A nomograph is a device used to relate the physical quantities in such a way that the value of an unknown quantity can be determined given the values of the other related quantities. Nomographs normally involve the relationship among three physical quantities. The scales are located in such a way that, when a straight line is drawn between the values of the known quantities on their respective scales, the line crosses the value of the unknown quantity on its scale. Figure 10 is a typical nomograph that relates the distance traveled, the average speed, and the time traveled. It should be noted that, as with any graphical representation, the values determined are only approximations.

Figure 10 Typical Nomograph

Example:

Using Figure 10, find the distance traveled if the average speed is 20 mph and the time traveled is 40 minutes.

The line labeled A in Figure 10 connects 20 mph and 40 minutes. It passes through 14.5 miles.

Thus, the distance traveled is 14.5 miles.

Example:

Using Figure 10, find the time required to travel 31 miles at an average speed of 25 mph.

The line labeled B in Figure 10 connects 31 miles and 25 mph. It passes through 70 minutes.

Thus, the time required is 70 minutes.

Summary

The important information in this chapter is summarized below.

Graphing Summary

Ordinate - x-coordinate

Abscissa - y-coordinate

Cartesian Coordinate System

Rectangular Coordinate System

Divided into four quadrants by x- and y-axis

Logarithmic Coordinate System

One or both of the scales are divided logarithmically Semi-log graphs contain linear x-axis and logarithmic y-axis Log-log graphs contain logarithmic x- and y-axis

Linear functions are usually plotted on Cartesian coordinate graph.

Exponential functions (y = e^x) are usually plotted on semi-log graphs to provide a straight line instead of the resulting curve placed on a Cartesian coordinate graph.

Power functions (Y = ax², y = ax³, etc.) are usually plotted on log-log graphs.