There's a website - really for the technically minded - on which things like the effect of tiller (which may cause the long-rod to flick upwards during the execution of the shot) arrow spinning, bracing height, Archer's Paradox etc. are pretty definitively discussed. I don't understand the mathematics as much of this is about engineering and ballistics,
but there are some very clear explanations in some parts of the site. It's called Topics on bow mechanics and is regularly updated.
Another possible reason for the long-rod flicking upwards of course might be "heeling" the grip.
Here's the website.
http://homepage.ntlworld.com/joetapley/