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Professor Lars Larsson asks how smooth should the hull be in order to reduce resistance? Is there a ‘roughness height’ below which there is no resistance increase?
The flow of water near the hull
When a yacht moves through the water it drags the water along in a rather thin layer outside the hull called the boundary layer which is a few centimeters thick for most yachts.
Water sticks to the actual surface of the hull and so at this point there is no relative motion.
Thus, within the boundary layer the speed increases from zero, relative to the hull, to approximately the yacht speed at the boundary layer edge.
In the boundary layer the flow of the water is very irregular and turbulent, but there is a very thin region close to the hull, the viscous sub-layer, where the flow is mostly smooth, or laminar.
Permissible roughness of the hull
If any roughness of the hull is embedded in the viscous sub-layer it will not influence resistance; the surface is hydraulically smooth. This is good news, as it means there is a limit beyond which there is no point in further smoothing the surface.
This limit is dependent upon three factors: the hull shape, position on the hull and speed of the boat. The speed is the most important factor and a reasonable estimate of the permissible roughness height can be based on speed alone, as shown in Figure 1 below.
Here the roughness is in microns (1/1000 mm) and the speed in metres per second (knots divided by two, approximately).
Figure 1. Permissible roughness.
As an example, a 36ft yacht will seldom go faster than 8 knots, i.e. 4 m/s – unless planing. This yields a permissible roughness of 25 microns, which is the grit size of sandpaper P600.
So we can say that there should be no roughness elements on the surface higher than the grits on this sandpaper! This is a tough call which would not normally be accomplished on a brush or roll-painted surface without sanding afterwards.
Brush and roll-painted surfaces
The unevenness left from a brush or a roller varies depending on the paint viscosity, which in turn depends on temperature and humidity. Other factors are the brush/roller quality, the skill of the painter and how fast the paint dries. In addition, the original surface may contain roughness elements caused, for instance, by old paint. In Figure 2 the increase in frictional resistance of the yacht for varying roughness size is shown. The results were obtained for a 25 foot traditional yacht, but are applicable to other yachts as well, as speed is the dominating factor.
Figure 2. Increase in frictional resistance due to roughness.
At 7 knots, increases in frictional resistance as large as 20% may occur, even for a modest roughness of 100 microns which is common for a brush-painted surface.
For 500 microns (0.5 mm) the roughness resistance is 80% of the smooth frictional resistance. Upwind in a good breeze the frictional resistance is about 1/3 of the total. For a yacht that makes 7 knots under these conditions, the 100 micron roughness would yield around 7% increase in total resistance, which corresponds to a speed loss of 1.5%, roughly 3 boat lengths per nautical mile.
Other factors which will increase frictional resistance are barnacles, the keel and rudder.
If you want to learn more then sign up for the course in Sailing Theory and Yacht Design, offered to RYA members with a 15% discount. Find out more and book your place.
Lecturers are Professor Lars Larsson, from Chalmers University of Technology in Gothenburg - a former adviser to Americas Cup Teams in Sweden, Italy and the USA - and two faculty members at the Solent University in Southampton: Dr Robin Loscombe and Mr Giles Barkley. All experienced yachtsmen.