do some searching on FOC.
Realize the energy formula you're using gives you a figure that really doesn't pertain to the way an arrow uses energy to penetrate.
Just use a simple inertia formula...wt x speed.
wtpops has a good point...but...some bows might be able to get that "VW" arrow going 60mph but can't get the "big diesel" going 60mph. so the question ends up being more like a VW going 60 and a truck going 40...hard to figure in your head right.
SO...you need to figure is it better to have a lt arrow going faster or heavy going slower....just as you questioned in your post.
Don't double the speed in the energy equation it just gives a number that doesn't pertain to what we care about.
if possible...Take a heavy arrow that shoots straight out of your bow. I mean a heavy total arrow. at least 13grns/# hopefully more.
Then find a lighter arrow that shoots straight 10grn/# or less.
Shoot them into something side by side. Something that'll not have voids or give much..like a new block target or something. If you really want to see a difference suspend the target so it swings.
You'll hear a diff when the arrow hits.
You WILL see a movement diff and/or a penetration difference.
Here is a REAL example from my bow and my chrono.
Guess which arrow I use?
Hint..568 grn.
Also. if you do any reloading think about sectional density being important...not so much ft/#'s. our arrows aren't blowing up inside the animal to use up energy...just passin thru.
Fun stuff!