The next question became, how to exactly describe a hulls shape and how to alter only a single or limited number of variables in the hull so as to independently test the influence of each variable in resulting performance? You cant just say that this hull looks this way and the next hull looks like that. You must be able to describe the hull shape mathematically in exact terms. I found some equations in the Proceedings of the US Naval Institute, but they were far too complicated for my simple project. I found the trajectory curve in physics textbooks, a parabolic equation form, had the right characteristics. Such a curve has the appearance of a boat waterline; it can be integrated to find its length; it can be differentiated to find the slope at any point. It is easy to work with. It describes the motion of an object displaced at some angle from its rest position by an external force which then is brought back to its rest position by gravitational forces. Not exactly the Navier-Stokes equation of general fluid mechanics, but at least it is analogous to the motion of a water molecule displaced by a passing hull form. The research project was successful but very limited in extent due to the complexity of the many variables and the need to build a new model for each design change.
Fast forward a few years: I changed careers forever, leaving engineering for a new profession. I didnt dislike engineering intellectually; I just didnt like the environment, being viewed as just a technical nerd, a contract-following migrant laborer. But I didnt want all my engineering knowledge to atrophy. So I picked up my senior research subject and, as a spare-time evening hobby, started playing with the mathematical hull design concepts to create hull forms of interest. Mathematical techniques match very well with the concept of conic projections to produce entire surfaces. Conic projections match very well with the use of plywood hull sheathing which speeds actual construction time. You have to actually build a boat occasionally to prove that your ideas really work (and that you are not completely crazy).
Over the next thirty years I mentally designed a number of hulls for various purposes and I ended up building six of them. My family and I have lived in many places. Each hull was designed for a particular set of circumstances and an envisioned purpose. Ive learned something from each boat. If I were to revisit any design, I could find improvements to make, but that just makes it interesting. In subsequent entries I hope to post photos of some of the boats I have built and the lessons I learned from them.
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