A nomogram is a two-dimensional diagram designed to allow the approximate graphical computation of a function. Like a slide rule, it is a graphical analog computation device; and, like the slide rule, its accuracy is limited by the precision with which physical markings can be drawn, reproduced, viewed, and aligned.
The slide rule is intended to be a general-purpose device. Nomograms are usually designed to perform a specific calculation, with tables of values effectively built in to the construction of the scales.
A nomogram typically has three scales: two scales represent known values and one scale is the scale where the result is read off. The known scales are placed on the outsides (ie the result scale is in the center). Each known value of the calculation is marked on the outer scales and a line is drawn between each mark. Where the line and the inside scale intersects is the result.
Straight scales are useful for relatively simple calculations, but for more complex calculations, simple or elaborate curved scales may need to be used.
Examples of nomograms:
- Spiral-shaped nomogram -- the Cornu spiral
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The nomogram below performs the computation
A and B are entered on the horizontal and vertical scales, and the result is read from the diagonal scale. This formula has several uses: for example, it is the parallel-resistance formula in electronics, and the thin-lens equation in optics.
In the example below, the green line demonstrates that parallel resistors of 56 and 33 ohms have a combined resistance of about 21 ohms. It also demonstrates that an object at a distance of 56 cm. from a lens whose focal length is 21 cm. forms a real image at a distance of about 33 cm.
The nomogram below can be used to perform an approximate computation of values needed in the statistical chi-squared test. This nomogram demonstrates the use of curved scales with unevenly-spaced graduations.
The blue line demonstrates the computation of
(9 - 5)2/ 5 = 3.2
The red line demonstrates the computation of
(81 - 70)2 / 70 = 1.7
More examples
Parallel-resistance/thin-lens nomogram
This nomogram is interesting because it performs a useful nonlinear calculation using only straight-line, equally-graduated scales. Parallel-resistance/thin-lens nomogram
