Thursday, April 21, 2011

Forbes' fictional rich list

Forbes has released their list of the top 15 richest fictional characters. Scrooge McDuck tops the list with $44.1 billion with Carlisle Cullen, Artemis Fowl II, Richie Rich and Jed Clampett rounding out the top 5. My favourite, though, is the inclusion of the dragon Smaug, always depicted curled around his pile of gold and silver. Michael Noer breaks down how they calculated the dragon's wealth based on descriptions in the book of his treasure pile, his belly crusted with diamonds and gems and the Arkenstone of Thrain. Just his description of how they calcultated the worth of the precious metals makes me want to head straight back to The Hobbit.


"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."
Love that they used the AD&D Monster Manual as a reference.

Photo source: Smaug by John Howe c/o www.johnhowe.com

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