The Point.

 

Everything in war is very simple. But the simplest thing is difficult.

Carl von Clausewitz, On War

I'm currently re-reading a digital copy of K. J. Parker's fantasy novella Mightier Than The Sword. At 75 pages it's a fun little read, clever, witty, and imaginative, that just sort of sits on my iPhone and gets opened now and then when I'm out of fresh reading material.

However, during this re-read, I began to wonder about the actual numbers involved in the story's climactic battle. (This is a thing that happens now and then when I'm reading, something in the math gets my attention.)

Here's the scenario: the bad guys have 4,000 to 7,000 warriors - we don't know exactly how many, because it's based on reconnaissance, rather than actual knowledge. On the other side, there are 575 archers who are supported by a thousand heavy infantry and 1,500 untrained local militia - not great odds, even if we take the low end count for the enemy, but let's average them out at 5,500 light infantry - more accurately, tribal barbarians, who apparently aren't even wearing shoes.  (Which may actually be a factor in all of this - wait, you'll see.)

Here's how the narrator, who happens to be commanding the defending army, lays things out.  He puts his militia in line, with the Steelnecks - his heavy infantry - on the flank, and hides his archers in a ditch behind the militia.  His opponents sensibly decide to launch their attack on the weaker target of the militia, and begin their charge.

The militia had sworn me a solemn oath to stand their ground, no matter what.  When the enemy were two hundred yards away, they turned and ran like deer; one moment they were there, the next they weren't, and who can blame them?

At this point, his concealed archers stand up and start to shoot.

Okay, time for math.  First, it looks like the general may have made a bit of a mistake.  Historians have determined (lord knows how) that a trained archer in the time of Edward III could shoot an arrow 365 meters.  Accuracy isn't an issue here, the target is an army of over 5,000 people, it would probably be hard to shoot an arrow at that many people and NOT hit someone.  So the good guys have already wasted 182 meters of opportunities to put arrows into the enemy.

The second factor is speed - on both sides.  A sprinting man can run at about 32 kilometers an hour, and a normal running speed is 24 kilometers an hour.  Realistically, in this situation the barbarians will obviously be running as fast as they can, but they're also carrying swords, axes, spears, shields and so forth, which most casual runners don't have to deal with.

So again, let's split the difference and give them a speed of 28 kilometers an hour, which breaks down to about 22 seconds to cover that 182 meters - presumably, like African marathon competitors, they're not handicapped by running in their bare feet because they do it all the time.

The next speed question is how long it takes to fire an arrow.  Again, we're not looking at careful target selection, the archers just need to pull an arrow from a quiver - probably on the ground - nock it to the bow, raise, pull and let go.  The internet suggests that there's some show-off out there who can fire three arrows in .6 seconds, but we're looking at a longer sustained volley, so let's say an arrow a second.

Given the 22 seconds that it's taking the charging infantry to reach the archers, that gives us 22 arrows each from 575 archers for an impressive total of 12,650 arrows.  However, that's in a perfect world.  Let's face it, by the time the barefoot people with axes and swords are three meters away, you've probably stopped shooting and starting running yourself.  If you don't run, you get stabbed or chopped, which is what happens to about half of the archers in the story.*

Even so, that's going to be about two arrows per attacking barbarian, although, again, a lot of this isn't targeted shooting, so a few lucky souls may not get any arrows at all.  (And a few less lucky souls will get four, after all, they have to end up somewhere, and as already discussed, 5,500 people makes for a big target.)

Does that wipe out the attacking horde?  At this point, we enter the realm of supposition, since the only ready sources of information about the results of volleyed arrows are the movie 300, the Battle of the Five Armies from the third Hobbit film, or Ian McShane's character in Hercules, none of which can really be considered as science.

You'd have to think that it would at least put a big dent in the attacking army - even if you've only been hit by one arrow, having three feet of birchwood with an iron tip stuck somewhere into your body is going to make you a less effective fighter when the thousand heavy infantry take you in flank. On the other hand, we don't really know what they're wearing or carrying in terms of protection, although there has to be some kind of inverse relationship between amount of armour and ability to sprint up a hill while archers snipe away at you and your companions.

The author, oddly enough, seems to feel that the archers would only be shooting at the front row of the attacking army, which feels like a mistake - or is it?  Hmmm...575 archers in a line, 5,500 running men, let's call that 10 ranks of 550 each (although probably not that organized) - let's slow things down a bit because our archers are aiming a bit, but even then, the math suggests that ten carefully aimed arrows per archer pretty much wipes out the attacking army.

The narrative suggests otherwise, with half the archers dead and half of them running, as a thousand heavily armed and armoured killing machines hit the barbarians in flank and wipe them out.  And even then, there's a suggestion that it's not a walkover, there are enough remaining barbarians that the first century of Steelnecks that comes into contact with them experiences 83% casualties. 

Ultimately, in that situation, I'm willing to admit that math might not be the only factor that determines the results. As von Clausewitz points out, even the simplest thing is difficult in war.

- Sid

* But why would the archers not have swords as well? Or sharpened poles as a defense to slow down the enemy - something, ANYTHING other than just a bow and arrows.
 
Postscript:

A couple of late-breaking comments on the above.  First, it turns out that the general hasn't wasted that first 182 meters - an earlier note in the book mentions that the maximum range of the bows used by his archers is 200 yards, so he's actually waiting for the enemy to get into range, not wasting time. (His archers must be using some kind of shorter compound bow, rather than the full longbow that made the English archer such a dangerous opponent.)

Second, after writing this all up, I checked in with my archery consultant, Her Ladyship Anika Styfe - aka my co-worker Christi -  and here's her comment:

Hmmm...in a 30 second round, I can comfortably shoot 8 arrows, with the first arrow ready to be loosed when the marshal says go.

For 20 arrows I'd say about 90 seconds, maybe a little faster for the lack of aim. But can't help muscle memory. :-)

So it would appear that an arrow a second would be an unrealistic timeline - but four seconds seems like a LONG time.