Technical » Hull Cross Sections for Multihulls

Release Date: 1/25/2010

Hull Cross Sections for Multihulls

Most multihull design books include a section about the pros and cons of various hull cross sections. They dont 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 changes the picture considerably and is not addressed here.

When a boat moves through the water, the friction between the boat hull surface and the water flowing past it 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.

  1. 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.
  2. Second is the wetted surface of the hulls.
  3. 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 semi-circular one has the shortest perimeter. Thus a hull based on a semi-circular shape should have the lowest wetted surface. All others will have greater wetted surface related to the numbers shown on the figure below, which was taken from Derek Harveys Multihulls for Cruising and Racing.

 

 

Another thing to observe from the shapes in the figure 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 semi-circular shape to minimize wave drag, he would have to select a shape that was narrower but deeper, for example, an oval shape. But the deeper shape would have greater wetted surface. This is a trade-off between friction drag at low speed and wave drag at high speed.

Another thing to note is that very few hull designs retain the same shape from bow to stern. Most are basically semi-circular at the mid section, more vee shaped toward the bow and flattened toward the stern. The elliptical and multi-chine shapes are good choices to get slimmer hulls that approximate semi-circular in skin surface area. The multi-chine and deep vee shapes offer construction advantages to amateur builders.

Bernd Koehler of K-Designs favors hard chines which he incorporates in symmetrical and asymmetrical trapezoid shapes with flat bottoms. He argues that the chines have hydrodynamic benefits that offset the additional wetted surface. He says I design for an optimum performance neglecting low speed situations.

Rudy Choy used an asymmetrical vee hull in most of his designs in the 1950s and 60s. James Wharram uses a symmetrical rounded vee hull for many of his designs. Both are attempts to achieve hulls that sail well without boards or keels. Some of Choys 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 semi-circular hull shapes with dagger boards, centerboards or keels. The debate over which was best was documented primarily in the Amateur Yacht Research Society publications. Today, the semi-circular 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.