This is my first post here. I have been reading the forum off and on for several years and would like to thank all the contributors for the great information provided, and of course Nick Schade for hosting this forum. When I built a Yost SOF a few years ago, I found many answers to my questions on this forum.

I am planning to design and build a hard-chine stitch-and-glue kayak, possibly with a strip built deck. I wrote some non-linear optimization routines to compute developable rulings between 3D Bezier curves and a small program to unfold plates based on the generated rulings.

This seems to work really well for the sheer panel, but the panel between keel and chine is a different matter. For all the designs I have tried, the developable ruling lines are very slanted in profile view except in the center and near the stems. The developable rulings are approximately described by three conic sections with one cone tip at either end near the bottom and one cone tip in the center above the chine. Despite being developable, I do not believe the shape that is described by these ruling lines to be buildable because the curvature in the direction perpendicular to the ruling lines is very high. Furthermore, plotting cross sections through the ruling lines shows that this shape has a pronounced bulge or "soft" chine below the hard chine described by the Bezier curve outside the center of the kayak. Compared to a straight line between keel and the hard chine, there is a substantial increase in volume for the developable shape, for some designs I have tried more than ten percent. This additional volume is near the ends of the kayak and can result in a substantial increase in prismatic coefficient as well.

Initially, I thought I must be doing something wrong or might have some bugs in my code, but I have become more and more convinced that what I have observed more or less applies to all designs where the deadrise angle changes from near horizontal in the center to near vertical at the stems. I cannot picture a geometry that would lead to a developable ruling different from the three-cone geometry described above. Has anybody else observed this? Are there designs with developable ruling lines that are not heavily slanted in profile view?

Because of the problems with developable rulings mentioned above, I have experimented with non-developable rulings instead by allowing some twist along the ruling lines. By twist I mean the change in surface normal along the ruling line, which must be zero for a developable ruling. I implemented this by introducing a penalty function for the slant in the ruling lines, so I can generate rulings with a compromise between twist and slant. While there are a number of issues with this code, e.g., ruling lines can cross for some weights of the penalty term, this looks promising and I have been able to generate rulings that closely approximate the design shape by allowing a few degrees of twist. In a large area around the center of the kayak, the twist angle can generally be kept below one degree with near vertical ruling lines. Towards the stems, however, I have found it to be much more difficult to minimize twist and slant, and the amount of twist is very sensitive to small changes in the transition at the stems. I am now wondering what makes for a good compromise between twist and slant, and how much twist I can introduce and still be able to force the plywood into the designed shape.

I have found a number of articles that discuss using non-developable rulings for boat building, but not really anything specific to kayaks and thin plywood construction. In one article, the authors suggested that for steel, twist angles of up to six degrees can be tolerated. I am not sure how valid this is, as there was no mention of plate thickness or the length of the ruling lines over which the six degree twist would have to be spread out. Nevertheless, I am wondering if there are any design guidelines or practical experiences relating to the permissible amount of twist for 3-4mm plywood construction. Any information would be greatly appreciated.

Hubert.