Rich, I'm a bit of a duffer when it come to mathematics but I can offer a "lay-mans" interpretation.
There will be an optimum weight of the whole projectile, the lighter it is, the further it is likely to fly, but it will be more susceptible to side winds etc. At the other end of the scale, a heavier arrow will need more energy to fly a similar distance though it will hold a steadier course, and is likely to "strike" harder.
There are a whole lot of trade-offs in the final item;-
Spine (the springiness) of the shaft, too thick and it will not bend - leading to a dead feeling, too thin and it will "porpoise" leading to excess drag as it settles into straight flight. I don't think a pre-bent shaft will do you any favours as it will probably "corkscrew" in flight and throw accuracy out of the window.
Weight of the arrow head (which makes the arrow bend as it resists acceleration due to it own inertia), too light will not get the best out of the shaft and too heavy is in danger of snapping the shaft on launch or causing a permanent bend which will destroy accuracy.
Flights or fletches (which will stabilise the arrow by increasing drag on the rear end, to name a few, again too small will not hold a steady trajectory, and too big will cause excess drag.
I've seen some atlatl launchers with weights bound to the middle section which causes bending of the launcher, also because the throwing action is in an arc, the arrow shaft is bent during launch.
I think theres a whole lot of fun to be had in experimentation with lengths of arrow and launcher, weights, spine etc to get the best set-up for the individual as no two sets are likely to be the same. I've adapted this from a few years of longbow archery but the theories are very similar.
This is going to be a great winter project.
ATB
Ogri the trog