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Team Number: 1917933 Page Number: 1
1 Executive Summary
Although George R.R. Martin’s series A Song of Ice and Fire falls under the category ”hard
fantasy,” we doubt he expected this level of rigour applied to his dragons. In our paper
we address realistic concerns of raising dragons, as well as their impact on the earth. We
analyze their growth and caloric requirements, their impact on local ecosystems, as well as
the required human-intervention needed.
For our growth and calorie estimations, we modeled the rough size limit of a dragon us-
ing the largest known dragon, Balerion the Black Dread. We used fanciful descriptions of his
teeth being as long as longswords to estimate his size and weight. We then estimated how
young dragons would grow by using a model geared towards indeterminately growing species,
which matched the description of dragons growing forever. We ultimately found an accurate
applicable equation to model dragon growth over time.
For their calorie consumption, we took several approaches and evaluated each one in or-
der to find a plausible caloric requirement of the dragons based on their size and activity.
We used the novel unit of cows in order to better process the gargantuan number of calories
that they need. We were able to obtain a equation for caloric needs based on the dragon’s
basal metabolic rate and the Harris-Benedict approach to account for activity levels.
In order to determine land requirements for dragons in different environments with different
resource levels, we assumed that dragons could be compared to apex predators of different
biomes. The model aimed to ensure environmental sustainability while also fulfilling dragon
requirements. We combined data on the caloric requirements and land requirements of var-
ious carnivorous predators in different biomes to find the available calories from prey per
square mile. We then used this value and the dragon’s caloric requirements from the previ-
ous model to determine the total land requirements.
To account for the effects of climate on dragons, we considered both water availability and
temperature. In the case of arid climates, we compared dragons to existing migratory birds,
which create a net increase in water during metabolism. Using data from a Game of Thrones
episode, we found the necessary water requirements of a dragon. After dividing this value
by caloric intake, we compared the mass of water per kcal of dragons to that produced by
birds. We then used data on bird flights to find that the metabolic rate comparison has the
implication that dragons can fly for 7.5 hours without water before needing more resources.
We also determined that dragons use more energy at low temperatures and conserve energy
at high temperatures.
To determine how large a community would need to be to sustain these dragons, we consid-
ered both people needed for dragon management and people needed for food. Ultimately,
including management of a cow farm, security, and dragon riders, we determined that 3
dragons would need to be 61x + 48 people, where x is the amount of people per day.
1
Team Number: 1917933 Page Number: 2
Contents
1 Executive Summary 1
2 Global Assumptions and Justifications 3
3 Caloric Intake and Growth 3
3.1 Defining the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.2 Assumptions and Justifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.3 Growth of the Dragons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.3.1 How big is Balerion? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.3.2 Selection of a Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.3.3 von Bertalanffy Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.4 Caloric Intake—The Basal Metabolic Rate . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.4.1 Metabolic Rate and Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.4.2 Reasonable Bounds on Dragon BMR . . . . . . . . . . . . . . . . . . . . . . . . 8
3.5 Effect of Activity level on Calorie Consumption . . . . . . . . . . . . . . . . . . . . . . 9
3.6 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.7 Strengths and Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.8 Extensions of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4 Land Requirements 11
4.1 Defining the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.2 Assumptions and Justifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.3 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.4 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.5 Evaluating the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
5 Effects of Different Climates on Caloric Intake 14
5.1 Defining the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.2 Assumptions and Justifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.3 Effect of Travelling through Arid Environments . . . . . . . . . . . . . . . . . . . . . . 15
5.3.1 Supply of Freshwater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
5.4 Effects of Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
5.5 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5.6 Strengths and Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5.7 Extensions of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
6 Human Intervention 17
6.1 Defining the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
6.2 Assumptions and Justifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
6.3 Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
6.4 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
6.5 Evaluating the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
7 Consideration of Reproduction 20
8 Letter to G.R.R.M. 21
9 Citations 23
2
Team Number: 1917933 Page Number: 3
2 Global Assumptions and Justifications
• The dragons in the paper have the characteristics of those in the Game of Thrones series.
Justification: While there are a wide range of descriptions and functions of dragons, the
problem uses Game of Thrones as its basis for lore.
• Dragons can be biologically compared to animals existing in our world.
Justification: Dragons must have a physical basis for their existence. In cases where the
series is unclear, dragons will be modeled off of existing animals biologically.
• The flight of dragons is not in question.
Justification: In the context of the problem, it is given that dragons can both appear
and function as they do in the fictional world in Game of Thrones. Therefore, while the flight
of a dragon may contradict traditional laws of physics, we can assume that, like the pterosaur,
certain biological mechanisms are in place that allow dragon flight. This allows us to account
for flight in our model without question.
• Dragons can be modeled consistently across the species, that is to say, there is no significant
variation between individuals in terms of growth or resource intake.
Justification: In the series, there are not significant differences between the needs of the
three dragons. In the scope of the problem, minor variations become unimportant. This allows
us to uniformly apply our model across all three dragons.
3 Caloric Intake and Growth
We’ll need to feed our dragons. The dragons in Game of Thrones seem to vary in their food consump-
tion: In Season 5 episode 5 Daenerys feeds her dragons a human each (roughly 125,000 kcal), then
holds off on killing any more humans, saying ”Don’t want to overfeed them. Tomorrow, perhaps.” Just
5 episodes later, we see Drogon feast on several animals, each exceeding the 125,000 kcal of a human.
Because of this, we instead model the dragon’s caloric necessities by analysing similar animals.
3.1 Defining the Problem
Our aim is to:
• estimate the basal metabolic rate of dragons
• estimate calories burned through daily activities
• predict impact of climate change on caloric requirements
3.2 Assumptions and Justifications
• Dragons are endotherms, meaning that they regulate their internal body heat.
Justification: Dragons are said to be fire made flesh, and even steam on cold nights. [2]
• Dragons have a similar basal metabolic rate per unit mass as Earth animals.
Justification: Since dragons do not have a fixed diet in Game of Thrones, we instead
have to assume that they obey similar laws as Earth animals.
3
Team Number: 1917933 Page Number: 4
• Dragons grow like similar organisms with indeterminate growth.
Justification: The dragons, which grow without limit so long as they have food and
freedom, seem very similar to the description of Earth organisms with indeterminate growth.
Their growth is linked to caloric intake, to competition, the amount of space they have, as well
as their age.
• Dragons’ maximum age is about 250 years old.
Justification: Balerion, the oldest known dragon, lived to be about 220 years old. We
do not know whether dragons would live longer or shorter in captivity; it varies between dif-
ferent animals. And although Balerion’s lifespan may have been shortened by his use in war,
descriptions of the time before his death where he was sluggish and unable to fly great distances
indicate that Balerion died of old age. [2]
• Balerion is around the limit of the size that a dragon can grow.
Justification: Balerion was the largest known dragon. No skulls seen in the series are
larger than Balerion’s skull. Furthermore, growth slows as the dragon grows bigger. Thus,
dragons are not likely to grow much beyond Balerion’s size.
• Dragons’ caloric intake can be fulfilled with red meat and red meat alone. The dragons can
also eat fish. Our model does not need to account for food or nutrition groups, only caloric
requirements.
Justification: In the series, there is no indication of dragons eating any sort of plant life.
It is indicated that their bones and blood have a high iron content, which might not be fulfilled
completely by fish. Thus, they need only iron-rich red meat. [2]
• Dragons are given enough free space and food to grow freely.
Justification: Although it might prove beneficial for dragons’ growth to be stunted, for
our initial models we want to find the limits of their growth.
3.3 Growth of the Dragons
There are several models of indeterminate growth. Given the facts from the series we know that
dragon growth is affected by:
• surrounding space, or habitat
• caloric intake
This lines up with factors that impact the growth of most indeterminately growing vertebrates. Before
using Balerion as our upper limit, we’ll have to estimate his size.
3.3.1 How big is Balerion?
Looking at pterosaurs and lizards, dragons are somewhere in between. They clearly do not have the
scrawny look of a pterosaur, but must be able to fly. Thus, we averaged a scaled up pterosaur and a
scaled up lizard to approximate Balerion’s weight.
As length increases by a factor of x, volume, and thus weight if a uniform density is assumed, scales
upwards by a factor of x
3
. Estimates of Balerion’s size puts him at roughly 42 meters long, with a
wingspan of 150 meters. He truly seems to be a limit of dragon size: he struggles to move in his old
age and his hefty weight gives him difficulty in flying.
4
Team Number: 1917933 Page Number: 5
We took this by taking a crocodile, which has similar proportions to a dragon, and scaling it up-
wards by one of the only explicit mentions of size, that Balerion’s teeth were as long as longswords.
Balerion’s teeth were from 1 to 1.5 meters, then. A saltwater crocodile’s teeth are about 4 inches, or
.1 meters long, but their teeth actually seem smaller, proportionally, than depictions of Balerion. An
estimate of scaling up a saltwater crocodile, 6 meters long, puts Balerion at 50 meters long. Propor-
tional to a bat’s wingspan, his wingspan is about 150 meters long.
Now for the weight estimates:
Pterosaur: Wingspan 9 meters, weight 250 kg [23]. Balerion would weigh 115,740 kg.
Komodo dragon: length 3 meters, weight 70 kg [24]. Balerion would weigh 324,074 kg.
Taking an average of these two estimates, Balerion would weigh roughly 219,901 kg, or roughly 220
metric tonnes. For reference, a blue whale can reach up to 30 meters and 180 tonnes.
3.3.2 Selection of a Model
Common models used for indeterminate growth of the nature indicated by Martin’s book include an
asymptotic sigmoidal curve, or use of the von Bertalanffy equation (although the latter is used more
commonly in fisheries than for land vertebrates, it sees use in other animals as well). However, the
asymptotic sigmoidal model has an issue: Martin seems to imply his dragons grow without limit, thus
meaning there should be no asymptote. Instead, the growth likely attenuates over time but never hits
an asymptote.
The von Bertanlanffy equation hits an upper limit of size. It states
L(t) = L
∞
1 − e
−K(t−t
0
)
And we can see from examination of the equation that L will never exceed L
∞
.
Another potential approach is to use a simpler function with attenuating growth but no limit. Any
function y such that
d
2
y
dx
2
< 1 fits this category. However, we believed that the dragons exhibited
exponential growth at the beginning of the season, limiting the possible graphs. Because of these
factors we chose to use the von Bertalanffy Equation, which has tested applications in modeling the
growth of indeterminate growers [24].
3.3.3 von Bertalanffy Equation
We will use the von Bertalanffy Equation modified for weight.
W(t) = qL
3
L(t) = L
∞
1 − e
−K(t+t
0
)
thus becomes
W(t) = W
∞
1 − e
−K(t+t
0
)
3
5
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