Having a pathologically critical mind set, I could not help but noticing a large number of “here” links. They make up one possible area for improvement (see e.g. http://www.w3.org/QA/Tips/noClickHere).

Far too often, people think “old = bad, new = good”. Nomograms may be arcane, but definitly not useless! BTW, I still use a slide rule occasionally…

You’re welcome, Dule! — Ron

Hi Adam. Nomograms for celestial navigation and calculation go back to D’Ocagne’s treatise, with more provided in Soreau’s books on nomography. Since your situation with the rising/setting of a star means the altitude is zero, you have a simpler situation than usual, and you can use several different forms of nomogram from three parallel lines, N-chart, etc. I sent some information on general celestial nomograms to you by private email, and I’m trying to gather more. I’ll send it as soon as I can locate it. — Ron

I’ve only just started reading the PDF form of these three nomogram posts, and I’m very glad to see them! I wish they were there half-a-decade ago when I wanted to make some simple parts-calculators for op-am circuits!

I do have one minor quibble: “It’s interesting to note that the nomogram has outlived the slide rule.” This is not so! Just as nomograms take many forms, so do slide rules. I know of one company which markets a (very cheaply made and in accurate) wooden slide rule as a promotional, “your logo printed on the back” deal, but also the Concise company makes and still sells very fine circular slide rules. There are other companies making both slide charts (cardboard sliderules, sometimes ruled and sometimes just with selection text on them) and slide rules (one company is selling ruled slide charts and slide rules specific to the medical industry.) So don’t count them out, yet!

One other aspect: it is likely that many people have used nomograms without knowing. In addition to the more obvious cases where the word “nomogram” is not used to describe them, the operation of some nomograms just don’t seem to fit the bill. I was a bit surprised to see the venerable Smith chart presented as the first of your nomogram examples, simply because we never used them like a nomogram, per se. Instead of laying a straight edge across two variables to get a calculated answer from a third line or some such, we simply plotted measurements involving phase and amplitude as frequency varied, then drew lines to connect the dots and analyzed the resulting figure to understand the RF system! It is a way of considering the nomogram which adds a few more dimensions to its fascination!

Hi Ray. I just looked up the Concise company. You’re right, they do sell circular slide rules—I had no idea. I still have my pocket circular slide rule from my high school days,so I’m partial to those. I’m not surprised as much by companies making custom cardboard slide rules for specific products. (I plan on writing an essay on designing custom slide rules at some point, BTW.) I will have to modify my statement so that it doesn’t imply the death of slide rules. But the use of nomograms, particularly in the medical field, is not uncommon today, so I think it’s fair to say that the use of nomograms surpasses that of slide rules today.

I was trying to design something for risk assessment, extending an idea that had been used, I believe, by the US military and then modified by the New Zealand authorities for the purposes of the assessment of risk of injury from defects with consumer products. I wanted to extend it for the risk assessment of food, to assign suitable frequencies of sampling for analysis to detect problems for consumer protection/safety.

With not even the slightest concept of appropriate mathematical relationships, and being unable to find anything to help, I approached this entirely non-mathematically. In the end my design was based on trial and error with practical experimentation. Once I had gone beyond the New Zealand basics I struggled a lot to get the model to do what was needed, until hitting on the idea of non-parallel axes, when all of a sudden it started to come together. Had I seen your essay first it may have prompted me down that line much earlier!

What I’d be interested to know is how to extract formulae that effectively lie behind the nomogram - I’m not a mathematician, and whilst I might get there sometime the methodology has eluded me so far! Extraction of the formulae would enable a calculation of risk to be done on a computer, which unlike the nomogram would then lend itself to multiple rapid assessments.

In case you are interested in the risk assessment nomogram, there are a pair of documents on www publicanalyst dot com /News/Historical_Documents/ Risk_Based_Sampling_Vol_1.pdf and Risk_Based_Sampling_Vol_2.pdf

I’ve read through your papers and I’m impressed with your success with empirical nomography! The creation of nomograms from empirical data is sometimes covered in books, but I understand that you are looking for the reverse–to find the equations from nomograms. The only thing I’ve seen on that is the paper http://eldredgeengineering.com/Reverse%20Engineering%20Nomographs%20Paper.pdf but the author’s approach is definitely ad hoc–he knows the form of the engineering equations and he has a nomogram that has a grid that can easily be separated into x and y components. The general method seems to be curve fitting based on the expected form of the equation from the configurations of the scales. I had a quick go at deriving something from your risk assessment nomogram but the equation got very complicated very quickly, to the point that it would not be useful. If you only assumed discrete values on some scales as it appears in your papers, it would make such a curve fit much simpler, I would think. — Ron

Thanks for your comment, Chris! I really knew very little about nomograms when I started gathering references, and I was stunned by what I found. Since I’ve accumulated a lot of articles and books on nomography, I’m now planning on writing a blog essay that will just be a showcase of scans of the coolest nomograms I’ve run across. There are many that are a lot more inspirational than the simpler examples in my essays, and it would be a fun and easy article to write after I finish the one I’m working on now.

Nomography is an actively growing topic on the web. Sites on nomograms that have recently been updated include William Chung’s site, Leif Roschier’s Pynomo site with free software to generate nomograms (see the “Basics” and “Examples” links or the links under the Software Documentation area to see beautiful examples), and Eric Sumner’s newly-launched site. And there is the relatively young nomography forum as well for ongoing discussions. — Ron