Friday, April 08, 2011

The Forbes Fictional 15

Here is the yearly list Forbes makes of the net worth of the richest fictional characters around. Most are from video and comics, but two from books have made it: Artemis Fowl and Smaug the dragon. The introduction:

The members of our 2011 list of wealthiest fictional characters have an average net worth of $9.7 billion, up 20% from last year. In aggregate, the Fictional 15 are worth $131.6 billion --more than the gross domestic product of New Zealand. To qualify for the Fictional 15, characters must be known, both within their fictional universe and by their audience, for being rich. Net worth estimates are based on an analysis of the fictional character's source material, and where possible, valued against known real-world commodity and share price movements. All figures are as of market close, April 1, 2011.

I look forward to this list for the novelty of it, and I really enjoy the way Forbes comes up with their calculations. Here's a bit of how they computed Smaug's wealth:

We know from the novel that Smaug’s wealth comes down to three primary components, the mound of silver and gold that he sleeps on, the diamonds and other precious gemstones encrusted in his underbelly, and the “Arkenstone of Thrain,” which is depicted as something like the Hope Diamond on steroids. (There are certainly other valuable items in Smaug’s hoard – rare suits of armor and so on – but the point of the exercise is to establish a minimum, conservative, net worth and the total value of a pile of ancient weaponry is probably no more than a rounding error in a fortune measured in the billions of dollars.)

Let’s start with the metals.

The book describes Smaug as “vast,” “centuries-old” and of a “red-golden color.” According to the Advanced Dungeons & Dragons’ site The Hypertext d20 SRD a true-dragon of that age and color measures around 64 feet from snout to tail. However, a great deal of that length is likely tail. By way of reference, Komodo Dragons are 70% tail by length, so we can estimate Smaug’s body to be approximately 19.2 feet long.

Dragons are long and narrow, so we can safely assume that Smaug can curl comfortably up on a treasure mound with same diameter as his body length – 19.2 feet.

How high is the mound? Well, at one point in The Hobbit, Bilbo climbs up and over the mound, and we know that Hobbits are approximately three feet tall. Assuming the mound is twice the height of Bilbo, we can say that the mound has a height of approximately 6 feet – like a six foot tall man climbing over a 12 foot mound of coins; substantial but not insurmountable.

To keep the math relatively simple and to avoid complications like integrating the partial volume of a sphere, we can approximate Smaug’s bed of gold and silver to be a cone, with a radius of 9.6 feet (1/2 the diameter) and a height of 7 feet (assuming the weight of the dragon will smush down the point of the cone by about a foot).

Now we can calculate the volume of Smaug’s treasure mound:

V= 1/3 π r2 h = 1/3 * π * 9.62 * 7 = 675.6 cubic feet

But, obviously, the mound isn’t solid gold and silver. We know it has a “great two-handled cups” in it – one of which Bilbo steals – and probably human remains, not to mention the air space between the coins. Let’s assume that the mound is 30% air and bones. That makes the volume of the hoard that is pure gold and silver coins 472.9 cubic feet.

We know that Bilbo eventually takes his cut of the treasure in two small-chests, one filled with gold and the other filled with silver, so it seems safe to assume that the hoard is approximately ½ gold and ½ silver, or 236.4 cubic feet of each metal.

A Kuggerrand, the South African Coin containing 1 troy ounce of pure gold, measures 32.6 mm in diameter and is 2.84 mm thick. Solving for the volume of a cylinder( V= π r2 h), then converting cubic millimeters to cubic inches, then cubic inches to cubic feet gives a volume of 8.371354e-05 (or 0.00008371354) square feet for a single coin, containing one ounce of gold.

Using similar logic, an American Silver Eagle coin (40.6 mm in diameter, 2.98 mm thick), which contains one troy ounce of silver, has a volume of 0.000136 square feet.

It’s then a trivial matter to determine the number of 1-ounce gold coins (2.8 million) and silver coins (1.7 million) in the heap. At the moment gold is trading at $1423.8/ounce and silver at $37.5/ounce making the gold coins worth a little more than $4 billion and the silver ones worth $65 million, or $4.1 billion for them combined.

Now for the diamonds:

After all those decades of sleeping on the top of his hoard, Smaug’s soft underbelly has become encrusted with diamonds (“what magnificence to possess a waistcoat of such fine diamonds!”), making him largely invulnerable to arrows and lances, except of course for the “large patch in the hollow of his left breast” which is “as bare as a snail out of its shell.”

How much are all these diamonds worth?

Well, we know that Smaug’s body (with tail) is 64 feet long, and we know that dragons are long and narrow, so it seems safe to assume that the ratio of length to width for a full-grown true dragon is about 6 to 1, leaving us with 10.7 feet for the beast’s body width. Six-inches by six-inches seems a reasonable guess for the size of individual dragon scale, meaning that there are 822 individual scales on Smaug’s underbelly. Subtracting 5% for the bare patch, leaves us with 781 diamond-encrusted dragon scales.

According to Diamond Helpers, diamonds above 5.99 carats are priced individually, so let’s simplify and assume that all of Smaug’s diamonds are 5.99 carats, priced at approximately $16,700 per carat or just over $100,000 each. Fifty diamonds per six-inch square dragon scale seems adequate to ward off most arrows, so Smaug is encrusted with 38,900 diamonds, with a total value of $3.9 billion.

Adding the diamonds to the $4.1 billion in precious metals gives us a value of $8.0 billion.

Finally the Arkenstone of Thrain:

In the narrative the Arkenstone is explicitly valued at exactly 1/14th of the entire treasure, since Bilbo takes it as his full-share then altruistically trades it away to prevent all-out war between the dwarves and a coalition of men and elves. If 13/14ths of the treasure is worth $8.0 billion, then the whole treasure must be worth approximately $8.6 billion, comfortably placing Smaug in 7th place on the 2011 Forbes Fictional 15.

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