I'd rule a "strength-based bow" to have the normal stats of a long or short bow, but with the ability to add their strength modifier to the damage roll. Definitely don't let it apply to the attack roll.
Presumably, the choice of a Strength-based bow over a Dexterity-based bow is being made because the character has a higher Strength score than their Dexterity score, so the increased accuracy and damage from the higher ability modifier will already cover the bow's heavier draw weight resulting in more damage (and it's fine to use Strength for the attack roll modification because A) Strength bonus to attack rolls of bows was the default in AD&D, though exceptional strength (the % stuff above 18) required a more expensive than normal bow), and B) higher draw weight means more force exerted on the arrow, means faster flight, means harder to get out of the way of - and complicating things by making up the only weapon in 5th edition that requires 2 stats to shine isn't worth it). So the only unrepresented advantage of a higher draw rate is potential for longer range. And since the range of a bow is already long enough to be practically the same as "the entire battlefield", there isn't much meaningful about increasing the range.Strength based bow
Iron bow, 1d10, short bow ranges.
For simplicity's sake, why not just have the use of an Atlatl increase the range of darts or javelins thrown with it to 80/320?Atlatl
Uses Darts as ammo, 2d4(too little?) Have not settled on a range, maybe same as Short bow as well, for simplicity sake.
Out of curiosity, why shouldn't strength be allowed on the attack roll? If I was trying for big damage and big range, I would agree with you, but in my mind the small effective range is because of the lack of finesse applied to the shot.
One of the few weaknesses for strength-based characters is their general ineffectiveness at ranged combat. Get them in close, and they'll outdamage most other dex-based melee characters with a gap that only widens as they get more and more attacks each round. By giving these characters strength-based ranged weapons, you're removing a disadvantage that seems to have been intentionally added by design.
Also remember that a short bow has a range of "only" 80 feet before penalties get applied, and since so few combat encounters deal with ranges beyond that, it's just really not much of a penalty or form of balance. It just makes them pretty much equally effective in ranged combat as they would be in melee combat, other than not having the GWM feat apply.
The player assures me that he will be ranged, only using melee in the most dire of circumstances. Also, I will not be allowing feats yet, so GWM is not a variable in the equation.
Famous last words.
Anyway, what exactly are they trying to accomplish with strength-based ranged attacks?