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# Game of Thrones Analysis

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## Kyle Camacho

on 22 May 2015

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#### Transcript of Game of Thrones Analysis

Range= Vo * Cos(Theta) * time

Vy= (V0 * Sin(Theta)) - gt
Vx= V0 * Cos(Theta)

Now to Derive Formulas Needed...
Vertical Velocity
Vy = (V0 * Sin(Theta)) - gt
At the heighest point Vy = 0
So: Vy = 0
and :
Vy = Vo * Sin(Theta) - gt
so:
0 = Vo Sin(Theta) - gt

Solved for t
t = (Vo * Sin(Theta))/g

However, this is time to Max Height

Total time in air = (2Vo * Sin(Theta))/g
Inputting this into normal range formula
Range= ((2Vo^2) * Sin(Theta) * Cos(Theta))/g
Therefore, R = 2V0^2 * Sin^2(Theta)/g
A Song of Ice and Fire: Physics Analysis
By Lord Kyle Camacho and Ser Justice Centrello
What is a Song of Ice and Fire?
A fantasy book series by George R.R. Martin
Takes place in another world during a medieval-esque era (but with dragons)
Features many chracters with a lot of depth and intriguing story arcs/plot twists
Physics in Scene
Formulas
Scene Chosen
This scene occurs in Season 3 of the television show based on the book series
It is a funeral tradition of House Tully to light the funeral boat on fire with a flaming arrow
Edmure Tully, the eldest son of Hoster Tully (the man in the funeral boat), fails to hit the funeral boat after three attempts; his uncle, Brynden "Blackfish" Tully, takes the bow from him out of frustration and manages to hit the funeral boat on his first shot
The Sigil of House Tully is presented to the left.
The topic in physics covered here is projectile motion
We will analyze the physics in this scene and then give it an appropriate physics rating
Video Clip
Formulas - Horizontal Direction
Vx = Vox
Dx = Voxt
Finding Needed Values
Formulas - Vertical Direction
Vy = Voy + gt
Dy = Voyt + 1/2gt^2
Dy = (V^2y - Vo^2y/2g)
Dymax = Vo^2y/2[g]
[g] = 9.8^m/s^2
Edmure's Shot
Finding Bow Initial Velocity
Using Data from Bow Lee's Bows, bow most like the one used within the Clip is the "Palmer"
Has an average FPS ( feet per second) of 170 - which equates to ~52 meters/second

Finding Angle of Shots
Using GIMP Software, the angles of both Edmure's shot and Bryndyn's Shots can be obtained

Angle = ~41 degrees
Angle = ~ 44 Degrees
Bryden's Shot
Quick Analysis
Conclusion
Since Both Bryden and Edmure are physically fit, it is assumed they both pulled the bow to its maxium tension, and in turn had the same Inital Velocity
Range = ((2Vo^2) * Sin(Theta) * Cos(Theta))/g

R = (2 * (52 m/s ^2) * Sin(41) * Cos ( 41))/ 9.81 m/s

R = (2 * (2704 m^2/s^2) * Sin(41) * Cos ( 41))/ 9.81 m/s

R = (5408 m^2/s^2) * Sin(41) * Cos ( 41))/ 9.81 m/s

R = (5408 m^2/s^2) * Sin(41) * Cos ( 41))/ 9.81 m/s

R = (5408 m^2/s^2) * .6561* .7547)/ 9.81 m/s

R = (2678 m^2/s^2)/ 9.81 m/s
Range = 273.0 Meters

Range = ((2Vo^2) * Sin(Theta) * Cos(Theta))/g

R = (2 * (52 m/s ^2) * Sin(44) * Cos ( 44))/ 9.81 m/s

R = (2 * (2704 m^2/s^2) * Sin(44) * Cos ( 44))/ 9.81 m/s

R = (5408 m^2/s^2) * Sin(44) * Cos ( 44))/ 9.81 m/s

R = (5408 m^2/s^2) * Sin(44) * Cos ( 44))/ 9.81 m/s

R = (5408 m^2/s^2) * .6947* .7193)/ 9.81 m/s

R = (2702 m^2/s^2)/ 9.81 m/s
Range = 275.5 Meters

Finding Actual Distance to Boat ( x)
In Chapter 58 of the Book
A Clash of Kings
it states...
"They could not dress more than twenty ships abreast, lest they risk tangling their oars and colliding with each other."
The width of a galley is about 10 feet wide, meaning the river is most likely 200 feet wide, or 60.96 meters
. By looking at the picture on the next frame it can be seen that the boat is nearly directly in the middle of the river so its X distance is equal to 30.48 Meters
Finding Distance to Boat ( y)
Using the picture, it appears that the funeral boat is approximately 100 meters away, or slightly longer than a football field
Actual Distance to Boat
Use the Pythagorean Theorem
Hypotenuse = Sqrt( a^2 + b^2)
D = Sqrt ( 30.48^2 + 100^2)
D = Sqrt ( 929.0+ 10,000)
D = Sqrt (10,929)
D = 104.5 Meters

The range of Edmure's shot was 273.0 meters

The range of Brynden's shot was 275.5 meters

The estimated distance the funeral boat was from them was 104.05 meters

Simply Put, both men overshot the funeral boat by about the same distance
In order to use the Range equation, we needed to find a) the angle in which the shots were fired and b) the initial velocity of the shots. The angles were found using GIMP software. The initial velocity was obtained from Bow Lee's Bows. Assuming that both men pulled the bowstring to its maximum tension, the arrow would have been released at ~52 m/s.

Both men overshot the funeral boat by approximately the same distance, since they both shot the arrow at about the same angle and both had the same initial velocity. Hitting a boat that distance with an arrow is difficult for even trained professionals anyway. In a world filled with White Walkers, warlocks, red priests, and draagons, you can't expect it to be too realistic. The final verdict for this particular scene is...

PGP. Pretty good physics in general. Yes, there may be flaws, but it isn't completely unrealistic in hitting the boat with an arrow. If their initial velocities were decreased or if their angles changed, they would have hit the boat if they were aiming correctly.
Sources
GIMP 2.8.10,The GIMP team, www.gimp.org, 1997-2014, retrieved on 31.07.2014.
Martin, George R. R. A Game of Thrones. New York: Bantam, 1996. Print.
Martin, George R. R. A Storm of Swords. New York: Bantam, 2000. Print.
"Walk of Punishment." Martin, George R. R.. Game of Thrones. HBO, . 14 Apr. 2013. Television.
"The Science behind a Bob Lee Bow." Bob Lee Archery/Wing Archery. Web. 22 May 2015.
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