‘Scale’ models

 

The scaling issues with model testing revolve around stability, resistance values and reynolds number effects.

Stability is a function of displacement and varies with  the cube of the scaling factor. The heeling force is a function of the sail area, which varies with the square of the scaling factor and the force due to windspeed, which varies with the square of the windspeed. It works out that the equivelent windspeed for the full size vessel = the models windspeed multiplied by the square root of the scaling factor.

Hull resistance has two major components, namely wavemaking resistance, which varies with displacement (the cube of the scaling factor)  and frictional resistance, which varies with the wetted surface area (the square of the scaling factor). Consequently, resistance curves for models and full size vessels, although similar in shape, are not the same. To correct for this in resistance model testing, an estimate of the frictional resistance is subtracted from the model results, the resulting wavemaking resistance component is then scaled up for the full size vessel and an estimate for the full size friction component is added back in.

Fluid flow characteristics are not the same at scale speeds vs full size speeds. This is basically because fluid molecules are the same size regardless of the scale of the model. To compare fluid flow, Reynolds numbers are used, which are a function of fluid velocity and length. In wind tunnel testing, models are compared to full size objects by testing at the same Reynolds number, which usually involves adjusting the test air speed to suit. In tank testing, the model must be tested at the scale wave resistance speed, so other trick have to be used to correct for the Reynolds number effects, such as roughening the hull surface and/or mathematical correction factors.

While we can learn a lot from model testing, these factors can lead to errors and must be borne in mind when interpreting the results.

 

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