What is Similitude?

Emma G.
Emma G.
Scientist with beakers
Scientist with beakers

Similitude is the standard used to measure how accurately a particular model will represent real-life conditions. A model is said to have similitude if it meets the three basic requirements of geometric, kinetic, and dynamic equality. If these three parameters match those of the system being modeled, then the model has similitude. The concept is most often used in hydraulic and aerospace engineering.

In engineering, models of systems are used to represent how the system will behave under certain conditions. The model can be either much smaller than the real system, such as a model of a hydroelectric dam, or it can be much larger, like a model of a nanobot. The purpose of the model is to allow engineers to test the system without building a full-scale one, which may be both expensive and labor intensive. In order to be of use, this model must behave exactly as the actual size system would.

Engineers use three criteria to gauge the accuracy of a model. Geometric similitude refers to the shape of the model. All of its lines, curves, and angles should be smaller or larger than the actual system by a given ratio. For example, if an engineer is building a model of a dam in 1:72 scale, then each of the sluice gates cannot be in 1:55 scale or it will misrepresent the physics involved.

The second test of similitude is kinematic similitude. This means that the fluid or air moving around and through the model must move in the same way as it would through and around the full-scale system. The focus is on recreating the motion without worrying about the implications of the motion.

Finally, a model must have dynamic similitude. Here the engineer deals with forces. The forces acting on the model must be scaled versions of the forces that would act on the full-scale version. So the water pressure acting on the 1:72 scale dam must be a 1:72 ratio of the pressure acting on the full-size dam.

It is not always possible to achieve absolute similitude with a model. The more complex the forces working on a system, the more difficult that system is to model, especially if the full-scale version will be subject to several conditions simultaneously. Engineers can sometimes overcome this problem by creating multiple models, each of which is designed to test a specific aspect of the scale version and then combining the results.

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Discussion Comments


@nony - Speaking of airplanes, anyone who has ever built a toy model airplane understands similitude - at least in terms of geometry.

Many of these models are built to exact specifications and they’re nearly perfect in their ratios of body proportions, compared to full scale models.


@SkyWhisperer - I’ve seen how they test car aerodynamics too. They put them in these air chambers to test the flow of air around the vehicle.

I think they use these calculations to determine the best design and shape of the car for ultimate fuel economy.

Of course, the same principle would apply to testing aircraft wings as well. I’m sure they put them in chambers to see how well they take to air lift.


@MrMoody - Yes, water is a perfect environment for creating similitude. I remember watching a television program about tsunamis and killer waves.

Scientists were trying to understand the forces that shape tsunamis and the effects they have on the ocean. Obviously it would be impractical, not to mention impossible, to create a tsunami.

So they created a model in a box, filled with water. They had small motors generate waves to create currents and they had meters and stuff measure the ripples and the impacts of the waves.

I’m pretty sure that since they were using a water model to simulate an ocean event, the ratio of similitude would be pretty close to perfect in that setting.


The principle of similitude is easy to understand, but sometimes you have to use certain substitute forces to emulate a model’s actual behavior in a real life setting.

I’ve seen astronauts in training for example. Part of their rigorous programs involves simulating weightlessness. Obviously there is no place on Earth that is weightless, so they try to simulate an approximation of what weightlessness would feel like.

They do this by having astronauts do stuff underwater. The buoyancy of the water gives the astronauts a lightness that would be similar to what they would feel in space; it’s not exact, but close enough.

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