Does anyone have a good resource for low temperature viscosities of metals? I’m trying to calculate the timescale for viscous creep of gold and how long it would take a dragon to flatten its hoard.

This calculation has many parts. Starting with simply the downward pressure of the dragon's weight on the gold pile. Per the v3.5 #DnD Monster Manual, the body of a Huge dragon takes up 15 ft square of space and weighs 16 tons or 14515 kg.

(Remember that when we say something weighs X lbs, we are usually actually referring to its mass rather than true weight, which depends on gravity. So in this case we convert the “weight” to kg. I hate imperial units.)

The downward force of an object on the Earth is the mass times gravity, and the pressure is the force divided by the area. -> P = F/A = mg/A

I make the approximation that, while lying down, its weight is equally distributed between all parts of its body touching the gold, but that its body covers the 225 square foot area due to the tail, neck, and wings to wrap around the edges.

Our simple calculation yields a downward pressure of ~7 kPa onto the gold pile.

Assuming they have the same foot to body size ratio as an elephant, this comes to 0.3 MPa of pressure while standing on all fours, or 0.6 MPa on their hind legs. This is substantially more than an elephant, which exerts only ~0.05 MPa of pressure due to their smaller mass.

Now, the Monster Manual says that creatures in the Gargantuan category are 20 ft square and weigh from 16-125 tons. This gave me pause though, because the volume of a 20 ft cube is only ~2.4x greater than the volume of a 15 ft cube.

So if a Gargantuan dragon weighed 125 tons that would suggest that, as a species, they become denser as they age. The researchers who wrote the Manual did not discuss any physiological phenomena that could explain this effect, so we’ll assume that a Gargantuan dragon is ~38 tons.

A Gargantuan dragon exerts a pressure of 9 kPa on the gold pile while lying down, or 0.4 MPa while standing.

I did this calculation for the pressure while laying, but let’s pause to appreciate the standing pressure here. Soft rocks like clays and limestones have tensile strengths of ~0.5-5 MPa and compressional strengths from 10s-100s of MPa.

(Tensile strength = resistance to breaking while pulling apart, compressional strength = resistance to crushing)

This means that a rocky outcrop made of a weaker rock type would break just from a dragon standing on it. And this is just while standing still- the extra force during takeoff and landing could easily crush weak rocks!

This suggests dragons have to careful where they choose to land if they don’t wish to destroy the landscape or cause rock falls. Landing in soil would cause it to displace and they would sink part way in, requiring extra energy for them to take off again.

This is consistent with the fact that dragons tend to live in caves. Such caves would need to be made of a strong rock type like basalt, which has a tensile strength of 100s of MPa and compressional strengths in the GPa.

Ok I’ll return later with more updates on the gold pile calculation :)

I’ll note here too that the Monster Manual states that some dragons live in other environments. Black dragons live in swamps (obviously very soft ground), so the fact that they would tend to sink in them is consistent with the fact that they can breathe under water.

Lots of interesting points in the comments about considering the metal quality and environmental conditions- all great input! But one thing at a time. First, let’s talk about the attributes of the hoard.

Let’s assume the dragon’s preference for treasure is gold. The gold pile is likely to have objects made of other metals (e.g., armor) and precious stones (e.g., jewelry) as well. But we’re building a first order model, so I’m going to ignore these effects for the time being.

Say the gold mostly comes in the form of coins, candlesticks, dishes, crowns, and other small objects. The random packing density of equally sized spheres is 64%. Coins would likely pack tighter, but the irregular shaped objects would increase porosity.

I’m going to approximate that these effects cancel each other out. We can always change this later and even add other kinds of materials once the model is built. So our gold pile has a density of 64%.

The size of the pile is likely to scale with the size of the dragon, as they will add to the pile to make it bigger as they grow. In order to lay on it comfortably it needs a flat area the size of the dragon at the top, but the edges would be sloped downward.

A large pile of coins would act as a granular material, so it would have a pretty low angle of repose- that is, the angle to which it can be piled up with avalanching. The angle for dry sand is ~30 degrees, whereas gravel with bigger irregular chunks is closer to 45.

We have some irregular chunks but coins are really smooth so let’s say 35 degrees. If the edges have 35 degree angles then the distance which the pile edges extended beyond the flat area on top would be equal to the pile’s depth divided by tan(35).

So let’s say the gold pile is 2 meters thick, that would mean for a 4.6 m (15 foot) square dragon the gold pile would be total of ~10.4 meters (~34 feet) across.

The volume of the pile can be quantified using the formula for the volume of a pyramid and subtracting the volume of a smaller pyramid from the top. For a 2 m thick gold pile, it’s total volume would be ~118 m^3.

Let’s check if this make sense: 118 m^3 of gold at a density of 19300 kg/m^3 but a packing density of 64% comes to 1462477 kg of gold. That’s a lot! It would be worth $88 billion in today’s economy.

The Byzantine solidus was a widely used medieval gold coin about the size of a nickel. With a diameter of ~21 mm and thickness of ~2 mm, each coin would have a mass of 0.013 kg. If the entire pile was coins this would be to a total of 112 million coins.

Per the Monster Manual, Huge dragons are considered adults having ages of up to 800 years. This would mean the dragon would have to add 141 thousand coins (or equivalent mass) to the pile per year.

I don’t know about you, but that sounds like a lot of gold! Per a random google search that’s ~0.5% of the total amount of gold discovered on Earth to date.

Considering this, I feel like realistically there would not be enough gold in a medieval kingdom in order to sustain a dragon’s hoarding. This suggests that either a) the pile is much smaller than I’d imagined, or b) much more of the pile is other materials.

Another possibility is that dragons inherit (or take by force) hoards from other dragons, and therefore they’re accumulated over longer time periods than their absolute age. In such a case, that will make it more complicated to assess how long the pile has been lain upon.

Perhaps I’ll reduce the pile thickness to 1 m instead as I move forward. I’ll mull this over. In the meantime, I have to go play video games now so I’ll pick back up another day. Have a good weekend folks!

Solid evidence that dragons can accumulate very large and deep gold piles. Worth more research. https://twitter.com/scottwx_twn/status/1330389474531037184