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Two Effects of Firepower: Attrition and Suppression

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Two Effects of Firepower: Attrition and Suppression Calhoun: The NPS Institutional Archive Faculty and Researcher Publications Faculty and Researcher Publications 1995 Two Effects of Firepower: Attrition and Suppression Hughes, Wayne P., Jr. Military Operations Research http://hdl.handle.net/10945/38442 ABSTRACT • Military force, or combat power, is a real phenomenon, the results of which are Anew basis for the quantitative study observed by its effects on the enemy in of ground combat is introduced that battle. argues the inadequacy of attrition • The observable effects of combat Two Effects models and the need to incorporate the power are not merely physical (producing effects of suppression of the enemy with fire- casualties) but also mental (persuading the of Firepower: power. A quantitative approach to suppres- enemy of our superiority) and spiritual sion of enemy fire is offered. Then an (diminishing enemy morale and will to con- Attrition and analysis shows that the effect of own fire in tinue fighting.) suppressing enemy fire will, in suitable, fre- For purposes of this paper, we will look Suppression quent circumstances, reverse the conclusions carefully only at the most measurable mani- derived from the Lanchester square law, so festation of combat power's mental effect, that the squared term determining the victor which is suppression of enemy actions, Wayne P. Hughes, Jr., FS is unit firepower instead of the numbers of specifically his return of fire. Its spiritual units engaged. effect to diminish enemy morale plays no Senior Lecturer A fundamental aim of physical science part in the computations that follow, but Department of Operations Research is to describe its processes with dynamic may be seen to be an unquantified bonus. Naval Postgraduate School models, mathematical if possible. The same Let us begin with a fresh look at the Monterey, California 93943 aim, often implicit, is true of descriptions of Lanchester square law from the perspective combat phenomena in military operations of combat science. As it was conceived and research. Models of military operations are employed by Chase [1902], Fiske [1905], necessarily more abstract and approximate Osipov [1915] and Lanchester [1915] the than those of physical science. This is espe- square law describes combat as a purely cially so because the scientific study of com- physical phenomenon: bat operations is complicated by human presence. The problem, of course, is to [Unit fire's physical effect in casualties reduce the enormous effects of "human fac- imposed/minute] tors," to an understandable construct, or paradigm. An excellent statement of the problem is in Davis and Blumenthal's mono- graph, The Base-of-Sand Problem: A White [# of physical units firing] Paper on the State of Military Combat Modeling [1991]. For more than a decade The Military [Fewer enemy units] Conflict Institute (TMCI) has been address- ing the problem via a theory of combat that Starting with Osipov, who reached his derives from six axioms. A goal of TMCI is own unique conclusion as to the appropriate to express the theory in a study, thus far relationships, there have been many objec- unpublished.1 As something of a status tions that the classical square law does not report, I undertook a Naval Postgraduate fit the historical battle casualty data for ground combat. The most commonly cited School research paper to digest what seemed reason is (properly enough) that the law can- to be the essence of TMCI's work. It is enti- not apply when the required conditions are tled "Combat Science: An Organizing not present in the battle. The conditions are Study" [1993]. The present paper is an expo- that each participant must be able to fire at sition of a small but important consequence each participant on the opposing side; and of the two endeavors. incapacitated opponents must be known at We may come at our subject with the once, so that fire is distributed only against following question which arises from the active opponents. Patently these conditions remarkable results of the Gulf War: are seldom fully met, with not-so-obvious What analytical proposition helps to explain the evidence that much superior effects on the square law's applicability. combat power when properly applied will There are probably three additional result in disproportionately small losses to major reasons, each related to the other two. the winner while he achieves his objective? One is insufficient attention to defender The relevant principles from Combat advantage. Unit fire effectiveness will nor- Science are: mally be greater on the defender side until Military Operations Research, Fall 1995 Page 27 TWO EFFECTS OF FIREPOWER the attack is nearly consumated. This advantage forces remaining at any later time t; and dA/dt comes from the defender's superior posture. and dB/dt are the rate of losses of A and B When identical unit effectiveness is (wrongly) respectively at time t. assumed for attacker and defender the results A solution to equations [1] for end time T is will appear to show a less-than-square-law effect the state equation: for the attacker's numerical advantage. The second reason is that a battle is usually a [A(0)2 - A(T)2] = ß [B(0V - B(T)2] (2) episodic, such that different elements of a force play predominant roles at different phases of the Equation [2] shows the well known square battle. A battle might involve disproportionate law phenomenon, in which A will win a fight losses upon the attacker during his assault and when the weaker side is annihilated: disproportionate losses upon the defender dur- ing his attempt to disengage. Different weapons aA(0)2>ßB(0)2 produce casualties more and less effectively during different phases. Historical battle data and vice-versa. The classic conclusion from the rarely specify casualty production in this way square law is that the "fighting strength" and so the episodic effects are disregarded out of (Lanchester's term) of a force increases in direct necessity. proportion to unit effectiveness and in propor- The third reason is shortage of data with tion to the square of the number of forces which to measure the effect of suppression of engaged. enemy actions from firepower.2 Since suppres- Notably, the casualty-producing effect of fire sion produces no casualties and is a transitory is regarded as a constant. There is ample evi- phenomenon that disappears when the battle is dence that unit effectiveness, a or ß, is not even over, the effect of its presence is overlooked (or is approximately constant but is highly variable. merely implicit) in almost all combat models, This is true when one is using casualty data including high resolution simulations. In taken battle after battle or day after day during a Chapter 18 of Understanding War, T. Dupuy campaign: see for example, D. Hartley [1990, pp. began his fine discussion of suppression with: 3-4; and 1991, p. 3]. It is true when one is using "There is probably no obscurity of combat casualty data taken from different places on a requiring clarification and understanding more battlefield: see G. Kuhn [1989], for example. It is urgently than that of suppression" [1987]. true during different phases of a battle: see The heart of the problem is not a refusal to R. Helmbold [1979], for example.3 Even though acknowledge the importance of suppression but data by phase is seldom available, the variability the lack of an analytical approach that describes of fire effectiveness is readily appreciated by the phenomenon and its importance. We wish reflecting upon a battle's sequence: for example, here to develop a quantifiable model of it. Then an artillery preparation phase, an armored we will fulfill the purpose of this paper, which is assault phase, and an exploitation phase after an to show how an appreciation of the cognitive enemy position is overrun. influence of fire can reverse present conceptions If a (t) and ß (t) are also variables, then the of the value of numbers relative to the unit fire- Lanchester square law equations must be writ- power of a fighting force. ten: We begin with the common form of the dA dB Lanchester square law: = -a(t)A(t) dt = -ß(t)B(t) dt (3) dA dB a A{t) (1) dt -ßB(t) dt Two important reasons that a (t) and ß (t) vary are: first, a change in range between the fighting units as the battle unfolds; and second, where a and ß are the constant unit effectiveness the suppressive effect of each side's fire on the coefficients for A and B respectively, measured in other's fire. For two forces fixed in place with no kills per shooter per unit of time. A(0) and B(0) change in range, the suppression suffered by A are the initial force strength; A(t) and B(t) are the will be in consequence of the volume and Page 28 Military Operations Research, Fall 1995 TWO EFFECTS OF FIREPOWER accuracy of fire by B, and vice versa. Let us pos- We may easily explore circumstances in tulate a constant of proportionality, g, such that which the volume and precision of fire have a g/3(t)B(t) is the time-rate at which each A-shoot- much greater effect to suppress enemy fire than er's fire is curtailed (measured in volume or to impose casualties. Define b(t) as the rate of fire accuracy or both). Similarly define a value, h, in shots by each unit B, and a(t) as the rate of fire such that ha(t)A(t) is the rate that each B-shoot- by each A. Define s as the rate of reduction of fire er's effectiveness is diminished by A's fire.4 We imposed on the other side per shot fired, such write: that: da dß da db ■ha(t)A(t) (4) Tt=-sBKt) -ä = -sAa(t) (5) The total effect of firepower represented by With equations [5] we measure combat equations [3] and [4] is twofold.
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