N PS ARCHIVE 2000.03 TURKES, T. NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS FITTING LANCHESTER AND OTHER EQUATIONS TO THE BATTLE OF KURSK DATA By Turker Turkes March 2000 Thesis Advisor: Thomas W. Lucas Second Reader: Ron Fricker Approved for public release; distribution is unlimited. \ THESIS j. T937255 REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington. VA 22202-4302. and to the Office of Management and Budget. Paperwork Reduction Project (0704-0188) Washington DC 20503. 1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED March 2000 Master's Thesis 4. TITLE AND SUBTITLE 5. FUNDING NUMBERS Fitting Lanchester and other equations to the Battle of Kursk Data 6. AUTHOR(S) Turkes, Turker 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER Naval Postgraduate School Monterey, CA 93943-5000 9. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING /MONITORING AGENCY REPORT NUMBER 11. SUPPLEMENTARY NOTES The views expressed in this thesis are those of the authors and do not reflect the official policy or position of the Department of Defense or the U.S. Government. 12a. DISTRIBUTION / AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE Approved for public release; distribution is unlimited. 13. ABSTRACT (maximum 200 words) This thesis extends previous research on validating Lanchester's equations with real data. The quality of the available historical data for validation of attrition models is poor. Most accessible battle data, contain only starting sizes and casualties, sometimes only for one side. A detailed database of the Battle of Kursk of World War II, the largest tank battle in history, has recently been developed. The data were collected from military archives in Germany and Russia by the Dupuy Institute (TDI) and were reformatted into a computerized data base, designated as the Kursk Data Base (KDB), and recently made available and documented in the KOSAVE (Kursk Operation Simulation and Validation Exercise of the US Army) study. The data are two-sided, time phased (daily), and highly detailed. They cover 15 days of the campaign. This thesis examines how the various derivatives of Lanchester's equations fit the newly compiled database on the Battle of Kursk. In addition, other functional forms are fit. These results are contrasted with earlier studies on the Ardennes campaign. It turns out that a wide variety of models fit the data about as well. Unfortunately, none of the basic Lanchester models fit the data, bringing into question their use in combat modeling. 14. SUBJECT TERMS 15. NUMBER OF PAGES Combat Modeling, Lanchester Equations, Battle of Kursk 15. PRICE CODE 20. 17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION LIMITATION OF ABSTRACT • OF REPORT OF THIS PAGE OF ABSTRACT Unclassified Unclassified Unclassified UL NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std. 239-18 298-102 Approved for public release; distribution is unlimited FITTING LANCHESTER AND OTHER EQUATIONS TO THE BATTLE OF KURSK DATA Turker Turkes ij First Lieutenant, Turkish Army B.S., Turkish Army Academy, 1993 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN OPERATIONS RESEARCH from the NAVAL POSTGRADUATE SCHOOL March 20,00 ABSTRACT This thesis extends previous research on validating Lanchester's equations with real data. The quality of the available historical data for validation of attrition models is poor. Most accessible battle data contain only starting sizes and casualties, sometimes only for one side. A detailed database of the Battle of Kursk of World War II, the largest tank battle in history, has recently been developed. The data were collected from military archives in Germany and Russia by the Dupuy Institute (TDI) and were reformatted into a computerized data base, designated as the Kursk Data Base (KDB), and recently made available and documented in the KOSAVE (Kursk Operation Simulation and Validation Exercise of the US Army) study. The data are two-sided, time phased (daily), and highly detailed. They cover 15 days of the campaign. This thesis examines how the various derivatives of Lanchester's equations fit the newly compiled database on the Battle of Kursk. In addition, other functional forms are fit. These results are contrasted with earlier studies on the Ardennes campaign. It turns out that a wide variety of models fit the data about as well. Unfortunately, none of the basic Lanchester models fit the data, bringing into question their use in combat modeling. VI 1 TABLE OF CONTENTS I. INTRODUCTION 1 A. COMBAT MODELING 1 B. LANCHESTER EQUATIONS 3 C. THESIS OUTLINE 4 II. PREVIOUS STUDIES ON COMBAT MODELING 7 A. PAST STUDIES WITH LANCHESTER EQUATIONS 7 1. Bracken's study 7 2. Fricker's study 10 3. Clemens' study 1 4. Hartley and Helmbold's study 13 5. A summary of previous findings 13 B. THE DATA AND THE STUDY METHODOLOGY 14 1. The data 14 2. Study methodology 15 III. HISTORY AND THE DATA OF THE BATTLE OF KURSK 19 A. SHORT HISTORY OF THE BATTLE OF KURSK 19 1. City of Kursk 19 2. The history of the Battle of Kursk 19 B. BATTLE OF KURSK DATA 23 1. Limitations and timeframe of the Kursk database 23 2. Assumptions made for Kursk database 24 3. Phases of the battle 24 C. METHODOLOGY USED FOR GATHERING DATA 25 1. Manpower data 25 2. Weapon systems data 25 D. COMPARISON OF MANPOWER AND WEAPON SYSTEMS 32 1. Personnel statistics 32 2. Tank statistics 34 3. Armored personnel carrier statistics 35 4. Artillery statistics 39 5. Air sorties 41 IV. COMPARATIVE AND EXPLORATIVE ANALYSIS OF BATTLE OF KURSK DATA , 43 A. APPLICATION OF PREVIOUS STUDIES 43 1. Application of Bracken's methodology 43 2. Application of Fricker's methodology 52 B. EXPLORATORY ANALYSIS OF BATTLE OF KURSK DATA 66 1. The scalar aggregation models 67 vn 2. Includingt air sortie data 71 3. Taking into account the change in offensive/defensive roles 76 4. Considering the tactical parameter d of the campaign 82 5. Considering the change points in the model 91 6. Using different weights 94 7. Force ratio and the fractional exchange ratio models 102 8. Fitting the standard Lanchester equations 1 17 9. Fitting Morse-Kimball equations 122 10. Fitting the parameters found by Bracken and Fricker 124 11. Summary of results 131 V. CONCLUSIONS AND RECOMMENDATIONS 137 A. CONCLUSIONS 137 B. RECOMMENDATIONS 148 APPENDIX A. DETAILED INFORMATION ON TYPES OF MANPOWER AND WEAPON SYSTEM LOSSES FOR BATTLE OF KURSK 151 LIST OF REFERENCES 169 INITIAL DISTRIBUTION LIST 171 Vlll EXECUTIVE SUMMARY War is a conflict between nations or states carried on by force of considerable duration and magnitude, by land, sea, or air for obtaining and establishing the superiority and dominion of one over the other for some cause. Throughout history, war has been a topic of analysis for scientists and researchers, especially following World War II. Soviets argue that Osipov [Ref.2] was the first to study and discover the equations most often used when modeling attrition in combat. The equations are widely known as "Lanchester's equations." Regardless of claims of prior or parallel discovery, Lanchester's equations for attrition provided the origin for modeling attrition in the United States and around the world. Today, with the advent of computers, Lanchester- based models of warfare are widely used in the decisionmaking process for research, development, acquisition of weapons systems, force mix decisions, and for aiding in the development of operational plans. The basic generalized Lanchester Equations are of the form [Ref.6]: p q B{t) = aR(t) B{t) (1) p q R(t)=bB{t) R(t) (2) where B(t) and R(t) are the strengths of blue and red forces at time t, B(t) and R(t) are the rates at which blue and red force levels are changing at time t, a and b are attrition parameters, p is the exponent parameter of the attacking force, and q is the exponent parameter of the defending force. Two versions of the Lanchester equations are of particular interest. When p = q = 1, force ratios remain equal if aR(0) = bB(0), and hence this condition is called, Lanchester's linear law. The interpretation of Lanchester's linear law is that a battle IX governed by this model is characterized as a collection of small engagements, and was proposed by Lanchester as a model for ancient warfare. The equation is also considered a good model for area fire weapons, such as artillery. Lanchester contrasted the Linear Law with the condition p = 1, g = 0, which is called Lanchester's square law, where the 2 2 force ratios remain equal when aR(0) = bB(0) . He theorized that the square law applies to modern warfare, in which both sides are able to aim their fire. His model suggests that in modern warfare combatants should concentrate their forces. A third version with/? = 0, q = 1 is called Lanchester's logarithmic law. Past empirical validation studies of Lanchester Equations include the work of Bracken on the Ardennes campaign of World War II, Fricker, also on the Ardennes campaign, Clemens on the Battle of Kursk of World War II, and Hartley and Helmbold on the Inchon-Seoul campaign of the Korean War.