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# Computer graphics in hull shape design. Pros and Cons.

Updated: Jan 16, 2020

Look at this wonderful picture of Cecil Beaton. It was made in 1943. But up to now not so many changes happened at loft flor. Only bending templates now cut by cutting machine. It is steel a lot of manual, work at shypyard for parts bending and preparation.

Two men cutting templates in the mould loft, Tyneside Shipyards, 1943

It so happened for a long time that the shape of the hull surface is determined by a set of intersecting orthogonal sections. A set of cross sections says a lot about the shape of the case for an experienced designer. The smoothness of the lines and the change in shape from one curve to another clearly represent the shape of the hull. Only twenty years ago we began to use analytical surfaces to determine the shape of the body. Prior to that, computer models used all the same grids of orthogonal curves as many years ago. For designers and shipbuilders, this choice is quite logical and natural. Hull structural elements are typically a set of frames in orthogonal sections of the hull. The current waterline determines the shape of the hull when the ship is immersed in water. In a word, a theoretical drawing is not only one of the most important drawings of the future vessel, but also an open book for the designer, according to which much can be said about the characteristics of the vessel.

Only hull lines builders use for hull shape definition and checking.

Modern ship surface design programs offer a variety of new forms of shape quality control for shipbuilders. Are all of them suitable for surface quality control?

Modern programs for modeling the hull surface instead of a grid of orthogonal curves use patches of parametric surfaces. This makes it possible to mathematically accurately determine any point on the surface. It would seem that the need for visualization of cross sections disappears. The graphical capabilities of computers allow you to visualize the surface of the hull both in shaded form and in the form of graphs of curvature, zebra and realistic reflection. Are these methods sufficient to control surface shape? Perhaps in other industries, such as jewelry and modeling the surface of the car body, this is enough. In shipbuilding, in addition to the aesthetic presentation of the surface, technological factors must also be taken into account. To assess the manufacturability of the hull surface is unlikely to help, for example, a color representation of the Gaussian curvature of the surface. It is rather a mathematical characteristic of a surface that says little to the designer.

Shaded hull shape for preliminary model.

Shaded hull shape for finally faired model. It is not so easy to see difference. Shaders design to hide app shape defects.

Zebra for finally faired hull. It is difficult to undersand hull shape quality.

Preliminary surface reflecition.

Faired hull surface reflecition.

Mean curvature for faired hull

Same hull, but with differen limits of curvature. What kind of information we can get from here?

For the designer, the shape of the lines of frames, waterlines and buttocks is still the most informative. It is these lines that are most often used to determine the geometry of hull structures adjacent to the outer skin. On these lines, plate and profiles hull parts are built. The shell plates of the outer shell bend along the same lines. If, when modeling body parts, a line is used that exactly repeats the contour, with all its defects, then the shell plates in this area will take a natural shape close to the shape of the spline. This leads to gaps between the shell plates and the internal structures. As a result of poor-quality smoothing of the ship surface, there is a need to fill the gaps with welding, overheating of the metal and deformation of the structure. This, in turn, creates internal stresses leading to the development of fatigue cracks in body structures. An opinion on the quality of the ship surface can best be obtained from shipbuilders at the shipyard. I myself saw a team of 5 people using a crane tried for four hours to install one sheet of skin on the body. The reason is an incorrectly smoothed surface in this area.

A poorly smoothed hull surface may not be optimal from the point of view of hydrodynamics and this makes the vessel more expensive to operate. According to data from various sources, for example, an average fishing vessel saves about 500 thousand dollars a year with a 10% reduction in hull resistance. In addition, a poorly welded and assembled body rusts faster and requires additional costs for cleaning and painting and eliminating fatigue cracks in the body.

In other words, despite the rapid development of programs for modeling the surface of the hull, the methods of controlling surface quality remain the same as a hundred years ago. So what methods are best used to control the quality of the hull surface?

As mentioned above, we imagine the shape of the hull surface in the form of lines of orthogonal sections. Consider several ways to control the shape of the curves.

All defects in the shape of the curve are easy to see when viewed along the curve. This method has been and is being used on a large scale to control paper drawings. An analog of this control method in computer modeling is the compression of a model along one of the coordinate axes. It is especially convenient if your program allows you to edit the model in a compressed form. An example of such a model is the NACA profile, usually having a very large elongation relative to the longitudinal axis. If in a compressed form the profile will look acceptable to the designer, then on a natural scale it will be all the more satisfactory. Compression along one of the coordinate axes is also very convenient to use when controlling the shape of the sections in the transition area to a flat side or flat bottom.

Frames in connection to flate side.

Same frames, but 10 times compressed in vertical direction. It is more easy to see all problems in connection to flat side.

The curves on the computer screen differ from the curves on paper, despite the high resolution of modern monitors. The best way to feel the shape of the curve is to plot a curvature. I prefer to visualize the radii of curvature of the curve at each point. In my opinion, this better shows the local flattenings of the curve. I note that the curves of curvature are very sensitive to changes in the shape of the curve. Often, moving a control point by 1-2 millimeters in real-time hull, can significantly change the graph of curvature. It is also important that your program allows you to directly visualize the curvature of the surface section, and not the curvature of the approximating section of the curve. I already wrote about this here. It also simplifies the work when editing surfaces. It is enough to enable the visualization of the curvature of the sections and, when the position of the control point of the surface changes, the curvature graphs will be dynamically updated. If the program that you use does not allow this, it significantly slows down the smoothing process. The only, in my opinion, drawback of the curvature graphs is that on a large scale, when displaying a set of curves on the screen, a mash of curvature graphs of different lines is obtained. Usually it is necessary to cut off too large values ​​of curvature for better visualization.

Difference between original lines (yellow) and faired shape (green).

Same as above, but with curvature radiuses.

One of the most important characteristics of the shape of the curve besides curvature is the presence of inflection points on the curve. These are the points at which curvature changes direction. The presence of several inflection points in a limited area of ​​the curve is visually perceived as undulation. This is exactly what the designer tries to avoid in the first place. The undulation of the frames will be transferred one to one to the corresponding details of the hull in the area. Sheathing sheets in this area will bend along more natural smooth curves. ShapeMaker has the ability to visualize the inflection lines of sections on the surface. I have not seen such an opportunity in any other program. The shape of the inflection lines on the surface is not only a means of controlling the shape, but also one of the most important characteristics of the surface itself. The correct location of the inflection lines allows you to accurately guarantee the absence of undulation at any point on the surface. We cannot directly influence the shape of the inflection lines, but when the position of the control point of the surface changes, the shape of the inflection line also changes. Note that the inflection line is a curve of a lower order than surface sections. In this case, only the continuity conditions of the curve segments in the case of NURBS surfaces of the 4th order or 3rd degree are satisfied on the inflection lines.

Inflection line for frames ( cian ) has several inersection with frame marked by red line. It means that frame has several inflection points and bad shape.

The above form control tools give us a complete picture of the hull surface. For more than 15 years, we have not printed theoretical drawings for verification. Following video show how ShapeMaker user can work with curvature and inflection lines.