Nomograph Notes
Nomographs
What do you think of nomographs as a way to show data? Are there any good software packages or books
on the topic?
-- Joe Iannucci (email)
I have not seen any current books on nomography, but I have an old one which you may be able to
find at used book sources:
Levens, Alexander S. _Nomography_, 2nd ed. New York: John Wiley & Sons, Inc.; 1959.
Levens was a professor of mechanical engineering at Berkeley. The book has 296 pages. HTH.
Regards,
Mike
-- Michael Rosenborg (email)
According to the dictionary at Wolfram research's web site, a nomograph (nomogram) is a graph that
is useful for solving an equation. An example is available on-line at Rice University's flood alert
center:
http://www.floodalert.org/BraysFAS/index.php?sPageID=Nomograph&sRadar=KHGX
It relates the intensity of rainfall to rainfall duration and expected waterflow in Brays Bayou, with
color coding (yellow to orange to bright red) indicating the level of danger of flooding at the Bayou.
A good narrative explains how to use the chart to solve the problem -- if it rains x inches in y hours,
how bad will the flooding be?
[link updated February 2005]
-- Scott Zetlan (email)
I liked to see nomographs (nomograms) when they were still being used, but I did not always gain a
complete understanding of the relationships among the variables from the nomograms. There is a nice
orderly contour-line type aesthetic pattern to some nomograms. But the equation behind the
nomogram usually gives a better theoretical sense of what was going on; that is, Y varies as log X,
taken at various levels of Z, for example. Still, to see the systematic contours--the shape of the
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equations--is quite helpful.
A great virtue of nomograms is that they are usually multivariate, showing relationships among
variables in quite complex systems.
It is surely helpful to have both an analysis of the underlying equation along with nomogram
visualization of the curves generated by the equation. Nomograms show how equations perform.
Nomograms remain useful for understanding; their computational use has passed. Computational
power is so cheap now, we don't need look-up tables or nomograms; we can just plug the numbers
into the equations and solve.
Recently nomograms appear to be used mainly as practical workaday graphics in local applications
and particular trades. Nomograms don't appear often enough in scientific textbooks. Nomograms are
routinely used in engineering statistics books in order to show operating characteristic curves. The
original graphic of Moore's Law is a nice nomogram.
The article by Thomas L. Hankins, "Blood, Dirt, and Nomograms: A Particular History of Graphs,"
Isis, 90 (1999), 50-80 is excellent, a helpful history and depiction of nomograms. It can be seen at
http://www.journals.uchicago.edu/Isis/journal/demo/v000n000/000000/000000.text.html . Hankins'
article at this link shows spectacular high-resolution images of many great nomograms.
-- Edward Tufte
See an excellent website: http://www.projectrho.com/nomogram/index.html with extensive literature
references: http://www.projectrho.com/nomogram/reading.html
-- Zenon Kulpa (email)
I have written a three-part article on nomography that might be of interest. It includes some references
as well as links to online examples and programs. It starts here with the first part:
http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-i-geometric-design
-- Ron Doerfler (email)
From: http://www.edwardtufte.com/bboard/q-and-a-fetch-msg?msg_id=0000Bc
Books
Pretty much every one of these are out of print, but can be obtain from places
like http://www.bookfinder.com and Google Books
Nomography: Theory and Applications
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Douglas P. Adams, (Archon Books Inc., Hamden, Conn.) 1964. I haven't seen this
book.
The Nomogram: The Theory And Practical Construction Of Computational
Charts, 3rd ed.
H.J. Allcock and J.R. Jones, (London: Sir Isaac Pitman and Sons, Ltd.) 1946. Get this
book. Very comprehensive, with a nomogram classification system and step by step
instructions. Covers determinants. Includes appendices that will make your task easier.
A first Course In Nomography
S. Brodetsky, (G. Bell and Sons, Ltd., London, England) 1949. Download it Here. A
good solid book.
Graphical Techniques for Engineering Computation
W. H. Burrows, (The Chemical Publishing Company, New York, N.Y.) 1965. Get this
book. Covers determinants. Also has extensive information on other kinds of
mechanical computing (integrators, slide rules, etc.)
Nomography and Empirical Equations
Dale S. Davis, (New York: Reinhold Publishing Corp.) 1955. A good solid book.
Technical in spots. Has a chapter on custom slide rules. The book is a revision of
"Empirical Equations and Nomography".
Empirical Equations and Nomography
Dale S. Davis, (New York: McGraw-Hill Book Co.) 1943. Very similar to his other
book, but not as complete. This book was republished by Reinhold Publishing
Corporation, New York, N.Y. (1962)
Traite' de Nomographie
Maurice d'Ocagne, (G. Villars Publishing LTD., Paris, France) 1899. Download it from
Google Books Here. Unfortunately, I cannot read French.
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Exposé synthéthique des principes fondamentaux de la nomographie
Maurice d'Ocagne, 1903. Download it from Google Books Here. Unfortunately, I
cannot read French.
Elements of Nomography
R.D. Douglass and D.P. Adams, (New York: McGraw-Hill Book Co.) 1947. A good
solid book. Includes a "nomogram worksheet" form to make the task more systematic.
Nomography
L. Ivan Epstein, (Interscience Publishers) 1958. Good solid book, abet sparse. Covers
determinants.
Falk's Solutions
Karl H. Falk, (Columbia Graphs) 1954. This is an engineer's book of pre-made
nomograms to solve specific problems, not a book on nomograph theory. Mostly fancy
graphs.
Nomography
John H. Fasal, (New York, Frederick Ungar Pub.) 1968. I haven't seen this book.
Alignment Charts
Lester R. Ford, 1944. Download it Here. I haven't seen this book.
ABACS or Nomograms-An Introduction to Their Theory and Construction
A. Giet, (London: ILIFFE and Sons. LTD, Dorset House, Stamford Street, London,
England) 1953. A good solid book.
Stereo nomograms
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N.D. Haasbroek, 1962. Download it Here. Interesting method for making threedimensional nomograms.
The Design Of Diagrams For Engineering Formulas And The Theory Of
Nomography
Laurence I. Hewes and Herbert L. Seward, (New York, McGraw-Hill) 1923. I haven't
seen this book.
Graphic Aids In Engineering Computation
Randolph P. Hoelscher, Joseph Norman Arnold, and Stanley H. Pierce, (McGrew-Hill
Book Company, New York, N.Y.) 1952. Get this book. The section on nomograms is
lucid and comprehensive. Covers determinants. It also has valuable information on
creating custom slide rules.
Nomography and Empirical Equations
Lee Johnson, (New York: John Wiley and Sons) 1952. A good solid book.
Best Approximation by Linear Superpositions (Approximate Nomography)
S. Y. Khavinson, (American Mathematical Society) 1997. I haven't seen this book.
Alignment Charts: Construction and Use
M. Kraitchik, (New York: D. Van Nostrand Co.) 1944. Get this book. It is slender, but
don't let that fool you, it is packed with meat. It is easy to read for those with shaky
mathematical backgrounds, and has some techniques I have not seen in other books. It
also has many unique techniques from other books collected in one volume.
Nomographic Charts
C. Albert Kulmann, (McGraw-Hill Book Co., Inc.) 1951. This is an engineer's book of
pre-made nomograms to solve specific problems, not a book on nomograph theory.
Useful for examples.
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Applied Nomography 3 volumes
J. F. Kuong, (Gulf Publishing Co.) 1965. I haven't seen this book.
Nomography
Alexander S. Levens, (New York, N.Y: John Wiley and Sons, Inc.) 1948. A good solid
book. Covers determinants. Also was copyrighted under the title " Alignment Charts" in
1937
Graphical And Mechanical Computation, Part I - Alignment Charts
Joseph Lipka, (New York, John Wiley and Sons) 1928. Download it from Google
Books Here. A good solid book. Be sure you do not get Part II by accident as it has
nothing on nomograms.
Fundamental Formulas of Physics, Vol. 1
D. Menzel (Ed.), (New York: Dover) 1960. Very minimalist and terse. There are only
four pages covering nomograms.
Construction Of Nomographic Charts
F.T. Mavis, (Scranton: International Textbook Company) 1939. Get this book. Covers
determinants. Has some hints on creating determinants that I have not seen in any
other books.
Nomographs: What They Are and How to Use Them
J. Molnar, (Ann Arbor Science Publishers Inc.,Butterworth Publishing Group,
Stoneham, Ma.) 1981. I haven't seen this book.
Nomography, Vol.42, International Series Of Monographs On Pure And Applied
Mathematics
Edward Otto, (Oxford/Warszawa, Pergamon Press/PWN) 1963. Get this book. This is
the book to have if you can only have one book. However, be warned that it is not for
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beginners, it is quite heavy on the math. It covers most everything, and has information
that isn't in any of the other books I've seen.
The Construction of Graphical Charts
John Bailey Peddle, (McGraw-Hill) 1919. Download it from Google Books Here. I
haven't seen this book.
Nomographs for Electronics: Instant Calculations for Designers
Robert L. Peters, (Boston, Cahner's books) 1972. I haven't seen this book.
Über die Nomographie von m. D'ocagne: Eine Einführung in dieses Gebiet
Friedrich Schilling, Fr Schilling, Maurice d' Ocagne, 1900. Download it from Google
Books Here. I can't read German, either. It appears to be a German translation of
Traite' de Nomographie, but I'm not sure.
Contribution à la théorie et aux applications de la nomographie
Rodolphe Soreau, 1902. Download it from Google Books Here. Unfortunately, I cannot
read French.
A Collection Of Tables And Nomograms For The Processing Of Observations
Made On Artificial Earth Satellites
I.D. Zhongolovich and V.M. Amelin, (New York, Pergamon Press) 1961. I haven't
seen this book.
Links
PyNomo for the Python programming language. A marvelous software library that will
allow a Python programmer to easily create PDF files of your nomograms.
The Nomography Discussion, second era of graphical computation. An online forum
about nomography.
Dead Reckonings lost art in the Mathematical Sciences. The blog of Ron Doerfler, it
often has important details about nomograms. Do not miss the following posts: 1, 2, 3, 4, 5.
Birds of Prey is a paper and cardboard war game of air combat. The game makes
extensive use of nomograms as game play aids.
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Society for the Conservation and Advancement of Nomography Barbecue Joe's
nomography page.
From:
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