Posted by & filed under CSAG blog, Frontpage.

December 2013 saw the release of the second instalment of the film adaptation of J. R. R. Tolkien novel, The Hobbit. The events of The Hobbit: The Desolation of Smaug are set some 60 years prior to Lord of the Rings, and chronicles the quest of Bilbo Baggins and Co. to rid Lonely Mountain from the dragon Smaug. Dragons are a winged species that breathe fire and have an affinity for gold[1, Ch. 1], and are critically endangered, with Smaug being the last documented specimen.

The climate of Middle Earth has recently been under the spotlight, with the current and future climate of Middle Earth simulated using the HadCM3L General Circulation Model[2]. However, to the best of our knowledge, there has been little work investigating the historical carbon emissions of Middle Earth. Specifically, what impact has the demise of dragons had on carbon emissions? To shed some light on this question, we start by considering the carbon footprint of the antagonist, Smaug.

Tolkien’s Middle Earth is based on European tradition, taking inspiration from the dragon of Earnaness in Beowulf[3]. This suggests that Smaug is likely descendent from reptiles, and although no exact measurements are provided, his length is estimated to be around 60 m[4]. In order to approximate Smaug’s overall mass, we assume that a dragon’s proportions are roughly the same as that of a Komodo Dragon (the largest species of reptiles). A typical Komodo Dragon is 3 m in length, and weighs 70 kg, which when scaled proportionally to a 60 m length, gives an estimate of 560 tonnes (ignoring the additional mass of the wings, which is assumed to be negligible).

The energy consumption of a living organism can be estimated using empirically-determined allometric laws. For fauna, it has been found that the logarithm of energy required is proportional to the logarithm of mass. More specifically, statistical analysis resulted in the formulation of Kleiber’s Law, which relates the Basal Metabolic Rate (kCal/day) to mass through the expression

$E_{\text{BMR}}=70m^{\frac{3}{4}}$,

and the Maximal Metabolic Rate has empirically been shown to be[5]

$E_{\text{MMR}}=69m^{0.872}$.

Smaug’s net available energy output (Joules) per day  is therefore given by

$\Delta E=E_{\text{MMR}}-E_{\text{BMR}}=23.7\ \text{GJ}$.

This represents the maximum sustainable energy expenditure per day for activities such as breathing fire, flying and cataloguing treasure. In order to give an upper bound on emissions, we look at the extreme (and perhaps somewhat artificial) case where all energy is expended through fire-breathing.

There has been speculation on whether the mechanism that generates dragon flames is of magical or biochemical origin[6]. To misquote Arthur C. Clarke, any sufficiently advanced biochemical process is indistinguishable from magic, and we therefore take the view a sufficient explanation exists without resorting to paranormal phenomena. The current school of thought is a fuel-based fire, with a tooth-initiated spark igniting the fuel as it leaves the mouth[4]. Some deductions regarding the chemical composition of this fuel can be made. It has previously been noted that dragon fire could (and did) melt some of the “rings of power”, with the exception of the One Ring[7, Ch. 2]. These rings are described as being “gold”, which is confirmed in most artistic depictions from various sources[1,7].

The structure of flames can be broadly divided into two categories, based on the mechanism of oxidiser mixes with the flame: either pre-mixed in a set ratio, or via diffusion of oxidiser. The resultant flames can either be laminar (e.g. a Bunsen burner), or turbulent (e.g. a wood stove). From video footage, it is clear that dragon fire is turbulent, and the variations in flame colour between tip and base suggest that diffusion is the primary mechanism for oxygen to much with the fuel source. The theoretically calculated maximum temperature of the flame, referred to as the adiabatic flame temperature, is rarely reached in real-world (open air) situations. This is due to heat loss, and inefficient mixing of air and fuel.

Gasoline has maximum flame temperature of 1026 oC for turbulent diffusion flames[8, pp. 2-4], which would be insufficient to reach the melting point of gold (1066 oC). A more likely candidate of dragon fuel would be a methane-based natural gas, which commonly reaches temperature of 1150-1250 oC in open-air flames[9]. The production of methane is common in a class of animals known as ruminants, where food is digested several times through a bacterial-assisted fermentation, with methane gas produced a by-product. The storage of methane would also increase the buoyancy of dragons, further adding weight to this theory.

At this point, it is useful to draw parallels between the production of dragon flames and the practice of “gas flaring” from the petroleum and natural gas refining industry. This refers to the practice of venting (and burning) excess flammable gas during unplanned over-pressurisation of equipment. Flare gas (technically known as “associated petroleum gas”) is a form of natural gas, composed of 81% Methane, 5% Ethane, 6% Propane, 4% Butane, 1% Nitrogen, and trace amounts of other chemicals. A typical gas stack has a diameter of 75 cm[10, pp. 29—30], and a typical release rate of 45-90 kg/h[11, Ch.13.5-3], which is comparable to the dimensions and physical properties we would expect from a dragon.

From conservation of energy, the maximum amount of gas produced by the dragon per day is determined by the net available energy, previously determined from estimating the metabolic rates. The heat of combustion of natural gas is 48.95 kJ/g[12,  pp. 283], and assuming perfect efficiency of burning, this implies that Smaug can release gas for 5.3-10.75 hrs per day while keeping within the 23.7 GJ energy limit.

According to the US Environmental Protection Agency, typical gas flare combustion efficiency has been estimated at 98%. The total hydrocarbon content of the resultant waste is quantified by means of an “emission factor”, measured in methane-equivalent emissions per unit energy. For flare gas, this factor is 6×10-11 kg/J[11, Ch.13.5-4], with Methane being the primary component of the waste gas (55% by volume).

Assuming that Smaug’s combustion efficiency is of the same order of magnitude as typical gas flares, this equates to 1.43 kg CH4 per day, or 260.6 tonnes over a 500 year life-span. Compare this to the typical Methane-equivalent output of a horse; 18 kg CH4 per year, or 49 g/day. [11, Ch.14.4-6] The armies of Rohan from the Lord of the Rings trilogy consisted of horsemen, with as many as 250 riders depicted at any given time[12], with up to 2000 riders in total[13]. Even this small subset of the total horse population of Middle Earth equates to a carbon footprint of over 68 dragons.

Given the dragon species’ status as an apex predator, we can conclude that their likely efficiency of combustion, coupled with low population numbers resulted in minimal impact on carbon emissions in Middle Earth. Consequently, Smaug’s demise would not significantly offset the effects of the deforestation of Fangorn forest, the industrialisation of Isengard or the volcanic activity of Mount Doom over the course of the following century.

References

[1] Tolkien, J. R. R. 1937. The Hobbit, or, There and back again. London: George Allen & Unwin.

[2] Brown, R. 2013. The Climate of Middle Earth. J. Hobbitlore, pp. 1-8. Available at: http://www.bristol.ac.uk/university/media/press/10013-english.pdf.

[3] Tolkien, J. R. R. and Tolkien, C. 1984. Beowulf: The monsters and the critics, and other essays. Boston: Houghton Mifflin.

[4] Sullivan, K. P. 2013. What Happened To Smaug’s Other Legs? ‘Hobbit’ FX Expert Explains. [online] Available at: http://www.mtv.com/news/articles/1719502/smaug-hobbit-fx-explained.jhtml [Accessed: 21 Jan 2014].

[5] Painter, P. R. 2005. Allometric scaling of the maximum metabolic rate of mammals: oxygen transport from the lungs to the heart is a limiting step. Theoretical Biology and Medical Modelling, 2 (31).

[6] Hill, K. 2014. Smaug Breathes Fire Like A Bloated Bombardier Beetle With Flinted Teeth. Scientific American, [blog] 2nd January, 2014, Available at: a href=”http://blogs.scientificamerican.com/but-not-simpler/2014/01/02/smaug-breathes-fire-like-a-bloated-bombardier-beetle-with-flinted-teeth/”>http://blogs.scientificamerican.com/but-not-simpler/2014/01/02/smaug-breathes-fire-like-a-bloated-bombardier-beetle-with-flinted-teeth/ [Accessed: 21 Jan 2014]

[7] Tolkien, J. R. R. 1954. The Lord of the Rings. London: George Allen & Unwin.

[8] Schmidt, C. W. and Symes, S. A. 2008. The analysis of burned human remains. London: Academic Press.

[9] Smith, D. and Cox, G. 1992. Major chemical species in buoyant turbulent diffusion flames. Combustion and flame, 91 (3), pp. 226–238.

[10] Rahnama, K. 2012. Plume Dispersion: A New Flare Combustion and Plume Rise Model. M.Sc. Thesis. University of Calgary: Canada.

[11] US Environmental Protection Agency. 1995. AP42, Fifth Edition. Compilation of Air Pollutant Emission Factors, Volume 1: Stationary Point and Area Sources. [report].

[12] Girard, J. 2005. Principles of environmental chemistry. Sudbury, MA: Jones and Bartlett Publishers.

[12] Lordoftherings.net. 2014. Lord of the Rings Guide. [online] Available at: http://www.lordoftherings.net/guide/horses_home.html [Accessed: 22 Jan 2014].

[13] Wikipedia. 2014. Rohan (Middle-earth). [online] Available at: https://en.wikipedia.org/wiki/Rohan_(Middle-earth)#Horses_and_warfare [Accessed: 22 Jan 2014].

(image from MRC Aviation)

4 Responses to “From Smaug to Smog: Historical carbon emissions due to dragons in Middle Earth”

1. Agent Green (Dragon Whisperer)

Your insights will be most helpful to my work as lead draconics officer at DCHQ [Dragon Conservation Headquarters, Cotswolds, England]. That’s a mite more scientific detail than I’m accustomed to but I’m sure my companion dragon Fuse can explain it to me. Indeed I was asked a quesetion on this very subject at my last seminar On The Care & Training of Dragons.

One thing: dragons produce no waste. It’s all consumed in internal processes.

Wishing you happy landings in 2014.
Agent Green
DCHQ
“Only the keenest survive”

2. Alex

Those are fair points, Brendan. For simplicity, I’ve omitted Smaug’s impact on the surrounding environment. Regarding other emissions, I’ve made the implicit assumption that natural gases typically released by ruminants are captured completely by dragons, and the associated natural gas emissions associated with dung are zero. While this is somewhat naive, it serves as a first-order approximation (best case), and would also make sense from an evolutionary standpoint. Using this methane in a (relatively) efficient combustion process then reduces the overall emissions of GHGs (compared to typical livestock).

As for smelting gold, natural gas emits 51% of CO2 per unit energy compared to (e.g.) Anthracite coal. The combustion efficiency of dragon flames would also be significantly more efficient than that of a primitive blacksmith. Wired magazine recently published an article on the physics of melting gold in The Hobbit (which partially inspired this blog post): http://www.wired.com/wiredscience/2013/12/melting-gold-in-the-hobbit/

3. Brendan Agrent

Although I think this is a great start, I fear there are some weighty carbon sources that have been left out of this calculation.  Firstly, dragons have to eat. And since they reportedly live on a largely human- and livestock-heavy diet (Prof Noakes would surely approve!), the GHG emitted by these creatures should be added to the tally. The Food and Agriculture Organization of the United Nations report ‘Livestock’s Long Shadow’ (available at ftp://ftp.fao.org/docrep/fao/010/A0701E/A0701E00.pdf) states that livestock contribute 18% of all green house gas emissions (on planet Earth) and since dragons eat by the barnful, this would add up dramatically over a 500-year lifespan. Another major emission omission is that released by the burning that dragons tend to spread in their vicinity. The whole of Smaug’s Mountain was ‘charred and smoking’ according to Bilbo, and I think it’s safe to assume that traveling Dragons burn vast tracts of farming land, as well as urban areas (should we include albedo effects?). Then there are the land use changes – imagine the forest fires!

Dragons, I’d imagine, would also result in significantly greater transport emissions as people go far out of their way to avoid them (although this would admittedly be lower without cars and planes – imagine the air traffic problems they would cause on planet earth). And let’s not forget about dragon dung, which must be a pretty hefty source of GHGs! And the increased demand for precious metals? Smelting gold is a carbon-intensive process, any dwarf will tell you that! Just as we humans have carbon footprints far greater than those from the energy our bodies consume, surely Smaug and his kin would have a carbon footprint significantly larger than the methane they breathe? Perhaps a vegetarian dragon that cycled to work and avoided long distance flights (and excess city demolition) would have the carbon footprint calculated here, but for some reason I have trouble imagining an eco-friendly Smaug.