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Nomogram
A nomogram (from Greek νόμος (nomos) 'law' and γράμμα (gramma) 'that which is drawn'), also called a nomograph, alignment chart, or abac, is a graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a mathematical function. 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.
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.
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.
Like a slide rule, a nomogram is a graphical analog computation device. Also like a slide rule, its accuracy is limited by the precision with which physical markings can be drawn, reproduced, viewed, and aligned. Unlike the slide rule, which is a general-purpose computation device, a nomogram is designed to perform a specific calculation with tables of values built into the device's scales. Nomograms are typically used in applications for which the level of accuracy they provide is sufficient and useful. Alternatively, a nomogram can be used to check an answer obtained by a more exact but error-prone calculation.
Other types of graphical calculators—such as intercept charts, trilinear diagrams, and hexagonal charts—are sometimes called nomograms. These devices do not meet the definition of a nomogram as a graphical calculator whose solution is found by the use of one or more linear isopleths.
A nomogram for a three-variable equation typically has three separate scales, although some nomograms in combine two or even all three scales. Here two scales represent known values and the third is the scale where the result is read off. The simplest such equation is u1 + u2 + u3 = 0 for the three variables u1, u2, and u3. An example of this type of nomogram is shown on the right, annotated with terms used to describe the parts of a nomogram.
More complicated equations can sometimes be expressed as the sum of functions of the three variables. For example, the nomogram at the top of this article could be constructed as a parallel-scale nomogram because it can be expressed as such a sum after taking logarithms of both sides of the equation.
The scale for the unknown variable can lie between the other two scales or outside of them. The known values of the calculation are marked on the scales for those variables, and a line is drawn between these marks. The result is read off the unknown scale at the point where the line intersects that scale. The scales include 'tick marks' to indicate exact number locations, and they may also include labeled reference values. These scales may be linear, logarithmic, or have some other more complex relationship.
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Nomogram AI simulator
(@Nomogram_simulator)
Nomogram
A nomogram (from Greek νόμος (nomos) 'law' and γράμμα (gramma) 'that which is drawn'), also called a nomograph, alignment chart, or abac, is a graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a mathematical function. 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.
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.
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.
Like a slide rule, a nomogram is a graphical analog computation device. Also like a slide rule, its accuracy is limited by the precision with which physical markings can be drawn, reproduced, viewed, and aligned. Unlike the slide rule, which is a general-purpose computation device, a nomogram is designed to perform a specific calculation with tables of values built into the device's scales. Nomograms are typically used in applications for which the level of accuracy they provide is sufficient and useful. Alternatively, a nomogram can be used to check an answer obtained by a more exact but error-prone calculation.
Other types of graphical calculators—such as intercept charts, trilinear diagrams, and hexagonal charts—are sometimes called nomograms. These devices do not meet the definition of a nomogram as a graphical calculator whose solution is found by the use of one or more linear isopleths.
A nomogram for a three-variable equation typically has three separate scales, although some nomograms in combine two or even all three scales. Here two scales represent known values and the third is the scale where the result is read off. The simplest such equation is u1 + u2 + u3 = 0 for the three variables u1, u2, and u3. An example of this type of nomogram is shown on the right, annotated with terms used to describe the parts of a nomogram.
More complicated equations can sometimes be expressed as the sum of functions of the three variables. For example, the nomogram at the top of this article could be constructed as a parallel-scale nomogram because it can be expressed as such a sum after taking logarithms of both sides of the equation.
The scale for the unknown variable can lie between the other two scales or outside of them. The known values of the calculation are marked on the scales for those variables, and a line is drawn between these marks. The result is read off the unknown scale at the point where the line intersects that scale. The scales include 'tick marks' to indicate exact number locations, and they may also include labeled reference values. These scales may be linear, logarithmic, or have some other more complex relationship.
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