Nomographs

A forgotten tool

What is a Nomograph

• Also called a nomogram• nom·o·gram• ˈnäməˌɡram/• noun• noun: nomogram; plural noun: nomograms; noun: nomograph;

plural noun: nomographs• a diagram representing the relations between three or more

variable quantities by means of a number of scales, so arranged that the value of one variable can be found by a simple geometric construction, for example, by drawing a straight line intersecting the other scales at the appropriate values.

Slide rule

Smith Chart

Custom Slide rules

BINOMIAL NOMOGRAPH FOR SINGLE SAMPLE ACCEPTANCE SAMPLING

n = ______ c = ______

How do you build a nomograph

• Geometric Design for Parallel Lines

• Nomograms composed of straight scales can be designed by analyzing their geometric properties.

How do you build a nomograph

• N or Z Charts• An N chart can be used to solve a

three variable equation involving a division

How do you build a nomograph

• Proportional Nomograms

• The proportional chart solves an equation in four unknowns

• Concurrent-Scale Nomograms

• The concurrent-scale nomogram solves an equation of the type

How do you build a nomograph

How do you build a nomograph• Compound Nomograms

• A compound nomogram can solve an equation of four or more variables by

concatenating a series of three-variable nomograms of any type.

How do you build a nomograph

• Using Determinants• A determinant is denoted by vertical bars along the sides of a matrix of

values or functions. The determinant of a 3 × 3 matrix

• Is denoted by

• Is the quantity given by

How do you build a nomograph

• Straight-Scale Nomograms using Determinants

How do you build a nomograph

• Curved-Scale Nomograms built with determinants

How do you build a nomograph

• Grid Scale Nomogram using determinants

Bibliography• Adams, Douglas P. 1964. Nomography: Theory and Application. Hamden, CT: Archon.• Douglass, Raymond D., and Douglas P. Adams. 1947. Elements of Nomography. New

York: McGraw-Hill.• Epstein, L. Ivan. 1958. Nomography. New York: Interscience Publishers.• Hoelscher, Randolph P., Joseph N. Arnold, and Stanley H. Pierce. 1958. Graphic Aids in

Engineering Computation. New York: McGraw-Hill.• Johnson, Lee H. 1952. Nomography and Empirical Equations. New York: John Wiley

and Sons.• d’Ocagne, Maurice. 1899. Trait´e de nomographie. Paris: Gauthier-Villars.• Otto, Edward. 1963. Nomography. New York: Macmillan.• Roschier, Leif, andTapaniMakkonen. StarNavigation.

http://www.pynomo.org/wiki/index.php/example:Star_navigation. Accessed 10 September 2009.

• A Nomogram for Confidence Limits on Quantiles of the Normal Distribution with Application to Extreme Value Distributions NEVILLE F. DURRANT Target Training Ltd., Scalford Hall, Melton Mowbray, Leicestershire, England

More Bibliography• Levens, A.S. Nomography. New York: John Wiley and Sons (1937). Masse, Yvon. Central

Projection Analemmatic Sundials, The Compendium, Journal of the North American Sundial Society, Vol. 5, No. 1, Mar. 1998, pp.4-9.

• Sawyer, Fred. Ptolemaic Coordinate Sundials, The Compendium, Journal of the North American Sundial Society, Vol. 5, No. 3, Sep. 1998, pp.17-24.

• Sawyer, Fred. A Universal Nomographic Sundial, Bulletin of the British Sundial Society, Oct. 1994. 94(3):14-17, also in Sciatheric Notes, a collection of sundial articles by Fred Sawyer from this publication.

• Vinck, Rene J. Samuell Foster’s Circle, The Compendium, Journal of the North American Sundial Society, Vol. 8, No. 3, Sep. 2001, pp.7-10.

• Creating Nomograms with the PyNomo Software Version 1.1 for PyNomo Release 0.2.2 Ron Doerfler http://www.myreckonings.com/wordpress

• The Art of Nomography ©2008 Ron Doerfler Dead Reckonings: Lost Art in the Mathematical Sciences http://www.myreckonings.com/wordpress January 8, 2008

• The Lost Art of Nomography Ron Doerfler Naperville, IL http://www.myreckonings.com rondoerfler@myreckonings.com

Software

• PyNomo can be found at http://www.pynomo.org. The software is OS-independent in principle, as Python interpreters exist for all major operating systems. It runs at least onWindows XP/Vista, Mac OSX and Linux. It requires installation of several other software packages, including the Python language, the PyNomo package for Python, four other Python add-on packages, and the MiKTeX distribution of the typesetting language LaTeX/TeX. Detailed instructions for the installation on Windows platforms are found on the PyNomo site.