Scale representation

A scale model is most generally a physical representation of an object, which maintains accurate relationships between all important aspects of the model, although absolute values of the original properties need not be preserved. This enables it to demonstrate some behavior or property of the original object without examining the original object itself. The most familiar scale models represent the physical appearance of an object in miniature, but there are many other kinds.

Scale models are used in many fields including engineering, architecture, film making, military command, salesmanship and hobby model building. While each field may use a scale model for a different purpose, all scale models are based on the same principles and must meet the same general requirements to be functional. The detail requirements vary depending on the needs of the modeler.

To be a true scale model, all relevant aspects must be accurately modeled, such as material properties, so the model's interaction with the outside world is reliably related to the original object's interaction with the real world.

In general a scale model must be designed and built primarily considering similitude theory. However, other requirements concerning practical issues must also be considered.

Similitude is the theory and art of predicting prototype (original object) performance from scale model observations. The main requirement of similitude is all dimensionless quantities must be equal for both the scaled model and the prototype under the conditions the modeler desires to make observations. Dimensionless quantities are generally referred to as Pi terms, or π terms. In many fields the π terms are well established. For example, in fluid dynamics, a well known dimensionless number called the Reynolds number comes up frequently in scale model tests with fluid in motion relative to a stationary surface. Thus, for a scale model test to be reliable, the Reynolds number, as well as all other important dimensionless quantities, must be equal for both scale model and prototype under the conditions that the modeler wants to observe.

An example of the Reynolds number and its use in similitude theory satisfaction can be observed in the scale model testing of fluid flow in a horizontal pipe. The Reynolds number for the scale model pipe must be equal to the Reynolds number of the prototype pipe for the flow measurements of the scale model to correspond to the prototype in a meaningful way. This can be written mathematically, with the subscript m referring to the scale model and subscript p referring to the prototype, as follows:

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