much energy is used. The caster does the same with a level line also. The fly line behaves according to the laws of physics. If it is cast in a wide loop, more energy is required to cast the line, a tight loop requires less energy to extend the cast.
Because of the taper of a fly line a tapered line requires less energy to cast a given distance with a given fly and the tip of the line lands more gently, there is NO disadvantage to a tapered fly line vs a level line other than cost but the line taper must be appropriate for the type of fishing that is being done.
Other than cost, a possible disadvantage is the increasing number of fly line tapers. This is like going out to a restaurant and having a 10 page menu vs a one page menu. Some may complain that there are too many choices. I really don't understand the logic of complaining about too many choices. You can always order off the first page of the menu and buy a vanilla WF or DT fly line.
Here is a primer on WF fly lines: