It's a common misconception that size has anything to do with the range of a bow.  It's all about pull. (leaving aside arrow characteristics)

Most games have the yew longbow as the pinnacle of archery, but that's simplification at best and ethnocentrism at worst.  Given time and technology, humans will come up with a bow that matches the pull of a human male, that uses the materials available locally, and that fits a style of warfare that suits the environment.

The English had yew, and developed the longbow.  The Mongols lived in steppes, had access to a range of animal materials, and developed the composite bow.  The Japanese had no access to cheap and plentiful metal, and developed the yumi.

And guess what?  The average Yew longbows and Mongolian horse bows have pretty much the same pulls.  Why?  Because there aren't many homo sapiens who can pull more than 120 pounds, and even less than can hold it.  We have preserved Mongolian bows with higher pulls than any preserved longbows, and I won't comment why that may be.  I must have spent a 100 hours debating, yelling, and shooting (targets) over that argument. 

Yumi have much lower pulls, but this can be explained by the simple fact that armor and shields played a much lesser role in Japanese warfare.  50-60 pounds was enough, and accuracy was a lot more important that penetration.

I think too many people get there knowledge of weapons and armor from games, video games or things like Dungeons and Dragons.  Understand that games tend to want to balance things and make them fun to use, not be as historically accurate   Take the Scythe in D&D 3rd edition.  This was the weapon of choice for power gamers, 4x criticals.  Do you know how Scythes were really used in war?  By peasants who moved the blade so it worked like a really shitty spear.  It was a terrible improvised peasant weapon.  But, in a fantasy setting, you could be a bitchin' Grim Reaper with it.  

Quite. A bow's range shouldn't come into play except for in really BIG maps

1) You should add the [eInfo] tag at the start, as it seem more like a question than instructions.

2) A possible fix for this issue, is as follows: create 2 sets of weapons. The first is used by the player, the way you described.

The second is a melee weapon, a copy of the bows, that adds the ability to shoot. This way, the AI (whos units are already built with this!) have the correct programming, since he has no reason to charge with the archers (I hope).

3)Regarding ranges, you could set an optimal range, and add with abilities lesser ranges, with different accuracy.

Also... I'm pretty sure that the British longbows reached up to 400 yards.

For the same "tech level" of bow, the longer a bow the higher the pull.  The higher draw weight short bows are laminated, composite or both.  Those would require more research so length is relevant.  Long bows also used longer, heavier arrows which gives them both a longer effective range (the higher mass of the arrow makes indirect, plunging fire more effective) and a higher effective draw weight (the same draw weight applied over a longer distance).

To sum up what needs to be done for bows and techs, ranges, and accuracy over range.

I believe you about the pull weight as I used a compound bow myself as a teenager when I did most of my archery and also when I did my research and now it makes more sense.  So what makes sense in game as well as staying as close to reality as reasonable.

Should there even be a short bow in the game?  A crude bow for tier 1, longbow for tier 2, yew bow for tier 3 and composite bow for tier 4?  is this acceptable given the present conversation?

For as far as ranges go what should the final verdict be?  Have the AI updated so it can deal with range limits on bows or ask for them to implement a accuracy reduction beyond a certain point?

Obviously this is a somewhat subjective list of things to answer or to even ask to begin with. However, can we please answer these questions or as a community can we come up with good questions that need to be answered to deal with this problem constructively.

Sounds like we want tapering armour penetration.

Fine against unarmoured opponents at all ranges, worse against armoured opponents at range, but don't lose effectiveness when the enemy tries to close in on them? Or will this STILL make bows too shitty when trying to gun down opponents?

First tier should have both a long and short bow.  The long bow should not be usable while mounted and have about double the range and higher damage.  Second tier (laminated?) should increase range and damage on both.  Short bow should have about 3/4 the range as the basic long bow.  Long bow should now require either the Strong or Muscled trait.  Third tier (composite?) should increase range and damage on both.  Short bow should have the same range as the basic long bow.  Long bow should now require both the Strong and Muscled traits.

The AI should be updated to deal with range and an accuracy reduction should be implemented.  This would allow for differentiation between weapons with similar ranges (throwing axes and knives) and tweaking those with unlimited range (magic, perhaps?).

In order for any changes to matter, however, combat needs to be rescaled.

No. Definitely not true for modern replicas, let alone cheapos, and I do not see why it would be true for historical bows, either.  When you have the luxury to make (have made) a custom bow, the length is decided by your height and arm length, and then you try for a particular pull by varying the thickness of materials and the proportions/mounting points. I'm talking about composite bows, of which I have three, one of which I helped make. 

True, but irrelevant.  If you do not have lamination/composite tech, there's only a few woods that can make a high pull longbow, and no wood that will produce a short bow that's more than a hunting tool.  The composite bow would not have been developed in the British Isle, because there was no need. You can use longbows from horseback, and not just the asymmetrical yumi.

A heavier arrow will receive less velocity from the same stored torsion (and the same energy)  It will not go noticeably higher (and thus accumulated more potential energy), and it will not have a noticeably higher kinetic energy at the point of impact. 

It is true that a heavier, longer arrow suffers less from air resistance. But the effect is minimal, especially since there no reason that a horse bow has to use lighter arrows.

Another common misconception.  Few people realize that a composite horse bow bends in a COMPLETELY different way from a long bow.  If I could still I pull my Hungarian, the distance between the tips would be barely half the distance between my hands.  The angle formed by the string is such that I could not use a Mediterranean draw even if I wanted to. 

I did not draw my horse bows any shorter than I drew my longbow. If anything, because I used a thumb ring, my draw was about an inch longer than it would have been if I were a medieval English longbowman who would not have known about thumb draw.  Every archer usually draws to the same point, no matter whose bow he uses, and strives to own as heavy a bow as he can handle comfortably.

So then how do we handle this in game?  I love the interesting correction in my knowledge base but how do we fix this in game?  How do we solve this showing technological progression from not so good bows to great bows?  What stats do we use?

I think that significantly improvements to the way bows work have to come from the developers, because the AI must be changed to take advantage of them.  And if Stardock does not think that tactical combat need to be made more complicated, they may not do anything about it.

As for realism and historical accuracy, do we really care?  I should apologize about my ranting, it was not very useful.  If I was making a game for my buddies, I would go "hunting bow", "crude long bow", "seasoned yew longbow", "composite bow", with only an small initiative bonus for the last one.  And then I would not do anything for the rest of my days but defending my choices. And the names would confuse everyone conditioned to think that "longbows are just better" (the same crowd that think "katanas are just better")

By the way, historically, composite bows would be inferior to longbows in a humid climate.  But this is a level of detail we do not need.

So, to recap, I would love the developers to introduce cover, obstruction, and units that shield others.  Until then, we will have cavalry charging from outside an archer's range, and archers picking out familiars without the opponent having any options.

Actually those names work for me and lets face it people will understand the point if you put them in a specific order in the research tree and the attack/penetration values.

About penetration values, Should bows all have a similar but linearly scaling base attack value and a exponential growth in penetration?

So the hunters bow does close to a yew but the yew can penetrate armor far better.  Making it so that while bows may not do a great deal of damage they do consistent damage against all armor types.  

The balance against bows is large shields that give bonuses to dodge against range thereby avoiding bow fire.  This was something I sort of solved with the armor mod I have been working on.  Tower / arrow shields are specifically used to avoid missile fire.  I do agree about the cover system needing to be implemented with a LOS system.  That and increased tactical battlefield sizes would make for really interesting tactical battles.