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Graphical Techniques for Engineering Computations



 
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Product Code: 9780820604015

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ISBN-13/EAN: 9780820604015
ISBN: 0820604011
Author: Walter Herbert Burrows
Chemical Publishing
Book - Hardback
Pub Date: Feb 9, 1965
454 Pages
Features

CONTENTS -

1. SCALES -
Nature and Properties of Scales -
Methods for Constructing Scales -
Altering Moduli of Scales -
Standard Scales -
Mechanical Aspects of Scale Construction -
Exercises -

2. CALCULATING WITH SCALES -
Adjacent Scales -
Parallel Scales With Index Line -
Standard Slide Rules -
Slide Rule Routines -
Special Slide Rules -
Methods of Reproduction -
Other Forms of Special Slide Rules -
Differential Gear Rules -
Exercises -

3. GRAPH PAPERS -
Common Types of Graph Papers -
Construction of Graph Papers -
Exercises -

4. CALCULATING WITH GRAPH PAPERS -
Hyperbolic Paper -
Linear Paper -
Semilogarithmic Paper -
Logarithmic Paper -
Exercises -

5. GRAPHS -
Relationship of Graph to Table and Function -
Graphs of Regular Functions -
Interpolation and Extrapolation -
Graphs of Empirical Data -
Complex Graphs -
Condensed Graphs -
Exercises -

6. CALCULATING WITH GRAPHS -
Position Relationships -
Vertical and Horizontal Displacements -
General Distance Relationships -
Isometric Translation -
Slopes; Graphical Differentiation -
Areas; Graphical Integration -
Exercises -

7. NOMOGRAPHY -
Nomographic Methods -
Some Characteristics of Nomographs -

8. NOMOGRAPHS BY SYNTHETIC METHODS - Synthetic Methods -
Figures With One Straight Index Line -
Figures With Two Parallel Index Lines -
Figures With Perpendicular Index Lines -
Review of Synthetic Methods -
Exercises -

9. NOMOGRAPHS WITH CARTESIAN COORDINATES, -
Relationship of Defining Equation to Type -
Matrix Transformations -
Exercises -

10. NOMOGRAPHS WITH HYPERBOLIC COORDINATES -
The Semihyperbolic Coordinate System -
Application to Construction of Nomographs -

11. PRACTICAL ASPECTS OF CONSTRUCTING NOMOGRAPHS -
Nomographs With Parallel Scales -
Nomographs With Oblique Scales -
Nomographs With Curved Scales -
Exercises -

12. USE OF GENERAL HYPERBOLIC COORDINATES -
Hyperbolic Plane Coordinates -
The V-Type Nomograph -
Fitting Nomograph to a Rectangle -

13. THREE-DIMENSIONED NOMOGRAPHS -
Three-Dimensional Hyperbolic Coordinates -
Defining Equation for Nomographs -
Applications -

14. PROPERTIES OF HYPERBOLIC
COORDINATE SYSTEMS -
Hyperbolic Plane Coordinates -
Semihyperbolic Coordinates -
Hyperbolic Solid Coordinates -
Semihyperbolic Solid Coordinates -

15. NOMOGRAPHS FROM GRAPHS AND TABLES -
Relationship of Graph to Nomograph -
Constructing Nomographs From Tables:
Symmetrical -
Constructing Nomographs From Tables:
General -

APPENDIX -
Values of x = -p/p-r- and 1 - x
INDEX -

PREFACE
There is a steadily growing interest in the capabilities of graphical methods in the field of computation and an increasing demand for applications of these methods to a broad spectrum of scientific and engineering formulas-scientific principles or laws expressed in mathematical symbols. Over the years, man's scientific endeavors have resulted in the accumulation of ponderous volumes of these formulas involving computation for their application to engineering problems. At the same time, man has developed a number of devices for reducing the labor of these computations, numerical devices such as the abacus and tables of logarithms, mechanical devices such as adding machines and desk calculators, electronic devices such as the modern computer, and graphical devices such as the slide rule and the nomograph. It is this last class of devices with which we are now concerned.

The calculation of a series of values required for the solution of an engineering problem (e.g., the design of a column for the fractionation of a hydrocarbon mixture) can be quickly performed with all required accuracy by the use of charts contained between the covers of a handbook at the engineer's fingertips.

Many scientists and engineers that use graphical devices have little idea of the relative merits and applicability of the various types of devices, and virtually no knowledge of the underlying theory of their construction. Yet, the mathematics of this theory is so simple that mathematics advisers on projects for high school science fairs would do well to consider some of the methods described herein, such as construction of special slide rules, nomographs for formulas of current interest, and three-dimensional nomographs. There is no lack of technical literature in this field, but what is lacking is a systematic approach to the subject as a whole, from the standpoints of both organization and theory.

This book is an outgrowth of very earnest efforts towards unifying my own knowledge in this field. Having made a thorough study of nomographic methods and theory, I nevertheless found myself in poor shape to produce a series of nomographs based on certain polynomials describing the characteristics of flight of helicopters.

A modification of existing theory greatly simplified the procedure for representing polynomials; however, it also pointed the way towards the development of a new theory of nomographic representation, the hyperbolic coordinate method from which have grown generalizations and extensions covering the entire field of nomography. At the same time, extension of the idea of the scale equation into the areas of graph papers, graphs, and slide rules has simplified the application of these devices in the field of computation.

Although some topics (e.g., the hyperbolic coordinate method of nomography) are treated in much detail because of the lack of thorough treatment elsewhere, other topics (e.g., graphical integration and differentiation) are recognized as being adequately covered in other sources and are here given only introductory discussions by way of recognizing their family relationships.

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