Introduction to Scale Modeling

Scale Models

Jana Dunphy

History of Scale Modeling

The use of scale models began early in the 1800s. A French mathematician by the name of A. L. Cauchy studied a model of vibrating rods and poles in 1829. In 1869 W. Froude, who was to have a dimensionless number named after him, made the first water-basin model for designing watercraft. Model experiments performed on fluid motion in pipes were published in 1883 by O. Reynolds. He also had a dimensionless number named after him. Finally, the Wright brothers built the first wind tunnel to test wing models (Schuring, 1977).

What is a Scale Model?

A model can be defined as a variety of things: an outstanding student, a futuristic home, a new car, an attractive person, an idea, an image, a concept . . . the list goes on and on. Specifically, a scale model is a system similar to the prototype which keeps the relative values and proportions of the prototype (Schuring, 1977). A prototype is the original system of the problem. In other words, scale models are pieces of hardware proportioned after the original systems in length, velocity, force, density, etc. The purpose of scale models is to reduce the time and cost of solving technical problems. They are most often used when the original problem is too complex for an analytical solution (Skoglund, 1967). The two main objectives of using them are to verify a hypothesis about laws and to predict the performance of a prototype (Schuring, 1977).

The use of scale models is increasing due to the demands of modern technology. In fact, since a new scale model must be derived for every problem, scale modeling could be more accurately called an art rather than a technique (Schuring, 1977).

When studying the prototype, only the physical laws which govern the phenomenon are required. The physical laws consist of such things as geometry, pressure, stress, deformation, weight, velocity, electric current, magnetic field strength, plus many more. The physical laws responsible for a certain phenomenon can be determined through experiments.

There are two systems of five primary factors to scale modeling: mass, length, time, temperature and electric current (MLT(), and force, length, time, temperature, and electric current (FLT(). These are the only quantities that must be accounted for when scaling. Secondary factors, such as area, acceleration, velocity, power, and moment of inertia, are derived from primary factors. These quantities can all be written in terms of either MLT( or FLT(. For example,

acceleration = l/t²
power = F*l/t = m*l²/t³

Dimensionless numbers, or pi groups, have been developed to relate these factors. Common pi groups would be the Reynolds number, Re = V*L/nu or the Nusselt number, Nu = h*x/k.

Many fields exist in which scale models can be applied. The simplest type, which are built by architects, are table models of cities. Architects also can study the lighting in a room through the use of a scale model. Some toys, such as model cars or airplanes, can be used as very simple scale models. In navel architecture water basins are used as model-testing tanks. They are used to test frictional and wave-making resistance, propeller performance, cavitation, ship bending, and maneuverability in smooth and rough water. In the field of hydrology, scale models are used to study the flow of water at coastlines, tsunamis, open channels, rivers, and harbors. Cyclones and glacier movements are studied by meteorologists and geophysicists. Outside of all of these general topics, scale models are also used to study the spread of fire, acoustics, rocketry, earthquakes, and tunnels, among other things. As you can see, many, many applications exist for scale models (Schuring, 1977).

Why Use Scale Models?

Several advantages go along with scale modeling. The most important is reduction of costs of the fabrication and operation of the prototypes. They allow a trial-and-error procedure of design at a reasonable cost. They shorten the time of experimentation and promote a deeper understanding of the phenomenon. Unfortunately, even though the model may be relatively cheap compared to the prototype, testing facilities are still expensive (Baker, 1973).

References

Baker, Wilfred E., Peter S. Westine, Franklin T. Dodge, Similarity Methods in Engineering Dynamics: Theory and Practice of Scale Modeling, Hayden Book Company, Inc., Rochelle Park, NJ, 1973.

Schuring, Dieterich J., Scale Models in Engineering: Fundamentals and Applications, Pergamon Press Inc., Elmsford, NY, 1977.

Skoglund, Victor J., Similitude: Theory and Applications, International Textbook Company, Scanton, PA, 1967.