Analysis of the Effect of Longbows (Work in Progress)

Work in Progress (open) Work in Progress (close)

Alright, so a concern with the planned operations against Jagon and his men is the fact that, with only two aerial mounts available, attacking safely from the air is quite difficult. While I do not suggest that the mounts will be untouchable, I am quite of the opinion that with only longbows and crossbows to contend with, the mounts will be quite difficult to hit and kill. Here is why:

To present a comparison between Jagon's likely cababilities and some historical reference, I will use WWI-era air-defense using two weapons of the British Empire, the Short-Magazine Lee Enfield Mk III bolt-action infantry rifle and the Vickers Mk I machine-gun, both of which used the exact same .303 British (7.62x56mm) cartridge, when pitted against a common bomber of the Imperial German Air Service, or Luftstreitkräfte, the Gotha G.IV heavy bomber.

Now, first of all, let us establish the characteristics of the weapons being used. To analyze the effects of a single marksman shooting at an aerial target, I will compare Jagon's longbow, with data gathered from research about professional longbowmen of medieval England, and the British Short-Magazine Lee Enfield Mk III service rifle. First of all, one must consider the two most important things about these weapons when comparing them: muzzle velocity and fire rate.

Now, you may be thinking, Jagon's longbow is massive and fires lance-sized arrows, and I have considered this, and have decided that it is very likely that the construction of this bow is mainly proportional to a real longbow, yielding much the same characteristics of trajectory and projectile flight. Keep in mind, a big force on a big object can yield the same effects as a small force on a small object.

In any case, I was unable to find a flight speed of an arrow fired form a longbow, but my readings have told me that, at the time of King Edward III of England, a professional longbowman could fire to a range of 400 yards, or 365.76 meters. Setting this as the maximum range of a longbow, I can assume that this would be fired at the angle which yields maximum range (when not considering air resistance, which I would need calculus to consider), being 45 degrees of elevation. This allows me to calculate the speed of an arrow from such a longbow to be 59.9 meters per second.

The muzzle velocity of a Lee Enfield rifle is listed as being 744 meters per second. Now, my readings do not yield a firing rate for a bolt-action Short-Magazine Lee Enfield, but I will provide a reasonable estimate of one aimed shot every five seconds, while the English longbowman would never fire an arrow faster than once every ten seconds, given that firing faster is quite exhausting. Let us therefore suppose that aimed shots from an Enfield can be twice as fast as those of a longbow.

For later reference, the Vickers Mk I medium machine-gun shares an identical muzzle velocity to the Lee Enfield of 744 meters per second, with a rate of fire of 450-500 rounds/min.

Numerical Values So Far (open) Numerical Values So Far (close)

English Longbow
"Muzzle" Velocity=59.9 m/s
Rate of Fire=6 rounds/min

Short-Magazine Lee Enfield Mk III
Muzzle Velocity=744 m/s
Rate of Fire=12 rounds/min

Vickers Mk I medium machine-gun
Muzzle Velocity=744 m/s
Rate of Fire=450 rounds/min (safer to assume lower value in this case)

Now, let us compare the targets these weapons are shooting at.

In the longbow's corner is the mythological Wyvern/Dragon mount, capable of carrying one passenger in flight.

In the rifle corner is the German Gotha G.IV heavy bomber.

For these mounts, we must consider a few factors: altitude, wingspan, and airspeed. To further simplify my work, I will also have to assume that the mounts/bombers are experiencing no head winds or tail winds, therefore their indicated airspeed is equivalent to their ground speed.

The analysis I will provide will illustrate the characteristics of shooting at a target that is approaching head-on toward the shooter. The aerial target will not be directly overhead, and I will calculate altitude and slant range from shooter based on the transit time of the projectiles. This may seem complicated and difficult to understand, as I've explained this is one short paragraph, but all will become clear.

Now, first to address is airspeed of these aerial bombers. Let us first deal with our historical reference point: the Gotha G.IV. This was a World War One-era heavy bomber operated by Germany, meaning that shooting at it was about as primitive as air-defense has ever been. The Gotha G.IV had a maximum airspeed of 83 miles per hour, or 135 kilometers per hour, to put it in metric for ease of calculation, and a service ceiling of 5,000 meters (16,400 feet).

Of course, size is also an important consideration. The Gotha G.IV had a wingspan of 23.7 meters (77 feet 9 inches), a height of 3.9 meters (12 feet 10 inches), and a length of 12.2 meters (40 feet).

Now, I can estimate the speed of aerial mounts based on the speed of relatively fast birds, as I imagine the dragons can be fast, but are not the fastest things in the air.

Therefore, I estimate, based on what I have deemed reasonable after looking at Wikipedia's chart of the five fastest birds in the world, that either of our mounts will manage a maximum airspeed of 70-80 miles per hour (112.65-128-75 kilometers per hour), but with a rider and whatever bombs we plan to drop, let's be slightly conservative and say the mounts will manage and airspeed of 65-70 miles per hour (104.6-112.65 kilometers per hour).

As for dimensions, let us base our one-man mounts on WWI-era fighters. Therefore, let us suppose these dragons will have a wingspan of 10 meters (32 feet 9 inches), a length of approximately 6 meters (19 feet 8 inches), and a height, while flying, of about 2 meters (6 feet 7 inches).

Numerical Values So Far (open) Numerical Values So Far (close)

English Longbow
"Muzzle" Velocity=59.9 m/s
Rate of Fire=6 rounds/min

Short-Magazine Lee Enfield Mk III
Muzzle Velocity=744 m/s
Rate of Fire=12 rounds/min

Vickers Mk I medium machine-gun
Muzzle Velocity=744 m/s
Rate of Fire=450 rounds/min (safer to assume lower value in this case)

Gotha G.IV heavy bomber
Maximum Airspeed=37.5 m/s (135 kph)
Service Ceiling=5,000 m
Wingspan=23.7 m
Length=12.2 m
height=3.9 m

Wyvern/Dragon Aerial Mounts
Maximum Airspeed=31.3 m/s (112.65 kph)
Service Ceiling=Altitude to be Illustrated
Wingspan=10 m
Length=6 m
Height=2 m

Now, I will address two situations in which Jagon will be firing at an approaching aerial mount, and these scenarios will be made parallel with a rifleman of the British Expeditionary Force firing at a Gotha G.IV in 1917.

First, we will look at the difficulties of firing at an airborne target flying in a straight line toward the shooter, or rather in a line that would take it over the shooter's head.

Then, I will look at a scenario in which the aerial target flying over a bombing area to the side of Jagon, where Jagon and/or the rifleman will be shooting at the aircraft from the side.

First of all, I will calculate the transit time of an arrow from Jagon's bow to the point of the approaching aerial target. For this scenario, we will say that Jagon will try to shoot straight-on, that is to say, no hitting the target while the arrow has begun its descent. We will also say that the mount is coming in at a reasonable altitude of 100 feet (30.48 meters). First, we must calculate the maximum range at which the arrow will hit an altitude of 30.48 meters. Therefore, I must simply calculate the y-axis vector component of the arrow's velocity that would see it be rising at 0 m/s at an altitude of 30.48 meters. We must keep in mind that a reasonable estimate for the starting height of the arrow is 2.45 meters, the height at which Jagon would likely loose the arrow.

Formulas (open) Formulas (close)

v=v0+at
x=x0+v0t+(at^2)/2
v^2=v0^2+2a(x-x0)

I have thereby calculated the y-component of the arrow's velocity to be 23.45 meters per second, meaning that the arrow will reach its peak height of 30.48 meters after 2.39 seconds. The vector components of an arrow traveling along such a trajectory will be a vertical component of 23.45 m/s and a horizontal component of 55.11 m/s. Therefore, it can be found that Jagon will be firing this arrow at an angle of elevation of 23.05 degrees.

As the arrow will travel at 55.11 m/s horizontally, the horizontal range at which the arrow will reach its maximum height I have calculated to be 131.7129 meters.

Since the arrow will take 2.39 seconds to reach the point of impact, Jagon must fire when the aerial mount is 206.5199 meters away, as it will approach 74.807 meters closer in that 2.39 seconds.

To calculate the angle by which Jagon must lead his target, I will use the law of cosines.

Law of Cosines (open) Law of Cosines (close)

c^2=a^2+b^2-2abcosC

In order to lead his target by 2.39 seconds, or 74.807 meters, Jagon must pick a point that, when looked at straight on, is an angle of elevation of 4.28 degrees higher than the angle of elevation to the moving target. That is to say, he may not have to aim 4.28 degrees higher when evelating his bow, but he must aim at a point that is colinear with a line 4.28 degrees above the line through the approaching dragon. Given the distance to his target, any small variation in aiming will yield a miss. Keep in mind, this is also assuming Jagon has Straight Shooting.

In order to hit his target, he must aim to an area that is ten meters across, two meters high, and six meters long. At 131 meters, this yields a target area only 1.36 degrees of arc vertically and 4.25 degrees horizontally.

Now, it would make sense to try and shoot the dragon as it comes closer, but, the thing is, as it flies overhead, the angle to the target changes rapidly, while, if it is farther away, it does not change so quickly, and is therefore actually easier to aim at. In addition, Jagon has the time for only one shot, as ten seconds will pass before he can shoot again, and, by that time, the target will have passed overhead. It makes no sense to fire a longbow at a target that is traveling away from you, because the speed of the arrow relative to the target would be so low that it would be far insufficient to score a kill, or even injure the target to any significant degree.

I really hope this isn't for serious use, but for just shits and giggles.

You seem to forget this takes place in a universe where the laws of physics don't always apply. Plus there's, you know, magic. Treasures for perfect aim, etc.

Nah, there are small, weaker birds that fly much faster. I don't think 70 is really that bad. Keep in mind, it is a maximum speed, which you would likely only reach when within striking distance of the enemy.

I'd hope the same thing, but, to be honest, I take this seriously only because I am interested in exactly this sort of analysis... Well, not this sort, but this is close enough. It's what I do. The fact that I get to do it here is just a perk.

And, in any case, I do know about Straight Shooting, which is why I am not taking into account wind effects, aside from the fact that it would also make calculations more difficult. These numbers are as perfect as an arrow can be. Realistically, you won't get these nice, clear-cut trajectories.