# Article

# Article

- Mathematics
- Applied mathematics
- Nomograph

# Nomograph

Article By:

**Douglass, Raymond D. **Formerly, Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts.

Last reviewed:January 2020

DOI:https://doi.org/10.1036/1097-8542.455000

- Scale
- Types of nomographic charts

- Determinant as a basis of a nomograph
- Circular nomographs

- Related Primary Literature
- Additional Reading

**A graphical relationship between a set of variables that are related by a mathematical equation or law.** The fundamental principle involved in the construction of a nomographic or alignment chart consists of representing an equation containing three variables, *f*(*u*,υ,*w*) = 0, by means of three scales in such a manner that a straight line cuts the three scales in values of *u*, υ, and *w*, satisfying the equation. The cutting line is called the isopleth or index line. Numbers may be quickly and easily read from the scales of such a chart even by one unfamiliar with the construction of the chart and the equation involved. **Figure 1** illustrates such an example. Assume that it is desired to find the value of *E* when *D* = 2 and *Q* 50. Lay a straightedge through 50 on the *Q* scale and through 2 on the *D* scale and read 11. 8 at its intersection with the *E* scale. As another example, it might be desired to know what value or values of *D* should be used if *E* and *Q* are required to be 10 and 60, respectively. A straightedge through *E* = 10 and *Q* = 60 cuts the *D* scale in two points, *D* = 2. 8 and 9.4. This is equivalent to finding two positive roots of the cubic equation *D*^{3} − 10*D*^{2} + 56. 25 = 0. It is assumed that *g* = 32 ft/s^{2} in this equation.

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