Very cool !
Bowmaking was a hobby of mine for several years, good strong wooden bows in mesolithic to medieval style. For prehistoric hunting games or medieval reenactment as well as experimental archeology. Can't do it any more because where i live now there is not the right wood and these things are weapons here and the country is pretty restrictive with that.
Be it as it may, you said simulation, and like anything physical it is not trivial. The flight of an arrow is not just a parabolica under the influence of air drag.
Let's start with the bow, when it is opened, there is stretched on the front and compressed on the back. The energy it can release before it breaks is determined by the amount of such deformation and the speed with which the material returns to the state of a stretched cord (except those shooting bycicles aka compound bows). Btw., bows are kept with the string taken off.
An arrow is stabilized by its shaft and not the feathers, these are mostly just decorative props. The shaft is set into a swinging vibration when the arrow is accelerated. The "stiffness" is defined by tapering the arrowshaft so that its strength corresponds to the shooting strength of the bow. This is, of course, done by machines these days and one can buy sets with given strengths en gros in wood or plastic or fibre ....
The shooting strength is measured in lbs, the spine of the shaft in grains (them 'Murricans, can't help ...). Every arrow in a set must be of equal strength, or some will turn the one or other way before they hit, which can be equally funny and annoying ...
An arrow in flight: Arrow in flight
Traditional Bowyer's Bible (Volumes 1 to 4)
A whole lot of papers from experimental archeology, like for instance:
https://www.cambridge.org/core/journals/antiquity/article/experimental-archery-projectile-velocities-and-comparison-of-bow-performances/2C1D9F880201D2EDBBAFDEB3A283048F
... and more. If they are behind paywalls, try arxiv.org with the doi as a search criterion.
Further search terms will reveal a plethora of information: Physics of Archery, Experimental Archaeology, Bowmaking, Prehistoric Hunting.
Hope that helps and isn't slightly overpowered ?
Edit: try this, it has some of the formulas you need. You will eventually want to model the air drag by yourself. Big feathers, short flight, small feathers, long flight ?