Warfare is predominantly resolved in one of two ways, either by missile weapons or in hand-to-hand combat. During historical episodes wherein the dominant weapon is a hand-held weapon, the skill of the individual combatant is more significant than the number of combatants in a battle; conversely, when missile weapons dominate, the number of combatants is more significant than personal skill (i.e. in feudal times, when army sizes were limited, small numbers of highly skilled "professional" knights could control and defeat superior numbers but less skilled dismounted troops).

When armies of both opponents are small it is relatively easy to find terrain upon which the defensive army, usually the smaller, can anchor both flanks. The use of terrain for security will force the attacker into a situation where he must attack on an equal frontage, in numbers equal to the defender, because he is denied the opportunity to extend his front and thereby overlap the defender's frontage.

The increasing budgets of governments, universal conscription, and the use of low skilled weaponry allowed the size of armies to grow during the wars of the French Revolution and Napoleon. This increase in army size produced situations where a local superiority of numbers could be developed and exploited.

Limited by the available technology of the late 1700's, the military powers independently developed small arms that resembled each others to 2 high degree. Balancing the requirements for a weapon that is capable of a high rate of fire, while possessing a reasonable range, the primary method of inflicting casualties became the use of massed formations of infantry, using the smoothbore musket.

The advent of the industrial revolution and the mass production of standardized firearms and gun powder, allowed the impact of massed firearms to become significant. The smoothbore was inexpensive, capable of sustained action at two to three rounds per minute, and in action resulted in three percent of expended rounds resulting in the death or incapacitation of an enemy soldier.

Hypothetical Situation

Given a hypothetical situation where opponents had identical formations, weapons, tactics, and training, it is apparent that they would produce similiar rates of inflicting casualties. Therefore, in a firefight between two similiar formations in which both formations were able to fire to the last man, they would annihilate each other, as the last man in each formation fired a fatal shot.

In a firefight between two identical formations, each composed of 1,000 men, firing one volley every thirty seconds for 5 minutes, both formations will receive 263 casualties, about one-quarter of their original strength. As the casualffes are received and the number of troops decline, the ability of the formaffons to inflict casualties must decrease. There is a steady decrease in casualties inflicted by each volley, from 30 in the first volley to 23 in the tenth volley.

The use of missile weapons and the inability of armies to anchor upon terrain allows for the concentration of multiple units against a single enemy. In a firefight in which two 1,000 man formations are engaging a single 1,000 man opponent, with all formations identically trained, equipped, and capable of inflicting casualties equal to 3% of rounds fired, the casualties inflicted will be equal to the ratio of combatants. Initially the casualties will be 2 to 1 (in proporffon to the combatants), however, since the smaller formation is receiving more casualties than the larger formation, the ratio will change from volley to volley.

Therefore, the ratio of the larger force to smaller force grows thoughout the combat. The ratio of casualties per volley are 2.00:1, 2.10:1, 2.20:1, 2.33:1, 2.47:1, 2.65:1, 2.83:1, 3.06:1, 3.34:1, and 3.67:1 for the first through tenth volley respectively, with the ratio of casualties for the entire firefight being 2.55 to 1. Notice how the final ratio of casualties (2.55 to 1attacker to defender) approximates the initial ratio of attackers to defenders (2 to 1). I consider the correlation of inflicted casualties to the initial ratio of combatants as "proportionate casualties".

Taken to the extreme, a firefight that is extended until the last man of a formation becomes a casualty will see 19 volleys, the defending formation of 1,000 men is eliminated due to the fire of a 2,000 man opponent. The steadily increasing ratio of attackers to defenders prior to each volley will grow from 2 to 1 for the first volley to 3.34 to 1 in the tenth to 25.55 to 1 in the 18th volley.

Finally, the ratio of casualties at the conclusion of the combat (3.54 to 1 ) is approximately equal to the square of the original ratio of combatants (22:12 = 4:1). This rule of squares was first presented by E.W. Lanchaster, which he termed the N-square law.

Firefight Myths

Firefights to the point of annihilation of a formation are nearly the thing of myth. There are occasional references to such actions in history, but they are the unusual encounter wherein the losing formation cannot run, nor engage their opponent. A likely instance to come to mind is the annihilation of a battalion of the French Old Guard at Waterloo, the 1st battalion/lst Brigade of Chasseurs.

However, the formation was not involved in a traditional firefight, this immortal battalion was deployed in open square, shielding the fleeing mass of French troops, when it was engaged by British cavalry and forced to hold its ground. The chasseurs were then fired upon to the point of virtual extinction by several batteries of cannister-firing artillery.

In most firefights, the opponents will fire at each other until the men of one unit reach the point where they refuse to take the punishment any more and retire, with or without their officers approval. The point at which the morale of a unit breaks is twofold. After the casualties start to become numerous, the men eventually may refuse to advance further into the maelstrom being quite satisfied to remain in place and trade shots with their distant and impersonal foes.

As casualties continue to mount, men may begin to fall back without orders. For a while the officers and NCO's, enforcing their authority with threats and blows, will contain this encroaching retreat. However, since the enlisted men of a unit outnumber the officers and warrant officers of a unit, by at least ten to one, the enlisted ranks will eventually filter through in one's and two's, which in turn will inspire more men to retire -- ultimately evolving into a torrential flood toward the rear. The focus of all combat is to drive the men of opposing formations to this point of disillusion of command.

Local Superiority

A number of options are available when trying to obtain a local superiority. The most direct is simply to concentrate on the weakest point in the defensive array. By choosing this place to engage the enemy, the attacker has selected a place where the defender has extended frontages and limited reserves, therefore, the obtainment of local advantages will be easily obtained without extravagant movements or evolutions at the point of attack.

Another method to obtain local superiority of firepower is to utilize initiative of movement to concentrate superior numbers at a critical point in the opponent's defense Plans for coordinating units can be made and reviewed in advance, resolving conflicts and oversights before they occur, instead of working them out on the march.

Simply by taking the initiative, a commander knows what he is doing and where he is going. A general who awaits an opponent's action will by necessity be delegating himself to the local defensive, and will be reacting to opposing concentrations instead of developing his own. In addition. and more importantly, often an enemy concentration is employed before it can be discovered and, therefore, the attack is executed and resolved before reserves can be deployed -- denying value to any response. The failure to respond to an enemy's concentration of units will result in the enemy having a superiority of firepower at his point of attack.

These strategies can be combined, by using movement to create a weakness in the defensive lines. The attacker can require the defender to extend his front, either linearly or by committing to a flanking action, the defender will be required to pull local resources and commit reserves to counter the movements of his opponent.

When the assault lands, the defense - missing the resources that were pulled to counter the extended front - will be considerably less resilient to combat. Jena and Austerlitz are prime examples of Napoleon's use of flanking actions on a grand scale.

Risky

Although a strategic maneuver - rather than a tactical development - and taken further than a flanking action, an indirect approach can be used to create a superiority of firepower, but is considerably more risky than a flanking action. In the indirect approach a small diversionary force remains to the enemy's front engaging it's attention - while the majority of the attacking force makes a distant flanking movement, making for the enemy's rear. Properly designed, an indirect approach can effectively cross terrain that secures an opponent's flank, which might otherwise would be unbreakable.

The frontal diversion is not meant to seriously engage the defender, only keep its attention long enough for the flanking action to concentrate at the point of attack and deliver the attack from behind the opponent's flank.

At Ulm, the premiere example of an indirect approach on a grand scale during the Napoleonic period, Napoleon distracted the Austrians with a cavalry corps of 17,000 men and proceeded to make an encircling march of 80 miles with 200,000 men, crossing the Rhine, Danube and Lech rivers. Having cut the Austrian line of communications, Napoleon effectively seized the entirety of Bavaria, taking 50,000 prisoners, in the face of considerable opposition.

Regardless of the method of concentration, the key issue related to local superiority of firepower is the ability of a smaller force to defeat a larger one. Many issues impact when a formation will quit the field, but the most significant factor must be the amount of casualties that the formation has suffered. But given an environment where antagonists will retire after receiving 50% casualties, it is critical to inflict 50% casualties before receiving them yourself.

Two units can decisively defeat the three opponents by reducing each of them, in turn, to less than 500 men, while remaining themselves above 50% of effectives. The attacking units have a combined strength at the conclusion of combat 1291 men, or approximately 65O of their original effectives. Increasing the ratio of combatants will result in the defending units breaking more quickly. Therefore, increasing the local super ority of firepower (3 to 1 instead of 2 to 1} will correspondingly increase the ability of smaller forces to defeat larger forces.

To accomplish the defeat of a numerically superior foe, economy of force must be utilized - all the units of an army must be employed to full effect. While it is necessary at all times to form and keep reserves, it is equally necessary to restrict the placement of units into inactive roles. Each of these inactive units reduces available resources and limits opportunities to develop further points of superiority of firepower.

Tactically, proportionate casualties result in the opponent losing significantly more casualties - killed and wounded - than will the attacker. This accelerated rate of casualty infliction wil1 result in a corresponding increase in the opposition retiring, withdrawing, and breaking from firefights. The ability of two units to defeal singly, three opposing formations allows an army of 20,000 to defeat an army of 30,000 exclusively by firepower.

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