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Minor Alchemy allows you to transmute one object into a different material. What happens if the object is in motion (example: arrow in flight) when it reverts? What is the effect of mass changing while in motion? Does it stay at the same speed, and somehow the reverting just gives it a huge increase in momentum? Does it slow down, conserving the amount of momentum? If the rules specify (doubtful) then great. If not, I'd like some sort of a physics perspective on the question.

I'm mostly worried about two things:

  1. If it doesn't change speed, you could just throw a very heavy object that has been transmuted to be really light, then release the transmutation right at the end, landing with a hugely powerful amount of force?
  2. If it does change speed based on mass and momentum, then you could shoot a ballista with a spear of a very light metal transmuted into a very heavy one, then reverted once it was airborn, giving it a huge speed boost. No way you would normally be able to send that light of a spear with that much force.

Either way, either you get an advantage from going from light to heavy, or you get an advantage in going from heavy to light.

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Alright, as both a physicist and a DM these are the questions that also haunt me. I'll answer the second case first.

Althought it'll never happen in real life (an object of macroscopic size won't change mass drastically in an instant without that mass going somewhere or being converted into energy), there should be no difference in the energy of a heavy bolt being shot by a ballista and transmuting into a lighter bolt than in the energy of a light bolt being shot in the first place. This is simply due to the law of conservation of momentum and to the mechanics involved in an inelastic collision. This is due to the fact that a heavy bolt shot by a ballista will initially be going much slower than the light bolt, and the transformation between the two should just compensate for this. Same thing for a light bolt being shot then becoming a heavy bolt, it'll lose speed so that the momentum is conserved. This is keeping in mind that the momentum affects the force of the impact, and therefore there should be no difference in impact damage. This would be the physically accurate answer, but it's also the less entertaining one for gameplay. As @Lexible mentioned in the comments, in heavy-to-light transmutation, the range could be doubled, but that is up to you the DM.

In the first case, well then that's your call as a DM. This could be hugely fun for your characters (polymorph a tiger into an ant then throw it and release polymorph, have your barbarian throw it to create a pseudo tiger catapult), but could also be a handicap if the enemy does the same. The rules don't cover this, and since D&D is by design open to this kind of thing, don't hesitate to break some of the laws of physics to improve gameplay!

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    \$\begingroup\$ Your first paragraph almost covers it. The important difference is not in the penetration/damage of the heavy projectile that become light and fast, it is in the range of that lightened projectile. The much faster traveling spear should, perhaps, have it's range multiplied, potentially by quite a lot. For example, my spear now travels miles. \$\endgroup\$
    – Lexible
    Oct 19, 2016 at 18:12
  • \$\begingroup\$ Whoops, should have written second paragraph. :) \$\endgroup\$
    – Lexible
    Oct 19, 2016 at 18:19
  • \$\begingroup\$ Well, if we're gonna get physical about it, while it would be greater I wouldn't say the range is increased by all that much for two reasons: wind resistance, which will slow down the lighter spear more quickly, and the fact that the presence of cold/warm cross air currents and the coriolis effect would affect its accuracy on a range of almost a mile (much like a sniper's bullet). So yes increased range, but doubled at most. \$\endgroup\$
    – QuantumDM
    Oct 19, 2016 at 18:19
  • \$\begingroup\$ I have a question, since I'm not a physicist I may have some misunderstandings: does the conservation of momentum implies that the (des)acceleration will be the same? I ask because as far as I know f=ma, if m changes but a is constant, would not it mean a change in "damage"? \$\endgroup\$
    – Chepelink
    Oct 19, 2016 at 18:24
  • \$\begingroup\$ The force of impact is the equivalence of the change in momentum over time, which we'll assume to be constant since those calculations are too complex for this kind of exercice. But conservation of momentum implies that the heavy spear will go slower, and therefore while m increases (decreases), a would decrease (increase). \$\endgroup\$
    – QuantumDM
    Oct 19, 2016 at 18:27
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Neither condition results in different damage per se, but both conditions result in changes to the range of the missile.

Assuming momentum is conserved, condition 1 would result in a light-to-heavy missile dramatically slowing, but potentially being placed so as to easily drop on those below. If the timing of the flip can be precisely known by those hurling the missile, then in game-play terms they could effectively create either a longer range for their heavy object if it transforms at the end of its flight (e.g. I can easily throw a ball 120 feet, but I cannot easily throw a sledgehammer 120 feet; now if that ball transforms back into a sledgehammer at 119 feet...), or could effectively create a "hammer drop" maneuver (like the overhand Frisbee hammer throw) for the heavy-to-light missile if it transforms back into heavy mid flight and effectively dropping it's velocity to near zero, allowing precise targeting from above for a practiced attacker.

Assuming momentum is conserved, condition 2 does not change the amount of force of the projectile, it changes the velocity of the projectile. Any resulting damage will be a consequence of velocity * mass. The game-play consequence is that with greater velocity your heavy-then-light projectile travels farther. The earlier in the flight the transition occurs, the faster the light missile will fly. The DM will need to rule on how the added velocity affects the missile's range.

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This is the DMs call, in most cases there is no difference

It is well established that the D&D rules do not adhere to the rules of physics, just look at falling damage. D&D is not a physics simulation, it values speed of resolution and simplicity of rules far over accurate modeling of physics. The reason for this is that for most players it is no fun to break out the calculators and compute acceleration or solve trigonometry problems in the midst of a heroic fantasy session.

For cases where this would lead to egregious deviations from expected outcomes and break immersion of the game's fiction, the game relies on the DM and common sense to make ad-hoc adjustments and rulings as needed. For example if you could turn an arrow into water in mid-flight, this might call for such an adjustment.

However, look that the materials that Minor Alchemy offers:

You perform a special alchemical procedure on one object composed entirely of wood, stone (but not a gemstone), iron, copper, or silver, transforming it into a different one of those materials.

So your arrow will consist of wood, stone, iron, copper or silver. They are all hard solids, and their flight behaviour will be quite similar. The simplest way to deal with this is to rule that it has no effect, unless you are trying to hit a werewolf and you just lost your silver projectile.

Why only "in most cases"?

There might be special situations where it is worthwhile to get into the details, for example if you come up with an elaborate plan between sessions and can clear this with the DM without wasting everyone's time. At most you can create an object of 5 cubic feet because the feature also says

For each 10 minutes you spend performing the procedure, you can transform up to 1 cubic foot of material. After 1 hour, (...), the material reverts to its original substance.

Let's say you obtained and want to abuse a trebuchet. The DMG (p. 256) says it is typcially throwing a Trebuchet Stone for 8d10 bludgeoning damage. Trebuchts came in all forms and sizes, but a typical medieval one apparently threw stones of about 100-200 lbs, so lets assume it can throw that.

If you look at the specific weights below, that would allow you to throw a wood ball of all five cubic feet in light wood. You could turn an iron ball weighing close to 3,000 pounds into this wood (worth 300 gp; a copper ball would cost you 1,500 gp in material, and silver, 15,000 gp but would be even a bit heavier ... which is unlikely to be needed, read on).

If you let it revert at the top of its arc, timed everything just right and calculated correctly how much slower it would progress from there to pinpoint where it will drop, it could deal considerable falling damage from a height of 200 feet. Possibly 1500d6 bludgeoning using the assumption it linearily multiplies the damage it deals for dropping 10 feet.

That amount might be worthwhile going through the motions. Of course, it would depend on your DM playing along. They might just say nope, it's 15 times the heaviest stone, so it will be 120d10, or, they might say, nope, we'll use the CR 17-20 deadly trap (DMG p. 121), and the cap is 24d10.

Substance Specific Weight Comment
Wood 20 lb/ft3 Cedar
Wood 94 lb/ft3
Stone 145 lb/ft3 Sandstone
Iron 491 lb/ft3
Copper 559 lb/ft3
Silver 655 lb/ft3
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