Scale Model

A scale model is a representation of a figure, structure or other phenomenon that maintains the overall shape and appearance of the original but alters (usually reducing) its dimensions in terms of length, width, height and so on. A common example of a scale model is seen in the architectural models used to represent buildings that are planned for construction. A scale model is usually intended to represent a real world object in miniature, in order to study the object in ways that would be either impossible or extremely difficult or inconvenient if the original object were used. For example, one might create a scale model of a skyscraper in a computerized, virtual reality environment in order to test how the building stands up to extreme conditions such as earthquakes and hurricanes. This would allow one to learn about how the building could best be designed without having to first construct the building (at great expense), test its behavior under destructive conditions, and then have to rebuild it in order to incorporate the improvements that had been discovered during testing. Architects use scale models for similar purposes, because the scale model allows them to see what a building will look like without having to go to the expense and effort of building it in real life.

Overview

One of the most important features that must be kept in mind when one is constructing a scale model is to keep measurements consistently in proportion to one another. The word "scale" in the phrase scale model refers to this idea, which assigns a particular ratio to all measurements the model seeks to reproduce. For example, if a scale model of an amusement park is constructed to a scale of 1 inch to 100 feet, that means that each linear inch of distance on or within the scale model is meant to represent a distance of one hundred feet in the real world. In this way, an amusement park that actually takes up thousands of square feet can be modeled in miniature on a tabletop.

If the scale model is to provide useful information, however, all of its parts must be constructed according to the same scale. In the example of the scale model of the amusement park, the model would look very strange if distances were given at a scale of 1 inch to every 100 feet but buildings were constructed to a scale of 1 inch to every ten feet—the scale model amusement park would be crowded with enormously oversized buildings, making it difficult if not impossible to extract any useful information from the inspection of the model. Some types of scale models have challenges beyond those presented by the need to maintain linear proportionality. For example, scale models of automobile prototypes are often used to test how aerodynamic a particular design for a car is, so in addition to the concern for the size of the model to be accurately proportional, designers must also ensure that its material properties behave in proportion to their real world counterparts.

Bibliography

Adam, John A. Mathematics in Nature: Modeling Patterns in the Natural World. Princeton, NJ: Princeton UP, 2003.

Bay-Williams, Jennifer M, and William R. Speer. Professional Collaborations in Mathematics Teaching and Learning: Seeking Success for All. Reston, VA: National Council of Teachers of Mathematics, 2012.

Ceccato, Cristiano, Lars Hesselgren, Mark Pauly, Helmut Pottmann, and Johannes Wallner. Advances in Architectural Geometry. Wien: Springer, 2010.

Cook, William. In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation. Princeton, NJ: Princeton UP, 2012.

Dunn, Fletcher, and Ian Parberry. 3D Math Primer for Graphics and Game Development. Boca Raton, FL: CRC, 2011.

Kutz, Jose N. Data-Driven Modeling & Scientific Computation: Methods for Complex Systems & Big Data. Oxford : Oxford UP, 2013.

Roth, Richard, and Stephen Pentak. Design Basics. Boston: Cengage, 2013.

Serway, Raymond A., John W. Jewett, and Vahé Peroomian. Physics for Scientists and Engineers with Modern Physics. Boston: Cengage, 2014.