I don't know I you have seen this news yet, but Adam Karpowicz has been conducting a number of flight shooting experiments with his horn bows using a shooting machine. Up until now, most of his test shots landed at a distance of 500-600m, but just recently he was able to send an arrow a distance of 790 yards! This is truly amazing, regardless of how the arrow was shot. Adam is quickly approaching the holy grail of flight performance.
The bow he used is 120lb at 27 inches. Arrow is split cane bamboo, 208 grains, and 24.5" long. The string is Dacron, but I imagine a good linen string or even a silk string would improve performance even more.
Here's another interesting fact. The place where Adam runs his tests is several feet below sea level.
Alan