Like most things in archery, particularly traditional archery, I think this is more of an art than a science, and there are a lot of variables in play, especially your loose and how well spined your arrows are.
Having said all that, I have recently seen the light and converted to longbow after 25-odd years with the devil’s toys.

As a result, I have done a lot of testing and experimenting with (among other things) fletching size and shape; which accounts for why my kitchen looks more like an arrow factory than somewhere you’d like to make food!
For what they are worth, my personal conclusions are:
- There are more problems associated with fletchings that are too big than too small.
- For me, no normal longbow arrow (ie excluding mediaeval bodkins, hunting broadheads and the like) needs a fletching more than about 3 inches long, provided it is not cut to an exceptionally low profile. I have successfully used 2.5 inch low parabolics or shields on arrows as heavy as 600 grains, although, just for peace of mind, and because cast is not an issue, I usually use 3 inch shields, 3/8” high.
- If speed/cast are an issue, avoid high profiles, and many off-the-shelf shapes are too high for optimum performance. High profile shapes tend to flap and vibrate along their edge, increasing drag out of proportion to their area.
- Similarly avoid shapes that have ‘swept-back’ tail ends (eg so-called ‘traditional’ ‘mako’ and ‘ninja’). These also flap and vibrate. If you just like the look of them, that's fine, but you may pay a price in cast.
- I can discern no difference in cast or stability between shields, parabolics or any of the other curved shapes, provided, they are have more or less the same total area, and are of much the same (lowish) height.
So the upshot is that I now use 2.5 or 3 inch low profile parabolics or shields on all my target arrows ranging in weight from around 300 to 600 grains with no problems – or at least, none concerned with the fletchings.
Like I said, very personal, but I hope this helps - keep 'em short, keep 'em low.