Assume that the line has a mass m per unit length. When the angler brings the rod forward, he imparts a certain amount of kinetic energy to the line. At the point where the forward motion stops and the line continues forward with a velocity v, a certain kinetic energy T is imparted to the line. In the absence of air resistance and other dissipative forces, this kinetic energy is constant. In the more detailed models discussed below, the feature that the maximum fly velocity occurs just as the loop unrolls is more or less retained.
Air resistance affects the motion of a real fly line considerably.
We can make an effort to include it in our simplified model as follows. We now take h, the vertical extent of the loop, to be non-zero and constant. Denote the time derivatives of x and z as xdot and zdot, respectively. Now, v is the velocity of the fly. The force of air resistance can be included by imagining the loop to be a vertical cylinder of height h and radius r.