Similitude of ship models

Many research workers, hydraulics specialists and engineers have used scale models for over a century, in particular in towing tanks. Manned models are small scale models that can carry and be handled by at least one person on an open expanse of water. They must behave just like real ships, giving the shiphandler the same sensations. Physical conditions such as wind, currents, waves, water depths, channels and berths must be reproduced realistically.

Manned models are used for research (e.g. ship behaviour), engineering (e.g. port layout) and for training in shiphandling (e.g. maritime pilots, masters and officers). They are usually at 1:25 scale.

Worldwide, manned model schools have chosen to apply the similitude law of William Froude (1810-1879) for its manned models. This means that gravity is considered to be preponderant over the other forces acting on the hull (viscosity, capillarity, cavitation, compressibility, etc.).

The different aspects of similitude may thus be defined as follows:

Similitude of shape: The model has exactly the same geometric shape as the real ship. This means that all the length (L) dimensions of the real ship are divided by the same factor, the scale factor. The designers of Port Revel chose a scale (S) of 1:25, so:

S_(L) = 25 (smaller, hence distance is 25 times less)

It should be noted that in this similitude, the proportions are kept (the ratios between the various dimensions of the ship are identical). This is also the case with the block coefficient. Furthermore, the angles are a length ratio, so they are also identical to the original ones. The scale factors of the areas and volumes are deduced from this, i.e.:

S²_(L) = 25² = 625

S³_(L) = 25³ = 15 625

Similitude of mass (M): The model used for shiphandling training must not only resemble the original but also move in the same way as the original when subjected to similar forces. Consequently, the scale factor for the mass (M) and displacement is the same as that for the volumes, i.e.:

S_(M) = S³_(L) = 25³ = 15 625

Similitude of forces (F): If the external forces on the model are in similitude, like the shapes, masses and inertia, the model's movement will be in similitude. It can thus be shown that the forces (F) must be at the same scale as the masses and weights, so:

S_(F) = S_(M) = 25³ = 15 625

Similitude of speed(V): In agreement with Froude's law, the velocity scale is the square root of the length scale, so:

S_(V) = S^1/2_(L) = sqrt(25) = 5 (times slower than in real life)

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Wikipedia