The hard edges of the transport template’s planar convergences will likely suffice for a home-made dinghy intended for limited use. But the more a vessel sits and/or is engaged in moving through its intended medium, the more important rounding becomes in easing stresses caused by unruly waters and facilitating smooth efficient passage through them.
Spheres are appropriated extensively to guide design of GDCode-designed marine craft largely because of their omnipresent availability in the pattern of the transport template. This follows from the fact of spheres being the basic building unit of the code’s conceptual model, a choice influenced by nature’s spherical ubiquity from the innumerable electrons surfacing everything we see, touch, smell, taste, breath, and hear to stars to the detectable universe at large from any point of reference – including the place where you are right now, for example.
Aside from the sphere’s common familiarity, it is also the easiest to use, formulate, and program into rounding schemes whether realized by hand or computerized machinery. What’s more, the form that follows from locating a point rotated around a sphere’s plane cross-section according to its separate dimensions is the wave which also results from any disturbance to the surface of water.
A rounding scheme for marine vessels framed according to the manner of the last post’s simplest of application examples requires some special considerations.
The first pertains to the separation of the template’s 2 infinitely expandable and divisible geometries – that of the cuboda and that of the triangular prism-based HXP which share common (hexagonal) planes and which correspond roughly to the vessel’s hull and superstructure.
If no deck extends outboard from the HXP superstructure, spheres of one radius may be appropriated for the rounding process. As with the elementary rounding method described in Rolling Transport, spheres are first conceptually centered on the vertices of the vessel’s framework.
If there is a separating deck, the cubodal hull and HXP superstructure can easily be rounded with spheres of differing radii, with the latter typically being smaller, and in some cases much smaller to the extent of nothing at all. As with rolling transport and aircraft frameworks, cylinders join the spheres and then planes paralleling those of the framework meld to the cylinders tangentially.
In viewing the bow head-on, the cubodal side caps are omitted from the superstructure to more clearly depict the rounding procedure. Once this is done, the resulting shell is sliced back along the original deck plane, the sealing planes, and up along the inside of the hull.
Slicing around the region of the gunnel can follow any of a few alternative directions consistent with template geometry. As always, spheres rolled along creases define concave curvatures where desired. As far as the superstructure is concerned, any one or two of the 3 plane sets comprising its HXP geometry may be sliced off similarly.
The deck and other horizontal planes are not exactly flat but are shaped by very shallow wave forms with maximum slopes of about the 1.8° angle derived from the edge/triangle transformation.
A couple of clarifications are in order regarding the “framework” of the rounding process. The region between the outside of the rounding framework and the inside of the rounded shell may be framed further by the template pattern as long as the pattern geometry is retained where contacting the shell. This should cause no problems where planes and their edges are concerned, but care for the spherical and cylindrical curves will be necessary. Meeting these curved surfaces perpendicularly with whatever is projected from the framework is a safe bet.
Framework extension is necessary in the next big rounding consideration – regaining a sharp bow and keel after the rounding. The simplest way to do this is to first extend the framework’s intrinsic plane past the shell.
This plane can be rounded in profile circularly or with half or quarter 60° max sloped waves. For the bow only, the wave can be keyed to the sphere radius and its maximum slope extended linearly as needed.
The extent of the central planar extension may be defined by twin spheres rolled along them in a manner similar to how concave curvature seams are dealt with.
As viewed in cross-section the change in dihedral angle between matched squares and matched triangles means the extension of the bow from the hull will be about 40% more than that of the keel with the difference continuously smoothed around what is exposed of their common rounding spheres. If the triangle down template is employed the situation is reversed.
Design of submarine vessels centers around (spherically capped) cylinders to deal with pressure differentials.
The template supplies structural support, guidance in how spheres and cylinders are arranged, and exterior planes to protect them if necessary.
Indeed, one might look to rolling transport and aircraft approaches for other design possibilities. The simplified examples offered here don’t evoke broken speed records or fuel efficiency gains per se. But I believe one of the template’s potential virtues lie in economy of construction* that will advance efficiency when viewed wholistically. Another virtue is the potential for reusability of components before recycling; and yet another from a pattern as pliable to variation as there are species of fish in the sea.