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 to 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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Added resistance in waves: “Pinkster” solver versus “Keuning 2006” comparison

In 1980, Johannes Albert Pinkster defended his doctoral thesis “Low frequency second order wave exciting forces on floating structures”. His work focused on how these forces acted on stationary vessels in regular and irregular waves and developed a method to predict them. His method can also be used to predict the additional resistance in waves experienced by a ship by adjusting the frequency of encounter of the waves.
Twenty-six years later, in 2006, Jan Alexander Keuning et al. presented the paper “An Approximation Method for the Added Resistance in Waves of a Sailing Yacht,” which aimed to develop a calculation method for the assessment of the added resistance of a sailing yacht when sailing in waves. Their approach uses a polynomial expression that considers the primary design parameters of interest as far as added resistance in waves is concerned.
Jean-Francois MASSET compares these both methods developed at TU Delft by applying them to a day-boat project and analyzing the results.

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