Hydrodynamics of a sailboat. Fairing and strength

What happens below the waterline of a traditional sailboat? What is hydrodynamics and why do hull and appendages affect the speed of a boat? Starting with the basics, Professor of Naval Architecture at the University of Genoa, Paolo Gemelli*, former author for us of the articles“The Carrying Capacity of Sails,” “Mainsail and jib. How to regulate them with the help of science“,“Mainsail and Jib Interaction, Boundary Layer and Stay” that have been widely read.

Introduction to sailboat hydrodynamics

In the past months we have been interested in how wind generates lift through sails and how sails interact with each other.

Let us now change perspective and focus on what happens below the waterline, the realm of hydrodynamics: that is, how the hull and appendages affect the speed of our boat. This is a very broad topic involving concepts that are sometimes difficult to digest, so the approach will be gradual, sometimes didactic, and for this I do not begrudge discerning readers.

The hull of any vessel or nautical craft is designed to meet two specific needs: to transport a cargo to its destination and in the shortest possible time. This implies that its shape must be able to bear a certain weight and have a shape such that it needs as little power as possible to move from one point to another. These issues are addressed by naval architecture, which describes the shapes of floats, characterizes their statics and describes their resistance to motion.

The construction plan, which provides a representation of the hull in different planes (horizontal, vertical and lateral), is the starting point for evaluating some of the most important features of any hull.

The straight fairing table

Through a series of calculations, the straight fairing table is derived within which, for a series of dives corresponding to as many planes of buoyancy, it is possible to find important information such as the displacement of the hull (corresponding to Archimedes’ buoyancy) and the coordinates of the centers of buoyancy (where Archimedes’ buoyancy is applied) and of gravity where the resultant of all weights is considered to be applied.

The reciprocal position of the center of thrust (B) with respect to that of the center of gravity (G) plays a decisive role in the stability characteristics of the vehicle.

The shape of the hull determines the resistance of the hull to motion and the power required for propulsion at the required speed. Traditionally, tank tests on a scale model have been the gold standard for determining the total strength of the medium. A model is dragged through water of known density and temperature until it reaches the required velocity; the force exerted is then measured, which corresponds, precisely, to the resistance of the medium.

Hydrodynamics – The role of CFD

Currently, there is an established use of computational fluid dynamics (CFD ), which, through the numerical solution of a set of equations, allows results comparable to ship tank tests to be obtained at lower cost and with greater flexibility of use. The use of computer-generated three-dimensional models of the hull, instead of physically constructed scale models, allows for greater simplicity in the modification of design details and almost immediate verification of the effects on the motion of the boat.

It is normally used to divide the resistance of a hull into its components, which in the case of sailboats can be divided as follows: component due to water viscosity and residual component mainly related to the formation of wave systems by the hull. Additional terms due to heeling, and swell present in the area should be considered in conditions of heeled boat and formed sea. An additional term, induced drag, associated with lateral hull motion in the presence of drift is considered.

The coefficient of friction and the resistance

The viscosity-related component of water is manifested as frictional force, expressed through a coefficient of friction that is calculated by the formula:

Like all quantities related to viscous resistance, the coefficient of friction depends on the Reynolds number Rn-a dimensionless quantity widely used in fluid dynamics to which we will return later.

To know the value of the drag component due to friction, it is necessary to multiply the coefficient by the speed squared, the density of the water and the wetted surface area of the hull.

This is expressed by the formula:

Theoretical calculation of residual hull strength can be done by using hull series such as the Delft series (a series of hulls produced by the Dutch University of Delft for which the strength has been evaluated. If you design a hull with similar characteristics to one in the series the strength will also be similar, ed.).

Over the years, the resistance values of a series of hulls have been measured in the tank, and by means of these values, using the hull in the series that comes closest to the one of our interest, a formula can be applied to estimate the residual component of the total resistance.

The numerical value of residual strength is obtained by calculating a formula containing coefficients relating to one’s own hull combined with others relating to the similar hull in the series. Studies, which are quite promising, are currently underway regarding the application of machine learning to this particular need, which could be an interesting evolution of a traditional method.

Hydrodynamics and foil

Analysis of the effects of appendages follows the assessment of hull strength; however, we enter territory where innovations in recent years are radically changing the design approach. The advent of foils in particular has radically transformed the possibilities of hulls in terms of speed by making them achieve previously unthinkable performance. We have seen races, such as America’s Cup races in which hull contact with the water is almost occasional. We will talk about this issue, however, in the coming months.