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MATHEMATICAL THEORY OF ROCKET FLIGHT BY J. BARKLEY ROSSER, PH. D. Professor of Mathematics at Cornell University Formerly, Chief, Theoretical Ballistics Section Alleyany Ballistics Laboratory ROBERT R. NEWTON, PH. D. Member of Technical Staff, Bell Telephone Laboratories, Inc., Murray Hill, N. J. Formerly, Research Associate Allegany Ballistics Laboratory GEORGE L. GROSS, PH. D. Research Engineer in Applied Mathematics, Grumman Aircraft Engineering Corporation Beth page, N. Y. Formerly, Research Associate A lleyany Ballistics Laboratory Office of Scientific Research and Development National Defense Research Committee NKW YORK AND LONDON MCGRAW-HILL BOOK COMPANY, INC. 1947 MATHEMATICAL THEORY OF ROCKET FLIGHT PRINTED IN THE UNITED STATES OF AMERICA PREFACE This is the official final report to the Office of Scientific Research and Development concerning the work done on the exterior ballistics of fin-stabilized rocket projectiles under the supervision of Section H of Division 3 of the National Defense Research Committee at the Allegany Ballistics Laboratory during 1944 and 1945, when the laboratory was operated by The George Washington University under contract OEMsr-273 with the Office of Scientific Research and Devel opment. As such, its official title is Final Report No. B2.2 of the Allegany Ballistics Laboratory, OSRD 5878. After the removal of secrecy restrictions on this report, a consider able amount of expository material was added. It is our hope that thereby the report has been made readable for anyone interested in the flight of rockets. Two slightly different types of readers are antici pated. One is the trained scientist who has had no previous experience with rockets. Theother is the person with little scientific training who is interested in what makes a rocket go. The first type of reader should be able to comprehend the report in its entirety. For the benefit of the second type of reader, who will wish to skip the more mathematical portions, wo have attempted to supply simple explana tions at the beginnings of most sections telling what is to be accom plished in those sections. It is our hope that a reader can, if so minded, skip most of the mathematics and still be able to form a general idea of rocket flight. Although this is a report of the work done at Allegany Ballistics Laboratory, it must not be supposed that all the material in the report originated there. We have been most fortunate in receiving the whole hearted cooperation and assistance of scientists in other laboratories. Many of them, notably the English scientists, were well advanced in the theory before we even began. Without the fine start given us by these other workers, this report could certainly not have been written. However, we were fortunate enough to discover two means of avoiding certain difficulties of the theory. The first is that of using some dynamical laws especially suited to rockets in deriving the equations of motion, and the second is that of using some mathematical functions especially suited to rockets in solving the equations of motion. The explanation and illustration of these simplifying devices take up a considerable portion of the report, although for completeness we have included material not involving them. vi PREFACE In attempting to acknowledge the contributions of other workers, we are in a difficult position. Approximately a hundred reports by otherworkers were useful in one way or another in the preparatf on of this report. However, most of them are still bound by military secrecy, so that only the few cited in our meager list of bibliographical references can be mentioned here. Many figures are copied from these unmentioiied reports. Sizable portions of our report, such as Chap. II and Appendix 1, lean very heavily on certain of these unmentioned reports, but no specific credit is given...
This is the official final report to the Office of Scientific Research and Development concerning the work done on the exterior ballistics of fin-stabilized rocket projectiles under the supervision of Section H of Division 3 of the National Defense Research Committee at the Allegany Ballistics Laboratory during 1944 and 1945, when the laboratory was operated by The George Washington University under contract OEMsr-273 with the Office of Scientific Research and Development. As such, its official title is “Final Report No. B2.2 of the Allegany Ballistics Laboratory, OSRD 5878.” After the removal of secrecy restrictions on this report, a considerable amount of expository material was added. It is our hope that thereby the report has been made readable for anyone interested in the flight of rockets. Two slightly different types of readers are anticipated. One is the trained scientist who has had no previous experience with rockets. The other is the person with little scientific training who is interested in what makes a rocket go. The first type of reader should be able to comprehend the report in its entirety. For the benefit of the second type of reader, who will wish to skip the more mathematical portions, we have attempted to supply simple explanations at the beginnings of most sections telling what is to be accomplished in those sections. It is our hope that a reader can, if so minded, skip most of the mathematics and still be able to form a general idea of rocket flight.
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This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Aerospace Engineering/Mechanical Engineering The definitive text on rocket propulsion-now completely revised to reflect rapid advancements in the field For more than fifty years, this seminal text has been regarded as the single most authoritative sourcebook on rocket propulsion technology. More comprehensive and coherently organized than any other book on the subject, Rocket Propulsion Elements guides readers evenhandedly through the complex factors that shape propulsion, with both theory and practical design considerations. With more than a third of the text and illustrations either completely new or extensively revised, this latest edition includes current information on engine structures, nozzle theory, gas properties, thrust chambers, launch vehicles, and more. With a detailed table of contents breaking down each chapter into subsections-as well as an expanded index of key words-the Seventh Edition efficiently steers readers quickly to the information they need. Other highlights include: * Separate chapters on liquid, solid, and hybrid propulsion systems and a new chapter on thrust chambers including the new aerospike nozzle * Comprehensive coverage of rocket propulsion technology, with applications to space flight, satellite flight, and guided and unguided missiles * Problem-solving examples and exercises relevant to actual design situations * More than 340 illustrations, including photographs, tables, and graphs * Coherent, up-to-date chapter on electrical propulsion balancing fundamentals with practical aspects and applications For professional engineers in the aerospace and defense industries as well as undergraduate and graduate students in mechanical and aerospace engineering, this time-honored resource is indispensable for its scope of coverage and utility.
International Series of Monographs on Aeronautics and Astronautics, Division VII, Volume 5: The Flight of Uncontrolled Rockets focuses on external ballistics of uncontrolled rockets. The book first discusses the equations of motion of rockets. The rocket as a system of changing composition; application of solidification principle to rockets; rotational motion of rockets; and equations of motion of the center of mass of rockets are described. The text looks at the calculation of trajectory of rockets and the fundamentals of rocket dispersion. The selection further focuses on the dispersion of finned rockets. Topics include the critical section of the trajectory; standard formula for calculating angular deviation; dispersion of actual rockets; and effective launcher length. The text also describes the dispersion of finned rotated rockets and of finned anti-tank rockets. The book also examines the effect of wind on the flight of rockets. Topics include correction to the coordinates of the point of impact for finned rockets; general effect of wind on dispersion; and general treatment of powered flight in the presence of wind. The text is important for readers interested in the ballistics of uncontrolled rockets.
The book follows a unified approach to present the basic principles of rocket propulsion in concise and lucid form. This textbook comprises of ten chapters ranging from brief introduction and elements of rocket propulsion, aerothermodynamics to solid, liquid and hybrid propellant rocket engines with chapter on electrical propulsion. Worked out examples are also provided at the end of chapter for understanding uncertainty analysis. This book is designed and developed as an introductory text on the fundamental aspects of rocket propulsion for both undergraduate and graduate students. It is also aimed towards practicing engineers in the field of space engineering. This comprehensive guide also provides adequate problems for audience to understand intricate aspects of rocket propulsion enabling them to design and develop rocket engines for peaceful purposes.