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(June 2016) ( Learn how and when to remove this template message )
A scale model of the Tower of London. This model can be found inside the tower.
Scale model of water powered turbine L to R with 12 inch ruler at bottom: 1:64 Matchbox Chevrolet Tahoe, 1:43 Ford F-100, 1:25 Revell
Monogram 1999 Ford Mustang Cobra, 1:18 Bburago 1987 Ferrari F40
Model ships and castle
A
scale model
is most generally a physical representation of an object that maintains accurate relationships between all important aspects of the model, although absolute values of the srcinal properties need not be preserved. This enables it to demonstrate some behavior or property of the srcinal object without examining the srcinal 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 srcinal object's interaction with the real world.
[
citation needed
]
Contents
1Requirements
o
1.1Similitude requirements
1.1.1Scaling
o
1.2Practical requirements
2Classes
3Examples
o
3.1Structural
o
3.2 Aircraft
3.2.1Static
3.2.2Flying
o
3.3Plans-relief
o
3.4Buildings
o
3.5 Architectural
o
3.6House portrait
o
3.7Buses and trucks
o
3.8Cars
o
3.9Construction vehicles
o
3.10Railways
o
3.11Robots
o
3.12Rockets and spacecraft
o
3.13Living creatures
o
3.14Ships and naval wargaming
o
3.15Manned ships
o
3.16Tanks and wargaming
o
3.17Engines
o
3.18Miniatures in contemporary art
4See also
5Notes
6References
7Further reading
8External links
Requirements
[edit]
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 requirements
[edit]
Similitude is the theory and art of predicting prototype (srcinal object) performance from scale model observations.
[1]
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.
[2]
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: where
is the mean velocity of the object relative to the fluid (SI units: m/s)
is a characteristic linear dimension, (travelled length of the fluid; hydraulic diameter when dealing with river systems) (m)
is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/(m·s))
is the density of the fluid (kg/m³).
Observing the equation above it is clear to see that while the Reynolds numbers must be equal for the scale model and the prototype, this can be accomplished in many different ways, for example, in this problem by altering the scale of the dynamic viscosity of the model to work with the scale of the length. This means, the scales of different quantities, for example a material's elasticity in the scale model versus the prototype, are governed by equating the dimensionless quantities and the other quantity's scaling within the
dimensionless quantity to ensure the dimensionless quantity of interest is of equal magnitude for the scale model and prototype.
Scaling
[edit]
With the above understanding of similitude requirements, it becomes clear the scale often reported in scale models refers only to the geometric scale, (L referring to length), and not the scale of the parameters potentially important to consider in the scale model design and fabrication. In general the scale of any quantity i, perhaps material density or viscosity, is defined as: where
is the quantity value of the prototype
is the quantity value of the scale model This relationship must be applied to all quantities of interest in the prototype, observing similitude requirements
—
so the scale model can be built using dimensions and materials that make scale model testing results meaningful with respect to the prototype.
[3]
One method to determine the dimensionless quantities of concern for a given problem is to use dimensional analysis.
Practical requirements
[edit]
Practical concerns include the cost to construct the model, available test facilities to condition and observe the model, the availability of certain materials, and even who will build it. Practical requirements are often very diverse depending on the purpose of the scale model and they all must be considered to have a successful scale model experience. As an example, perhaps an aerospace company needs to test a new wing shape. According to the similitude requirements the test must be carried out in a wind tunnel that
can drop the temperature of the air to −128
°C (−198
°F), such as the 0.3-meter (12 in) Transonic Cryogenic Tunnel at NASA Langley Research Center .
[4]
However, if a facility such as this one can't be used, perhaps due to cost constraints, the similitude requirements must be relaxed or the test redesigned to accommodate the limitation.
Classes
[edit]
For a scale model to represent a prototype in a perfectly true manner, all the dimensionless quantities, or
π
terms, must be equal for the scale model during the observational period and the prototype under the conditions the modeler desires to study. However, in many situations, designing a scale model that equates all the
π
terms to the prototype is simply not possible due to lack of materials, cost restrictions, or limitations of testing facilities. In this case, concessions must be made for practical reasons to the similitude requirements. Depending on the phenomena being observed, perhaps some dimensionless quantities aren't of interest and thus can be ignored by the modeler and the results of the scale model can still safely be assumed to correspond to the prototype. An example of this from fluid dynamics is flow of a liquid in a horizontal pipe. Possible
π
terms to consider in this situation are Reynolds number , Weber number , Froude number , and Mach number .
For this flow configuration, however, no surface tension is involved, so the Weber number is inappropriate. Also, compression of the fluid is not applicable, so the Mach number can be disregarded. Finally, gravity is not responsible for the flow, so the Froude

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