Bezier Radius Chine

After reviewing various design and fabrication methods for steel and aluminum sailing hulls, something was very apparent. There was little information on construction methods for the individual builders wanting a true round bottom sailboat in steel or aluminum. Until now, the backyard builder with average skills and equipment has been limited to hard chine designs and depending on their skill level the constant radius chine design.

The following innovative construction method, Bezier Curved Chine, offers amateur builders the option of constructing a true round bottom design that's as easy to build as a hard chine constructed boat.

Types of metal hull surfaces

There are two basic types of surfaces used in hull design for boats of Steel and Aluminum. They are "developable" and "non-developable" surfaces.

A developable surface is any surface that can be formed from a flat sheet of material without deforming. Developable shapes are sections of cylinders, cones, or any other shape formed by pattern development methods know as triangulation, radial line development and parallel line development. In boat building they will lie naturally on framework. They are easily placed in position, since they are designed to only roll in one direction at a time.

A non-developable surface is one that is rolled in two directions at the same time. Rolling a piece of sheet material in two directions deforms the material requiring skill and equipment to produce the desired faired result. An example of a non-developable surface is a potato chip. Another example is a round bottom sailboat hull.

Backyard builders and hard chine boats

All hull shapes, from hard chine to true round bottom, can be fabricated in steel or aluminum. The success of construction lies in the available equipment and skill set of the builder.

For the backyard builder, hard chine boats are the easiest to construct. They can be achieved with average construction skills and limited equipment. If, for example, you are experienced with a tape measure in your day job, you can build a boat from steel or aluminum with developable hard chine construction. I experienced this myself, building a hard chine steel sloop that I sailed for many years.

There are many design adaptations for hard chine constructed boats. The single chine is the simplest, requiring the least amount of work. Double chine designs are more appealing to the eye, and give the feel of a round bottom hull underway. Labor for the double chine increases slightly over a single chine, but the skill level is the same. Choosing between a single or double chine is simply preference.

Various methods are used to soften the appearance of the hull at the turn of the chine. On adaptation to accomplish this is to add a narrow strip of flat bar or section of pipe to help soften the appearance of the chine.

The esthetic downside of a hard chine constructed sailboat hull is that it lacks the beauty of a true round bottom. No matter which variation is used, in the end they are all recognized as flat-sectioned hard chine hulls.

Round bottom hulls in steel or aluminum, are skill intensive. Understandably, this makes the hard chine hull building more attractive to amateurs. Although builders may prefer a round bottom hull, they are reluctant to take on the challenge.

Backyard builders and constant radius chines

An alternative method used to imitate a round bottom hull is a Constant Radius Chine design. This method uses a large radius, arc of a circle, for the mid-section of the hull between the upper and lower developable surfaces, For ease of construction, the radius used in the mid-section does not change along the length of the hull, therefore the name constant radius.

Even though a constant radius design requires more skill than a single or double hard chine boat, it is another choice for an above average skilled person to construct a hull similar to a true round bottom. However, it is not a true round bottom.

To construct a constant radius chine hull, a fabrication shop rolls or breaks the constant radius mid sections used to plate the hull along its length. The roll or brakes form the girth dimension (the distance around the shape of the hull).

To illustrate this construction process, imagine taking on of these pre-rolled pieces, cutting it as necessary to meet the curvature of the hull along its length. The builder places the pre-rolled section on the framework and begins to work the section closer and closer to the framework of the hull. This is done using clamps, mallets, line heating (can not be used on aluminum), and other fabrications methods until the plating lies against the framework in a fair way. These methods require professional metal working skill and equipment.

If you're putting professional skill into building a constant radius chine, the end result should at least imitate a round bottom design. Does it? To look like a round bottom, the constant radius section of the hull needs to be seen at or above the water line. Remember, if you cannot see the radius section when the boat is at rest, it may as well be a single or double hard chine design.

Backyard builders and true round bottom boats

Professional Builders are able to construct true round bottom hulls in steel or aluminum. They staff professional workers with years of metalworking, boat building, and surface finishing skills. Their shops contain the equipment, both heavy and light, needed to achieve this kind of construction. It is not, however realistic for the average hands on person to build a steel or aluminum round bottom hull equal in beauty and fairness to those being built by highly skilled professionals.

The Question:
Any hull shape is possible from steel and aluminum, but the real question is do you really have the skill and equipment to take on a round bottom design?

The Answer:

At last, there is another method for the "backyard builder" to achieve the beauty of a true round bottom hull using average skills.

Here is the solution - a pre-engineered process using a sectioned Bezier Curved design, together with an innovative construction method. It is not as complicated as it sounds, in fact, it's easier.

Bezier curved construction

The hull illustrated (Fig. 1) is drawn with a bezier curved surface between two developable surfaces, one above and one below the turn of the chine. Note that the hull surface at the turn of the chine is visible both at rest and underway.

Because the curved surface of the hull is a free-formed surface, there is more freedom in the design process. Bezier curved designs have no need to use the same radius along the length of the hull. It is a free formed curve that changes at every location on the surface to enhance the hull lines, similar to a fiberglass design.

An example for the need of the bezier curve design method is best seen at the transom. At this location, a much smaller free formed curve is required for a more pleasing hull proportion. Unlike the constant radius design, bezier curved designed hulls do not require the same radius at the transom as at amidships.

What about skill and tooling needed for construction of a bezier curved chine? No more than building a hard chine hull. Labor hours increase with this method, but not the skill required. Again, more hours, but not more skill to achieve a hull that is a true round bottom design. Read on to see how this is possible!

Design example

The design example, (Fig. #1), is a combination of developable and undevelopable surfaces use to complete this trued round bottom design.

There are four major surfaces:

  1. The upper developable surface;
  2. The non-developable surface at the turn of the chine;
  3. The lower developable surface; and
  4. The keel developable surface.

The upper, lower, and keel surfaces are developable and fabricated from flat sheet metal. They will not deform in the plating process. Hull plating for these three developable surfaces are the same as that of hard chine construction. The average skilled person will have no problem plating these areas of the hull surface.

The section of focus is the non-developable free formed area between the upper and lower developable surfaces. This is the section which cannot be formed from flat material and therefore, the most challenging for the average person.

Figure 1 shows the many-stationed sectioned view of the hull, while Figure 1A, a three dimensional view is used to further clarify the hull shape.

The longitudinal lines shown in the body plan and the tree dimensional view indicate the point of change from the developable surface to the non-developable surface and vice versa. There is no interruption of smoothness here because the curves of the joining surfaces are tangent.

To illustrate that the curve is free formed, look at the body plan in Figure #1. The right side of the body plan shows the first half of the hull from the Bow to midpoint. The left side picks up from the midpoint to the transom.

Note the tightness of the curves at the last stations ending with the transom in the non-developable section of the hull. Compare this to the ever increasing fullness of the stations in this section of the hull, as your eye moves forward from the transom along the hull. You can see that the free formed shape of the curve changes. Additionally, note that free formed curve between the developable surfaces is not a simple radius of a circle, as would be required with a constant radius hull design. Bezier curve design is free-formed. A true round bottom boat.

Framing methods

The boat is built using a longitudinal frame method. This means that the transverse frames will support the longitudinal frames, which then support the hull skin. The longitudinal frame method of construction is used because the developable and non-developable surfaces or any combination thereof, meets at the longitudinal framing and provides a fair curve to weld to. In this design 1.250" x .250" flat bar aluminum is used for the longitudinal framing.

The design process

For those familiar with Marine Design, the following paragraphs describe an abbreviated method of the design procedure.

  1. In this model, the subject surface is located between the two developable surfaces. The curves supporting the developable surface form the boundaries of the, for now, non-developable Bezier curved section in the chine area.
  2. The master curves for the curved chine section is constructed with six Type 2 "Bcurves". The master curves are then used to support a "Clofted surface". Since a Clofted surface is non-developable, a series of developable surfaces will need to be superimposed over the Clofted surface.
  3. The Clofted surface is divided into sub-surfaces, which will be developable surfaces of an arbitrary length, approximately seven inches - thirty-four per side for this model. To create developable sub-surfaces we will use rings and magnet entities, which are required to lie on the Clofted surface, to define the size and location of these sub-surfaces.

    The rings and magnets serve as the control points for the "snake entities" which are also required to lie on the Clofted surface. A total of thirty-five snakes lie on the Clofted surface, dividing up the length of the surface at the turn of the chine.

    Next, two adjacent snakes are used as the supports to create the developable surface for the arbitrary seven-inch sections of the chine surface.
  4. Each of the developable surfaces are saved as a file and developed with a utility program to obtain a flat pattern. The flat patterns are used to form three-dimensional steel or aluminum into the plating. The utility program shows the locations of bend lines to form the material. Three-degree bend lines are used for forming in a press break.

Cutting the patterns

The most direct method of transferring the pattern to the sheet material is by the use of CNC cutting equipment. This is pictured in Fig. 2. A CNC Plasma machine is cutting them directly from a computer file. This is accurate and fast but more costly.

A less expensive way is to print the layouts from a computer file onto paper. Tape the paper pattern to a piece of flat material. Then transfer the bend lines locations on the pattern to the material for future forming in a press break by center punching.

Fig. 3 shows a paper pattern being used to cut a sheet material blank in a vertical band saw. It is a good idea to reference the direction of each piece, marking left and right, top and bottom and number them to keep them in a workable order.


Since these developments are not simple sections of a radius, a press break is used to form the pieces. The tooling used in the press break is fairly standard, consisting of a short length of bottom "V" die and a short rounded top punch. The press break time to form these pieces is estimated at about eight hours.

Figure #4 shows two sets of seven surfaces developed into flat patterns - starting at the transom on the left end working forward. The upper set shows bend lines at three degrees, while the lower set uses six-degree bend lines. Any degree of bend angle can be used. The deciding factor is the effect the bending process has on the material.

Since a bend is actually a crease in the material, the larger the bend angle the more pronounced the crease. Preferably, the crease should be minimal so it is best to use the smaller bend angle, even if it requires twice the hits in the Press Break. (The smaller the crease marks - the less finishing will be required on the hull surface.)

Looking at Figure #5, (one of the patterns), notice that the bend lines are askew and cross in random directions. Additionally, the distances vary between the bend lines. This is typical of a bezier curved formed surface. Remember, it is not a constant radius where all the bend lines are parallel to each other and the same distances apart for any given bend line.

When all the sections are cut and marked, the forming is next. A press break requires accurate setup, it is advisable to have all the patterns ready for the break operation.

In the press break, twenty or more hits are required to form the pre-defined shape of each pattern for a hull skin section. Accurate hits are important - a error in the bend angle even a quarter degree for each will multiply itself, and the piece will end up being 5 degrees over or under the desired mark.

To determine if this distortion occurred see Figure #5 and note the diagonal dimensions given on the pattern. It references the finished corner-to-corner length of each formed hull section, If you make your twenty hits as required and you end up with this dimension, your press break bend angle is correct.

If this reference dimension is not reached, the bend angle should be adjusted accordingly - sacrificing a few pieces to get the proper bend angle. Figure #6 shows the press break operation.

Thirty-four preformed sections complete the chine section of the hull. Why Thirty-four?

  • In figure #5, twenty hits were used to achieve a sixty degree curve to form one of the small rolled girth sections between the upper and lower developable surfaces.
  • Since the hull rolls in two directions at the same time (like the potato chip), it also rolls along its length. The Clofted surface is divided into thirty-four smaller developable surfaces to achieve this.
  • The thirty-four individual segments of developable surfaces can be compared to the bend lines in each individual segments, this time, not along the girth of the hull but along its length.
  • For the same reason the bend line degrees are kept small, the change in degree along the hull is kept small by having thirty-four segments.


With the hull built upside down and the framework completed and faired, plating is then fitted to the hull working symmetrically from side to side.

First , completely plate the upper developable surface since it is nearest the building jig set on the shop floor. Then the lower developable surface is plated symmetrically from side to side.

Finally, the free-formed chine section is plated using the thirty-four preformed pieces. Remember that this rounded section of the hull has been pre-engineered to fit with seamless ease. Start at the transom and plate this section, also symmetrically from side to side.

A minimal one-sixteenth inch gap is placed between all joining surfaces and framing when fitting the plating. The plating itself is chambered to at least half the thickness of the material on the outside surface, since the welds are ground smooth on the outside of the hull. The hull is completely tack welded together inside and out before the welding sequence is initiated. All tack welds are no more than three inches apart - preferably two inches.


  1. Begin with a three inch weld, at any location
  2. Move forward or back about two feet and do another three inch weld
  3. Step another two feet and do the last three inch weld
  4. Next - go to the opposite side of the boat and repeat steps 1-3 in approximately the same location
  5. Repeat the same process in 1-4 at another location
  6. Continue until the entire hull is welded outside and inside

As the process continues the welds will inevitably start and stop on a previous weld. To achieve complete and proper weld penetration, use a burring tool to cut away some material at the ends of the existing welds.


Figure #7A thru Figure #7D illustrates the construction method of a mock-up of a small section of the hull.

Figure #7A shows the sections being tack welded together, on a workbench. Remember that the sections in this mock-up have no longitudinal framework to guide the fit as they do when applying to framework. Therefore diagonal dimensions are used to verify the shape along the hull, similar to the method used in the bending process

From the computer model, diagonal dimensions can be obtained for any section or groups of sections at any location along the hull. Using this method to form the mock-up establishes the true shape of the design.

Figure #7b shows the hull surface being roughed in by an aluminum hard grinding wheel. It is used for initial fairing between adjoining sections. Later, finish sanding is used to refine the surface of the hull

Figure 7c shows the curve (edge thickness of the plating) along the girth. The transom plating would join the hull plating here. It can be easily seen from its shape that the curve is a free-formed curve - not the arc of a circle.

Figure #7d shows the curve along the length of the hull, which consist of six sections of preformed plating. The change occurring along the length is less dramatic then the curve along the girth, but still can be seen in this picture.

To Sum It Up ...

A non-developable Clofted surface is converted into an arbitrary number of smaller developable surfaces. These developable surfaces are pre-engineered to fit a specific location on the hull, using full size flat patterns. The patterns provide forming line and reference dimensions markers to verify the bend angle and accuracy of the finished formed skin section.

The hull plating is simplified by shaping in a cold forming press break, using a consistent and predictable method of fabrication.

The curved sections of this hull fit together easily, with minimal adjustment into the framework.

The pre-engineered design and fabrication method enables an average person to build a true round bottom hull using the same skills as required in hard chine construction.

The result is the unmistakable beauty of a round hull - the uninterrupted graceful line curving to meet the water.

Yes, Watson ... it can be done!


For information, questions or any comments on bezier curved chine design, building, or designs using this method; simply use the Feed-Back page or drop me an e-mail at:

I look forward to hearing from you!

Dennis Schaffer

March 2010

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