Earticle

A developable surface is a surface that can be flattened onto a plane without distortion, neither in angle nor in area. In mathematics, it is a collection of points with zero Gaussian curvature. The developable surfaces are of vital importance in modern industry modeling, whereas current business modeling software could only transfer a 3D model into an approximation of a developable surface. In this way, a methodology that could directly generate developable surfaces with no intermediate transformation is in need. This paper illustrated a modeling method based on dynamic programming, and further proposed a method for variational developable surface design. Finally, algorithm in this paper would be verified as valid and practicable by some design cases.

In this paper, we study the position vector of a developable q-slant ruled surface in the Euclidean 3-space $E^3$ in means of the Frenet frame of a q-slant ruled surface. First, we determinate the natural representations for the striction curve and ruling of a q-slant ruled surface. Then we obtain general parameterization of a developable q-slant ruled surface with respect to the conical curvature of the surface. Finally, we introduce some examples for the obtained result.

Novel ships are commonly required iterative hull form modifications until she get reputation for new marine environment. Small FRP boats are manufactured in a identical shape with a mould. It implies that every modification step requires great time and expense which makes it difficult to improve the hull form promptly. Domestic hull form of small fishing boat of Korea has been evolved from the traditional hull form of developable shape. Utilizing this typical developable characteristics of small boats, New mouldless production method for FRP boat has been suggested and it is confirmed that the method is recommendable for a petty order of hull in evolving period of hull form development.

The Korea inshore fishing boats are the size up to 30G.T., and their construction commonly employs the traditional wide wooden planking. Nevertheless, the hull forms have been developed with chine-type straight-framed sections which give developable surface party, but not on the whole: especially not on the whole portion of the hull are preferable for them. Considering many merits in the boat construction, the author, excluding cases of the FRP construction by hand lay-up or spray-up method and of the ferro-cement construction, finds out no reasons to depart from the chine-type hull forms of a developable surface in future development of their hull forms, too. In this report, the author proposed new designs of the developable hull surface for four typical boats forming the main structure of Korean inshore fishing fleets; 5G.T.-class multi-purpose boat, 10G.T.-class angling and longlining boat, 20G.T.-class drift and gill netters, and 27G.T.-class stow netters, and presented the tank test results on their propulsion resistance. The tank test had two purposes; one is to present the powering schedule of the new designs and the other to investigate the resistance characteristics of this kinds of boat in comparision with those of equivalent round-type boats at operational speed ranges. Between the both types of the boat no material differences in powering are expected. Hence, the author is confident of that saving in the construction cost of the developable hull over that of the round-type boat may result in considerable contribution to the over-all boat economy.