I assume it is not a whole lot like the one handed and two handed critical hit perks just do base weapon damage. But the UESP does not specify what the damage it from archery's three critical shot perks. A quick google search also did not yield an answer. Does anyone here know?

Crit damage is the same across all weapons. it is based on a % of the "base" damage. This makes all the crit damage perks rather unattractive.

The 3rd rank of the bow, does do somewhat of a noticeable increase in damage, but still not enough to invest the extra perks to get it.

That's what I feared. Thanks. I had to get one rank to get the ranger perk but I think I will leave the other two ranks unfilled, especially since I like using fast bows that don't do that much base damage.

Crit damage is described in the corresponding weapons section. The crit damage amount is typically about half of the base damage of the weapon, but there are some exceptions. Some glass weapons do not do extra crit damge at all.

http://www.uesp.net/wiki/Skyrim:Malachite#Glass_Weapons
http://www.uesp.net/wiki/Skyrim:Ebony_Ingot#Ebony_Weapons
http://www.uesp.net/wiki/Skyrim:Dragon_Items

Crit damage perks are not very popular because it's not affected by smithing or enchanting. But for non-enchanting, non-smithing pure warrior builds, or bound weapon only builds, the impact of the crit perks are quite significant. It can be a fun build if you want to try it out.

Criticals are done much better in Fallout New Vegas. The variety of ways to enhance critical events allows 100% chance in some specific situations. Usually the amounts are not far from Skyrim's but in some situations, gear and consumables stack to allow much more critical chance.

You need to know what you are doing but one can build towards criticals as a useful RP method. Having Luck as a characteristic does allow a bit more believable critical build it's true.

I can see how they might be useful for specialized builds that don't smith or enchant or use bound weapons. I had a character that only used bound weapons and took all the bound weapon perks, but after level 40 or so, he gave up and started using corporeal swords that he smithed (no smithing perks) because he just was not doing enough damage with his bound sword. He still used the bound bow.

My current archer uses fast bows like hunting and forsworn bow, that have pretty low base damage. Seems like it would be more fun to put a couple extra perks into smithing and be able to craft more different types of arrows than get another five or six points of damage with those last two critical shot perks.