What's a Nomograph and How Do You Use It?

Inexpensive scientific and engineering calculators have pretty much eliminated the need for nomographs that embody complicated relationships that would prove cumbersome or difficult to calculate otherwise. A basic nomograph used to calculate reactance includes logarithmic scales for inductance, capacitance, reactance and frequency, as shown below. In this example, the straight line, called an isopleth, connects the 10 cycles/second (cps) to a 5-Henry inductance. To obtain the 10 cps resonance, you will need a 50 μF capacitor. The nomograph also lets you determine the XL or XC reactance, too.

I still find this type of graphical representation of information handy for quick assessments of electrical conditions and quantities. If you had to perform the calculation: f = 1/(2π √(LC)) time and again as you try to find a capacitor-inductor combination to create a given resonant circuit, you might resort to a spreadsheet or programmable calculator. And you would have to rearrange the equation to calculate L or C for a given value of the other quantity and the needed frequency. With a nomograph, you need only a straight edge.

A nomograph can get more complicated, as shown below. This graph helps you find the inductance of number of turns in a single-layer coil–one with only one layer of windings. In this case, you have a coil with 80 windings that take up 4 inches on a core 2 inches in diameter. On this chart, the Ratio corresponds to the coil diameter divided by its length, or 2/4 = 0.5. So, draw a line (Example 1A) between the number of turns (80) and the ratio (0.5). Mark where the line crosses the Axis, which simply serves as a reference point. Next, draw a line (Example 1B) between the Axis point and the diameter of the coil (2.0) and read the coil inductance, which looks like 125 to 130 μH.

Again, you could calculate the inductance from the formula:

L = (N * A)^2 / (9A + 10B)

Where:

These examples come from “Handbook of Electronic Tables & Formulas,” D. Herrington and S. Meacham, editors, 1959. The 2009 edition of the “ARRL Handbook for Radio Communications,” includes a nomograph for helical resonators, which helped me remember the utility of this type of “calculating” graph. Also, the Smith chart is a form of nomograph.

For more information about nomographs, visit “The Art of Namography,” a three-part series at: /myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-i-geometric-design. –Jon Titus