Graphing with dissimilar units

I’m working on a graphing project for which I’d love to get your advice.

I’m the editor and designer of a large compilation of material information related to the electrical steels used in motors and generators; over past several years, the organization I belong to, The Electric Motor Education and Research Foundation, has published two sets of data on CD-ROM and I’m now working on the third edition. One essential property of these steels is Magnetization, which can generally be thought of as the amount of magnetic induction, or flux density, you get with a given electrical input; this is commonly presented on a log-log Magnetization or “B-H curve” graph (you may recognize this as the first leg of a hysteresis curve). The data I work with is provided to us by various steel mills, produced either from their own tests or from curve-fit algorithms they’ve developed. There are several material properties covered in the complete document; the question I put before the forum will apply to all of them.

A quick note about the images that follow. They’re a workout on a complete page from the Lamination Steels CD-ROM; the core element of this disk is set of massively linked pdf files of which this page is but one (there are over 600 pages in the second edition with over 1000 planned for the third edition). The navigation bar at the left contains location information as well as links to other pages in the document. These graphs were prepared with the intention of their being used in pdf format; hence the small minor scales that help keep the curves in place should one wish to zoom in on them with Acrobat’s zoom utility (they should be apparent if not entirely readable in this posting). I wanted to keep the graphs as large as possible so the accompanying datasets are presented on the pages following the graphs. I’ve tried to keep these graphs as clean, attractive and readable as possible, with careful attention not only to plot accuracy but such compositional elements as line weight, colors, type (typeface, size, weight and color) and type placement (I’m still working on a few issues with the very small type in the minor scales). It was important that the navigation elements reside on the page so I had to carefully consider the composition of the entire page, making the navigation bar readily available and large enough to be used easily without distracting from the graph. One thing I worried over (and still don’t know if I got just right) was the visual depth of the elements; I tried to set the color of the body of the navigation bar and the ground of the graph so that they appear to be on the same plane visually, with the hope of getting the curves to “float” just a bit above them thus enhancing their essential importance on the page.

This graph, from our second edition, is a B-H curve for a common grade of electrical steel “M-19” and shows the magnetization characteristics for this material at a number of switching frequencies. You’ll see that the magnetizing force on the x axis is in the unit “Oersteds” (Oe) and induction on the y axis is in “Gausses” (Ga). (The red grid lines at 10,000 Gausses and 15,000 Gausses refer to the two standard testing points for these materials.) These units are those routinely used by U.S. producers; for the next edition, I’m developing data and accompanying graphs using what may be called “metric” units: Teslas for induction and Ampere Turns per Meter (A/M) for magnetizing force. Therein lies the rub. While the relationship of Gausses to Teslas is easily handled (1 Tesla equals 10,000 Gausses and you’ll see that on this graph I referenced Tesla units), the conversion of Oersteds to A/M is a bit dicey as 1 Oersted equals 1.256 x 10-2 A/M. I’d like to be able to plot both units on the same graph, yet am concerned about confusing the units or overly cluttering the graph. I’ve considered several approaches. First, keeping the graph as it is and placing converted A/M values along the major and minor x axis scales:

This graph keeps the log decades on Oersteds with the corresponding A/M units underneath. While appealing in the ease of converting the data points and in having just one grid system on the x axis, I found this solution uncompelling as I’d like to be able to represent both Oersteds and Ampere Turns per Meter as complete systems. This will make it easier for those used to reading these graphs in one or the other set of units and also helps make the relationship of the two unit systems more readily apparent. I was still worried that having two x axis systems would be visually confusing. So, to help get a handle on the workings of two unit graphs, I prepared one with differently colored Oe and A/M grids on their respective decades, reducing it to a bare essential set of elements by removing all the minor scales, just to see how it would look:

After plotting this, I felt that there might indeed be hope for a graph with both x axis systems. Still concerned that a layout similar to the first graph with two grid systems would result in an unreadable spider’s web of grid lines, I plotted the minor scales just in the areas of the curves:

My final thought was to produce two separate graphs on separate pages, appropriately linked, but I found a lot to like about this graph and stopped.

So, to the question, Dr. Tufte (and the others on the forum): Do you have any thoughts about producing a graph with these multi-unit issues? Are there improvements you see for my general scheme or should I entertain a different approach?

Thanks for taking a look at these. Steve Sprague