This dissertation has been microfilmed exactly as received COLVOCORESSES, Alden Partridge, 1918- A UNIFIED PLANE COORDINATE REFERENCE SYSTEM. The Ohio State University, Ph.D., 1965 Geography University Microfilms, Inc., Ann Arbor, Michigan A UNIFIED PLANE COORDINATE REFERENCE SYSTEM DISSERTATION Presented in Partial Fulfillment of the Requirements for The Degree Doctor of Philosophy in the Graduate School of The Ohio State University Alden P. Colvocoresses, B.S., M.Sc. Lieutenant Colonel, Corps of Engineers United States Army * * * * * The Ohio State University 1965 Approved by Adviser Department of Geodetic Science PREFACE This dissertation was prepared while the author was pursuing graduate studies at The Ohio State University. Although attending school under order of the United States Army, the views and opinions expressed herein represent solely those of the writer. A list of individuals and agencies contributing to this paper is presented as Appendix B. The author is particularly indebted to two organizations, The Ohio State University and the Army Map Service. Without the combined facilities of these two organizations the preparation of this paper could not have been accomplished. Dr. Ivan Mueller of the Geodetic Science Department of The Ohio State University served as adviser and provided essential guidance and counsel. ii VITA September 23, 1918 Born - Humboldt, Arizona 1941 oo.oo.o BoS. in Mining Engineering, University of Arizona 1941-1945 .... Military Service, European Theatre 1946-1950 o . o Mining Engineer, Magma Copper Company,. Superior, Arizona 1951-to date . Military Service 1959 o.oo.oo M.SCo in Geodetic Science, The Ohio State University 1959 ......... M.SCo in Civil Engineering, The Ohio State University PUBLICATIONS "Flood Prediction in Korea," Military Engineer, 1954 "Map Reliability," ARMY, 1958 "Engineering Data for Disaster Planning Purposes," thesis, The Ohio State University, 1959 "A National City Mapping Program," thesis, The Ohio State University, 1959 "Unity of Effort?" Military Review, June, 1963 FIELDS OF STUDY Major Fields: Geodetic Science (Topographic Engineering) Civil Engineering Mining Engineering iii CONTENTS Chapter Page I. INTRODUCTION .................... 1 Scope and Purpose Background II. PHILOSOPHY OF PLANE COORDINATES .......... 4 III. ANALYSIS OF SUITABLE PROJECTION SYSTEMS ....... 7 IV. SPECIFIC CRITERIA FOR REFERENCE SYSTEMS ..... 11 Military Reference Criteria Civil Reference Criteria V. CURRENT STATUS AND DESCRIPTION OF REFERENCE SYSTEMS ......................... 18 Military Reference Systems The Universal Transverse Mercator Grid and Projection (UTM) Soviet Unified Reference System Other Reference Systems VI. SELECTION OF PROJECTION AND SCALE TOLERANCE . 24 Projection Choice Scale Tolerance VII. SCALE FACTOR MAPPING........ 28 Projection Scale Factor Elevation Reduction Scale Factor Combined Scale Factor Development of Scale Factor Mapping Consideration in Scale Factor Mapping Application of Scale Factor Mapping VIII. ZONE WIDTH AND DESIGNATION ............ 49 Zone Width Zone Boundaries Zone Designation Alternate System of Zone Designation iv Chapter Page IX. GRIDS AMD COORDINATES ....... ....... ..... 56 X. THE GENERALIZED TRANSVERSE MERCATOR REFERENCE SYSTEM. 58 Specifications of the GTM XI. POLAR REGIONS ......... 62 XII. IMPLEMENTATION OF THE GTM . ...................... 67 General Specific Regions Impleaientation Procedure XIII. SUMMARY .......... ^ ..... ........... 74 Basic System Auxiliary System Conclusions Appendix A. DEFINITION OF TERMS AS USED IN THIS PAPER ....... 78 B. LISTING BY COUNTRY, AGENCY AND NAME OF THOSE CONTRIBUTING TO THIS PAPER....................... 80 C. SUMMARY OF THE PRINCIPAL PROJECTION IN USE BY VARIOUS COUNTRIES..................................... 82 D. SELECTED ELEVATION DATA OF THE WORLD. ........ 84 E. TABULATION OF POLAR DISTANCE (r) AND SCALE FACTOR (k) ON THE POLAR STERBOGRAPHIC PROJECTION ........ 88 F. APPLICATION OF THE GTM TO THE UNITED STATES ........ 92 G. DIGITAL COMPUTER PROGRAMS FOR THE GENERALIZED TRANSVERSE MERCATOR PROJECTION (GTM)............ 99 BIBLIOGRAPHY................ 157 v LIST OF TABLES Table Page 1 Elevation Increments of the Earth . .. 31 2 TM Combined Scale Factor Based on Central Scale Factor of 1.0000 ...... 0 . .......... 34 3 TM Combined {icale Factor Based on Central Scale Factor of 0.9999........................... 35 4 TM Combined Scale Factor Based on Central Scale Factor of 0.9996. ........ ..... .... 36 5 Width of Subzones of ±1:10,000 Scale Error....... 41 6 No. of ±1:10,000 Scale Error Subzones in a 6° TM Zone . 43 7 Mean Elevations of the Continents ....... 84 8 Elevation Breakdown of Continents Based on the 1,000 Meter Contour ........ 85 9 Elevation Breakdown, U S S R .......... ............. 85 10 Elevation Breakdown, CHINA (Continental)....... 86 11 Elevation Breakdown, Conterminous United States .... 86 12 Elevation Breakdown, Alaska .............. ..... 87 13 Elevation Breakdown, Hawaii . ................... 87 14 Polar Distance (r) and Scale Factor (k), CSF = 1.0000 . 90 15 Polar Distance (r) and Scale Factor (k), CSF = 0.9727691 91 16 Ellipsoid Parameters in Terms of Semi-Major Axis (a) and Inverse Flattening (1/f)............... .. 100 LIST OF FIGURES Figure Page 1 Graph of Projection Scale Factor (TM) Based on Central Scale Factor of 1.0000 ........... 30 2 Sea Level Scale Reduction Due to Elevation ...... 32 3 Schematic Cross Section of a 6° Transverse Mercator Zone Divided into Subzones ......... ....... 42 4 Graph of Projection Scale Factor (PS) Based on Pole Scale Factor of 1.0000 i ............ 65 5 Index to Suggested Regions for the GTM Reference System ...... ....... ....... 69 vii CHAPTER I INTRODUCTION Scope and Purpose The problem of depicting a portion of the earth's surface on a'- plane has been the subject of intense study for over 2000 years. Since man first realized that the earth was curved, many of the greatest minds have been applied to mapping this surface in two dimensions. Thus the science of map projections has developed pro­ viding the geometric and mathematical solutions to this problem. Once the earth's surface has been depicted on a plane, a coordinate system (usually a rectangular grid) can arbitrarily be imposed and thus develop a convenient reference system for defining the horizontal location of any point on or related to the earth's surface. Un­ fortunately, several of the basic terms used in this field are am­ biguous or ill-defined. Such terms are marked with an asterisk (*) at their early appearance and are defined, for purposes of this re­ port, in Appendix A. This paper encompasses the problem of developing a reference system of plane coordinates by which any point on the earth can be described within certain degrees of positional accuracy. Since the selected degrees of accuracy are high, the mapping^ involved is .necessarily of relatively large scale*. The small-scale* depiction 1 Actual zone width may vary depending on specific geographic problems. 3. The concept of Scale Factor Mapping or alteration of the central scale factor offers a solution to many regional and local scale problems. 4. Formulas and machine programs as presented provide the means for obtaining required transformations with specified ac- curary of a high order. 5. The system derived is best described as the Generalized Transverse Mercator Reference System or GTM. 6. The north polar region (above 84° N) can be ignored for the present but a plane coordinate system is required for Antarctica. 7. A single Polar Stereographic projection on which "polar" (as opposed to rectangular) coordinates are utilized was determined as the most suitable reference system for Antarctica. Implementation of the GTM offers no serious problems to countries now using six degree transverse Mercator zones based on the Inter­ national Map of the World (UW). This includes the Soviet Bloc (in­ cluding continental China) and the large number of Western countries that have adopted the Universal Transverse Mercator Grid (UTM). Certain island areas might retain transverse Mercator zones which vary from those of the MJ. Countries not using transverse Mercator zones would require a complete conversion in order to apply the GTM. The problems and advantages of converting an area such as the United States to the GTM are also discussed. It is concluded that the GTM Background In addition to the study of published texts and papers on this subject, a considerable effort was made to obtain information and suggestions from various mapping authorities. This latter effort was in the form of correspondence and interviews with concerned in­ dividuals and included a questionnaire which was distributed to pertinent organizations. A list of the agencies and personnel answer­ ing the questionnaire or who otherwise contributed to this paper are included as Appendix B. Since the mapping and reference system within the Soviet Bloc and Continental China is unified, well documented, and was fully studied, all major reference systems in use today received consideration even though the questionnaire and personal contacts were restricted to the Western World. Various departments of the U. S. Army Hap Service prepared tabulations and graphics which are found throughout this paper. The machine programs proposed for use were developed and tested on the International Business Machine (IBM) 7094 Digital Computer of the Ohio State University. These programs, ex­ planations, and test results are presented in Appendix 6 . 3 CHAPTER II PHILOSOPHY