Technical » Hull Cross Sections for Multihulls Mostly Catamarans
Release Date: 11/28/2006
Hull Cross Sections for Multihulls" Mostly Catamarans "
Most multihull design books include a section about the pros and cons of various hull cross sections. They don't always agree with each other, and when that happens, it begs the question of why not. The intent of this piece is to shed a little light on that question.
It must be understood that the following discussion deals with "Displacement Hulls". "Planing Hulls" change the picture considerably and are not addressed here.
When a boat moves through the water, the friction between the boat hull surface and the water causes a drag force on the boat. This drag force is the predominant resistance to boat movement through the water at low speeds. Since the drag force is proportional to the area of the wetted surface of the hull, designers seek to minimize this area. Rounded hull cross sections are often the choice way to do this.
However, as the boat speed increases, the hull begins to cause a wave to form at the bow that propagates away from the boat but also forms a hump toward the front and a dip towards the rear of the boat hull itself. The positioning of the hump and dip are dependent on how fast the boat is moving. If this wave is pronounced, the dip moves toward the rear as speed increases until it fails to support the stern. The stern drops and the bow rises and the boat stops accelerating. This is called reaching “hull speed” and the force needed to make it go any faster increases significantly. This wave making is the second force involved in boat dynamics.
To minimize the second force, multihull designers have learned to design very slim hulls so that the amount of wave making is reduced to where the hump and dip are eliminated for all practical purposes. Edmond Bruce did model studies that showed that a waterline length to beam ratio of 8:1 or higher would accomplish this.
Of course, the hull or hulls of a sailboat must also resist the tendency of the wind on the sails to push the boat sideways. Asymmetrical (notably Hobie and Rudy Choy) and deep vee (notably James Wharram) hull shapes, keels, dagger boards and centerboards are design approaches to do this.
Another design choice, once a designer has decided how long, deep and slim he wants the hull to be, is how to shape the underwater portion of the hull to carry the weight of the boat and the payload he wants to put in it. Often this choice is at odds with one or both of the drag reducing choices.
There are three things involved in hull design that must be considered.

First is displacement, the planned weight of the boat itself plus the planned payload. That is the total weight that should make the boat float on its design waterline.

Second is the wetted surface of the hulls.

Third is the hull length to beam ratio (Lwl/Bh) at the waterline.
If a designer considers several cross sections and makes them all have the same area (implies same displacement) as shown in figure 1 below, geometry tells us that the semicircular one has the shortest perimeter. Thus a hull based on a semicircular shape should have the lowest wetted surface. All others will have greater wetted surface related to the numbers shown on figure 1, which was taken from Derek Harvey’s “Multihulls for Cruising and
Racing”.
Figure 1
Another thing to observe from the shapes in Figure 1 is that the waterline width (Bh) is different from one shape to another. If a designer wanted a more slender boat with the same displacement as the boat with the semicircular shape to minimize wave drag, he might opt for an oval or elliptical shape. But the oval or elliptical shape would have greater wetted surface. This is a tradeoff between friction drag at low speed and wave drag at high speed.
Figure 2
Notice that the Sharpie (rectangular) hull shape offers the lowest wetted surface! The geometric truth about the semicircle having the lowest wetted perimeter is no longer valid because the waterline beam was fixed to achieve a given length to beam ratio for the hull. If a designer fixes displacement, waterline beam and draft, the hull shape that gives the most displacement is the rectangular one. The semicircular shape (Round in the figure) has to have a rectangular block added to it to get the given displacement while holding the beam fixed. Similar adjustments have to be made to the other shapes. Without these adjustments, the shapes may give less wetted surface, but will not give the chosen displacement and hull length to beam ratio. So the contention that the Sharpie hull shape offers the lowest wetted surface is correct under a very strict set of constraints. Otherwise, geometric truths still hold.
Another thing to note is that very few hull designs retain the same shape from bow to stern. Most are basically semicircular at the mid section, more vee shaped toward the bow and a flattened oval toward the stern. The elliptical and multichine shapes are good choices to get slimmer hulls that approximate semicircular in skin surface area. The multichine and deep vee shapes offer construction advantages to amateur builders but may not give as smooth a water flow around the hull as a more rounded shape.
Rudy Choy used an asymmetrical vee hull in most of his designs in the 1950s and 60s. James Wharram uses a symmetrical vee hull for many of his designs. Both are attempts to achieve hulls that sail well without boards or keels. Some of Choy’s boats had small skegs that were added primarily to make the boats tack well. During that time period, other multihull designers, notably in Great Britain, Europe and Australia, favored semicircular hull shapes with dagger boards, centerboards or keels. The debate over which was best is documented primarily in the Amateur Yacht Research Society publications. Today, the semicircular shape and some close approximations to it dominate the designs offered.
To summarize, there are many factors that go into choosing a hull shape, and one must be careful not to attempt to oversimplify it.
Calvin H. Markwood
Engineering Analyst
Multihull Dynamics Inc.