A Verification of Lanchester's Law

Abstract

The validity of Lanchester's equations is demonstrated in an actual combat situation where U.S. forces captured the island of Iwo Jima. The equations tested are dM / dt = P ( t ) − AN , and dN / dt = − BM , with t the time elapsed since the beginning of the engagement, measured in days; M ( t ), and N ( t ) the number of effective friendly and enemy troops, respectively; A and B the friendly and enemy combat loss rates, respectively, per opposing combatant; and P ( t ) the rate friendly troops enter combat. Information required for the verification is the number of friendly troops put ashore each day and the number of friendly casualties for each day of the engagement, knowledge that enemy troops are not reinforced or withdrawn, the number of enemy troops at the beginning and end of the engagement, and the time T at the end of the engagement. If the number of enemy troops at the beginning of the engagement is not known, but the time, T , when the enemy is destroyed is known, it is still possible to determine whether Lanchester's equations are valid. In the analysis of the capture of Iwo Jima, the equations were found to be applicable. The value of such analyses increases when repeated often enough to permit general conclusions to be drawn. Operations Research , ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.