Whats the damage of a colossal non-magical longbow under the effects of shrink item and a medium arrow?

Question

What is the damage of a Colossal non-magical longbow when under the effects of shrink item spell?

Now, your standard medium longbow does 1d8 and weights 3 pounds. Scaling it up 4 size categories means its now does 6d6 according to the damage dice progression chart and should weigh 3x2x2x2x2= 48 (originally used x8 from enlarge person, but YogoZuno pointed out on the weapons page). 12k pounds. Under the weapon rules, a large weapon costs 2x as much as a medium weapon, so said colossal longbow should cost 75x2x2x2x2=1200 (found on the weapons page and scrolling down to weapon qualities).

It is also worth mentioning that this weapon MIGHT also have a -8 on attacks roles due to the weapon being sized for a larger creature. Found on the weapons page by scrolling down to Weapon Size.

Inappropriately Sized Weapons: A creature can’t make optimum use of a weapon that isn’t properly sized for it. A cumulative –2 penalty applies on attack rolls for each size category of difference between the size of its intended wielder and the size of its actual wielder. If the creature isn’t proficient with the weapon, a –4 non-proficiency penalty also applies.

Now having shrink spell cast on this colossal longbow now makes it back into a medium sized weapon and weighs 48 / 4000 = 0.012 pounds. Since shrink spell makes no statements about what damage the weapon would do, we are forced to rely on spells such as enlarge person and reduce person, of which they do not agree on this topic.

Enlarge person

Any enlarged item that leaves an enlarged creature’s possession (including a projectile or thrown weapon) instantly returns to its normal size. This means that thrown and projectile weapons deal their normal damage. Magical properties of enlarged items are not increased by this spell.

Reduce person

Any reduced item that leaves the reduced creature’s possession (including a projectile or thrown weapon) instantly returns to its normal size. This means that thrown weapons deal their normal damage (projectiles deal damage based on the size of the weapon that fired them).

So on one hand, reduce states its the weapon that matters, while enlarge says it does normal damage. So the best examples we have contradict each other for what happens. Since shrink item is more in tune with reduce person as both deal with shrinking, this would imply that a shrink item(colossal longbow) firing a medium arrow should deal 6d6 damage. Are there any rules, errata, FAQs that say otherwise? Crying DMs/GMs do not count.

There are two similar questions, but they ask different things. Shrink Item and the Oversized Starknife is asking about a thrown weapon. How viable is shrink item and massive projectiles? is asking about the projectile and not the launching weapon.

Answer 1

The shrunk Colossal bow would deal 1d8P damage, just like a Medium Bow, regardless of arrow size.

In the absence of any special rules in Shrink Item regarding weapons, the damage of a shrunk item would be calculated as for any other smaller-than-normal weapon. The Colossal Bow might deal 6d6 damage, but after reducing the size four steps, the damage goes back down to 1d8, just like a bow that started life at Medium Size.

Unlike Reduce Person (or Enlarge Person), Shrink Item does NOT affect the ammunition fired by a projectile weapon. Even if the user also shrank some ammunition with Shrink Item, it would not automatically resize upon leaving the user's possession, and striking a creature or object is different to striking a solid surface.

In addition, the damage for a projectile weapon is determined by the bow, not the ammunition. If you look at the equipment tables, arrows do not have damage ratings, but bows do. Therefore, the size of the projectile is immaterial to determining the damage done. In fact, Short and Long Bows use the same ammunition, despite having different damage ratings. Clearly, the size of the ammunition is not the determining factor in the damage.

As reinforcement to this idea, see this related question about using ammunition with a different size to the weapon.

If you would prefer a real-world physics justification, the damage done by a missile weapon is likely some function of relative momentum. Momentum is a combination of the velocity and mass of an object. This is made clear by better bows in the game using the same ammunition - they propel the same projectile faster. Thanks to the conservation of momentum, if nothing else changes, an object in motion that somehow changes mass would change it's velocity inversely proportionately, leaving the momentum the same. In other words, if your bow propelled a small arrow at a certain speed, and the arrow suddenly grew heavier, it would likely slow right down. Magic, of course, might change this, but only if it says it does. Enlarge Person says it does (likely as an irl balance to, for some reason, prevent Enlarge Person from improving missile weapons).

Answer 2

Shrink Item reduces the Size Category

Shrink Item states that "This change effectively reduces the object’s size by four categories." Since the 6d6 damage came from being 4 size categories higher, reducing the size category by 4 reduces the damage back to 1d8.

I would avoid comparison to Enlarge/Reduce Person since they are separate spells with their own sets of rules. I would also avoid comparison to magical weapons, wands, or spells as this spell exclusively applies to non-magical items.

The spell specifies the damage change by using the specific term "size category". The spell first defines the dimension and weight changes, then defines how those changes interact with the item/weapon size category rules. Those rules apply as normal since there are no exceptions stated in the spell.