i think the fishing line shape is kind of like diagram below. (turned 90* vertical, the lines below would represent a supple rope or chain hanging under its own weight, ie constant weight/unit length.
http://en.wikipedia.org/wiki/Catenary )
but as shown below, the lines would represent fishing line being pushed back by water resistance, but held down by the weight of a lure (that has no resistance itself). i don't think this is a completely accurate model of trolling situation because the water resistance on the line is probably not constant/unit length, but is probably determined at least partially by its angle to the flow.
for horizontal force varies by angle - see the wiki non-uniform chain derivation. i think you would just need to substitute an equation for water resistance of the line as a function of its angle for 'w', then solve for rho.
in any case, i think there is a line length where there's sum total enough water resistance on the line that the lure won't go any lower. instead, any additional line is basically going straight out along the water.
but given the choice between charts, equations, guessing - i would just do whatever Skip says,...
