Nomograms in the History and Education of Machine Mechanics

Computing formulae and solving equations are essential elements of scientific analysis. While today digital tools are almost always applied, analog computing is a rich part of the larger history of science and technology. Graphical methods are an integral element of computing history and still find some use today. This paper presents the history of nomograms, a historically-relevant tool for solving mathematical problems in various branches of science and engineering; in particular, we consider their role in mechanical engineering, especially for education, and discuss their mathematical properties. Each nomogram is a graphical description of a specific mathematical equation, designed such that the solution can be found through a simple geometric construction that can be performed with a straightedge. By design, using nomograms requires little skills and can be done even in adverse environments; a solution of sufficient accuracy for most purposes can then be found in a very short time. Another important advantage of nomograms is that they offer clear insight on the relationships between the variables, an insight which can be lost by looking at a complex equation. First introduced in the late 19th century, nomograms were used by engineers and scientists due to their speed with respect to manual calculations, before being superseded by computers. While now mostly obsolete in practice, nomograms can still prove useful in workshops and teaching classes: we thus also discuss their educational applications and present a few original examples.