Giants are really, really strong.
(Light spoilers ahead.)
On last night’s Game of Thrones, we saw a scouting force of the wildling army attack Castle Black and attempt to scale the Wall. Their effort was largely successful until the Crows used exploding oil barrels and conveniently frozen giant scythes to beat back the invaders.
The wildling’s initial defeat wasn’t from lack of military might—they had giants riding frickin’ wooly mammoths on their side. Giants are strong enough to pull cold-rolled steel bars from their hinges, lift the Wall’s enormous gates by themselves, and effectively become ballistas by firing man-sized arrows. It’s with this last ability where we can quickly get a sense for how strong giants are, with physics!
According to the A Song of Ice and Fire novels, giants are rather trollish beings that are between ten and twelve feet tall, ride mammoths, and have no kings, only great warriors. In the latest HBO episode, we got to see just how great their warriors are when one giant fired an arrow that easily cleared the Wall, pierced and then launched an unfortunate Crow over to the other side. Because of the conservation of momentum, we know that take some real strength.
Like energy, momentum is a physical property that is conserved in nature. When something with mass moves with some velocity, that object gains momentum. If that object then hits something else, that momentum is transferred or changed, but never lost. For example, when a moving billiard ball cracks into another ball on a pool table, the first ball loses some velocity and the other gains some velocity (how much depends on the masses involved). Very simply, that is conservation of momentum.
We have equations that tell us what will happen when objects collide and their momentums meet. In the case of the giant’s arrow connecting with the unfortunate Crow, we have one object (the arrow) let loose with some velocity and hitting/sticking with a stationary object with no initial velocity (the Crow). In equation form, all that put together looks like this:
Mass of Arrow*Velocity of Arrow=(Mass of Crow+Mass of Arrow)*Velocity of Crow and Arrow
The left side of the equation represents only the initial momentum of the arrow, and the right describes the final momentum of the Crow stuck with the giant’s arrow.
To make a quick estimation of giant strength, we need some rough guesses. I’ll guess that the pierced Crow is the weight of an average adult male, or around 180 pounds. Next, I’ll assume that the giant’s massive arrow was long yet light at two pounds. Finally, let’s guess that the Crow in the episode was flying backwards at 10 feet per second (fast but not too fast).
Plugging that all into the equation above, we can solve for the initial velocity of the giant’s arrow: 910 feet per second. If that sounds fast, it is. To make the Crow fly the way he did (given the assumptions we made), the giant’s arrow would have to leave his bow at 80 percent the speed of sound. When it hit the Crow, it would impart almost 26,000 foot-pounds of energy right to his chest—like being shot with an elephant gun, only the elephant gun is five times more powerful than normal.
Just how fantastical are Game of Thrones’ giants? Just 65 foot-pounds of energy behind an arrow will take down a grizzly bear or African elephant (but launching one is another thing entirely) and our fastest bows release arrows at less than half the estimated velocity giants do. A giant’s bow would have to generate incredible energy from the pull of its bowstring and withstand that stress. The giant himself would also have to be strong enough to draw one of these incredible bowstrings backwards. We are talking pulling back the equivalent of hundreds if not thousands of pounds. The wildlings have a whole army of these things?
At least Jon Snow now knows one thing: whether you are firing a massive arrow or charging headlong towards a steel gate, momentum matters.
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Kyle Hill is the Science Officer of the Nerdist enterprise. Follow the continued geekery on Twitter @Sci_Phile.
Thinking into this more, there were a significant number of factors not taken into account. What all happened in this scene?
The arrow is fired upwards at a variable degree angle.*
The arrow travels about 713 feet until the arrow strikes the man.
The man and arrow travel upwards and strike a wooden platform.
The man and arrow break through this platform (consisting of 3 2×6 planks and a 2×8 beam)
The man and arrow continue at about 18.25m/s** at an angle of about 45 degrees.
The man and arrow continue on until they encounter the ground on the far side of the wall.
I assumed the man weighed (with kit) 90kg.
I assumed wind resistance was not a factor.
I assumed that the beam was Northern Red Oak.
I assumed that friction was not a factor.
I assumed that the acceleration of the parts of the beam from the impact was not a factor
Now, with these factors, can we figure out the initial velocity and the amount of energy needed to push an arrow that fast?
First thing I did was find and calculate the amount of energy needed to break a wood beam with a breaking strength of about 1000psi. This gives about 16000lbs to break it, or 21693J. Now this brings kinetic energy into the equation, as this would be lost from the man/arrow after hitting it.
The kinetic energy of the man/arrow after passing through the board and while on their way over the wall was calculated to be approximately 36675J (Ke=0.5mv^2).
Breaking through the beam used 21693J, putting the Ke of the man at 58373J and the velocity of the two at 36.02m/s
Using the M1V1=M2V2 formula, I calculated that the arrow was traveling at 1620.73m/s as it hit the man.
At this speed, the distance traveled from the giant to the man would be almost negligible compared to the 26km the arrow would travel unaided, so I put out my final solution at:
The arrow left the bow at approximately 1620m/s (5315fps for you americans) with about 58500J of kinetic energy.
These guys have really good bows.
*This will be a point of debate, so I’m letting it be whatever it will be since the man hit the beam which was about six feet behind and above his centre of gravity.
**The man travels his own length in three frames, and at 30fps, that ends up being about 6′ in 1/10 of a second.
Please, anyone who isn’t overtired at 0340 check this over and make sure everything is about correct. I’m too tired to really work on this anymore.
I think you are underestimating the energy transferred to the Night’s Watchman. After being hit he was pushed through the beams above him and then still several feet in the air. I put 10 ft/s at 75° as a trajectory in Wolfram Alpha and it places the peak height at less than 2 feet. I think he traveled higher than that.
So this come out tobe 3-5 times faster than the average longbow. Its not impossible. But the Night’s Watch man flying back like that was a bit comical, even if physics can back it up. Also, i didnt look at the arrow, but its head must have been very broad for it to send the man flying rather than passing right through him
Thank you for honoring the NERDIST name. Great post. I love that you’re not all, “Pshaw, that was impossible!” but instead you’re saying, “Dude, thems some strong giants.” BTW, that picture above, the torch sconces really look like they are holding light bulbs.
I was told that there would be NO math.