LongBows and Archers

[JCoyote]

out to about 100 yds you might possibly still get a slight horizontal angle against soldiers but beyond that they will be descending more vetically i think.and the cross section of the target is several times less than it is horizontally.

You guys are off on this. You keep imagining an archer targeting a single soldier, and that's just not how it worked back then. Sure up close, but not past 40 yards. Imagine the enemy groups. They are lined up and stacked deep. Going down vertically, the area total of the group of soldiers can actually exceed it's surface area at the front horizontally. When you are firing at a group like that, you are matching surface area to probability. In this case, a narrow line has advantages over a deep column, exposing your troops less to falling shots.