Numerical/mathematical methods for hullform lines to Modern Vessels

Yes, that does like it will be helpful. Thank you, Sir : )

 

As a small-time amateur, I routinely use parabolic curves, with the aid of a Texas Instruments TI-36 calculator, to create hull shapes for the boats I build (15 so far) in the range of 13-20 feet length. Those parabolic curves (really, trajectory curves) are first used to create a major chine describing the general dimensions of the hull. From that I use projections (conic, cylindrical, or planar as appropriate) downward to form the bottom and upward to create the topsides.
You could think of a lapstrake/clinker hull as a developable shape with each projected surface one plank-width wide. For my small boats, I usually use only about four sequential projections.\ to create the transverse frame shapes.
The entire process is done mathematically. From that major chine (a constructed mathematical curve), exact dimensions can be taken off every few inches and used for further projections.

 

I think that the shape of the boat should fulfill its intended purpose, regardless of what mathematical curves it follow or doesn't. Mathematical methods have been around for a long time and were criticized by many of the best designers; for example Herreshoff.

 

I absolutely agree. The concept is to create numerical methods to describe the desired shape, not to bend the shape to conform to some numerical formula.

 

Isn't a DXF file what you describe? It is a numerical representation of a shape.

 

No, not at all. A DXF file is simply a binary file (which you can open, edit, and correct with, for example, Windows Notepad) in which a series of keys are written so that CAD/CAM software can generate various objects, both graphic and non-graphic.
A DXF file contains more text, or at least as many, than numbers.

 

There remains a huge disconnect between the act of mathematically describing a waterline or section taken from a hull, and the ability to manufacture a set of formula that will parametrically describe a decent, buildable, hull. For instance, natural cubic splines, varied parametrically, don't produce developable surfaces. They sorta can if you add restrictions to the shapes of developable plate (restricting the ruling lines to very uninteresting, unboatlike forms), but why do that?

If the goal here is to generate, not describe, hulls; then you have to include things like stability curves, hull material properties, dimensional constraints, and cost factors as hull generation parameters. Stability curves depend on cg location, center of buoyancy, and weight, so ballast weight and ballast density matter. Hull material properties effect weight, cg, and sensitivity to volumetric efficiency. Cost factors influence the different materials and construction methods that can be used, as well as operational requirements such as propulsion options.

I wrote a toy program a long time ago that spat out hull shapes based on those parametric inputs. It wrote input files for Michlet as part of it's iterations, which I hand cranked and then fed some data back to the proggy. I was rather dumbfounded that it could produce anything from Comanche to Napoleon's L'Orient by specifiying ballast density, cargo cg (moveable ballast also), hull material strength, a box rule, and some simplistic sail power ratios. Specific strength of hull materials, ballast location, and ballast density had the strongest influence on hull shape.

When generating a hull, it has to accommodate box rules (internal and external), float right side up, be a shape that can be manufactured at a reasonable cost, and operate efficiently. These are the parameters that must generate the shape of the hull. The important factors are how each trades off against the other. How important is build cost compared to annual operating cost? How much weight does 1 knot more speed add and how much does it cost? What does lead and steel ballast cost to install internally and externally. You can craft a measure of merit that combines desired performance into one score and then optimize that score. I pounded this all into an Excel spreadsheet over a weekend, mostly making stuff up as I went, and I learned a hell of a lot by doing it. Start REALY simple and add in new relations one at a time.

 

A very technical and comprehensive answer about what a ship's overall design should be. What I don't understand (my English is getting worse and worse) is what all that has to do with the mathematical definition of hull shapes.
And, by the way, a cubic spline can certainly generate developable surfaces, of course.

 

@TANSL -
Feel I must quibble with a few points about your paper. #1 - could be semantics, but a 4'th order or 4'th degree polynomial would assume a quartic curve fit (highest polynomial of degree four), not a cubic curve. Constants don't count. #2 - why would one assume your cosine and slope condition at the endpoint? The next point (not shown) affects those conditions. Mirror your example points over the X/horizontal axis and shift it right any amount.

 

@tropostudio, Thank you for taking the time to read my writing. That's very kind of you.
It must be a semantic issue, but I don't understand your statements. What I do know is that a third-degree polynomial is a fourth-order polynomial, and it contains constants, which can be zero, that multiply the variables. And it's these constants that need to be determined. Some of these constants can, of course, be zero.
The rest of what you say in your post, starting with "Constants don't count. #2 - why ....", I don't understand. I'm sorry.

 

TANSL , Yes It looks only semantic ! To my knowledge, a Nth order polynomial has its highest degree term with exponent N. It has N+1 terms, including the constant term corresponding to the zero degree exponent term of the polynom .
For example a 4 order polynomial is C0+C1* X+C2*X^2+C3*X^3+C4*X^4 .

 

A Nth orden polynomial is a (N-1)th grade polynomial. I don't see there any semantic issue.