building the great pyramid in a year
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BUILDING THE GREAT PYRAMID IN ONE YEAR
BUILDING THE GREAT PYRAMID IN ONE YEARAN ENGINEERS REPORT
Gerard C. A. Fonte
Algora Publishing New York
2007 by Algora Publishing. All Rights Reserved www.algora.com No portion of this book (beyond what is permitted by Sections 107 or 108 of the United States Copyright Act of 1976) may be reproduced by any process, stored in a retrieval system, or transmitted in any form, or by any means, without the express written permission of the publisher. ISBN-13: 978-0-87586-521-8 (trade paper) ISBN-13: 978-0-87586-522-5 (hard cover) ISBN-13: 978-0-87586-523-2 (ebook) Library of Congress Cataloging-in-Publication Data Fonte, Gerard C. A. Building the Great Pyramid in a year : an engineers report / Gerard C. A. Fonte. p. cm. Includes bibliographical references and index. ISBN 978-0-87586-521-8 (trade paper: alk. paper) ISBN 978-0-87586-522-5 (hard cover: alk. paper) ISBN 978-0-87586-523-2 (ebook) 1. PyramidsEgyptDesign and construction. 2. Great Pyramid (Egypt) I. Title. DT63.F66 2007 932dc22 2007004713
Front Cover: One man moving a 4200-pound block using technology that was available to the ancient Egyptians.
Printed in the United States
To Nellie, who enjoys the unconventional and whose support and encouragement made this book possible.
TABLE OF CONTENTSCHAPTER 1. THE EGYPTIAN PYRAMIDS Introduction Other Books The Great Pyramid Evolution of the Pyramid Pyramid Construction The Pyramid at Maidum Great Pyramid Construction Clues General Pyramid Geometry Conclusion CHAPTER 2. PYRAMID FALLACIES Introduction Slaves Pyramid Blocks Passageways and Chambers Secret Passages Still Secret Passages The Great Pyramid and Pi Numerology The Nose of the Sphinx Conclusion CHAPTER 3. SCALE FACTORS IN CONSTRUCTION AND ENGINEERING Introduction Order of Magnitude Size versus Strength Forces 1 1 2 4 10 12 12 14 15 17 19 19 19 20 21 24 26 27 30 31 32 33 33 33 35 37
Building the Pyramid
Energy Management Energy Management Cost Scale Factors and the Pyramids Energy Management and the Pyramids Conclusion CHAPTER 4. MOVING BLOCKS Introduction Sledges Wheels Why Things Roll Quarter Circles Quarter Circle Track Block Size Quarter Circle Shape Egyptian Quarter Circles versus Catenaries Time Estimate Conclusion CHAPTER 5. ROLLING BLOCK EXPERIMENT Introduction Manually Moving Heavy Objects Creating the Curve Preliminary Quarter-Circle Evaluation Fabricating a Block Block Specications Building the Quarter Circles First Tests Modications Second Tests Public Demonstration Block Moving Scenario Gross Movements Fine Movement Conclusion CHAPTER 6. LIFTING BLOCKS Introduction Ramp Principles A Practical Ramp Simple Lifting Machines Designing a Practical Raised Fulcrum Lifting Machine Lever Details
39 40 41 42 43 45 45 45 46 48 50 52 55 59 60 62 63 65 65 65 67 68 69 69 70 72 72 73 75 80 80 82 85 87 87 87 89 93 93 96
Table of Contents
Supporting Evidence Forensic Analysis of the Mystery Tool Miscellaneous Points Time Estimate Conclusion CHAPTER 7. QUARRYING BLOCKS Introduction Limestone Practical Limestone Information Available Tools Quarrying Blocks Using the Standard Methods Alternative Quarrying Methods Spear-Chisel Performance Removing the Block Miscellaneous Notes First-Order Time Estimate to Build the Great Pyramid Discussion Conclusion CHAPTER 8. ADDITIONAL CONSTRUCTION DETAILS Introduction The Great Pyramids Internal Design Finishing the Casing Stones Machining the Blocks Squaring the Sides Positioning the Top-Most Blocks Order of Assembly Wooden Tool Quantity Available Wood Additional Time Required for Minor Tasks Second-Order Time Estimate to Build the Great Pyramid Realistic Schedule Conclusion CHAPTER 9. SOCIAL CONSIDERATIONS Introduction Egyptian Psychology Available Population Problem Volunteer Workers The Big Picture A Question of Timing Conclusion
102 102 104 105 106 107 107 107 108 110 111 114 115 118 120 122 122 123 125 125 126 126 127 130 132 133 134 136 137 138 138 139 141 141 141 142 144 146 149 150
Building the Pyramid
CHAPTER 10. OTHER APPROACHES Introduction Cast In Place Concrete Davidovits versus the Evidence Kites The Standard Theories: Lehner The Standard Theories: Smith Discussion Conclusion CHAPTER 11. CONCLUSION The Approach The Archaeological Evidence Circumstantial Evidence Other Ideas Goals and Objectives Numbers and Engineering Conclusion APPENDIX 1. TABLE OF 100 EGYPTIAN PYRAMIDS APPENDIX 2. COURSE BY COURSE LAYOUT OF AN IDEAL GREAT PYRAMID BUILT WITH IDENTICAL BLOCKS APPENDIX 3. TIME/MOTION ANALYSIS FOR LIFTING A BLOCK Introduction 3-Person, 2-Stroke Lever Analysis 2-Person Considerations Conclusion REFERENCES INDEX
153 153 154 158 159 162 164 170 171 173 173 174 176 177 178 179 179 181 187 193 193 194 197 197 199 203
CHAPTER 1. THE EGYPTIAN PYRAMIDS
INTRODUCTIONThis book represents a forensic-engineering exploration of the construction of the Egyptian pyramids. Most archaeologists believe that about 25,000 workers spent about 20 years to build the Great Pyramid (or Khufus Pyramid) at Giza in Egypt over 4,500 years ago (Lehner, 224). But, by closely examining the clues and relics left behind, and by assuming that the Egyptians were intelligent and creative, it is found (conservatively) that about 10,000 workers could have built the Great Pyramid in about 346 days. However, there is evidence that 4,000 workers were used (Lehner, 225). And by using a relaxed production schedule, a value of four to six calendar years is probably a more reasonable estimate. These values are based entirely upon archaeological evidence, logic, common sense, and scientic and engineering principles. Every aspect of pyramid building will be examined in detail. This includes quarrying the blocks, moving the blocks, lifting the blocks, tting the blocks, placing the top-most blocks and nishing the outer casing blocks. It will be shown that each of these challenges can be successfully addressed using the materials and crafts that the Egyptians are known to have possessed. Additionally, tool specications, wood requirements and machine designs will be appraised. Surprisingly, such an analysis has not been done before. Not all of the important factors that allowed the pyramids to be built are directly related to these construction procedures. General pyramid geometry, available worker population, the social effects of large works, and scale factors 1
Building the Great Pyramid in a Year
in engineering are critically important as well. Lastly, there is the concept of Energy Management or, more simply: work smarter not harder.
OTHER BOOKSThere are many, many books and papers about the pyramids. Generally these can be broken into three main classes: picture books, specialized approaches, and archaeological works. Interested readers most often turn to picture books. They provide a general history of the pyramids with many beautiful pictures of Egyptian constructions and antiquities. And without any doubt, Egyptian artifacts can be exquisitely beautiful. Most often these books only briey discuss the mystery of how the pyramids were built. Typically they provide a few pages of speculations that are based on the generally accepted view that it took 25,000 workers about 20 years. Little original work is found here. The specialized approaches usually examine one aspect of pyramid building, often without regard to the archaeological evidence. These writers often have a specic idea that they believe could be applied for moving blocks, or lifting blocks, etc. These works have a very focused approach, typically with application to a single aspect of pyramid building. Unfortunately, while the work is often very imaginative and original, it doesnt match what has been found in Egypt. Nor are these approaches applicable at the massive engineering scale necessary for the Great Pyramid. Some of these will be examined in more detail later. The archaeological works are where the important information comes from. But archaeologists are not engineers. They cannot be expected to recognize important engineering functions of various artifacts or specialized tools. Generally, their works are descriptive. They offer drawings and photographs of things found at the pyramid sites. Of course, since their interest is in archaeology, they tend to focus their effort on items that relate to ancient Egyptian society. Tools that have no obvious function are, naturally, only mentioned in passing. One very important archaeological work is J. P. Lepres The Egyptian Pyramids (1990, McFarland & Company). This is an extremely detailed compilation of information from all of the Egyptian pyramids. Lepre is also extremely precise in his descriptions and drawings. For these reasons his book will be referenced with regularity in the following pages. Note that there are many variations in the spelling of Egyptian names and places. Unless otherwise noted, the spelling that Lepre uses will be incorporated here. It is also important to note that Lepre is an archaeologist, not an engineer or mathematician. As such, there are a number of mathematical errors in his book.
Chapter 1. The Egyptian Pyramids
Currently there seems to be increasing interest in the building techniques employed for the Great Pyramid. In particular, Dr. Mark Lehner, in association with the NOVA television program, went to Giza and actually built a small pyramid using the standard methods of sledges and ramps. This work is documented in his book The Complete Pyramids (1997, Thames and Hudson) and of course, the television program, This Old Pyramid. This experiment provides some useful benchmark information that will be examined closely. Additionally, Dr. Lehner is arguably the foremost archaeological authority on pyramid construction today. For