[Small Chirp] Weight of the Golden Fleece, or math in fantasy concepts

I’m the kind of reader who can get caught up on the details. One of the delightful and delicious things about fantasy and science fiction is the freedom authors have to craft crazy worlds and play with speculative concepts. But I also expect these worlds to have internal integrity – in other words, I want it all to make sense. So when an author tells me salt is a luxury and people live on the very basics in a medieval village far from any trading routes, I find myself wondering why the village windows are made of glass. Devil in the details.

A couple days ago, author @ilona_andrews posted a tweet about something most writers encounter at least half-a-dozen times when writing a book: “What would this cool idea really mean for my fantasy world?”

In this case, the question was about the weight of a pelt of gold:

By the way, the answer to her question is 18.9 pounds, assuming sheep fur – and that my calculations are right!

I was curious too, but the numbers I first kept getting seemed just too high (over 200 pounds of gold? Surely not.) and different every time as I kept tweaking my formulas and reinterpreting what “surface area” really meant.  My housemate saw me scribbling rows of numbers in the margins of a grading rubric, and asked me what I was doing:

“I’m calculating the weight of a fur pelt made of gold. Assuming each hair is 6 inches and there are 12 per millimeter…”

“Is it an assignment?”

“Nope. Someone tweeted the question.”

“Someone you know?”

“No.”

“Why do they wanna know?”

“No clue.”

But half an hour of mini-scribbles, nose-scratching, and strange results later, I gave in. Google would save me. I told it to fetch me an answer I could use a baseline for comparison. And I knew just how to do it:

“How much would the golden fleece weigh?”

“Golden fleece weight”

“Gold fleece weight or else”

Nothing. Jason stole the golden thing over twenty nine centuries ago. That should have been plenty of time for someone to do the math and schedule the answer forward as a blog post. But Google was stubbornly unhelpful and the internet singularly un-forthcoming.

The next morning, over lunch, I found myself doodling my way through the problem – and enjoying myself way too much.

I realized it was time to get down to business.

So how much would a golden fleece weigh?

You could always use it to scrub pots.

Here are a few assumptions and givens:

  1. Each fur follicle is solid gold. Yep, you probably don’t want to curl up on this throw rug.
  2. I did the calculations with skin and without. Maybe the pelt got touched by Midas, or maybe it’s just the fur. Let’s explore both options.
  3. For number of hairs per surface area, I’m using an average between male and female sheep, not merely ram. And generally, I’m assuming ram = sheep and leaving it at that.
  4. According to a conveniently on-hand and google-able online store, a sheep rug is about 2.5 feet by 3.3 feet. Gonna run with that. That’s 7,665.7 cm sq.
  5. After entirely too much time reading articles with titles like “Determination of wool follicle characteristics of Iranian sheep breeds,” I’m going to go with 16  hair follicles per millimeter.
  6. Found a chart listing average hair shaft diameters across a dozen species (from 25 micron diameter for dogs to 160 for cows, huh). Sheep came in at 90 microns.
  7. Assuming it’s super-pure (since it’s gonna be organic, after all), a cubic centimeter comes in at 19.32 grams of gold.

Where does that leave me? Well, assuming the skin is organic, a sheep wearing 6-inch-long fur would be carrying a load of 48 pounds on itself. If the fur is closer to the average 2.5 inches, then we’re looking at 20 pounds of gold fur. At current rates, the little guy’s fur would be worth about $500,000. Still, it begs the question about how you’d go about the shearing side of things (that’s a question for later).

Now if you’re gonna go with the King Midas Touched That Sheep Theory, let’s assume the skin is solid gold too. I have no idea how thick sheep skin is, and while I found out that hippo skin can be 2 inches thick and leather comes in a great range, the internet wasn’t very helpful when it comes to sheep. So I eyeballed it. Two millimeters look about right.

One Length-times-Width-times-Height-formula later, I had the volume of the skin part of the pelt. Multiply it by grams per cubic centimeters, convert it to pounds, and we have our gold sheep skin, coming in at 62 pounds of gold, with a total weight of either 110 pounds for our long-wool sheep and 82 pounds for the sheep with the average 2.5 fur.

Conclusion – The Weight of a Golden Pelt

And there it is. It seems like a lot, but a sheep can weight anywhere from 90 to 300 pounds, so a 300-pound winged ram could probably wear 20 pounds of fur without toppling over (whether it would fall out of the air is a whole ‘nother question). And if both the pelt and skin were solid gold, Jason is just a bit more impressive, sneaking that heavy thing off from under the nose of the dragon.

CORRECTION UPDATE: There was an error in one of my conversions. Having fixed it, the number of the 6-inch fur for a sheep would be 50lbs, and 21lbs with 2.5 inch-long fur. If the numbers of hair per sq mm is adjusted up to 55 (instead of 16) and all else is held constant, then the weight of the 6-inch fur pelt goes up to 174lbs (??? surely not?) (without gold skin).

Go math!

___

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4 thoughts on “[Small Chirp] Weight of the Golden Fleece, or math in fantasy concepts

  1. “The live weight of ewes on farms of all types is 48-54 kg and on breeding
    farms it is 52-58 kg (max. 122 kg). The live weight of rams is 115-123 kg
    (max. 160 kg). The carcass weight of adult ewes is 23.5 kg and of 7-month
    castrates 15.2 kg with meat/bone ratios of 3.85:1 and 3.75:1 respectively.
    The wool is white; the fleece and staple are uniform. The fleece has a
    blocky staple; the outer part is dense and has a square or oblong crosssection. The crimp is regular, distinct. The wool is usually of 64s quality
    (20.6-23.0 m), the ram’s wool is 60s-58s quality (24-26 m). The length of
    ewe’s wool is 8.0-8.5 cm, and of rams 9-10 cm. Yolk is predominantly light
    cream, rarely white.
    Fleece weight of ewes on farms of all types is 4.8-5.4 kg and on breeding
    farms 5.1-5.8 kg (max. 14.0 kg). In rams, fleece weight is 16-20 kg (max.
    25.4 kg).” Fancy Sheep Wool Resource

    My calculations:

    Hair length: 10 cm

    Hair diameter: 26 microns

    Hair density: 550 per square centimeter

    Fleece weight (ram): 25 kg

    Pelt size(ram): 1724 sq inches or 11123 sq cm

    Total number of hairs: 6117650 per pelt

    Mass of individual hair: 25,000 g/6117650 = 0.0041g

    V of cylinder = pi * radius2 * height

    Hair radius: 13 microns

    V=3.14 x (0.0013 cm) 2 *10 cm = 0.000053066cm3

    Gold density= 19.3 g/cm3

    Individual hair mass= density * volume

    Individual hair mass = 19.3 g/cm3* 0.000053066cm3 = 0.0010241738 g

    Total fleece mass = 0.0010241738 g * 6117650 =6265.57g

    O_O

    That said, I checked your review list and we’re not on there, so I figured you haven’t really read our books, or I would totally try to snag you as a beta reader.

    • Re-calibrating my brain!

      I just ran through it again with your numbers (I made a basic mistake in converting in sq to inch sq originally), and got the same number.

      The fur part of the pelt (assuming just the fur is gold) ought to weigh about 6kg or 14 lbs, about the weight of a large, medium-fat cat. (11-17 edit: It’s probably almost the exact same number as a regular pelt because we aren’t taking into account the weight of the skin. I used to have a sheep throw rug pelt thing, and it was heavy and unwieldy. But not because of the fur alone, I don’t think.)

      Fixing my error, I increased the surface area in my calculations, but I also decreased the hair length and hair diameter from 6 inch and 90 microns to 3.9 in and 26 microns. That affected the number down more than up, so a drop from 19 lbs to 14 makes sense. Though we did increased numbers of hair per cubed cm threefold. (Two days ago I was worried the numbers looked too big. Now I’m worried they’re too small! But I think it’s solid.)

      Re the book-reading: I’m afraid I haven’t, but Meg, my canary-partner-in-crime (theothercanary) is a huge fan. As far as I know, she’s read everything by you ever – aaand is the reason I have the first Kate Daniels book on my shelf. (That, and the fact I hear the series is set in Georgia; I’m trying to read a UF for every state. 20 down, 30 more to track down! [Hawaii, anyone?])

      I know she’d love even a whisper of the word Beta. Lemme know if I should ask her what she’s read. 🙂

      Math notes:,

      Ram weight = around 115-160 kg (253-352lbs)
      Gold = 19.32
      Hair = 10 cm (3.9 inches)
      Hair diameter: 26 microns (0.0026 cm)
      Hair radius: 0.0013 cm
      Density: 550 per cm^2 (so that’s 55 per mm^2) [ ***Very different than my estimate of 16 hair follicles per mm. Some more research says it was my bad: “Merino sheep has 53-87 hair follicles per square mm. ]
      Pelt size: 1724 sq inches (11123 sq cm) [aha! Here I missed the squared in my calculations]

      Weight of each hair:
      Volume = pi * r^2 * h
      Volume = 3.14 * .0013^2 * 10
      Volume = 0.000053093 cubic cm
      Weight of single hair = 0.000053093 * 19.32 grams
      Weight of single hair = 0.00102575676 grams

      Number of hairs on pelt:
      Pelt = 11,123 cm sq * 550 hairs per sq cm
      Pelt = 6,117,650 hairs

      Weight of gold wool:
      Weight = 6,117,650 hairs * 0.00102575676 grams per hair
      Weight = 6275.220842814 grams
      Final Weight = 6.28 kg or 13.83lbs

      11-17 edit:
      For the hide itself, I couldn’t find any info on how much a sheep hide weights, but a calf hide is 12 pounds uncured. It drops to 8 pounds if dry-salted. So if we have a ram the size and dimensions of a calf, gold wool and hide would weigh about 22 pounds.

  2. Couldn’t agree more about the need for internal/external consistency and accuracy, especially in speculative fiction. Loved (okay, kind of liked) DaVinci Code until I found out that 80% of everything in the book was complete bullish*t. Spent an inordinate amount of time calculating rate problems, researching locations, distances and time of travel, relative timezones, and a hundred other things in the writing of God Bless The Dead. Not only must it hang together for the casual reader, the author is required to meet the standard of “Will this cause an expert in the field to suddenly stop and say, ‘This is ridiculous.’ ” Even the venerable Tom Clancy got all too sloppy at times, especially regarding medical issues. It’s just a matter of how much effort the author puts forth, plain and simple. Readers deserve the effort if they’re making the effort to read your stuff.

    • Thanks for the great comment!

      I think space/sci fi is the only genre where I’m completely okay with science hand-waving. And even then I get irritated with writers who try to do technobabble when it’s clear that what speculating has no ground in science (shape-shifting pnr aliens who have magic- err, I mean, science powarz… Despite a promising blurb, I ended up giving up on Koch’s alien/MIB/UF series for that reason.). Don’t try to explain how spaceships fly or genetics work if you can’t, I say. The author should just take it as a given and do what they’re good at – like character-building and plot-greatness.

      That’s not an option in historic, literary, or any kind of modern story, though. There’s only so much handwaving I’ll buy on faith alone…

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