Book Description

Excerpt from The Design of Diagrams for Engineering Formulas: And the Theory of Nomography It is intended in this volume to present in a practical way the principles of the design of diagrams or nomograms for the solution of engineering and other formulas. The usefulness of a diagrammatic solution of a formula is becoming increasingly recognized and it is generally in proportion to the resistance of the formula to calculation and to the frequency of the application of the result sought. The aim of the present writing has been, therefore, not merely to give elementary methods of drawing simple diagrams but also to develop the grasp of the reader so that he will be able to analyze the more complex formulas of engineering practice. The entire subject would only be handicapped by attempting to avoid the use of the third order determinants and consequently that notation is introduced in the third chapter and continued throughout the book. A sufficient treatment of determinants is given in Appendix A and is indispensable to those who are not familiar with that branch of college algebra. The use of the projective transformation is mentioned, but the reader may proceed independently of that notion In Appendix B, however, is given a simple treatment of that subject sufficient to enable anyone who is interested to understand its application to the present theory. By the determinant notation the identification of given formulas with known types is much helped although it is not completely furnished in all cases. It is hoped, however, that the necessary identification for these cases has been made much more complete by the introduction of an entire new class of diagrams or nomograms which it is proposed to call "Diagrams of Adjustment." These diagrams are new and are treated in the last chapter. All other diagrams of alignment are special cases of these more general types for they may naturally be regarded as diagrams of adjustment in which the adjustment reduces to zero. The list of fifty-four illustrative examples is selected to avoid trivial instances. It is hoped that the careful presentation of the general theory of the introduction of scale factors and units of length into the diagram will enable the reader to produce designs that are practical. For this reason several difficult examples have been worked out in considerable detail. The geometric theory governing the position of component elements such as curves, lines or points which constitute the permanent diagram must always be modified by the application of certain limits of accuracy and by a choice of the range of values of the variables for which the formula is to be used. The construction of a permanent diagram does not consist in the plotting of an indefinite number of results computed directly from the formula, but rather in a neat segregation of the several functions in the formula so that when certain corresponding scales are plotted and suitable simple geometrical constructions applied, a useful diagram results. The labor thus involved is usually slight compared to the resulting economy in the use of the formula for direct computation. Diagrammatic representation of a formula permits the immediate determination of the value of any variable and usually also permits the determination of the rate of variation of any variable with respect to another variable when such variations are not readily determined or observed by direct inspection of the formula. The teaching of this subject of diagrammatic representation of formulas, or Nomography, at the Sheffield Scientific School for the past nineteen years has furnished opportunity to the authors to test its value as a supplementary course in applied mathematics and refined drafting, as well as in practice, and consequently all unnecessary theory has been sacrificed. A comprehensive set of problems is given at the close of each chapter and many of them may easily be varied .