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

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 D³ − 10D² + 56. 25 = 0. It is assumed that g = 32 ft/s² in this equation.

The content above is only an excerpt.