Quick Dips

Of Sailing Ships

Many of us have seen dolphins cruising almost effortlessly in the bow waves of ships and yachts on our travels over the water -- but how often have you reflected on how the waves they enjoy slow down your journey?

"The two major sources of drag for a ship are the viscous drag from the stickiness of water, and the wave drag from the waves it leaves behind", says Greg Marr, a member of the University of Auckland's Yacht Research Unit. "Straightforward methods for estimating the viscous part have been around for at least 30 years, but no-one really knows how to calculate the wave drag for a given shape yet, and that can be 30-60% of the total drag."

Currently, the only way of obtaining satisfactory values for wave drag is to make scale models and tow them down a huge towing tank. This is an expensive and time-consuming process -- hundreds of runs are often needed.

The wave drag problem is conceptually very simple, and most of the quite elegant mathematics for it has been known for at least a century. The problem, though, is far too difficult to solve exactly, even in a simplified form, as it involves many complicated mathematical functions called Bessel functions. These functions are difficult to calculate because of their oscillatory, open-ended nature.

Marr's current PhD research started from a set of papers published overseas in the late 1980s. These presented a new form of a computational approach which appeared to give superior results. Marr sought to expand on this to address the sailing yacht problem.

Refinements to the computational details improved the robustness and accuracy of the technique, and also reduced its computational expense -- a significant factor when a typical long run might take twelve hours on one of the School of Engineering's IBM RS-6000 workstations. A set of extensions was also implemented to enable some preliminary work on the yacht design problem.

Marr has also commented on the likely limits of some assumptions frequently used in yacht studies. One of the most common of these is to assume that a yacht leaning over (heeling) can be modelled in the same way as an aeroplane's upward-angled wings (called dihedral) is. The tool developed here has enabled an investigation of when this assumption breaks down.

While the PhD project's ultimate aim of being able to calculate the wave resistance of a given shape wasn't achieved, it did shed light on where the difficulty lies. Previous authors have suggested that the broad range of published results arises from numerical details and inaccuracies. The current study, by demonstrating that two previously published very different approaches give equivalent answers, has indicated that the problems are deeper than this.

Marr suggests that the next step is to investigate the term which represents the sea surface "inside" the ship or yacht (that is, as if the ship was full of water but still floating). This particular term, recognised about 20 years ago, has solved some difficulties for the theorists, but one of the foremost researchers in this field has labelled as "meaningless" current techniques for calculating it. For bodies which are completely submerged, this term is not needed, and the wave drag results are excellent.

Supervised by Professor Peter Jackson, of the Department of Mechanical Engineering, the recently completed PhD study is one of the latest investigations of the sailing yacht system carried out by staff and students of the Yacht Research Unit. Past and ongoing research includes studies of rig design, several aspects of sail design, performance prediction and material analysis.