CRANFIELD INSTITUTE OF TECHNOLOGY STEPHEN E. HOBBS A QUANTITATIVE STUDY OF KITE PERFORMANCE IN NATURAL WIND WITH APPLICATION TO KITE ANEMOMETRY Ecological Physics Research Group PhD THESIS CRANFIELD INSTITUTE OF TECHNOLOGY ECOLOGICAL PHYSICS RESEARCH GROUP PhD THESIS Academic Year 1985-86 STEPHEN E. HOBBS A Quantitative Study of Kite Performance in Natural Wind with application to Kite Anemometry Supervisor: Professor G.W. Schaefer April 1986 (Digital version: August 2005) This thesis is submitted in ful¯llment of the requirements for the degree of Doctor of Philosophy °c Cran¯eld University 2005. All rights reserved. No part of this publication may be reproduced without the written permission of the copyright owner. i Abstract Although kites have been around for hundreds of years and put to many uses, there has so far been no systematic study of their performance. This research attempts to ¯ll this need, and considers particularly the performance of kite anemometers. An instrumented kite tether was designed and built to study kite performance. It measures line tension, inclination and azimuth at the ground, :sampling each variable at 5 or 10 Hz. The results are transmitted as a digital code and stored by microcomputer. Accurate anemometers are used simultaneously to measure the wind local to the kite, and the results are stored parallel with the tether data. As a necessary background to the experiments and analysis, existing kite information is collated, and simple models of the kite system are presented, along with a more detailed study of the kiteline and its influence on the kite system. A representative selection of single line kites has been flown from the tether in a variety of wind conditions. The results from these experiments are analysed to obtain general performance measurements for these kites in real, turbulent, winds. The analysis is taken a stage further to evaluate the kites for anemometry, and to study the dynamics of the kite system. The most suitable kites for anemometry are identi¯ed, together with the wind conditions in which they may be used and the wind information available from measurements at the tether. The study ends with a review, and a discussion of useful areas of further work. This digital (pdf) version of the thesis was created in August 2005. The content is identical to that of the original paper copy of 1986, although the layout and pagination di®ers in detail. Readers should note that anemometer calibrations described in Hobbs (1994) suggest that the windspeed values given in this thesis are incorrect by a few percent: however, the general conclusions about kite performance stated in the thesis are una®ected by these changes. ii iii Acknowledgements It is a real pleasure to remember all those who have helped in one way or another towards the production of this thesis. I thank my supervisor, Professor Schaefer, for the opportunity to study a subject such as kites. I have learnt much during my time at Cran¯eld, and not only about kites. Ted Sills helped with the initial stages of the electronic design, and Ron Hussey did a good job building the Kite Tether Head. Without the cooperation of the farmer, Michael Nicholson, the ¯eld experiments would have been much more di±cult. Fellow students at Ecological Physics have helped in many ways, and in particular I must thank Dave and Patrick for technical help, and Jan, who was a surprisingly willing and much appreciated ¯eld assistant. Pam, Keith and Terry have played their part too. The friends (particularly Albert, Jane, Mark, Jane and Peter) who've helped over the last few years deserve special thanks for their friendship and encouragement. iv CONTENTS v Contents Contents v List of tables xi List of plates and ¯gures xiii Abbreviations xviii 1 INTRODUCTION 1 1.1 Background to the present studies . 2 1.1.1 Research 1885{1905 . 2 1.1.2 Royal Aircraft Establishment, 1938{1942 . 3 1.1.3 Recent research . 4 1.1.4 Kiteline and stability theory . 5 1.1.5 Kite anemometry . 5 1.1.6 Kite sailing . 6 1.1.7 Other kite applications . 6 1.2 Why study kites ? . 7 1.3 Outline of the thesis contents . 7 2 PRELIMINARY CONSIDERATIONS 9 2.1 Current Kite Types and Materials 2.1.1 Kite types . 9 2.1.1 Materials . 13 vi CONTENTS 2.1.2 Struts . 15 2.1.3 Coverings . 16 2.1.4 Lines . 17 2.2 Concepts from Anemometry . 21 2.2.1 The structure of the wind . 21 2.2.2 Frequency analysis of the wind . 22 2.2.3 Finite sampling and averaging times . 23 2.2.4 Finite measurement resolution . 24 2.2.5 Means and variance of the wind . 25 2.3 Concepts from Aerofoil Theory . 26 2.3.1 Basic ideas from aerofoil theory . 26 2.3.2 Aerodynamic theory particularly relevant to Kites . 29 2.4 Elementary Models of the Kite System . 32 2.4.1 Kite response to turbulence . 33 2.4.2 Kite system energy analysis . 34 2.4.3 Line length influence on angle measurements . 35 2.4.4 Kite azimuth dynamics and stability . 36 2.5 Longitudinal Kite Model . 38 2.5.1 Model description . 38 2.5.2 Qualitative features of the model . 39 2.5.3 Kite bridling . 40 2.5.4 Incidence change with windspeed . 41 2.5.5 Model of a kite anemometer . 42 3 THE KITELINE 43 3.1 Forces acting on the kiteline . 44 3.2 Static form of the line . 44 3.2.1 Equations describing the static line pro¯le . 44 CONTENTS vii 3.2.2 General Features of the Static Solution . 46 3.2.3 Examples of Calculated Line Pro¯les . 48 3.3 Dynamics of the kiteline . 50 3.3.1 Wave velocities along the kiteline . 50 3.3.2 Line vibrations . 53 3.3.3 Signal attenuation . 54 3.3.4 Signal distortion . 55 3.4 Summary and application of results . 58 4 EXPERIMENT EQUIPMENT 60 4.1 Kite Tether . 60 4.1.1 Mechanical design . 61 4.1.2 Tension measurement . 61 4.1.3 Angle measurements . 62 4.1.4 Practical calibration . 66 4.2 Anemometry . 67 4.2.1 3-d Field Anemometer System . 67 4.2.2 Porton Anemometer . 69 4.3 The Kite . 70 4.4 Kite Tether Instrumentation . 70 4.4.1 General KTI features . 70 4.4.2 Analogue inputs . 71 4.4.3 Multiplexor . 72 4.4.4 Analogue to Digital Converter . 73 4.4.5 Serial data formatting . 73 4.4.6 Control logic . 74 4.4.7 Radio . 76 4.5 Data Collection and Storage Equipment . 76 viii CONTENTS 4.6 Site Details and Experiment Procedure . 77 4.6.1 Site details . 77 4.6.2 Experiment procedure . 78 5 EXPERIMENT SOFTWARE 80 5.1 Data Collection and Validation . 80 5.1.1 Program STORE/TM . 81 5.1.2 Program FLAGFIND . 83 5.1.3 Program DATALOG/TM . 84 5.1.4 Program DATASUM/TM . 84 5.2 Raw Data Analysis . 87 5.2.1 Program ANGLEPLOT . 87 5.2.2 Program DATAPLOTv2 . 87 5.2.3 Program STATS1v5 . 88 5.2.4 Program STATS2v4 and v5 . 93 5.2.5 Program STATS3v3 . 95 5.3 Data Record Analysis . 99 5.3.1 Program ANEMOMETER . 99 5.3.2 Program ARR8FILE . 99 5.3.3 Program KITEDATA . 100 5.3.4 Program KITEDBASE . 100 6 EXPERIMENTS PERFORMED and ANALYSIS PROCEDURE 101 6.1 Kite Experiments Performed . 101 6.1.1 Experiments performed . 101 6.1.2 Kites flown . 103 6.2 Analysis Procedure . 105 6.2.1 Data preparation programs . 105 6.2.2 Data analysis parameters . 106 CONTENTS ix 6.2.3 Remaining analysis details . 109 6.3 Error Analysis . 109 6.3.1 Tether measurements . 111 6.3.2 Tension extrapolation to the kite . 112 6.3.3 Wind measurements . 113 6.3.4 Wind velocity extrapolation to the kite position . 113 6.3.5 Relating tether and anemometer measurements . 115 6.3.6 Analysis techniques . 116 6.3.7 Systematic errors . 117 7 KITE PERFORMANCE 118 7.1 Kite Performance Information . 118 7.1.1 Previous kite performance results . 118 7.1.2 Comparison between current and previous results . 119 7.2 Kite Performance . 121 7.2.1 Mean tension . 121 7.2.2 Mean angles . 123 7.2.3 Tension variation . 125 7.2.4 Angle variation . 126 7.2.5 Force coe±cients . 128 7.3 Kite Types . 129 8 KITE ANEMOMETERS 135 8.1 Ideal Kite Anemometer . ..