Added resistance in waves: Response Amplitude Operator (calculation)

How it works

When sailing against waves, a sailing craft experiences an additional resistance that penalizes its performance. To study how the boat is affected, one of the methods developed requires both a statistical model of the sea’s surface the yacht is sailing in (usually through the wave spectral density) and the Response Amplitude Operator (RAO) of the yacht (yacht’s response to waves of different amplitudes and frequencies).

This calculation estimates the RAO (Response Amplitude Operator) of an arbitrary yacht. The calculation needs basic hull data such as LWL, TC, BWL, ∇C, and CP and the value of the density of the water (default is 1026 kg/m3). The latter is necessary for transforming the non-dimensional RAO into a dimensional one.

The results are calculated for the combination of different values of the longitudinal radius of gyration, Froude number, and wave directions:

Calculation. Response Amplitude Operator results.
Response Amplitude Operator (RAO) curves of a sailing yacht.
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Sea state and wave forecasting

The performance of a sailing boat is affected by the presence of surface waves. To understand how the waves influence the boat’s performance, we need first to model the irregular shape of the water surface.

Frictional resistance of the hull (calculation)

The frictional resistance is a force that is generated when the underwater parts of the boat and the water around are in relative movement (the boat moves through the water, or, in other words, the water passes down the boat). Therefore, it is a hydrodynamic force, and as a resistance, it works in the opposite direction to the movement, trying to slow the boat down.


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