Homogeneous curve

:?:
Again I return to my last chance source. This time I’m hoping for some help in understanding this term, “homogeneous curve”, as used in the following text from Weston Farmer’s, From My Old Boat Shop.

“Another thing that will grab the eye of an old pro is the fact that the deck outline in plan fits the sheer sweep in profile. For lack of any better term, this is what is known as a “homogeneous curve” – that is, one curve belongs to another. They are related. …….

…… An easy way to make the two curves homogeneous is to cut the plan curve in cardboard, and take the sheer heights from the desired sag of the cardboard when in a catenary condition. (No charge for this tip; it is a good one.)”

Weston’s book is full of good ones, some I understand and some are confusing. This one, I would like to understand better. Is the homogeneous curve the secret to a sweet looking shear? Would anyone care to expand on this idea?

Below are the lines that accompanied the text.

Gary

 

Clearly, the curve obtained be Farmer's method would depend on the stiffness of the cardboard used, or alternately, on the scale used. (A 100" piece of cardboard would sag more than a 10" piece, etc.) Mathematically, the catenary of a chain with links of unequal weight would be tricky to work out.

LFH wrote that his father, Nathaniel Herreshoff, would determine the deck line in plan view by tacking a spline on top of a model in three places (bow, midship, stern). A line obtained this way will be very nearly quadratic. I suspect that if you use a three-point line fit to Farmers' sheer line, you will get a good fit there, too.

 

I don't know Farmer's book, but here's what Michael Pocock wrote on the same subject in his book "Inshore - Offshore":

"...Unless the hollow of the sheer is very carefully related to the curve of the deck outline the effect, when seen in three dimensions, will be very disturbing. There are in existence yachts whose sheer lines have been considered in two dimensions only and when heeled their curve becomes totally unrelated to the original concept.
The principle I use is that the sheer line is created by a flat plane cutting the topsides at an angle, rather as though a pitch roof was set up over the deck. The ridge of that roof is falling from the bow to the stern and the greater the angle of the pitch, the greater the sweep or hollow of the sheer line..."

 

Gary,

I may be wrong but I thought a catenary was formed by the sag of a line, beam, etc. of uniform cross section and weight. What Weston is saying is that the sag of the planform deck cardboard cutout will be in relation to its cross section at any point along the sheer. That is, the sheer curvature will be greater at points where the deck beam is lesser and will therefore sweep up more toward the ends than in the middle.

This makes sense to me when I read what I wrote. I hope it does to you. Maybe he did not take Seadrive's very long model into account, which will make a difference.

Whether this makes the prettiest sheerline is another matter. I do know that a sheer that looks just right in profile view may look awkward with hard spots in 3D. On boats which have a lot of curvature in plan view near the bow, I almost always need to take some height out of the sheer in this area to eliminate a hard spot. This only shows up in 3D so I can't exactly predict it.

 

I usually use a "planar sheer" to achieve the same idea. Directions? Hmmmm.....
1) Draw hull, not worrying too much about final sheerline.
2) Note: This does not work if drawing on paper... Make a plane that intersets 3 points:- Transom corner (assuming that at least is in the place you want it), bow at freeboard fwd, and some point on the final sheerline. The intersection of the hull and this plane is equivalent to laying sandpaper on a board and sanding the sheer of a half-model to a plane. you may have to dicker around with the plane to achieve a sheerline you really like, but it is worth it as you rarely get an "S" curve this way.
Steve

 

Steve -

Does using your "planar sheer" method on a computer require you model a hull surface that initially "runs wild" beyond your planar sheer? If so, how do you define the initial sheer so your body plan or sections assume the shapes your after?

Chris

 

Start with the planar sheer.

This method, BTW is also one John Letcher suggested many years ago.

 

Chris,
I usually model the hull to where the sheer looks "pretty good", and then drop the plane on. Anywhere there is no intersect, I tweak it up a little. It is more of a finishing tool than an initial tool, if ya see what I mean. With a little practice, you can get pretty goo at it. Also, with 3D modelling, you can line up the model on-screen in perspective mode, so that the bow and the transom corner are lined up, and sight along the sheer to see if if is close to planar before you drop on the plane. This ensures that things are pretty close to correct.
Steve

 

Thanks for the clarification, Steve. I get ya. I've never used this method per-se. I use Nautilus for my avocational designs, but usually start with a pretty good sized paper drawing to establish plan, profile, and a few sections. Once the sheer is put into the computer in 3D, it's easy spin it around for multiple views and be sure it looks good. When it's tweaked, surfaces are modeled based on those perimeter curves.

Regarding Gary's wanting to clarify Farmer's definition of a "homogenous curve," sound like the idea is to follow the curve of an end-supported plate of material of uniform density cut to the deck planform. "Thin cardboard" just happened to work for Farmer. Suppose carbon fiber would work too, if you we're looking for a really flat sheerline. Or paper, for that matter, if you wanted a really deep sheer.

The "planar sheer" method, ala Steve, Michael Pocock, and John Letcher looks a lot easier to use.

Chris

 

Thanks guys, what seems obvious to me now, was not, when I first started thinking about this. When Mr. Farmer says cardboard he is referring to the same stuff he builds his models from. Of course a different material would react differently.

I always knew one had to take care when determining the shear. For some reason I was still thinking in 2D and would fight with it back and forth from plan to profile. I thought I had the advantage using my 3D software. Weston and others used scale models and other props to help them, but I also believe they were skilled at thinking in 3D while drawing in 2D.

The more I learn the more questions I have.

Gary