The Cold Equations

In the movie and book The Killer Angels there is a scene where Confederate Lt. General James Longstreet is mentally running through what is going to happen to Pickett's men as they advance on the Union lines on July 3rd, 1863. When they come into view they will be hit with long-range artillery fire. Casualties will drop out and organizations will be stressed. At 200 yards they will begin taking rifle fire and formations will begin to come apart. At 100 yards it will be cannister howling through the air and cutting down men in groups. It will be up to leadership, then, because formations will be lost. In the end, 6500 men (more or less) fell, and every regimental and brigade commander was hit. The attack failed.

Longstreet's thoughts were the same numbers that guide everyone who writes a set of wargames rules for the black powder era. They are the presumed effectiveness of cannon and musket fire on advancing troops.

In the 1780's and 90's a series of experiments were conducted by the Prussian Army and the East India Company seeking those hard numbers. They fired at a canvas strip the height of a soldier and counted the hits scored at a variety of ranges.

Now a body of troops are not a solid wall. As troops advance gaps will appear between the men. There will be more gaps down lo around the legs. Further, the men doing the firing were not themselves under fire, nor was their command structure disrupted by hostile bullets. Despite all of that, these were numbers people could use.

There have been other attempts to codify the effects of fire. A number of years ago, in a book entitled Firepower, Brigadier B.P. Hughes studied the casualties in the Second Peninsular War (1808-14). One of the numbers that sticks in the mind is that every cannon shot (ball shot) will inflict 1 KIA and 3-5 wounded, at a minimum. This information was drawn from battlefield performance, and was seized upon by rules writers everywhere.

On the face of it the numbers Hughes derived appeared to be valid, but a careful reading of his work invites some skepticism and suggestions that these numbers are still a bit high. For example, the French fired at least 36,000 cannonballs fired at Wagram in 1809, but 36,000 dead and 180,000 wounded on the Austrian side. As they had some 150,000 men, this would have represented a 133% casualty rate.

A brief digression: the morale effects of fire is a lot harder to calculate, and falls into the sphere of anecdotes and memories. A Prussian general, speaking in 1870, opined that a unit could lose 2 min in 5 and still function adequately. In the American Civil War (a treasure trove of information like this) the numbers are, perhaps, higher. Dr. Christopher Duffy, in The Military Experience in the Age of Reason concluded that a regiment had one "good" fight in it (read "big" fight with high casualties), but a unit could go through a whole series of battles where they lost 4-10% casualties with little ill effect. S.L.A. Marshal investigated this very subject in his seminal work Men Against Fire about combat experiences in the South Pacific in WW2. Training, discipline, leadership, prior experience, and, yes, morale, all factor into this. Unit A might grind to a halt and return a desultory fire, while Unit B will continue to advance (albeit slowly). Look at what happened with the 26th North Carolina on the first day of Gettysburg when they ran into the 19th Indiana of the Iron Brigade.

Note, I listed morale and discipline as separate categories. A unit can be disciplined to the point of being brittle. Discipline might hold a unit in the firing line; morale will impel them forward or get them to maneuver while under fire. Not for nothing did the French inscribe "Valor and Discipline" on their colors during the French Revolution and Republic.

So what are we to do with the numbers so carefully collected in Prussia, Bombay and Spain? Is it too much to suggest we discount them by a healthy amount, say 75-90%?
Let us perform a thought experiment. A 600 man battalion of infantry drawn up in 3 ranks is going to attack a 6-gun battery 1000 yards away. The foot will advance at 75 yards a minute and halt when they come within 100 yards of their target to open fire. It will take them 12 minutes to cover those 900 yards. The 6-gun battery, all smoothbores, can fire as fast as 2 rounds/minute, but regulations specified otherwise. General Henry J. Hunt, the Commander of the Artillery of the Army of the Potomac, and therefore a subject matter expert, recommended a battery that is not in danger of being overrun, fire at one round per gun every two minutes. This would balance ammunition supply and usage, smoke, barrel temperatures (barrels that were too hot would "cook off" the ammunition, with unfortunate results for the crew), and the necessity to run the guns back into position in an era without recoil mechanisms on the gun.

Now 6 guns will, in 12 minutes, produce 36 shots. By the numbers derived in Hughes' book, this will generate 36 dead and up to 180 wounded, or 216 casualties (over 33%) just from this battery. Note that there isn't much cannister fire, no supporting musketry, and no fire from other batteries.

So how was it that batteries in the black powder era were captured? How was it that the battlefields of the black powder era weren't charnel houses that would rival WW1? There are several reasons: the effects of ground (these were direct fire weapons); the size of a battalion (don't think width, think depth - it takes very little to make the 4" cannonball miss); noise; distractions such as casualties; the effects (at least when facing the French) of sustained skirmish fire (by the way - you can shoot through skirmishers); and the difficulty of judging the effects of fire on a battlefield shrouded in smoke.

A brief anecdote here. A Union officer operating in the Peach Orchard at Gettysburg on July 2nd, 1863, was more concerned by the skirmish fire than the 44 guns aimed at his position from 400 yards away.

Unfortunately, without doing such things as walking the battlefields we've read about, rules writers have accepted a lot of the above numbers with little question. For example, a decade or so ago I played a dozen games of Battles for Empire, which was a slicked up rewrite of Garde du Corps, which was an attempt to rewrite/improve Scotty Bowden's Empire 2. I watched a single battery catch a column in the flank at 800 scale yards and blow away 10 of the 12 castings with one shot. This was not a fluke. I asked a rookie gamer about the rules afterwards. He offered the opinion that the guns were the killers, and everything else was just decoration.

As an experiment, when we did a large battle with 5,000 castings on a side, I tracked what happened to my lead infantry corps of 400+ castings (25,000 men in scale). Just over 60% of their 5,000 casualties came from 6# roundshot (almost all of it from two Royal Horse Artillery batteries; 30% came from one battalion of British Rifles that could move full and shoot at a full rate every turn; 10% came from smoothbore muskets and melee. The Young Guard at Aspern Essling in 1809 lost 10% due to artillery fire, 5% due to bayonet/sword, and 85% due to smoothbore muskets.

We stopped playing those rules just after that.

Some rules writers get it right by concentrating, not on the numbers, but on the effects of combat. Shako gives a quick game that more or less feels like some of the combat of the 1813-15 period. Be warned, things can go bad for you in a hurry, which is why I say a quick game. House Rules Napoleonic, 2nd ed. seems even closer, and can even be done without dice! I have been told my own Little Big Battles does much the same, though dice are a tad more important. Empire 2, preferably modified slightly, does much the same. Or you can write your own.

If you do (write your own), be prepared for someone to fire a 6# battery at a battalion in column 1200 yards away, and be vocally disappointed because that battalion wasn't vaporized (I saw it happen in a refight of Albuera). That is the residue of the use of the numbers I mentioned above.