Rocket and Spacecraft Propulsion Principles, Practice and New Developments (Third Edition) Martin J. L. Turner Rocket and Spacecraft Propulsion Principles, Practice and New Developments (Third Edition) Published in association with Praxis Publishing Chichester, UK Professor Martin J. L. Turner, C.B.E., F.R.A.S. Department of Physics and Astronomy University of Leicester Leicester UK SPRINGER–PRAXIS BOOKS IN ASTRONAUTICAL ENGINEERING SUBJECT ADVISORY EDITOR: John Mason, B.Sc., M.Sc., Ph.D. ISBN 978-3-540-69202-7 Springer Berlin Heidelberg New York Springer is part of Springer-Science + Business Media (springer.com) Library of Congress Control Number: 2008933223 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. # Praxis Publishing Ltd, Chichester, UK, 2009 First edition published 2001 Second edition published 2005 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: Jim Wilkie Project management: Originator Publishing Services, Gt Yarmouth, Norfolk, UK Printed on acid-free paper Contents Preface to the third edition ................................ xi Preface to the second edition ............................... xiii Preface to the first edition................................. xv Acknowledgements...................................... xvii List of figures ........................................ xix List of tables ......................................... xxiii List of colour plates..................................... xxv 1 History and principles of rocket propulsion ................... 1 1.1 The development of the rocket....................... 1 1.1.1 The Russian space programme ................. 6 1.1.2 Other national programmes.................... 6 1.1.3 The United States space programme .............. 8 1.1.4 Commentary . .......................... 13 1.2 Newton’s third law and the rocket equation .............. 14 1.2.1 Tsiolkovsky’s rocket equation .................. 14 1.3 Orbits and spaceflight. .......................... 17 1.3.1 Orbits.................................. 18 1.4 Multistage rockets ............................... 25 1.4.1 Optimising a multistage rocket ................. 28 1.4.2 Optimising the rocket engines .................. 30 1.4.3 Strap-on boosters .......................... 32 1.5 Access to space ................................. 34 vi Contents 2 The thermal rocket engine .............................. 37 2.1 The basic configuration ........................... 37 2.2 The development of thrust and the effect of the atmosphere . 39 2.2.1 Optimising the exhaust nozzle .................. 43 2.3 The thermodynamics of the rocket engine . .............. 44 2.3.1 Exhaust velocity ........................... 46 2.3.2 Mass flow rate ............................ 48 2.4 The thermodynamic thrust equation ................... 53 2.4.1 The thrust coefficient and the characteristic velocity.... 54 2.5 Computing rocket engine performance .................. 58 2.5.1 Specific impulse ........................... 59 2.5.2 Example calculations ........................ 60 2.6 Worked Example.... 62 2.7 Summary ..................................... 65 3 Liquid propellant rocket engines .......................... 67 3.1 The basic configuration of the liquid propellant engine ....... 67 3.2 The combustion chamber and nozzle ................... 68 3.2.1 Injection ................................ 69 3.2.2 Ignition................................. 70 3.2.3 Combustion instability ....................... 73 3.2.4 Thrust vector control........................ 78 3.3 Liquid propellant distribution systems .................. 81 3.3.1 Cavitation ............................... 83 3.3.2 Pogo .................................. 84 3.4 Cooling of liquid-fuelled rocket engines . .............. 85 3.5 Examples of rocket engine propellant flow . .............. 86 3.5.1 The Aestus engine on Ariane 5 . 87 3.5.2 The Ariane Viking engines .................... 88 3.5.3 The Ariane HM7 B engine .................... 90 3.5.4 The Vinci cryogenic upper-stage engine for Ariane 5 91 3.5.5 The Ariane 5 Vulcain cryogenic engine ............ 92 3.5.6 The Space Shuttle main engine . .............. 93 3.5.7 The RS 68 engine .......................... 96 3.5.8 The RL 10 engine.......................... 96 3.6 Combustion and the choice of propellants . .............. 98 3.6.1 Combustion temperature ..................... 99 3.6.2 Molecular weight .......................... 100 3.6.3 Propellant physical properties .................. 101 3.7 The performance of liquid-fuelled rocket engines ........... 103 3.7.1 Liquid oxygen–liquid hydrogen engines ............ 104 3.7.2 Liquid hydrocarbon–liquid oxygen engines .......... 104 3.7.3 Storable propellant engines .................... 106 Contents vii 4 Solid propellant rocket motors ........................... 109 4.1 Basic configuration .............................. 109 4.2 The properties and the design of solid motors............. 111 4.3 Propellant composition . .......................... 112 4.3.1 Additives................................ 114 4.3.2 Toxic exhaust. .......................... 115 4.3.3 Thrust stability . .......................... 115 4.3.4 Thrust profile and grain shape.................. 116 4.4 Integrity of the combustion chamber ................... 118 4.4.1 Thermal protection ......................... 119 4.4.2 Inter-section joints ......................... 120 4.4.3 Nozzle thermal protection..................... 122 4.5 Ignition ...................................... 122 4.6 Thrust vector control . .......................... 123 4.7 Two modern solid boosters ......................... 123 4.7.1 The Space Shuttle SRB ...................... 123 4.7.2 The Ariane MPS .......................... 125 4.8 Hybrid rocket motors. .......................... 126 4.8.1 Hybrid motor history ....................... 127 4.8.2 The basic configuration of a hybrid motor.......... 128 4.8.3 Propellants and ignition ...................... 128 4.8.4 Combustion .............................. 130 4.8.5 Grain cross-section ......................... 131 4.8.6 Propulsive efficiency ........................ 132 4.8.7 Increasing the thrust ........................ 133 5 Launch vehicle dynamics ............................... 135 5.1 More on the rocket equation ........................ 135 5.1.1 Range in the absence of gravity................. 137 5.2 Vertical motion in the Earth’s gravitational field ........... 140 5.2.1 Vehicle velocity . .......................... 140 5.2.2 Range.................................. 143 5.3 Inclined motion in a gravitational field ................. 144 5.3.1 Constant pitch angle ........................ 144 5.3.2 The flight path at constant pitch angle ............ 146 5.4 Motion in the atmosphere.......................... 148 5.4.1 Aerodynamic forces......................... 149 5.4.2 Dynamic pressure .......................... 150 5.5 The gravity turn ................................ 151 5.6 Basic launch dynamics . .......................... 153 5.6.1 Airless bodies. .......................... 154 5.7 Typical Earth-launch trajectories ..................... 155 5.7.1 The vertical segment of the trajectory ............. 156 5.7.2 The gravity turn or transition trajectory ........... 156 5.7.3 Constant pitch or the vacuum trajectory ........... 157 viii Contents 5.7.4 Orbital injection ........................... 157 5.8 Actual launch vehicle trajectories ..................... 159 5.8.1 The Mu-3-S-II launcher ...................... 159 5.8.2 Ariane4.... 162 5.8.3 Pegasus................................. 163 6 Electric propulsion ................................... 165 6.1 The importance of exhaust velocity .................... 165 6.2 Revived interest in electric propulsion .................. 167 6.3 Principles of electric propulsion ...................... 167 6.3.1 Electric vehicle performance ................... 168 6.3.2 Vehicle velocity as a function of exhaust velocity ..... 169 6.3.3 Vehicle velocity and structural/propellant mass ....... 170 6.4 Electric thrusters ................................ 171 6.4.1 Electrothermal thrusters ...................... 172 6.4.2 Arc-jet thrusters ........................... 175 6.5 Electromagnetic thrusters .......................... 177 6.5.1 Ion propulsion ............................ 178 6.5.2 The space charge limit ....................... 180 6.5.3 Electric field and potential .................... 182 6.5.4 Ion thrust ............................... 183 6.5.5 Propellant choice .......................... 184 6.5.6 Deceleration grid .......................... 186 6.5.7 Electrical efficiency ......................... 186 6.6 Plasma thrusters ................................ 189 6.6.1 Hall effect thrusters......................... 191 6.6.2 Radiofrequency thrusters ..................... 197 6.7 Low-power electric thrusters ........................ 199