I have done the math too and a heavier arrow will produce more KE at closer range and less KE than a lighter arrow at longer range.
I respectfully submit that you have done the math incorrectly. Going to a heavier arrow will increase the amount of initial KE and the advantage you gained over the lighter arrow increases the farther down range you go. All flight characteristics being equal, heavier arrows maintainke and momentumbetter then lighter arrows. Go to the web site I listed and then go to vortex shedding.
This is n argument that can be settled by no one here with out the quatitative fomulas. All it is is physycs.
I gave you the formulas and a web site that will confirm they are the correct formulas. You can also find them in a physics book. And btw there are a lot of people here that are more than capable of solving the equations and understanding the physics.
In theory, yes, a hevier arrow will broduce more PE and KE. However, the arrow will fly slower and have a different trajectory
Absolutely correct, and that's the tradoff. Going to a heavier arrow will give you more PE & KE but also a bigger arch in the trajectory. Whether or not it's worth it is open to opinion. Whether or not it's true isn't.