The next step would be defining haul distance and speed. How we measure them is something I think is best suited for the physics board.Pulling line through the guides during the casting stroke to increase line speed.
Given that the purpose of the haul is to increase line speed it makes sense that haul distance and speed would be derived from the motion of the line.
We know that if we take our line hand out of the equation by trapping the line against the cork with our rod hand and make a casting stroke we can measure the length of the stroke by how far the tip guide moves during the stroke. The speed of the stroke would just be the rate of change of the length/distance of the stroke. We can measure this at the tip guide or, since the line is not moving relative to the tip guide, we can measure the speed of the line itself up to the point of loop formation.
Since we've said that the haul occurs during the casting stroke, I suggest that the haul distance and speed be defined in terms of line movement relative to the tip guide during the casting stroke.
If we were to put a mark on the line near the tip guide the hauling distance would be the distance that mark moves relative to the tip guide during the casting stroke. In terms of an actual definition this would be movement of the line relative to the tip guide during the casting stroke (wordsmithing required).
The hauling speed would be the rate of change of the hauling distance (during the stroke).
Hauling speed can be average (total haul distance divided by the duration of the stroke) or instantaneous (the derivative of the hauling distance function at any point in time - since we are unlikely to generate an actual function for the haul distance in a measured cast, we would typically use numerical differentiation to estimate instantaneous speed, but that is a matter best discussed on the physics board).
