Why is the capacity of a barrel/bucket different for solids vs. liquids?

Question

The PHB states the following volumes on page 153:

• Barrel: 40 gallons liquid, 4 cubic feet solid.
• Bucket: 3 gallons liquid, 0.5 cubic feet solid.

Why is the volume for solids lower than that for liquids?

• Barrel: 40 gallons liquid ≈ 5.3 cubic feet solid (holds less solid)
• Bucket: 3 gallons liquid ≈ 0.4 cubic feet solid (holds more solid)

Could it that they are trying to estimate packaging losses in the case of the barrel?

A bucket could be filled past the rim when you put a heap on top of it. I could imagine this is why the bucket takes more solid.

Propably not very important, but it made me wonder.

Answer 1

A liquid has no definite shape and assumes the shape of whatever container it is, solids have their own shape

Because of this when you fill a barrel (or any container for that matter) with a liquid, it will perfectly utilise all available space without any losses. When filling the same container with solids, there will not only be empty spaces between the items and the walls of the container but also between the items themselves, this way you're losing some of the theoretical capacity. Imagine a barrel filled with potatoes, they will not perfectly fit against each other, some space will be wasted in the barrel. I believe this is the reason for the differences in capacity, they are taking into account that packing solids will be more wasteful than liquids. Exactly how much space you waste depends on what sort of solid you're filling the bucket with (e.g. potatoes will be more wasteful than grains of sand) but you will never get the sort of perfect fit that you can achieve with a liquid.

As to the difference in case of the bucket, it could indeed be due to the fact that you can fill it with a heap on top if you put something solid in, which you cannot do with a liquid but I think that this is more for convenience, 3 gallons (imperial) is about 0.48 cubic feet, this is very close to 0.5, which is easier to work with than, say 0.4 and unlikely to make a difference in the context of a game.

The volume lost in case of the barrel is around 25%, which is consistent with the densest sphere packing in 3 dimensions, the math behind this can be found here for those who are interested: https://mathworld.wolfram.com/SpherePacking.html. This does assume that you're using items spherical or close to spherical in shape but I think this is a fair generalisation given that D&D is a game, not a physics simulator.

Answer 2

No way to know

It's impossible to guess what the designers were thinking, and there have been no statements that I'm aware of that address this question.

Realistically, the whole concept is absurd. Even if we accept the historically unsupported idea that barrels are of standard size (even in systems where a Barrel was a defined unit, it has had multiple variants such as the Wine Barrel, Beer Barrel, or Oil Barrel, each with its own unique volume), the idea that a bucket is a standard measure is entirely silly. These numbers are, at best, suggestions and hand-waves and should probably not be taken too seriously.

For myself, I've always struggled with cubic foot measurements; without grabbing a calculator I couldn't possibly estimate how much stuff fits in a 4 cubic foot space, and that's ignoring the actual geometry of the storage space versus what you're putting in it. Technically, a steel rod 2 inches wide and 40 feet long is less than 4 cubic feet, but obviously that won't fit in an ordinary barrel. But would it fit if I cut it into 3-foot lengths? Heck if I know.