The Constraint Model Of Attrition

A mathematical model of attrition data

“…Lanchester laws that was devised to include the square and linear laws as special cases. Equations (7) give the generalization, where m represents the loser's strength, n the winner's strength, E some power of the exchange ratio, and g a function that is symmetric under interchange of m and n (such as g = mn or g = 1 ): dm f dt = -E-'/*nYg( m, n; t ) , dnfdt = -E''ZmYg(m, n ; t ) .…”

Termination decision rules in combat attrition models

“…They further observed that the S parameter in (4) is related to the ratio of the attrition rate coefficients and y . Hartley [2] used the same data as Helmbold to explain the distribution pattern in Helmbold space through constraint model of attrition assuming battle termination due to casualty rate, kill rate, casualty exchange rate, and force ratio. More recently, Hartley [ 3 ] studied the distribution pattern of the historical combat data with a view to improve the validity of the attrition model and defined the following attrition law:…”

“…The set of equations ( I ) are called Lanchester equations of modern warfare resulting in the square law of attrition, while Eqs. (2) are called Lanchester equations of area warfare resulting in linear law of attrition.…”

“…42 ( 1995) helmrat = ( R i -R 2 ( t ) ) / ( B i -B2(t)), ( 5 ) a and 6 are slope and intercept parameters of the regression line, respectively; RI, and B,, are initial force strengths of Blue and Red forces, respectively. This concept was further analyzed by Hartley and Kruse [4] and Hartley [2]. Hartley and Kruse (41 defined the following attrition equations:…”

“…Since the AOP rule represents the union of A rule and P rule, if kh 2 Ro/(fhBO), the proportional decision line for Blue will be contained in the absolute decision line and thus the AOP rule for Blue reduces to the A rule. Also, AAP rule being the intersection of A rule and P rule, the condition kb 2 …”