Nomography Main > Introduction


Paper and cardboard wargames have mostly died out, due to competition from computer games. But some wargame designers still persist.

An annoying limitation on wargames is that while a computer game can do massive mathematical calculations in a fraction of a second, wargames are limited to the speed and attention span of the human player. If the calculations are too difficult, nobody is going to play the game.

And it is prohibitively expensive to include a pocket calculator with each copy of the game.

Enter the Nomogram (Nomograph) or "Alignment Chart". This was invented by the French mathematicians Massau and M. P. Ocagne in 1889. It is a set of scales printed on a piece of paper that will solve a specific equation. Given the all but one of the values for the equation, it will solve for the unknown value. A ruler or straight edge is laid across the scales at the points corresponding to the known values, and the unknown value can be read off directly.

These were very popular with engineers up to about the 1950's. They were quicker than using a slide rule, since they were pre-set for a specific equation. Engineers had entire books filled with nomograms.

They were also popular with the engineer's (uneducated) assistants. They required little or no knowledge of the underlying equations, and were much less prone to error. They were easy to use and very idiot-proof.

Thus they are ideal for the wargame designer as well. Not only do they not require batteries, they can be inexpensively printed in the game manual or on data sheets. They also have an advantage over a pocket calculator in that the range of solutions can be visually inspected. A player can get a feel for the dimensions of possible solutions that is difficult to obtain from inspecting an equation.

The only problem is that constructing such nomograms is a dying art. (of course, the same can be said of wargames) The better books were written prior to 1950. As far as I am aware, courses in Nomography are no longer being offered. This website will attempt to give you enough of a working knowledge that you can create your own nomograms to enhance your wargame designs.

Nomogram designers should be familiar with how to plot points with Cartesian Coordinates. Some skill with algebra (especially factoring) is required for construction of the more complicated nomograms. Matrix mathematics is a plus but not strictly required. A good spreadsheet program that can create graphs will make your task much easier (I use Excel). Naturally a drawing program like Adobe Illustrator will allow the creation of more professional looking nomograms, but if such a program is outside of your budget pen and paper will do.

DISCLAIMER: My mathematical grounding is rather shaky. Any or all of the information in this site may be inaccurate. This is why the site will concentrate on the methods of construction while ignoring the theory of why they work (i.e., in many cases I don't know why they work either). A reading list will be supplied for those who want to go further. I would supply links to web sites about advanced nomography but there don't seem to be any. I found one! Ron Doerfler has a great series of articles about nomography: 1, 2, 3, 4, 5.

If you have any questions, don't bother trying to contact me. After you have read these pages, you will know just about as much as I do about Nomography. Read the books or consult with a real mathematician.

However, if you are a real mathematician and you catch a mistake I made, do feel free to draw my attention to it.

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