Do the suggested curves for boat hulls pertain to their volume progression?

Another newbie question. Whether it’s parabolic, Sears Hacck, sine wave, or other curves that are suggested for boat hulls, do these curves pertain to the boat’s outline, its waterline, or its volume (all of which would be same for a boat with perfectly vertical sides.) When dealing with varying hull cross-sections over a boat’s length, plots of these three could vary quite a bit. I’ve always assumed that it is the submerged volume should follow a mathematically described curve, and to a lesser extent, the waterline. Would that be right?

 

Parabolic, sine, or whatever curve, as a descriptive, usually refers to waterlines.

The area of various stations can be plotted as a curve. That will graphicly represent the changes and distribution of displaced volume. The curve is commonly a wave form of some sort.

In your reading, you may come across references to the Colin Archer wave form. His premise was that the area curve should follow the form of a surface wave in the water. You can construct such a graphic by plotting the involute of a circle. Archers postulate was in vogue at one time but I do not think that is considered gospel anymore.

Many modern boats such as kayaks and canoes use a planform called fishform, or alternatively, swedeform. That is to say that the widest point on the boat is not at the longitudinal center. That would tend to complicate the involute curve notion.

So what does a "proper" area curve look like? That question is fuel for argument or at least more in depth explanations..........Maybe some of the credentialed members will jump in to explain more precisely.

 

The "plot" only thickens

Thank you, though I would have thought just the opposite. That is, I naturally thought that as you push a wedge through the water, it is the progression of the volume of water moved aside that is more important than the actual outline of the wedge. It's reallly a question of 3 dimensions versus 2 dimensions.

I had designed a swedeform paddleboard (max beam at 62% of length) where I let the bow outline go a bit outside a parabolic curve so that the progression of displaced volume would be parabolic. That was necessary because the bow had both rocker and more rounded hull sections. If I put the bow outline back to parabolic, the volume curve would become "hollow" at the beginning. Hollow bows seem to be generally discouraged when pushing a displacement hull near Fn = 0.4. But that raises the same question -- does a hollow bow mean the curve of the outline or the displaced volume progression.

 

There are a lot of goofy theories for using a strict set of curves to design a hull. Successful boat are designed to fit a purpose regardless of what the curves are. Each type of vessel requires a design specific to it. Doing it the other way around is trying to force nature to conform to a rule that makes someone's mathematical theory work.

 

There are some rules of thumb for developing seactional area curves based upon speed-length and displacement-length ratios and sectional shape. Normally, a sectional area curve will show a "hollow" at the bow and stern and will be maximum just aft of midships. Other than that there is too much tied up in the overall use and design requirements of any vessel to say there is one "best" sectional area or waterplane curve.