Nomogram
A nomogram (from Greek νόμος nomos, "law" and γραμμή grammē, "line"), also called a nomograph, alignment chart or abaque, is a graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a mathematical function.
Contents
Origin
The field of nomography was invented in 1884 by the French engineer Philbert Maurice d’Ocagne (1862-1938) and used extensively for many years to provide engineers with fast graphical calculations of complicated formulas to a practical precision.
Nomograms use a parallel coordinate system invented by d'Ocagne rather than standard Cartesian coordinates.
Structure
A nomogram consists of a set of n scales, one for each variable in an equation.
Knowing the values of n-1 variables, the value of the unknown variable can be found, or by fixing the values of some variables, the relationship between the unfixed ones can be studied.
The result is obtained by laying a straightedge across the known values on the scales and reading the unknown value from where it crosses the scale for that variable.
The virtual or drawn line created by the straightedge is called an index line or isopleth.
Advantages
Nomograms flourished in many different contexts for roughly 75 years because they allowed quick and accurate computations before the age of pocket calculators.
Results from a nomogram are obtained very quickly and reliably by simply drawing one or more lines.
The user does not have to know how to solve algebraic equations, look up data in tables, use a slide rule, or substitute numbers into equations to obtain results.
The user does not even need to know the underlying equation the nomogram represents.
In addition, nomograms naturally incorporate implicit or explicit domain knowledge into their design.
For example, to create larger nomograms for greater accuracy the nomographer usually includes only scale ranges that are reasonable and of interest to the problem.
Many nomograms include other useful markings such as reference labels and colored regions. All of these provide useful guideposts to the user.
Limitations and applications
Like a slide rule, a nomogram 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.
While the slide rule is intended to be a general-purpose device, a nomogram is designed to perform a specific calculation, with tables of values effectively built into the construction of the scales.
Nomograms are typically used in applications where the level of accuracy they offer is sufficient and useful.
Alternatively, a nomogram can be used to check an answer obtained from another, more exact but possibly error-prone calculation.
Other types of graphical calculators
Other types of graphical calculators such as intercept charts, trilinear diagrams and hexagonal charts are sometimes called nomograms.
Other such examples include the Smith chart, a graphical calculator used in electronics and systems analysis, thermodynamic diagrams and tephigrams, used to plot the vertical structure of the atmosphere and perform calculations on its stability and humidity content.
These do not meet the strict definition of a nomogram as a graphical calculator whose solution is found by the use of one or more isopleths.
See also
- Cartogram
- Coordinate system
- Isopleth
- Philbert Maurice d’Ocagne
- Log-log graph
- Semilog graph
- Slide rule
- Smith chart
External links
- Nomogram @ Wikipedia
