# Archery on the Wall [Spoilers]

The wall in a song of ice and fire is roughly 700 feet tall. During the battle of castle Black, Jon Snow and the other brothers of the Night's Watch exchange arrow fire with wildlings on the ground. The wildling archers repeatedly hit the straw-men Jon Snow puts up as a distraction. So my questions are:

1. Would it be possible to accurately hit an enemy from the top of the wall, given its height?

2. Would it be possible to accurately hit an enemy on top of the wall from the ground, as the wildlings do?

• I smell a Mythbusters episode...
– TLP
May 30, 2013 at 10:17
• In a world where giants exist, it might not be a leap of the imagination that gravity is a wee bit weaker than here on Earth.
– user24620
Jul 13, 2014 at 21:00

Yes. The Great Wall of Westeros is 700 feet or 213 meters tall. On the face of it, it seems within the realm of plausibility to shoot and hit targets at that range.

• Looking at formulas for arrows and distance, the most important factor is the amount of force that can be applied to the arrow. Expect to see large bows (long bows, recurve bows) being used in such fight scenes because they are the only bows capable of generating the force required.

• Most bow hunters shoot at targets averaging 35 to 75 meters away. Target archers can shoot at ranges of 100 -200 meters. These distances are considering negligible elevation. Shooting at elevate targets reduce range.

• Using an advanced technology recurve bow might stretch target shooting to 225 to 250 meters. It takes an extraordinary archer to hit anything further than 200 meters.

So, is it possible to shoot from the top of the Wall of Westeros.

• Yes. The archer shooting down has the advantage of gravity working in his favor... The archer on the ground is at a distinct disadvantage but if there are enough of them, that might not matter as much.

• Is it possible to hit anything effectively at that distance? A highly-trained, well-equipped archer has a decent chance to hit anything from either position.

Are there examples of long range bow shooting?

The longest arrow flight until recently was 350 meters. Arrows shot this distance are not trying to hit a target. They are trying to cross distances. In the news on Tuesday, August 24, 2010:

Zak Crawford, 14, who dreamed of being Robin Hood, shot an arrow nearly 500 metres — equal to the length of five football pitches — using a recurve bow, in the senior under-35lb class, at the Northern Counties Flight Championships - setting the new world record for the Longest bow and arrow shot. He broke the previous world record of 350 metres in senior category by using a recurve bow in the championship.

Why is this relevant?

• It shows that it is quite possible to launch arrows considerable distances. The limitations are in the strength of the bowman, the pull of the bow, the weight of the arrow, and the elevation of the target.

• Elevation reduces range. Accuracy suffers for range but a range of 500 meters (1640 feet) gives credibility to the possibility of such archery being possible if a bit extraordinary.

The English Longbow statistics (range and penetration) from Wikipedia:

• The range of the medieval weapon is not accurately known, with estimates from 165 to 228 m (180 to 249 yds). Modern longbows have a useful range up to 180 m (200 yd). A 667 N (150 lbf) Mary Rose replica longbow was able to shoot a 53.6 g (1.9 oz) arrow 328 m (360 yd) and a 95.9 g (3.3 oz) a distance of 249.9 m (272 yd).

• A flight arrow of a professional archer of Edward III's time would reach 365 m (400 yd). It is also well known that no practice range was allowed to be less than 220 yds by order of Henry VIII.

• The longbow was capable of long range, and was highly accurate at short range. Most of the longer-range shooting mentioned in stories was not marksmanship, but rather thousands of archers launching volleys of arrows at an army.

• Longbowmen armies would shoot a rain of arrows landing indiscriminately in the target area. An archer could hit a person at 165 m (180 yards or 540 feet) "part of the time" and could always hit an army.

• Your examples are about horizontal distance, not height. Perhaps information about hight records could help. It should also be considered, that when firing upwards, the arrow loses a lot of its energy, so it might reach you, but not be particularly dangerous. It's not enough if an arrow just touches you, it has to have enough speed to pierce through clothing, skin, and flesh (and possibly armor).
– vsz
May 30, 2013 at 6:22
• There aren't a whole lot of records for shooting the HIGHEST arrow. Anyone able to find something, feel free to share it. May 30, 2013 at 15:51
• @Thaddeus, that's an interesting challenge. If I can get the proper equipment, I'll give it a go and do the experiment myself. If so, I'll get readings for a 55lb recurve, 200lb foot bow, 70lb longbow and 175lb crossbow. May 31, 2013 at 0:35
• For you maths mavens: kingsmountainarchers.org/tips/angle-shots.html May 31, 2013 at 1:56
• @Morgan I can see nothing that could possibly go wrong with that experiment Apr 11, 2014 at 20:51

Here's an answer I found on yahoo that I agree with:

For the arrow to just reach 800ft ignoring air resistance: 800 = Vyo^2/2g => Vyo = sqrt[2g*800] = 226.3ft/s. This is not impossible. For the arrow to reach 1000ft so that it would have some lethal velocity at 800ft Vyo = 253ft/s which is also possible ignoring air resistance. Including air resistance, the drag would prevent the arrow from reaching 1000ft.by a large margin. So the answer is NO. An arrow can not reach 800ft in height mostly because of air resistance/drag Source(s): http://cr4.globalspec.com/thread/36440/C

I've competed in several 'Flight Shoots' using specially made 'Flight Arrows' and overdrawing either a 70 pound draw English Longbow or a 55 pound draw Ben-Pearson recurve bow. One could possibly contort oneself sufficiently to shoot an arrow vertically to that height but not likely.

Also, just to achieve that distance/height the flight of the arrow would be near parallel to the plane of the wall. To actually hit a target would necessitate actually shooting over the lip of the wall in order to drop the arrows down on top of the target. This would in effect be like shooting arrows onto the top of the wall with just enough velocity to get there but not enough remaining energy on the downward arc to do anything but clatter harmlessly at their feet (unless you misjudged your angle or skipped the arrow off the wall and it came back down at you).

To actually aim at a target at that height, one would have to be shooting from some distance away from the wall, say about 45 degree line of sight. That would put you back 700 feet from a 700 foot wall. Line of sight then is around 1000 feet and the parabolic travel of the arrow much farther.

We're now well away from hand bows and into the 'potential' realm of the 200 pound+ draw weight of the foot bows and special 'flight arrows'. Even foot bows with their much heavier draw weights have the problem of body angle to be able to fire an effective shot to such an elevation.

Maybe an incline table to lay on?

• I agree with you here. The concept of shooting an arrow and killing someone who is 700 feet above you is crazy without especially powerful bows and lots of strength. And, afaik, the Wildlings are just using regular wood for their bows. Though, given GRRM's world, it's not inconceivable to believe he's made some sort of special superwood, since everything in the world seems to be grandiose and extreme. Jun 10, 2013 at 15:18

Assuming we have the launch velocity of the arrow (which I will take to be 82m/s (184mph)) and the force of gravity (9.8m/s) we can use the equations of motion to calculate the maximum height of the arrow.

# The equations we will use are:

v=at+v0
r=v0t+0.5*at2

Where `v` is the final velocity, `a` is the acceleration, v0 is the starting velocity, `r` is the distance from the starting position and `t` is time.

# The actual calculation:

We want to find the maximum height the arrow will get to, at that point the velocity will be 0, so `v=0`. We are ignoring air resistance so `a` is -9.8m/s. With that we can find the time at which the top of the arc is reached:

v=at+v0
0=-9.8*t+82
t=8.4 seconds.

Now we can plug that into our second equation to find the height at which that occures

r=v0t+0.5*at2
r=82*8.4+0.5*(-9.8)*8.42
r=343m

# So could an arrow get there?

Absolutely, ignoring air resistance the arrow could get to the top of the wall and keep going for a further 130 meters. This would clearly be reduced by air resistance (and not shooting straight up) but I'd be confident it would get there.

# Ok, so it gets there, but how deadly would it be?

As the arrow climbs it slows, and the slower it goes the less dangerous it becomes. We can again use the equations of motion to find how fast the arrow would be travelling at this point

v2=v02+2ar
v2=822+2*(-9.8)*213
v2=2549
v=50m/s (112 mph)

In other words still pretty damn fast.

However the energy that the arrow delivers is proportional to the velocity squared, as we know by Kinetic energy=0.5*mv2. For this we will need a mass, I've used 300 grams but it turns out not mattering since I'm just creating a ratio:

Energy at launch=0.5*0.3*822=1000 joules
Energy at the top of the wall=0.5*0.3*502=375 joules

This is starting to look a lot less impressive, for every joule of energy the archer puts in at the bottom of the wall a little over a third impacts the armour of a soldier standing at the top of the wall.

# Ok, the wildlings are in trouble, how deadly would the arrows from above be?

For this we just reverse the calculations above. Doing this we get the following arrow velocity when the arrow reaches the ground

v2=v02+2ar
v2=822+2*(9.8)*213
v=104m/s (230 mph)

Arrow energy: 1622 joules

(Incidentally terminal velocity for an arrow appears to be around 110m/s so an arrow could go this fast, although as always air resistance will reduce the actual velocity)

# Conclusion

The wildling arrows could certainly get to the top of the wall but they would have only 35% of the killing power of an arrow when launched. Furthermore the Night Watch's arrows would be around 60% more deadly than usual. While both parties would have difficulty aiming over such a distance the Nights Watch would find it far easier to penetrate armour. Additionally the wildlings would need to shoot at their greatest strength whereas the Nights Watch would need to exert less effort; this could impact accuracy.

Accuracy is ultimately going to be up to the skill of the archer, but it is worth noting that the slower the arrow is travelling the more its trajectory is affected by the wind.

• There is another factor hurting the wildlings. Impacts on armor would be at a rather severe angle, and likely to glance off. Even if they didn't, the effective depth of armor material would be enhanced markedly and thus give even more protection. Apr 11, 2014 at 18:45
• A person shooting a wood shaft 400gr bodkin tipped 'war' arrow from a 60 lb bow is going to get a maximum of about 190fps (57.9 m/s, 129.5mph) off the shelf. Depending upon the fletching size (drag surface), velocity goes down from there. I personally use a 4" 3 fletch w/RH twist for stability. Your numbers seem far too generous for traditional wood equipment. Apr 12, 2014 at 18:04
• @Morgan my reference used an 80 lb bow so that may explain the difference. Im trying to be as kind to the wildlings as possible, looking at this from a technically possible point of view Apr 12, 2014 at 18:08
• You did some good work there. They need all the help they can get, right? hehe You can definitely bump velocity by increasing draw weight and decreasing total arrow weight, but you then potentially get into weak arrow-spine issues. You can also decrease the control surface (fletching) to decrease drag and increase velocity but the payoff is decreased accuracy and stability at range. Apr 12, 2014 at 18:23
• This is nice work, but as you yourself say - you're ignoring the effect of air resistance/drag, and that should be not-insignificant. So the arrows will be slower, miss more and hit with less force. Jun 7, 2015 at 13:30

I could be wrong here, but I thought that the wall was 700 feet tall at its highest, implying that there were parts of it that were shorter. If this is the case (and I'm not saying it is), then it is possible that the wall is shorter at castle Black, making such feats more plausible, although still unlikely.

Actually it's mentioned that the wall is rather low (still probably several hundred feet) at the point the wildings used to climb over. They even used a tree to further reduce it.From what i got the wall has basically the same elevation over sea level over it's whole distance, but obviously the land isn't flat.

I don't think anything like this was mentioned for the area of Castle Black though.

Theres also the possibility that the wall is a bit lower near Castle Black, because it's one of the few castles always in use (and even the main one) so a lot more walk on the wall, melting the ice or eroding it.

• I would not consider 700 ft as 'rather low' May 13, 2014 at 14:46
• Its worth noting that everest has been climbed. Being climbable != small May 15, 2014 at 12:50

Using a trajectory calculator I found online that incorporates a rough estimate of air resistance I found that it would take an initial “muzzle” velocity in the area of 90 m/s just to reach (at this stage you could snatch the arrows out of the air before they turn back down again) the top of the wall at a 90 degree shot. If you shoot at an 45 degree angle the initial velocity would have to be about 190 m/s.

According to a friend whom shoots bows himself, British longbows plateau out around 60 m/s (200f/s) due to the arrow-weight-to-draw-weight-ratio. Given this I would call Myth Busted regarding wildlings firing over the wall at all with manpowered bows.

On the point of hitting wildlings form atop the wall, I doubt it is possible to pick individual targets from that distance. However they are never described as picking single targets, but fiering in volleys or firing blind, which is quite possible.

I used the following specifications for the simulator:

Initial speed: Several

Launch angle: 90 degrees

Initial height 1.5 m

Mass: 0.032 kg

Gravity 9.81 m/s^2

Air density 1.225 kg/m^3

Drag Coefficient: 0.02 (A number I honestly just heard from somewhere, but if you use it and plot a 45 degree shot with an initial velocity of 60 m/s you get a maximum range of ~200 meters which is a good estimate of the range of longbows)

Cross-sectional area: 0.0079 m^2

Things I laking "proper" sources for:

1 Max “muzzle” velocity of bow and arrow.

2 Drag Coefficient of an arrow.

3 The validity of the simulator.

Hope it helps!