ELEMENTS OF GRAPHIC DYNAMICS AN ELEMENTARY TEXT-BOOK FOR STUDENTS OF MECHANICS AND ENGINEERING BY EWART S. ANDREWS. 1919 All rights reserved PREFACE GRAPHIC methods have been successfully applied for very many years for the solution of mechanical problems, particularly those arising in engineering, and nearly all students of mechanics prefer the graphic methods to those based upon mathematical analysis. The reason is that argument based upon algebraic symbols does not give to most minds such a clear conception as that based upon diagrams we believe that in all walks of life the diagram method of appeal to the mind i. e. by pictures is the most effective. The champions of the mathematical method of argument have in the past laid great stress upon its value in the development of reasoning powers, suggesting that such reasoning is absent in the graphic method. Although this may be true in cases in which graphic methods are taught merely as mechanical processes, it is certainly not necessarily true. The application of graphic methods to the problems arising in structural engineering has been very fully developed under the name of Graphic Statics, but comparatively little attempt appears to be made in our schools and universities to develop the dynamic problems arising in mechanical engineering with the same logical sequence, the graphic constructions employed usually being introduced in a rather random manner. In the present book, which we call Elements of Graphic Dynamics, we have attempted to present the laws of elementary dynamics with particular reference to engineering vi PREFACE problems in a manner analogous to that employed in Graphic Statics. We wish to lay particular . stress upon the fact that by studying the subject from the graphic standpoint we are not forced to employ in our calculations graphic methods when numerical substitution in a formula will be more convenient we show that for certain special cases formula can be derived and we would remind our readers that it is only in special cases that formulae can be derived by the ordinary methods of mathematical analysis. We do not say that graphic methods arc better than mathematical analysis we do say that most engineering students will learn more from graphic methods than from the other. A considerable portion of the subject-matter of this book has already appeared in article form in Marhiwry the Knyincering Rcrinv, and the Mechanical Wot Id, and the author has to thank the editors of the two first - mentioned journals for the use of blocks. EWART S. ANDREWS. 20-1 I H NK CHAM UK us, T29 Ihf. ii Hor. MoKN, W. r. 1. March. 1919. CONTENTS CHAPTER I PAOK THE SUM CURVE AND ITS APPLICATIONS TO WORK CURVES 1 The Sum Curve or Graphical Integration Construction of Sum CurveEffort and Work Curves Special Cases Work against Resistance Graphical Representation of Effort and Resistance Mean Effort Indicated Horse-power of Engines. CHAPTER II SPACE, VELOCITY, AND ACCELERATION CURVES . . 17 Velocity Curve and its Relation to the Space Curve Accelera tionGeneral Relation between Acceleration, Velocity, and Space Curves Constant Acceleration liquations of Motion Gravity Acceleration tj Measurement of Kinetic Energy The Connection between Force and Acceleration. CHAPTER III CURVES OF ACTION AND CONSTRUCTIONS THEREFOR . 37 Auxiliary Parabola Construction Relation between the Curve of Resultant Effort aiid the Curve of Action Special Cases of Curves of Action The Inverse Sum Curve Application to Simple Harmonic Motion. CHAPTER IV POLAR DIAGRAMS ..........